JP6550654B2 - Orbit control device - Google Patents

Description

The present invention applies forced displacement or an external force to at least a part of the object to be controlled based on a target function that is determined based on the detected position and velocity of the mass of the object to be controlled. The present invention relates to a trajectory control apparatus and a trajectory control method that performs feedforward control of the trajectory of the controlled object so that the position and velocity of at least a part of the controlled object become a target value, and further performs sample value control using this. Is.

The controlled object is also called a controlled oscillator because it often has a vibrator inside. Further, the trajectory control device and trajectory control method of the controlled object are also called a vibration control device and a vibration control method because the vibration is operated when the controlled object is a vibrator.

The vibration phenomenon of a vibrating body consisting of an integral or multi-body vibrator is determined according to the equation of motion if the external force applied to the vibrator or the amount of forced displacement is determined, and the mass of each vibrator after an arbitrary time is determined. You can know the position and speed.

However, after an arbitrary time, it is possible to apply an external force or a forced displacement amount that is a non-conservative force that sets the position and velocity of the mass of each transducer constituting an integral or many-body transducer to an arbitrary target value. It becomes an inverse problem and generally cannot be determined unless specific conditions and closed systems are defined (Non-patent Document 1).

In addition, at the start and end points of any time, there are innumerable trajectories of the oscillators such that the mass position and velocity of each of the oscillators constituting the one-piece or many-body oscillator are set to arbitrary values. How to determine the correct path is related to what is used as a variation, and how to determine the variation has not yet been determined (Non-patent Document 2).

In recent years, in order to suppress residual vibration of the oscillator, a kinematic model consisting of kinematic information such as minimizing the squared integral of the mass of the oscillator within a defined time of the jerk is used. Although an optimal trajectory has been proposed (Non-patent Document 3), residual vibration could not always be suppressed.

In addition to this, although a criterion such as an endpoint error variance minimum model has been proposed as a method for determining the optimal trajectory of a vibrating body, the principle for determining the trajectory was not clear.

In the principle that defines the orbit, although free motion is the most natural, these methods do not satisfy the dynamic variational principle because the external force is a non-conservative force. There was not enough evidence to satisfy many.

Therefore, in conventional vibration control, a black box is regarded as a black box without setting a model in particular for the controlled object, and the position and velocity of the mass of the vibrator are measured at each moment, and an external force is calculated from the difference between this and the target value. And feedback control for determining the amount of forced displacement has been performed (Patent Document 1, Patent Document 2, Patent Document 3, Patent Document 4, Patent Document 5).

In addition, when feeding back the measurement signal, devices such as spectral separation and filtering have been made on the measurement signal so as to particularly cancel out the natural vibration of the controlled object (Patent Document 6, Patent Document 7).

Many of these feedback control methods have been defined based on analog feedback for continuous signals (Patent Document 8, Patent Document 9, Patent Document 10), or a sample that digitally feeds discrete signals. Although value control has been proposed (Patent Documents 11 and 12), the sampling period is half of the natural period of the controlled body, and the optimum period has not been determined.

Although these feedback controls are methods to bring them closer to the target values, it was not possible to determine a specific trajectory and to discuss the optimal trajectory.

On the other hand, an input shaping and preshaping command function based on positive cast control that attenuates residual vibration in a feed-forward manner by applying an impulse-like external force to the vibrator several times at the timing that matches the vibration of the system. Have been proposed, and various contrivances have been tried (Non-Patent Document 4).

On the other hand, energy transfer between different vibrators can be formulated and analyzed by defining a system and discussing modal vibration under natural vibration, so various ideas are made to define models and enhance their functions. It has come.

A representative of the system for defining and controlling the model is the two-system dynamic vibration absorber, the resonance condition between the vibrator and the dynamic vibration absorber is clarified, and the design is easy (Non-Patent Document 5) ). However, in these models, although there is a technique such as obtaining an external force function that satisfies the resonance condition to the damper (Patent Document 13), the energy transfer between the transducers constituting the system and the position and velocity of the transducers are controlled. A method has not been sought.

In addition, the motion of a multi-body vibration system with two or more vibration systems is generally complicated because three-body problems occur in linear vibration systems and chaos etc. occur, and analysis is conducted by defining three or more vibration systems as a system I could not do it until now.

The current state of vibration control is that no analytical method has been found to control even an integral vibrator when nonlinear elements such as collisions have entered. Approximate feedforward functions have been proposed, but they do not work universally under all conditions. In feedback control, the technology to correct the deviation is only speeded up with the development of computers. Conventional control methods that use only actual oscillators as state variables have required the following reforms for further development.

However, with recent advances in quantum information theory, quantum algorithms that run on quantum computers are being studied. The quantum algorithm expresses the whole wave as a state vector, and expresses the operation as an operator that is a matrix representing the operation. Quantum algorithms can also be applied to classical wave phenomena where entanglement between particles and focusing of wave packets due to observation do not hold. By expressing in, it becomes possible to express a series of operations of the vibration system as a wave algorithm.

For example, A. In Patel, two small oscillators with equal natural periods are connected in parallel to one large oscillator, and in a specially designed three-body collision vibration system, the small oscillator 1 and the small oscillation connected in parallel inside It has been reported that the energy transfer for each natural period of the small oscillator between the two small oscillators of the child 2 is equivalent to the Grover algorithm (Non-patent Document 6). Here, the natural period is the natural period of each single oscillator consisting of each small oscillator, and both are equal.

Takada et al. Analyzed in detail the conditions under which the Grover algorithm was established for the three-body collision vibration system, formulated the operator, and found that the Grover algorithm between two small-body oscillators connected in parallel We report that it is an almost periodic vibration with energy transfer between vibrators for every period (Non-patent Document 7).

Takada et al. Also reported that the Graze bifurcation in a small oscillator subject to a collision is a transition between different collision modes for each natural period (Non-patent Document 8). Furthermore, Kotake et al. Reported that the energy transfer between two small oscillators can be arbitrarily manipulated by changing the order of the collision calculation for each natural period (Non-Patent Document 9).

On the other hand, in the three-body collision vibration system in which the wave algorithm is established, although an interaction due to energy transfer occurs between the two small vibrators connected in parallel for each natural period, the internal resonance condition is entered. Since the remaining large oscillators that connect them do not affect the discrete dynamics, the motion of the system can be divided into two-body vibrations and one-piece vibrations discretely. It was possible to escape the occurrence of.

In the three-body collision vibration system, the state of the system is developed by free vibration during the collision operation for each natural period. Therefore, the trajectories of all the oscillators during the natural period are determined. In this sense, the optimal orbit for each natural period was given in the most natural way.

Further, since the energy transfer for each natural cycle between the two small vibrators changes depending on the position, the velocity, and the mass ratio of each small vibrator, it is possible to change the state of the small vibrator 2 for each natural cycle. Arbitrary energy transfer is possible, and the state of the other small oscillator 1 can be changed. However, since the position, velocity, and mass of the actual transducer cannot be changed arbitrarily, the state of the system cannot be arbitrarily controlled.

On the other hand, among the three-body collision vibration system, when the vibration system including one small vibrator is left as it is and the remaining vibrators are virtual, the position, velocity and mass of the virtual vibrator are arbitrary. Because it can be changed, it becomes possible to arbitrarily manipulate the position and velocity of the actual small oscillator in free motion between the natural periods from the collision of the virtual oscillator to the next collision.

Also, by doing this, the internal force of the system in free motion under Hamiltonian dynamics of the three-body collision vibration system during the natural period from the collision of the virtual oscillator to the next collision is extracted. The external force that could not be formulated as a non-conservative force can now be formulated by the variational principle under virtual Hamiltonian dynamics.

Therefore, Yagi et al. Derived an external force function and a forced displacement function that enable steady collisions between the natural periods of a two-body collision vibrator or a one-piece collision vibrator by extracting a part of the three-body collision vibration system. (Non-Patent Document 10). Moreover, Yagi et al. Proved that the steady-state vibration between the natural periods of the three-body collision vibration system is a stable vibration that describes a limit cycle (Non-patent Document 11).

Furthermore, Yagi et al. Studied the application to the collision machine using an external force function and a forced displacement function that enable steady collisions between the natural periods of the two-body collision oscillator and the one-piece collision oscillator. (Non-patent document 12, Non-patent document 13).

Furthermore, Kotake researched the mechanism of chattering in rolling mills using external force functions and forced displacement functions that enable steady collisions between the natural periods of these two-body collision oscillators and one-piece collision oscillators. (Non-Patent Document 14).

Furthermore, in this two-body collision vibrator and integral collision vibrator, Kobuchi differs from feed-forward control or sample value control using a vibration control function representing an external force or forced displacement operated at the natural period and a conventional control method. And the trajectory function of a trolley operating with reduced residual vibration in an overhead crane, using these vibrational operating functions operated at the natural cycle (Non-patent document 22, Non-patent document 23), residual vibration reduction method for robot hand (non-patent document 24), and application to wave power generation (non-patent document 25).

However, since the operation using the conventional vibrational manipulation function is determined using the entire natural period of each of the existing small oscillators, the feedforward control only has control at this interval, The sample value control could only be given for each natural period. As a result, trajectory control and vibration suppression control could not be performed in a shorter time, and operation could not always be performed faster than conventional feedback control.

In addition, the discrete points of the mass, root position, and velocity of the actual oscillator that determines the vibration operation function can only be determined for each natural period, and the trajectory plan cannot be determined more freely. Therefore, it could not be used in more complicated control, such as avoiding obstacles.

Also, in systems consisting of non-linear oscillators such as overhead cranes, the deviation due to non-linearity becomes large, so it was not possible to devise measures such as eliminating non-linearity deviations by operating at more arbitrary timing.

Other related prior art includes the following (Non-Patent Document 15, Non-Patent Document 16, Non-Patent Document 17, Non-Patent Document 18).

JP, 2005-147318, A JP-A-11-102858 JP-A-9-177873 Japanese Patent Application Laid-Open No. 7-337055 JP-A-6-137371 Unexamined-Japanese-Patent No. 5-340443 JP-A-5-240295 Japanese Patent Application Laid-Open No. 6-178570 JP-A-6-324744 JP-A-7-104856 JP-A-8-177966 Japanese Patent Laid-Open No. 7-42786 JP 2003-206979 A

Santilli, R.M., "Foundamentals of Theoretical Mechanics I, The inverse Problem in Newtonian Mechanics", Texts and Monographs in Physics, Springer-Verlag (1978). Bunji Kondo, “Optimum Control and Trends of Optimization Control”, Journal of the Japan Society of Mechanical Engineers, Vol. 66, No.530 (1963), pp.319-326. Hiroyuki Ito, Hideki Tsuji, Yasushi Ogasawara, Shinji Mitsuda, “Vibration Control by Optimal Trajectory Constrained by Jerk Value”, Transactions of the Japan Society of Mechanical Engineers, C, Vol. 59, No. 558 (1993), pp. 372-378 . Neil C. Singer, Warren P. Seering, Preshaping command inputs to reduce system vibration, ASME Journal of Dynamic system, measurement, and control. Vol. 112, 1990, pp. 76-82 Kazuto Sado, “Dynamic Vibration Absorber and its Applications”, Corona (2010). Patel, A. D., "Wave Algorithm: Optimal Database Search: Wave and Catalysis", International Journal of Quantum Information, Vol. 4 (2006), pp 815-825. Soichiro Takada, Shigeo Kotake, Yasuyuki Suzuki, “Analysis by the wave algorithm of the periodic perfect periodic vibration appearing in the internal resonant collision vibration system coupled to one oscillator (in the case of complete elastic collision at the balanced position)”, Japan Transactions of the Institute of Mechanical Engineers, C Ed., Vol. 77, No. 773 (2011), pp. 14-27. Soichiro Takada, Shigeo Kotake, Yasuyuki Suzuki, “Periodic Graze Phenomenon due to Energy Transfer due to Internal Resonance of Two-Body Collision Vibration System Coupled to One Oscillator”, Transactions of the Japan Society of Mechanical Engineers, C, Vol. 77, No. 777 (2011), pp. 1911-1925. Shigeo Kotake, Hiroaki Hanai, Yasuyuki Suzuki, “Wave Algorithm for Manipulating Energy Transfer Between Internal Resonant Two-body Small Oscillators Coupled to One Oscillator”, Transactions of the Japan Society of Mechanical Engineers, C, Vol. 77, No. 781 (2011), pp. 3337-3349. Kazunori Yagi, Shigeo Kotake, Yasuyuki Suzuki, “Excitation force and forced displacement to realize steady collision vibration in one-body, two-body, and three-body collision vibration systems”, Transactions of the Japan Society of Mechanical Engineers, C, Vol. 79, No. 800 (2013), pp. 918-930. Kazunori Yagi, Shigeo Kotake, Yasuyuki Suzuki, “Stability and Operation of Steady Collision Solution in Three-Body Collision Vibration System”, Transactions of the Japan Society of Mechanical Engineers, C, Vol. 79, No. 800 (2013), pp. 931- 942. Kazunori Yagi, Shigeo Kotake, Takahiro Kawamura, Yasuyuki Suzuki, "Inconsistent force that enables steady-state variable repetitive impact processing" Proceedings of the 20th Mechanical Materials and Materials Processing Technology Conference (M & P 2012) of the Japan Society of Mechanical Engineers. Kazunori Yagi, Shigeo Kotake, "Intermittent Forced Displacement Function Enabling Variable Steady-State Semi-Open-Loop Press Processing" Proceedings of the 25th Annual Conference of the Japan Society for Plastic Processing. Shigeo Kotake, “Possibility of Chattering due to Local Energy Propagation of Coupled Vibration Generated between Multi-Stage Rolls -Vibration due to Forced Displacement of Working Roll-” Proceedings of the 25th JSAP Spring Meeting . Oka, Hayashi Cho, Choshigo, Hiroaki Ozaki, Akio Kubo, “Optimization of Cam Curve Considering Residual Vibration Suppression of Cam Type Positioning Device”, Journal of the Japan Society of Mechanical Engineers, Volume C, Vol. 69, No. 682 ( 2003), pp. 1684-1690. Abe Akira, "Modeling and Vibration Control of Flexible Manipulators Considering Large Deformation", Proceedings of the Japan Society of Mechanical Engineers, C Ed., Vol. 72, No. 719 (2006), pp. 2177-2184. Hiroshi Yamaura, Kyosuke Ono, Naruyuki Yanagimachi, “Analysis and Control of Settling Process of High-Speed and High-Accuracy Positioning Mechanism”, Transactions of the Japan Society of Mechanical Engineers C, Vol. 60, No. 573 (1994), pp. 1676-1684 . Kyono Ono, "Optimal High-speed Trajectory Control of Oscillatory Mechanisms (1st Report, Analysis of One-Degree-of-Freedom Vibration Model)", Proceedings of the Japan Society of Mechanical Engineers, Volume C, Vol. 51, No. 469 (1985), pp. 2233-2243. Masahiro Mori, “Sample Value Control”, Automatic Control, Vol. 4, No. 3 (1957), pp. 172-182. Yasuhito Takahashi, “Optimum Control Theory Based on Maximum Principle”, Measurement and Control, Vol. 3, No. 1 (1964), pp. 1-10. Shigeo Kotake, Kazunori Yagi, Souichiro Takata, Optimal sampled-data vibration control functions for one mass-spring system obtained from three vibro-impact oscillators under Grover algorithms, Proceedings of the 12th International Conference on Motion and Vibration, 2014 Shigeo Kotake, Kazunori Yagi, Application of sampled-data vibration control function to suppress residual vibration of travelling crane, Proceedings of the 12th International Conference on Motion and Vibration, 2014 Shigeo Kotake, "Damping sample value control of suspended cask using vibration control function", Proceedings of the 19th Symposium on Power and Energy Technology, The Japan Society of Mechanical Engineers, 2014. Shigeo Kotake, Takahiro Kawamura, Yasuyuki Suzuki, “Residual Vibration Suppression of Elastic Robot Arm by Sample Value Control Using Vibration Manipulation Function”, Proceedings of JSME Robotomech 2014, 2014. Shigeo Kotake, "Sample value control of transmission lines by vibrational manipulation function to enable galloping prevention and power generation", Proceedings of the 19th Symposium on Power and Energy Technology, The Japan Society of Mechanical Engineers, 2014.

In the conventional techniques for controlling vibration, the control method of the vibrating body using feedback needs to calculate the deviation from the target value using a high-speed sensor, and a large output that follows the signal at high speed in response to the signal The actuator of was also required. In addition, the conventional modern control theory has a problem in terms of cost and on-site operation because it requires a high-speed computer to execute a complicated control theory.

On the other hand, the conventional model using a dynamic absorber etc. is generally a two-body vibration system, and the movement of the mass of one vibrator is affected by two different natural vibrations, and it is necessary to consider the whole vibration. there were. Moreover, in the conventional model, it was difficult to manipulate the motion of the vibrator under external force arbitrarily, and it was difficult to analytically derive the manipulation that gives the mass of the vibrator any position and velocity.

Furthermore, in the conventional vibration damping method, residual vibration remaining in the system after control can not be completely eliminated, and it takes time to drop the residual vibration below a certain level (Non-Patent Document 15, Non-Patent Document) 16, Non-Patent Document 17, Non-Patent Document 18).

Also, in the conventional sample value damping method, digitization is mainly performed by discretizing analog control, and although the control is affected by the difference in sampling period, the optimum sampling period is not particularly determined. (Non-patent Document 19).

In addition, in the conventional vibration control method, since the external force generally applied is non-conservative force, the optimal trajectory with a dynamic background using the variational principle cannot be obtained, and various evaluation functions are used. Although the optimum trajectory was found, the choice was not exempted. (Non-patent document 20).

The problem of these controls is that there is no target feedforward function, and it is impossible to obtain an optimal trajectory even if using an ambiguous evaluation function (Non-patent Document 18).

A control method using an input shaping function enables open-loop feedforward control, but the parameters to be input require information such as the frequency, amplitude, and attenuation factor of the oscillator, and the input function depends on conditions. There is no strict formulation. In addition, the control tends to diverge due to the difference in frequency, and the vibrator with a small attenuation rate has a problem such as external excitation. Since the force shaping function cannot be changed in a feedback manner according to the state of the system, it is necessary to devise measures such as using a robust input shaping function that does not depend sensitively on fluctuations in the system frequency. It did not obtain (nonpatent literature 4).

Various methods for determining the optimal trajectory of the vibrating body have been proposed so far in feedforward control, but no method that satisfies the dynamic variation principle has been proposed (Non-Patent Document 1, Non-Patent Document 1). Reference 2). Therefore, the external force and the amount of forced displacement that can arbitrarily determine the position and speed of the vibrating body after a predetermined operation time have not been formulated.

Here, the external force is a force that is applied to at least a part of the system from the outside of the system, and the forced displacement is a forced change in position that the system receives from the outside.

On the other hand, in the two-body collision vibrator shown by Yagi et al. Or an integral collision vibrator, a vibration manipulation function for determining an external force or forced displacement that enables arbitrary change in position or velocity is from the virtual three-body collision vibration system. Allows feedforward control to determine the optimal trajectory between the natural periods of the controlled oscillator.

Also, the vibration operation function, which is a feedforward function, is determined from the current mass and position and velocity of the root for each natural period of the oscillator to be controlled, and the current mass and position and velocity of the oscillator to be targeted. Therefore, it became possible to control the sample value of the oscillator at each natural period.

However, the vibration operation function shown by Yagi et al. Can control the vibrating body only in the natural period, and does not require high-speed feedforward control in a shorter time or slower power in a longer time. Was unable to control it. In addition, it was not possible to perform sample value control for trajectories consisting of more free target value sequences. (Non-Patent Document 21, Non-Patent Document 22, Non-Patent Document 23, Non-Patent Document 24, Non-Patent Document 25).

The vibration operation function proposed based on the ideal three-body collision vibration system where the characteristic wave (Grover) algorithm such as energy transfer between vibrating bodies is established, considers the virtual vibrator as a state variable together with the actual vibrating body. It has a viewpoint that is not found in conventional control methods. A virtual vibrator is a circuit or a power source that moves an actuator that has not been considered as a conventional system, and because it is physically a natural extension, it is possible to propose comprehensive control including the circuit and the power source. There is also.

However, in the ideal three-body collision vibration system that has been proposed so far, the desired energy transfer can not be achieved only by the natural period of the small oscillator, so the vibration operation function defined by assuming some of them is also It was impossible to remove restrictions such as not working on the natural cycle.

  The present invention has been made to solve the above problems, and a vibration control function derived by extending a three-body collision vibration system so as to make the time for achieving energy transfer between vibrators arbitrary. The main object of the present invention is to accurately change the position and velocity of the second support to be controlled among the objects to be controlled to a target position and velocity after a predetermined operation time.

As described later, in the present invention, Hamiltonian and Lagrangian are defined as the Hamilton system in which the energy of the entire system defined including the controlled object is stored during the operation time.

Therefore, in the following, position is expressed as generalized coordinates, velocity as generalized speed, acceleration as generalized acceleration, jerk as generalized jerk, force as generalized external force, mass as generalized mass, and momentum as generalized momentum. It is assumed.

[Invention 1]
The track control device of the present invention is
A trajectory control device for controlling a trajectory of at least the second support in a controlled object including at least a first support and a second support vibratably supported by the first support,
The second support reference generalized coordinates and the second support reference generalized speed, which are generalized coordinates and a generalized speed at a predetermined reference time of at least the second support among the controlled bodies, and the first support Reference information acquisition means for acquiring reference information capable of deriving a first support reference generalized coordinate and a first support reference generalized speed that are generalized coordinates and a generalized speed at a predetermined reference time of the body; ,
The object to be controlled is supported in parallel in a vibratable manner on a first support, which is vibratably supported by a fixed support in an inertial system, and on the first support, and has an equal natural period as a single vibrator. Two unique features of a two-body coupled vibration system comprising the second support and the third support, and comprising the center of gravity of the second support and the third support and the first support When it is regarded as a dynamic system which is a part of a three-body vibration system set so that the product of the absolute value of the difference in angular frequency and a predetermined operation time will be a natural number multiple of 2π, Based on the second support-based generalized coordinates and the second support-based generalized speed, and the first support-based generalized coordinates derived based on the reference information and the first support A reference generalization speed, and the second support at a time after the operation time from the reference time Determined based on the free motion of the three-body vibration system within the operation time determined from the second support target generalized coordinate and the second support target generalized speed, which are generalized coordinates and the generalized speed , based on the forced displacement of the objective function of the generalized coordinates given to said first support member in said operating time,
Between from the reference time to elapse the operating time, the first support to provide a forced displacement of the generalized coordinates, the second support generalized coordinates and generalized velocity feedforward control to control means When,
Equipped with
When the generalized coordinates of the first support when the entire three-body vibration system is in the balanced state are set as the origin of the generalized coordinates of the first support, and the entire three-body vibration system is in the balanced state The generalized coordinate of the second support is the origin of the generalized coordinate of the second support, and the generalized coordinate of the first support is forced to the generalized coordinate represented by the following (formula 1) Trajectory control device which controls to become displacement function X (t ₀ + t ').
However, Δt is the operation time,
Among the two natural angular frequencies of the two-body coupled vibration system, the large natural angular frequency is ω ₊ = (2p + 1) π / Δt, the small natural angular frequency is ω ₋ = π / Δt, and p is a natural number Do.
Further, the second support reference generalized coordinate is x _in , the second support reference generalized speed is v _in , the first support reference generalized coordinate is X _in , and the first support reference generalized speed is Is V _in , the second support target generalized coordinate is x _en , and the second support target generalized speed is v _en .
Further, (Equation 1) is a non-dimensionalization function with the characteristic period of the single oscillator consisting of the second support as 2π and a representative time, and the generalized mass of the second support as a representative mass, It holds in the range of t '= 0 to Δt. Α _p is any real number that satisfies (Equation 2).

  The trajectory control device determines at least at least the controlled object from the reference time to the operation time elapsed based on a forced displacement of the generalized coordinates given to the controlled object during the operating time or a target function of the generalized external force. Feedforward controls the generalized coordinates of the second support and the generalized velocity by applying a forced displacement or generalized external force to the generalized coordinates in part. The target function is a second derived from the reference information when the controlled object provided with at least the second support is regarded as a dynamic system which is a part of the three-body vibration system set as described above. A support-based generalized coordinate and the second support-based generalized velocity, a first support-based generalized coordinate derived from or virtually determined from reference information, and a first support-based generalized velocity, a second support It is determined based on the free movement of the three-body vibration system between the operation times determined from the target generalized coordinates and the second support target generalized velocity. The trajectory of the second support is controlled by applying the generalized coordinates or the generalized external force to the controlled object based on the target function, and the generalized coordinates and the generalized velocity of the second support from the reference time It is possible to accurately change the target generalized coordinates and the target generalized speed after the operation time. The reason will be described in detail later.

  Here, the reference information may be information from which the second support-based generalized coordinates and the second support-based generalized speed can be derived. That is, the reference information may be information representing the second support-based generalized coordinates or the second support-based generalized velocity itself, or the second support-based generalized coordinates or the second support-based generalized velocity. It may be indirect information from which can be derived. The control means may derive the second support reference generalized coordinates and the second support reference generalized speed based on the reference information. The control means may also perform derivation of the first support-based generalized coordinates and the first support-based generalized velocity or setting of virtual values. The control means may set the second support target generalized coordinates and the second support target generalized speed.

Also, the reference information acquisition means is not limited to the one that acquires the reference information at the reference time. If the reference information is “information that can derive the generalized coordinates and generalization speed of the second support at the reference time”, the time to be acquired may be, for example, a time before the reference time. For example, when the reference information is the acceleration of the second support and the control means derives generalized coordinates and generalized speed from the acceleration using a state observer (observer), the generalized coordinates and generalized coordinates are obtained from the acquisition of acceleration. Considering the time required for derivation, the reference information acquisition means should acquire the acceleration before the reference time. The reference information acquisition unit may acquire the reference information from the controlled body or may acquire the reference information from other than the controlled body. For example, when at least one of the second support-based generalized coordinates and the second support-based generalized speed is a fixed value, the reference information acquiring unit may read out and acquire a previously stored fixed value. Good. The reference information acquisition means may separately acquire information capable of deriving the second support reference generalized coordinates and information capable of deriving the second support reference generalized speed.

The target function is, for example, the second support reference generalized coordinate, the second support reference generalized speed, the first support reference generalized coordinate, the first support reference generalized speed, the second support target generalized coordinate. The second support target generalization speed, software or predetermined in advance with a time as a variable, to perform an output based on the input variable (a value representing a forced displacement of the generalization coordinates or a generalization external force) It may be configured as hardware.

[Invention 2]
In the track control device according to the present invention, the reference information acquisition unit repeatedly acquires the reference information every operation time of various lengths sequentially determined with the reference information set as a new reference time after the operation time has elapsed. The control means is configured such that the generalized coordinates and the generalized speed of the second support after the operation time has elapsed from the reference time are the second support target generalized coordinates and the second support target generalized. The feedforward control may be performed so as to approach the speed, and the feedforward control may be repeatedly performed by setting the new operation time after the operation time has elapsed from the reference time. In this case, the trajectory of the second support is controlled over a predetermined period constituted by the operation times of various lengths successively determined by repeating feedforward control during the operation time. Can do Here, the second support target generalized coordinates may be reset for each control between the operation times of various lengths each time, or may be between the operation times of a plurality of various lengths. It may be the same value throughout the control. Alternatively, the second support target generalized coordinates for each control during the operation time of each of various lengths so that the second support target generalized coordinates gradually approach the final target value. May be set. The same applies to the target generalization speed of the second support.

[Invention 3]
In the track control device of the present invention, the controlled object includes the first support movably supported by a fixed support A, and the second support oscillatingly supported by the first support. , And,
The fixed support A is a support fixed at an arbitrary stationary position as viewed from the fixed support, and the reference information acquiring means is the second support-based generalized coordinates, the second support-based generalized. Acquiring the reference information from which the velocity, the first support-based generalized coordinates, and the first support-based generalized velocity can be derived, and the target function performs the three-body vibration of the controlled object The second support-based generalized coordinates derived on the basis of the reference information, the second support-based generalized speed, and the first support-based generics when considered as a dynamic system that is a part of the system Based on the free motion of the three-body vibration system determined from the generalized coordinates, the first support reference generalized speed, the second support target generalized coordinates, and the second support target generalized speed. Determined to be given to the first support during the operation time. An objective function of forced displacement of generalized coordinates, and the control means performs forced displacement of the generalized coordinates on the first support from the reference time to the lapse of the operation time based on the goal function. The feedforward control may be performed by giving the value.

[Invention 5]
In the trajectory control apparatus of the present invention in the aspect of performing control using (Equation 1) described above, in the stationary coordinate system, the control means is configured such that both the first support and the second support are stationary. In this case, a method of moving the generalized coordinates of the second support by d, setting the first generalized reference coordinates of the first support to -d / 2, and setting the second generalized generalized target speed to 0 The feed forward control based on the forced displacement function X (t ₀ + t ′) may be performed by setting the second support target generalized coordinate to d / 2.

[Invention 6]
In the track control device according to the present invention, the controlled object is vibratably supported by the fixed support, the first support vibratably supported by the fixed support, and the first support. The second support, and the reference information acquisition means includes the second support reference generalized coordinates, the second support reference generalized speed, the first support reference generalized coordinates, When the reference information capable of deriving the first support-based generalized speed is obtained, and the target function considers the controlled object to be a dynamic system that is a part of the three-body vibration system, The second support reference generalized coordinates derived from the reference information, the second support reference generalized speed, the first support reference generalized coordinates, and the first support reference generalized speed; The second support target generalized coordinates and the second support target generalized velocity, A target function of a generalized external force to be applied to the first support during the operation time, which is determined based on the free movement of the three-body vibration system determined from the above, and the control means is based on the target function The feedforward control may be performed by applying the generalized external force to the first support from the reference time to the elapse of the operation time.

[Invention 7]
In this case, the objective function uses the generalized coordinates of the first support when the entire three-body vibration system is in balance as the origin of the generalized coordinates of the first support, and the three-body vibration A generalized external force function F _IIp (equation 3), where the generalized coordinates of the second support when the entire system is in a balanced state is the origin of the generalized coordinates of the second support It may be t ₀ + t ').
However, Δt is the operation time,
Among the two natural angular frequencies of the two-body coupled vibration system, the large natural angular frequency is ω ₊ = (2p + 1) π / Δt, the small natural angular frequency is ω ₋ = π / Δt, and p is a natural number Do.
Further, the second support reference generalized coordinate is x _in , the second support reference generalized speed is v _in , the first support reference generalized coordinate is X _in , and the first support reference generalized speed is Is V _in , the second support target generalized coordinate is x _en , and the second support target generalized speed is v _en .
Further, (Equation 3) is a non-dimensionalization function in which the natural period of the single oscillator consisting of the second support is 2π and the generalized mass of the second support is a representative mass, and t ′ = 0 to 0 It holds in the range of Δt.
In addition, γ is any positive real number.

[Invention 17-1]
The present invention is a power generation device for converting vibration energy into electric energy, comprising the orbit control device of the invention 7,
A magnetic field control unit capable of controlling a magnetic field of the magnetic field generation means, a magnetic field generation means attached to the periphery of the first support body, the first support integrated with a conductor; The reference information acquisition means capable of acquiring the position and speed of the vibration direction of the two support bodies and the first support body, and a power transmission means for transmitting electricity from the conductor to the outside,
The second support is devised so that vibrations are excited by external forces,
The conductor is arranged so that it can be energized in a direction perpendicular to the vibration direction of the first support,
The magnetic field generating means is arranged to be able to apply a magnetic field perpendicular to both the vibration direction and the energization direction,
Lorentz force acting on the current flowing in the conductor, which vibrates integrally with the first support,
A generalized external force function F _IIp (defined) to reduce the position and velocity of the vibrating second support based on the position and velocity of the second support and the first support in the direction of vibration. t ₀ + t '),
By controlling the magnetic field of the magnetic field generating means to be equal,
Suppressing vibration of the second support, and
In the conductor, a voltage due to speed electromotive force can be generated to increase a transmission voltage.
It is good also as a power generator which converts the vibration energy of the said 2nd support body into the electrical energy which flows through the said conductor.

  In the following, the controlled object may be referred to as a controlled oscillator. The reference time may be referred to as the operation start time. The generalized coordinates (position) at the reference time may be referred to as the initial position. The generalized speed at the reference time may be called the initial speed.

In the present invention, a three-body vibration system designed to cause energy transfer only between two specific vibrators is used, and one of the two specific vibrators is included in the controlled object, whereby the three-body vibration is generated. The trajectory of the controlled object is determined based on the free movement of the system.

The principle is clear and mechanically natural because the trajectory of the controlled object is determined by the Hamilton's principle of the dynamical system in the free movement of the three-body vibration system.

The three-body vibration system is designed so that Grover's wave algorithm is established so that energy transfer occurs only between two specific oscillators having the same natural period. By dividing into a child and the remaining one-body oscillator, the three-body problem does not occur and the movement of the entire system does not become complicated.

The Grover wave algorithm is the same as the Grover algorithm, which is one of the quantum algorithms in quantum information. The position and velocity vectors of multi-body oscillators, which are state quantities, are converted into time evolution operators, collision operators, and position conversion operations. By multiplying each operator such as a child, it is possible to freely manipulate the position and velocity vector of the many-body oscillator (Non-Patent Document 9).

By using the controlled object as one of the two specific vibrators, vibration energy of the controlled object can be freely moved to the other specified vibrator after a predetermined operation time, and every operation time can be changed. The position and velocity of the controlled object can be freely determined.

Further, the three-body vibration system is divided into a controlled body including one of the two specific transducers and a control body including the other of the two specific transducers, which is a portion other than the controlled body. Thus, vibration energy can be freely moved between the controlled body and the controlled body after the operation time.

Further, with the object to be controlled as a real body and the control object as an imaginary, the action and reaction of the force at the boundary between the object to be controlled and the control body are external force applied to the object to be controlled from the outside, and It is a force that can be applied from the controlled object to the outside. The change in the mass position at the boundary between the controlled body and the controlled body is a forced displacement from the outside of the controlled body.

Since the specific oscillator in the control body is a virtual system, its position and velocity can be freely determined every operation time. The trajectory of the control body is determined by determining the initial state of the virtual system so that the position and speed of the control body for each operation time become the target values.

The three-body vibration system according to the present invention comprises a first support vibratably supported by a fixed support in an inertial system, and a second support of equal natural period supported vibratably in parallel with the first support. A vibration system designed to move kinetic energy only between the second support and the third support for each operation time.

By regarding the controlled object having the second support, which is vibratably supported by the first support, as a part of the three-body vibration system freely moving in the storage force field, this three-body vibration system is characterized by Control function of external force or forced displacement capable of arbitrarily changing the position and velocity of the second support after the operation time in vibration systems under various restraints by utilizing energy transfer between certain vibrators. It derives analytically.

As a result, the external force that controls the controlled object and the control function for forced displacement are determined by the internal force of the three-body vibration system that freely moves in the conserving force field and the position of the virtual oscillator. It is optimized under the following mechanical conditions.

Further, in the present invention, as described later, a sample to which a control function is applied since discrete dynamic energy transfer is limited to only a part of two systems of the three-body vibration system, and conditions for separating speed and position control are further used. A special relationship, which will be described later, is established between the optimum operation time of the value control and the coupled angular frequency of the three-body vibration system.

By limiting discrete mechanical energy transfer in the present invention to a partial two-body vibration system, a three-body vibration system designed to satisfy the Grover algorithm is supported by a fixed support in a freely vibrating manner. A three-body vibration system comprising a first support, and a second support and a third support supported by the first support so as to be capable of vibrating in parallel, and a single vibration comprising the second support The natural angular frequency of the child and the natural angular frequency of the single oscillator including the third support are equally ω _t . Further, Δt is the operation time which can be various lengths, and the end point of each operation time represents a discrete time in the discrete dynamics. At that time, using a natural number p, two coupled natural frequencies ω ₊ and ω ₋ in a two-body vibration system consisting of the first support and the second and third supports with two centers of gravity By designing the three-body vibration system to satisfy 6), the internal resonance condition is established in the three-body vibration system. In this case, ω _+> ω _- is established.
As a condition of the three-body vibration system that satisfies this (Expression 6), there are design conditions for the three-body vibration system that satisfy the following (Expression 7) and (Expression 8).

When the three-body vibration system satisfies (Equation 7) and (Equation 8), as described later, an integrated vibration system consisting of a two-body vibration system consisting of the second and third supports and the first support Is an independent oscillator in the discrete dynamics whose end point is the operation time. On the other hand, except in special cases, the position and velocity of mass of each oscillator are coupled. In the following, we discuss the case where the three-body vibration system satisfies (Equation 7) and (Equation 8).

A schematic diagram of the three-body vibration system designed by this is shown in FIG. A vibrator composed of the first support 3 which is vibratably supported by the fixed support 7 via a spring 4 at one end is called a large vibrator, its mass is M, and a spring constant of the spring 4 is K. Further, of the two vibrators attached in parallel to the first support 3 so as to be freely vibrated, the vibrator composed of the second support 1 is a small vibrator 1 whose mass is m ₁ and a spring connected thereto Let the spring constant of 2 be k ₁ . Also an oscillator consisting of said third support 5 and the small vibrator 2, the mass m _2, the spring constant of the spring 6 connected therewith and k _2.

Since the natural angular frequency ω _t of the two small vibrators is equally expressed by the following (formula 9),
You can set m ₂ = γm ₁ and k ₂ = γk ₁ . Here, γ represents the ratio of mass and spring constant between the small oscillators. In the following, non-dimensionalization is performed with the mass m ₁ of the small oscillator 1 as the representative mass, its natural angular period 1 / ω _t as the representative time, and the unit length as the representative length. As a result, the natural period τ of a single oscillator consisting of the small oscillator 1 is made nondimensional as τ = 1 / ω _t = 2π.

The relationship of (Equation 10) and (Equation 11) is established between the coupled natural frequency, the mass of the dimensionless large oscillator, and the spring constant.

From these relational expressions and the above-mentioned conditional expression of the coupled natural frequency, the mass and the spring constant of the large non-dimensionalized large oscillator are expressed as in (Expression 12) and (Expression 13) below.

From (Equation 4) and (Equation 5), it can be seen that when ω ₋ = 1, the mass and spring constant of the large oscillator diverge infinitely. From (Equation 8), it can be seen that ω ₋ = 1 holds at Δt = π, so that the vibration control function to be obtained this time does not have physical meaning at Δt = π. The same can not be said for the case of Δt = (2n + 1) π. Since singularities of such models also appear as singularities such as functions, the discussion will continue below without particularly mentioning the existence of these singularities.

The position obtained from the balance position of the large oscillator when the entire three-body vibration system is in a balanced state is X, and the balance position of the small oscillator 1 when the entire three-body vibration system is in a balanced state The non-dimensionalized three-body system by setting the position obtained from the point x ₁ and the position obtained from the balanced position of the small vibrator 2 when the whole three-body vibration system is in balanced state as x _2. The equation of motion of free vibration in the vibrator is expressed by the following (Expression 14), (Expression 15), and (Expression 16).

The detailed definition of X, x ₁ , x ₂ which is the quantity of the position of mass of each oscillator appearing here, and V, v ₁ , v ₂ which is the quantity of velocity obtained from their time derivative is the end of the sentence Please refer to Fig.80 for a summary. Note that the origin of the coordinates of each position is different because X, x ₁ and x ₂ which are the amount of position of each vibrator have different locations such as the balanced position of each vibrator as the origin I want to be done.

In the explanation other than the theory, the object at the root of the large oscillator is the fixed support, the mass of the other large oscillator is the first support, the mass at the end of the small oscillator 1 is the second support, the small vibration The mass at the end of child 2 is also called the third support.

(Equation 14), (Equation 15), by solving the equation of (Equation 16), of the mass points of the three-body oscillator when the time is changed to t ₀ + t 'from t ₀ position X, x ₁ , X ₂ and speed V, v ₁ , v ₂ over time. The following (Equation 17) is obtained by representing these physical quantities in a vector.

Here, (Equation 18) is a state vector of the position of each mass point of the three-body vibrator at time t ₀ ,
(Equation 19) is the state vector of the velocity of each mass point of the three-body vibrator when the time is t ₀ .
Here, V is the mass velocity of the large oscillator, and v ₁ and v ₂ are the mass velocity of the small oscillator 1 and the small oscillator 2. Further, by arranging these vectors, a state vector of the position and speed of each mass point of the three-body transducer at the time t ₀ shown in (Equation 20) is obtained.

Further, A, B, and C are 3 × 3 matrices, and each component of the matrices A, B, and C is represented by (Expression 21-1) to (Expression 21-10) and (Expression 22-1) to It is represented by (Formula 22-10) and (Formula 23-1) to (Formula 23-10).

Furthermore, by replacing the time t 'of time evolution with a predetermined operation time Δt satisfying both (Equation 7) and (Equation 8), the interaction concerning the position and velocity of the large oscillator and the two sets of small oscillators The component to be represented is 0. The matrix A (t ′ = Δt) representing the time evolution during the operation time Δt determined in this way is U _a (Eq. 24) and the matrix B (t ′ = Δt) is U _b (Eq. 25) C (t '= Δt) is expressed as (Equation 26) as U _c . Therefore, (Equation 27) and (Equation 28) are obtained from (Equation 17).

As described above, in the time evolution of the three-body collision vibration system with the operation time Δt that satisfies both (Expression 7) and (Expression 8), the interaction between the small oscillators is separated from the large oscillator. Can do By this, the coupled vibration of the two small oscillators becomes a two-body problem under discrete dynamics, and a simple time evolution appears. Conversely, if this condition is deviated, the vibration becomes a three-body problem consisting of two small oscillators and one large oscillator, and complex chaotic oscillation may appear, but this condition prevents this.

On the other hand, the state vector of position and the state vector of velocity are discretely mixed with each other and can not be handled independently. This can only be done in special cases where the operating time Δt is an integer multiple of the natural period τ.

In addition to the time evolution operator this time, define the collision operator which causes one of the small oscillators to make an elastic collision, and operate the state vector | φ _v (t ₀ )> alternately to establish the Grover algorithm, Although almost periodic motion occurs in the system (Non-Patent Document 7), the present invention does not mention the collision operator because it is not always necessary.

Next, from the previous (Expression 28), the speeds of the small vibrators around the operation time Δt satisfy the following (Expression 29).
From this, the initial velocity v _in of the small vibrator 1 at time t _0, the target speed of the small vibrator 1 at time t ₀ + Delta] t When _{v en, v 1 (t 0} ) = v in, v since a _{1 (t 0 + Δt) =} v en, the initial velocity v ₂ (t ₀₎ of the small vibrator 2 may take a value that satisfies the following equation (30).

Similarly, from the previous (formula 27), the positions of both small vibrators around Δt time satisfy the following (formula 31).
From this, the initial position x _in of the small vibrator 1 at time t _0, when the target position of the small vibrator 1 and x _en at time _{t 0 + Δt, x 1 (} t 0) = x in, x _{Since 1} (t ₀ + Δt) = x _en , the initial position x ₂ (t ₀ ) of the small oscillator 2 may be a value satisfying the following (Equation 32).

On the other hand, from (Expression 17), the position of the large vibrator after time t ₀ + t ′ is expressed as (Expression 33) below.

_{x 1 (t 0) = x} in, x 1 (t 0 + Δt) = x en, v 1 (t 0) = v in, v 1 (t 0 + Δt) = v en, X (t 0) = X _in , V (t ₀ ) = V _in , and the coefficients defined in (Expression 21-1) to (Expression 21-10), (Expression 22-1) to (Expression 22-10) and ( The large vibrator which can change the position of the vibrator 1 from x _in to x _en and the speed of the vibrator 1 from v _in to v _en by substituting the equation 30) and the equation 32). A forced displacement function (Equation 34) is obtained. Since this forced displacement function is a function of ω ₊ = (2p + 1) π / Δt, the forced displacement function is a function that varies with the parameter p which is a natural number. In the following, the forced displacement function when ω ₊ = (2p + 1) π / Δt is expressed as X _p (t ₀ + t ′) and is shown in the following (formula 34).

Next, in the three-body vibration system, the position of the small vibrator 1 after time t ₀ + t ′ is expressed by (Expression 17) as follows (Expression 35).

_{x 1 (t 0) = x} in, x 1 (t 0 + Δt) = x en, v 1 (t 0) = v in, v 1 (t 0 + Δt) = v en, X (t 0) = X _in , V (t ₀ ) = V _in , and the coefficients defined in (Expression 21-1) to (Expression 21-10), (Expression 22-1) to (Expression 22-10) and ( The trajectory of the small oscillator 1 which changes the position of the oscillator 1 from x _in to x _en and the velocity of the oscillator 1 from v _in to v _en by substituting the equation 30) and the equation 32) The function (Equation 36) is obtained. Since the orbital function of the small oscillator 1 is also a function of ω ₊ = (2p + 1) π / Δt, it becomes a different function depending on the parameter p which is a natural number. In the following, the orbit function of the small oscillator 1 when ω ₊ = (2p + 1) π / Δt is represented as x _1p (t ₀ + t ′), and is represented by the following (Expression 36).

As shown by the dotted line A in FIG. 1, the small vibrator 1 is taken out from the three-body vibration system to form an integral vibrator, whereby the position of the large vibrator is X _p (t ₀ + t '). Is equivalent to the forced displacement function of the root of an integral oscillator. Fig. 2 shows an outline of an integrated oscillator that forcibly displaces the root.

As shown in FIG. 2, the integrated vibrator taken out in this way vibrates through a first support 3 that is movably supported by a fixed support A 7 a, and the first support 3 via a spring 2. It is a vibrator composed of the second support 1 supported freely. The fixed support A is a support fixed at any stationary position as viewed from the fixed support defined in the three-body vibration system.

By forcibly displacing the first support according to X _p (t ₀ + t ′) for t ′ = _{0 to} Δt, the trajectory of the second support becomes x _{1 p} (t ₀ + t ′), Before and after a predetermined operation time, the position of the second support can be changed from x _in to x _en and the speed of the second support can be changed from v _in to v _en .

On the other hand, the differential equation of the integral vibration system subjected to the forced displacement is expressed by the following (Equation 37).

In this differential equation, the differential equation shown in the following (Equation 38) is obtained by taking the linear sum of each parameter p. Thereby, the second support is required to draw the orbital function x ₁ (t ₀ + t ′) represented by (Equation 39). The displacement function X (t ₀ + t ') is defined. Therefore, during the operation time Δt, by applying a forced displacement represented by (Formula 1) to the first support, the position of the second support is changed from x _in to x _en and the second support You can change your body speed from v _in to v _en .
However, x (t ₀ + t ') and X (t ₀ + t') are not given, where 2π is the natural period of the single oscillator consisting of the second support and the representative mass is the mass of the second support. It is a dimensioning function, and holds in the range of t ′ = 0 to Δt, where Δt is the operation time. In natural numbers p, ω ₊ = (2p + 1) π / Δt, ω ₋ = π / Δt, and α _p is any real number satisfying the following (Expression 2).

On the other hand, the integrated oscillator for forced displacement of the root shown in Fig. 2 is rewritten in a non-inertial coordinate system fixed to the root. As a result, an inertial force is generated on the second support. This gives an equation of motion in the case where an external force acts on the mass of the integral vibrator whose root is fixed as shown in FIG. As shown in FIG. 3, the integrated vibrator thus taken out is a vibrating body composed of a second support 1 that is supported by a fixed first support 3 via a spring 2 so as to vibrate. An external force is applied to the second support 1.

In this case, during the operation time Δt, an external force function F _I (t ₀ + t ′) which is an inertial force applied to the second support is obtained, and an orbit function y _1p (t ₀ ) drawn by the second support + t ') is calculated. However, these physical quantities are only a result of rewriting the system that applies the forced external force shown in Fig. 2 to the root of the integral vibration system in the coordinate system of the non-inertial system. Absent.

Next, from the calculation of the three-body vibration system described above, the position of the small vibrator 2 at time t ₀ + t ′ after giving the operation from the time t ₀ to the operation time Δt is (Equation 40).

_{x 1 (t 0) = x} in, x 1 (t 0 + Δt) = x en, v 1 (t 0) = v in, v 1 (t 0 + Δt) = v en, X (t 0) = X _in , V (t ₀ ) = V _in , and the coefficients defined in (Expression 21-1) to (Expression 21-10), (Expression 22-1) to (Expression 22-10) and ( By substituting Equations 30) and (32), the trajectory function (Equation 41) of the small oscillator 2 which changes the position and velocity from x _in and v _in to x _en and v _en , respectively, is obtained. Since the orbit function of the small oscillator 2 is also a function of ω ₊ = (2p + 1) π / Δt, it becomes a different function depending on the parameter p which is a natural number. In the following, the orbital function of the small oscillator 2 when ω ₊ = (2p + 1) π / Δt is expressed as x _2p (t ₀ + t ′).

Furthermore, by multiplying the difference between the position of the large oscillator shown in (Equation 34) and the position of the small oscillator 2 shown in (Equation 41) by the spring constant γ, ω ₊ = shown in (Equation 3) The external force function F _IIp (t ₀ + t ′) (formula 3) _applied to the large oscillator in the case of (2p + 1) π / Δt is obtained.

However, F _IIp (t ₀ + t ′) is a non-dimensional function in which the natural period of a single oscillator consisting of the second support is 2π and the mass of the second support is a representative mass, and t ′ It holds in the range of 0 to Δt. Further, in the natural number p, ω ₊ = (2p + 1) π / Δt, ω ₋ = π / Δt, K = (γ + 1) (2p + 1) ² ω ₋ ⁴ / [{(2p−1) ² ω ₋ ² -1} (1-ω _- ² )}, and γ is any positive real number.

As shown by the dotted line B in FIG. 1, the position of the mass of the small vibrator 1 is obtained by taking out a two-piece vibrator comprising the small vibrator 1 and the large vibrator in series from the three-body vibration system. And an external force function to be applied to the large oscillator, which can be manipulated arbitrarily. The outline of the two-body oscillator is shown in Fig.4.

The equation of motion in the two-body oscillator using F _IIp (t ₀ + t ′) as the excitation force of the large oscillator is expressed as (Expression 42) and (Expression 43) below.

The two-body vibrator thus taken out is, as shown in FIG. 4, a first support 3 vibratably supported by a fixed support 7 defined in the virtual three-body vibration system via a spring 4. And a second support 1 vibratably supported by the first support 3 via a spring 2, and an external force is applied to the first support 3.

By applying an external force F _IIp (t ₀ + t ′) represented by (Equation 3) to the first support during t ′ = _{0 to} Δt, the trajectory of the second support becomes (Equation 36) It is possible to change the position of the second support from x _in to x _en and the velocity of the second support from v _in to v _{en as} shown x _{1 p} (t ₀ + t ′).

On the other hand, with respect to (Equation 37) in the integrated vibrator for forcibly displacing the root shown in FIG. 2, the second term of the right side of (Equation 37) which is a force generated by the forced displacement of the root By using the external force function F _IIIp (t ₀ + t ′), (Equation 44) holds.

(Equation 44) is an equation of motion that holds for a vibrating body composed of the second support 1 _vibratably supported by the fixed support D shown in FIG. from _{t 0 + t ') = X} p (t 0 + t') become possible, the external force function F _IIIp against said second support 1 (t ₀ + t ') is expressed as shown in equation (45) . The fixed support D is a support fixed at a balanced position of the first support defined in the virtual three-body vibration system.
Since the first support has no entity here, X _in the V _in is the parameter defining the external force at the reference time.

However, F _{III p} (t ₀ + t ′) is a non-dimensionalization function in which the natural period of a single oscillator consisting of the second support is 2π and the mass of the second support is a representative mass, and t ′ It holds in the range of 0 to Δt. In the natural number p, ω ₊ = (2p + 1) π / Δt and ω ₋ = π / Δt.

Even when the fixed support D 7d shown in FIG. 5 is an unfixed movable body, the acceleration is sufficiently smaller than the external force function F _IIIp (t ₀ + t ′). Is less likely to significantly change the position and velocity 'of the second support after the operation time.

Next, with respect to (Equation 38) in the integrated vibrator for forcibly displacing the root shown in FIG. 2, the right side second term of the (Equation 38) which is a force generated by the forced displacement of the first support 3 at the root. Is an external force function F _III (t ₀ + t ′) for the second support 1 shown in (Equation 46), so that (Equation 47) holds.
Where α _p is any real number that satisfies (Equation 2).

(Equation 47) is an equation of motion that holds for a vibrating body composed of the second support 1 vibratably supported by the fixed support D shown in FIG. An external force F _III (t ₀ + t ′) represented by (Equation 4) is applied to the support 1.
Since the first support has no entity here, X _in the V _in is the parameter defining the external force at the reference time.

However, F _III (t ₀ + t ′) is a non-dimensionalization function in which the natural period of a single oscillator consisting of the second support is 2π and the mass of the second support is a representative mass, and t ′ It holds in the range of 0 to Δt. In the natural number p, ω ₊ = (2p + 1) π / Δt and ω ₋ = π / Δt.

The second support is fixed by fixing the first support during t ′ = _{0 to} Δt and applying an external force F _III (t ₀ + t ′) represented by (Formula 4) to the second support. The trajectory described by is the orbital function x ₁ (t ₀ + t ′) shown in (Expression 39), and the position of the second support is from x _in to x _en and the velocity of the second support is v You can change from _in to v _en .

On the other hand, as shown by the dotted line C in FIG. 5, by taking out the second support 1 as a free object movably supported by the fixed support E, the position and speed of the second support 1 can be set arbitrarily. An external force function is obtained which is applied to the second support 1 which makes it possible to operate. The outline of the second support 1 is shown in FIG. The fixed support E is a support fixed at any stationary position as viewed from the fixed support defined in the virtual three-body vibration system.

As shown in (Equation 48), by setting the right side of (Equation 37) to the external force function F _IVp (t ₀ + t ′) with respect to the second support, an equation of motion (Equation 49) with respect to the second support Is true.

(Equation 49) is an equation of motion that holds for the controlled object composed of the movable second support 1 shown in FIG. 6, and the external force function F _IVp (t ₀ + t ′) for the second support 1 Is expressed as (Equation 50).
Since the first support has no entity here, X _in the V _in is the parameter defining the external force at the reference time.

However, F _IVp (t ₀ + t ′) is a non-dimensionalization function in which the intrinsic period of a single oscillator consisting of the second support which exists virtually as 2π and the mass of the second support as a representative mass Yes, and holds in the range of t '= 0 to Δt. In the natural number p, ω ₊ = (2p + 1) π / Δt and ω ₋ = π / Δt.

Similarly, by setting the right side of (Expression 38) to the external force function F _IV (t ₀ + t ′) for the second support shown in (Expression 51), it is an equation of motion for the second support (Expression 52) ) Holds.
Where α _p is any real number that satisfies (Equation 2).

Thus, the trajectory drawn by the second support is the trajectory function x ₁ (t ₀ + t ′) shown in (Expression 39).

By applying an external force F _IV (t ₀ + t ′) represented by (Expression 51) to the second support during t ′ = _{0 to} Δt, the trajectory described by the second support is expressed by (Expression 39) orbital x ₁ shown in) (t ₀ + t '), and the position of the second support to x _en the x _in, and alter the speed of the second support from the v _in v to _en be able to.

Therefore, the external force function F _IV (t ₀ + t ') given to the second support in order for the second support to draw the orbit function x ₁ (t ₀ + t') shown in (Expression 39) is (Equation 5).
However, F _IV (t ₀ + t ′) is a non-dimensionalization function in which the natural period of a single oscillator consisting of the second support is 2π and the mass of the second support is a representative mass, and t ′ It holds in the range of 0 to Δt. In natural numbers p, ω ₊ = (2p + 1) π / Δt, ω ₋ = π / Δt, α _p is an arbitrary real number satisfying (Expression 2), and X _in and V _in are at the reference time It is a parameter that determines the external force.

The function group that represents the forced displacement and external force applied during the operation time, arbitrarily operating the position and speed of the second support obtained as described above, is collectively referred to as “integral vibrator operation function”, or We will call it "oscillation control function" for short. In some cases, it is also called an "objective function" because it satisfies the purpose of the vibration operation.

Since the three-body vibration system is a Hamilton system in which energy is conserved during the operation time, Hamiltonian and Lagrangian are defined. Therefore, generalized momentum and generalized external force are defined as partial differentials of Hamiltonian and Lagrangian when generalizing the conventional concept of position and displacement of one-dimensional linear coordinates. General acceleration is defined as the time derivative of the generalized coordinate, and generalized acceleration is defined as the time derivative. Furthermore, the generalized mass is defined from the ratio of the generalized momentum and the generalized velocity.

Since the three-body vibration system satisfies the Lagrangian equation of motion during the operation time, the time derivative of the generalized momentum is equal to the generalized external force, and the same relationship as the Newton equation of motion holds. Therefore, the relational expression of the present invention is that the position is generalized coordinates, the speed is generalized speed, the acceleration is generalized acceleration, the jerk is generalized jerk, the force is generalized external force, the mass is generalized mass, the momentum is general The same holds true for the case of chemical momentum.

For example, when the generalized coordinates are taken as the angle of rotation, the generalized external force is the moment of force, the generalized mass is the moment of inertia, the generalized speed is the angular velocity, and the present invention is based on the equation of motion of rotation. The same holds for vibration. Of course, this also holds for physical quantities defined by other generalized coordinates.

According to the present invention, the position of the second support is set to Δx = x _en −x _in after Δt by applying forced displacement or external force for a predetermined operation time Δt in various vibrators and controlled bodies described above. , it is possible to feed forward control the trajectory of the controlled member so as to change its speed Δv = v _en -v _in.

As a result, the motion of the oscillator of interest is determined as an open box model, and the trajectory of the controlled body is determined analytically, so that reliable feedforward control is realized. This means that the three-body vibration system, which is the base, independently of the position and velocity between the small transducers independently and freely, regardless of the state of the large transducers, the end points of the sequence of operation times of various lengths. This is because it can be operated discretely as the reference time for each time, which is an advantage not seen in the conventional dynamic vibration absorber model based on the two-body vibration system. Furthermore, since the amount of forced displacement is given by a fixed function, it is also possible to use an inexpensive and high-speed control method such as a cam mechanism. Furthermore, since the magnitude of the external force can be selected by changing the function, the output of the device that applies the external force can be reduced, and the equipment can be given flexibility.

Further, according to the present invention, in the various vibrators described above, the target values of the position x _in and the velocity v _in of the second support are determined for each operation time Δt, and the target of the second support is determined for each operation time Δt. The operation time is obtained by obtaining information on the current value of the position x _in and the velocity v _in and applying a forced displacement or an external force according to a vibration operation function determined so as to eliminate the difference between the target value and the current value during Δt. For each Δt, the trajectory of the controlled body can be sampled so that the position of the second support can be brought close to x _en and the speed of the second support close to v _en . FIG. 84 shows a flowchart of sample value control using the vibration operation function X (t ₀ + t ′).

As a result, even when the position and speed of the second support are different from the purpose due to measurement error and control error, it can be corrected during the next operation time. In addition, even when the natural period and the operation time of the system are shifted with time, the position and speed of the second support can be brought close to the target values, so that the present method can be controlled with high robustness. .

Furthermore, in this method, since the vibration operation function is determined during the operation time, feedforward control is performed, and at each operation time boundary, the target position and speed are compared with the actual values to determine the vibration operation function. Because it can correct, feedback control becomes possible. As described above, this method can perform trajectory control of the controlled object that has both goodness of both feedforward control and feedback control in a natural way.

Furthermore, since the operation time that can be various lengths can be set as the sampling period, it is not necessary to apply higher-speed feedback for higher accuracy. This also eliminates the need to prepare high-speed sensors, computers with high-speed computing capabilities, and high-speed actuators. Furthermore, since control can be performed so as to gradually approach the target value for each operation time, it is not necessary to prepare a large output actuator. In addition, the vibrator can be damped without residual vibration after the operation time, and the fastest vibration can be controlled.

As described above, since the present method can set the operation time to be of various lengths as a sample period, it works effectively in a system in which feedback information can be obtained only in discrete time. For example, in seek control of a hard disk, the position of the head can read the position information written to the disk at constant intervals only at constant time intervals, but an integer multiple of the time interval at which position information can be obtained By designing the system so that the operation time is reached, the sample control of the present invention becomes more adaptable and the seek control with the fastest and less residual vibration becomes possible.

The conventional control method has been expressed by expressing the occurrence of feedback or feedforward flow, errors, etc. with a block diagram. On the other hand, this method is a method that has a feedback-like property by repeating this, since this function includes correction of deviation in addition to control using a ford-forward function at a constant operation time. Close to value control but not the same. Therefore, although it is extremely difficult, the flow of this control method is shown as a block diagram in the sense that it is easy to compare with the conventional control method (Fig. 85).

Block diagram is many of which represent the time evolution calculation U _s, after the feedback loop, by performing collision operator U _tp and speed of the collision operator U _tv position from the comparison with the target value, the It can be seen that the deviation is corrected.

On the other hand, the control method of this time is based on the theory of quantum algorithms, so the control method also suits the idea of a wave algorithm that performs operations sequentially on 6-dimensional state variables. Therefore, this algorithm is also written in the form of a wave circuit used in the field of quantum information (FIG. 86). This is easier to understand the history of calculated state quantities and operations.

The present invention is mainly in the discovery and application of vibration manipulation functions as analytical solutions, but it may be understood as a calculation process (algorithm) of a system including virtual state variables.

Three-body vibration system as a basis and integrated vibration system (A) and two-body vibration system (B) A controlled body comprising a first support 3 that is movably supported by a fixed support A 7a, and a second support 1 that is movably supported by the first support 3 A controlled body composed of a fixed first support body 3 and a second support body 1 supported by the first support body 3 so as to freely vibrate thereto, and an arbitrary external force is applied to the second support body 1 The first support 3 is composed of a fixed support 7, a first support 3 supported by the fixed support 7 so as to vibrate freely, and a second support 1 supported by the first support 3 so as to vibrate freely. Controlled body to which external force is applied A controlled body composed of a second support 1 that is supported by a fixed support D 7d so as to vibrate, and to which an arbitrary external force is applied to the second support 1 A controlled body composed of a movable second support 1 to which an arbitrary external force is applied to the second support 1 A controlled body composed of a first support 3a movably supported by a uniaxial actuator 8a attached to a fixed support A 7a and a second support 1a movably supported by the first support 3a. Trajectory controller A which measures the position and velocity of the first and second supports and controls the amount of movement of the first support 1a from the results A first support 3a, which is a cam follower 13a movably supported by a cam mechanism 12a attached to a fixed support 7a, and a second support 1a, which is movably supported by the first support 3a. A track control device A having a controlled body and measuring the positions and speeds of the first and second supports by the sensors 11aa and 11ab, respectively, and controlling the cam mechanism 12a from the results. It has a controlled object composed of a first support 3a movably supported by a cam 12a and a forceps mechanism 14a, and a second support 1a vibratably supported by the first support 3a. Orbit control device A for controlling the cam 12a and the lever mechanism 14a from the measured position and speed The position and speed of the second support are determined by a sensor 11db, which has a controlled object composed of a fixed support D 7d and a second support 1d vibratably supported thereto via a spring 2d. The trajectory control device B or vibration control device D for controlling the external force of 1d to the second support from the measurement result A fixed support 7c, a first support 3c vibratably supported by the fixed support 7c via a spring 4c, and a second support 1c vibratably supported by the first support 3c via the spring 2c Orbit control device C having the controlled object, measuring the position and speed of the first and second supports with sensors 11ca and 11cb, and controlling the external force applied to the first support 3c from the results. The second support 1e is movably supported and has a controlled body to which an arbitrary external force is applied to the second support 1e. The position and speed of the second support 1e are measured by the sensor 11eb, Trajectory control device E for controlling external force to second support 1e from the result Schematic diagram of a trajectory control device A comprising a robot arm 17 attached to an arbitrarily movable uniaxial actuator 8a A schematic illustration of a trajectory control device A comprising a cantilever 20 having at its tip a magnetic head 21 attached to an optionally rotatable arm 19 in a hard disk Schematic diagram of the trajectory controller A consisting of the entire semiconductor exposure apparatus including the vibration isolation table Change of position of modal mass of flexible structure when residual vibration removal operation is performed to the flexible structure which is residual vibration by orbit control device A Root position change when residual vibration removal operation is applied to flexible structure by trajectory controller A Changes of the modal mass and the position of the root of the flexible structure when the track control device A moves at the fastest speed from the stop position to another stop position Changes in modal mass and root position when residual vibration of a flexible structure moving at a constant speed is removed by using orbit control device A Changes in the acceleration at the base of a flexible structure that was gradually stopped in several steps Changes in the position of the flexible structure's root when the stop operation is performed while moving to the modal mass of the flexible structure at every operation time Change of the position of the mode mass of the flexible structure at the time of stopping operation while moving at every operation time and the cycloid curve as the reference of the trajectory Conceptual diagram of overhead crane using track control device A Time change of angle by residual vibration removal operation of overhead crane with initial deflection angle of π / 20 Time change of angle due to residual vibration removal operation of overhead crane with initial deflection angle of π / 4 Relationship between Initial Swing Angle and Residual Vibration Angle in Overhead Crane Temporal change of angle when removing residual vibration in two steps in the overhead crane whose initial deflection angle is π / 4 Difference in residual vibration removal ability due to deviation of appropriate swing angle and initial swing angle in vibration control operation of overhead crane Example of disk cam shape that realizes vibration control operation of an overhead crane that swings at a constant amplitude Conceptual diagram of a trajectory control device that controls a building built on a seismic isolation bearing using the trajectory control device A Conceptual diagram of a trajectory control device that controls sloshing in a large tank built on a seismic isolation bearing using the trajectory control device A Front view of an elevated transmission line tower equipped with a track control device that prevents galloping using the track control device C Side view of elevated transmission line tower with track control device that prevents galloping using track control device C A conceptual diagram of a galloping-preventing trajectory control device installed on the support of an elevated power transmission line steel tower using a trajectory control device C Side view of an elevated power transmission line tower equipped with a track control device for preventing hanging galloping using the track control device C Enlarged view of the trajectory controller that prevents the galloping by the suspension system using the trajectory controller C Enlarged view of track control to prevent hanging and non-contact galloping using track control device C Conceptual diagram of a relay for large current that does not cause chattering using track controller A Conceptual diagram of automatic door with fail-safe safety function using track controller A Conceptual diagram of a high-speed press with variable impact position and impact speed using orbit control device A Conceptual diagram of a trajectory control device that enables display with a pendulum using the trajectory control device A Conceptual diagram of a trajectory control device that enables display with cantilever beams using the trajectory control device A Cam curve that allows for a certain distance of movement without residual vibration Example of a disc cam that allows a certain distance of movement without residual vibration Change of the position of the follower mechanism moved by the cam which enables movement of a fixed distance without causing residual vibration and the cycloid curve as a reference Cam acceleration curve that allows for a certain distance of movement without residual vibration Relation between vibration ratio and ratio of cam rotation frequency to vibrator natural frequency A cam curve that allows a certain distance of movement by stopping at every operating time The track of the follower mechanism and the cycloid curve based on the cam curve that can be moved by a fixed distance by giving a stop operation every operation time Example of a disc cam that allows a certain distance of movement by stopping at every operating time Relationship between sloshing of liquid in container and virtual pendulum Trajectory control device that suppresses sloshing attached to transporter of liquid in container using trajectory control device A A model of a multi-stage rolling mill using linear vibrators. Increased vibration (chattering) of multi-high rolling mill due to fluctuations in sheet thickness Suppression of chattering of multi-stage rolling mill due to external force Orbit control device that suppresses chattering attached to each roll part of multi-high rolling mill using orbit control device D A trajectory control device that suppresses chatter vibration attached to a machining removal device using the trajectory control device D Side view of a track control device that suppresses vibration of a wind turbine support by controlling the phase of the blades of the wind turbine using the track control device D Front view of a trajectory control device that suppresses vibration of a wind turbine support by controlling the phase of a blade of a wind turbine using a trajectory control device D Conceptual diagram of electromagnetically driven valve consisting of orbit control device E Time change of external force applied to electromagnetically driven valve consisting of orbit control device E that opens and closes without residual vibration Time variation of electromagnetically driven valve position that opens and closes without residual vibration Conceptual diagram of the electromagnetically driven valve consisting of the orbit control device D Temporal change of external force applied to electromagnetically driven valve consisting of orbit control device D that opens and closes without residual vibration Temporal change in acceleration applied to a building by a large earthquake with a seismic intensity of 5 classes Time variation of the shaking of a building when a building without a damper receives a large earthquake of seismic intensity 5 class Time change of the shaking of a building subjected to a large earthquake with a seismic intensity of 5 class when the vibration suppression sample value control is performed by the vibration control device using the track control device A Flow chart of sample value control for each operation time Trajectory control device for vibration power generation using trajectory control device C Schematic of the active suspension of an automobile using the orbit control device A Automotive valve mechanism Time variation of surging of a valve spring excited by a cam with a cycloid curve shape Time variation of surging of a valve spring excited by a cycloid-curved cam with slight irregularities Time variation of contact pressure between cam and cam follower by surging valve spring Valve spring surging prevention device using orbit control device D Trajectory control device for suppressing pitching vibration of offshore wind turbine generator using trajectory control device D by blade pitch operation Conceptual diagram of an electromagnetically driven valve using a linear motor using the orbit control device E Time change of voltage applied to linear motor during opening / closing drive with valve lift of 10mm Time change of current applied to linear motor during opening / closing drive with valve lift of 10mm How to determine the position of each support in a three-body vibration system based on the balance position of the entire system Conceptual diagram of changes in position of first support and second support at each reference time viewed from fixed coordinate system Time variation of road surface position showing step-like change and time variation of actuator displacement when vibration control operation is performed using vibration function Time-dependent change in the position of the vehicle body when a vibration control operation using a vibration operation function is performed on a road surface change indicating a step-like change Flow chart of sample value control using vibration operation function X (t ₀ + t ') Block diagram of sample value control using vibration operation function X (t ₀ + t ') Wave circuit representation of sampled data control method using vibrational manipulation function X (t ₀ + t ') Dependence of target swing angle on operation time in overhead crane Dependence of target swing angle on operation time in vibration reduction operation of overhead crane Temporal change of trolley position and speed, wire deflection angle and deflection angular velocity in overhead crane transportation operation Integral rotating vibrator model of single-joint robot arm Conceptual diagram of wave power generator Image of wave power generators arranged on the coastline Trajectory control device for vibration power generation using trajectory control device D

According to the control signal created by detecting the position and speed of the mass of the first support and the second support constituting the controlled body at the operation start time, the present invention It is a trajectory control device that performs feedforward control or sample value control of the position and velocity of the second support by performing the trajectory control shown.

In the track control device A, the controlled object includes a first support movably supported by a fixed support A and a second support oscillatingly supported by the first support. In this case, the trajectory operation is a forced displacement to be applied to the second support, and the control signal is a forced displacement function X with a non-dimensionalization time t with an intrinsic period of 2π of the oscillator comprising the second support t ₀ + t ') (Expression 1). Thereby, the trajectory of the second support changes in accordance with the trajectory function x ₁ (t ₀ + t ′) shown in (Equation 39). These functions hold in the range of t ′ = 0 to Δt.

For example, as shown in the schematic view of FIG. 7, a specific example of the track control device A is subjected to forced displacement as the first support 3a is movably controlled by the one-dimensional actuator 8a. The two supports 1a are single vibrators connected to the first support 3a by springs 2a. Further, the position and the velocity of the first support 3a are measured by the sensor 11aa at each operation time, and the position and the velocity of the second support 1a are measured by the sensor 11ab at each operation time. The one-dimensional actuator 8a is controlled by the controller 10a so that the first support 3a is moved according to the forced displacement function X (t ₀ + t ′).

Further, as shown in the schematic view of FIG. 8, the cam follower 13a which is the first support 3a can be forcibly displaced by the cam 12a in accordance with the forced displacement function X (t ₀ + t ′). Or, as shown in the schematic diagram of FIG. 9, wherein the first support 3a, in accordance forced displacement function _{X (t 0 + t ')} , the displacement of the flat cam that born by the cam 12a and the cam follower 13a Forced displacement can also be performed by a mechanism which is expanded or contracted by the forceps 14a or the like.

On the other hand, in the case of the trajectory control device B in which the controlled object is composed of the fixed first support and the second support vibratably supported by the first support, the trajectory The operation is an external force applied to the second support, and the control signal is an external force function F _I (t ₀ + t ') with a non-dimensionalization time t, with the natural period of the oscillator comprising the second support 1d being 2π. It becomes. Thereby, the trajectory of the second support changes according to the trajectory function y ₁ (t ₀ + t ′). These functions hold in the range of t ′ = 0 to Δt.

For example, as shown in the schematic view of FIG. 10, a specific example of the track control device B is that the first support is the fixed support 7d itself, and the second support 1d is the fixed support by a spring. It is a single oscillator connected to the body D. The second support 1d is made of a soft magnetic material having a high magnetic permeability, and an external force is applied by an electromagnetic force generated from a coil or the like arranged around the second support 1d. Further, the position and the velocity of the second support 1d are measured at each operation time by the sensor 11db, and the current flows from the power source to the coil according to the external force function F _I (t ₀ + t ') determined from this information The amount of current is controlled by the controller.

On the other hand, a first support body vibratably supported by the fixed support body defined in the virtual three-body vibration system and a second support body vibratably supported by the first support body In the case of the orbit control device C constituted by the support, the orbit operation is the external force applied to the first support, and the control signal is the natural period of the oscillator formed of the second support 2π. This is the external force function F ' _IIp (t ₀ + t') of dimensionless time t. Thereby, the trajectory of the second support changes in accordance with the trajectory function x _{1 p} (t ₀ + t ′) shown in (Expression 36). These functions hold in the range of t '= 0 to Δt.

For example, in the specific example of the track control device C, as shown in the schematic view of FIG. 11, the first support 3c is connected to the fixed support 7c via a spring 4c, and further the second support 1c is connected to the first support 3c by a spring 2c to form a two-body vibrator connected in series. The first support 1c is made of a soft magnetic material having a high magnetic permeability, and an external force is applied by an electromagnetic force generated from a coil 15c or the like disposed around the first support 1c. Furthermore, the position and the velocity of the first support 3c are measured by the sensor 11ca at each operation time, and the position and the velocity of the second support 1c are measured by the sensor 11cb at each operation time. The amount of current flowing from the power supply 16c to the coil 15c is controlled by the controller 10c so that an external force is applied according to the function F ′ _IIp (t ₀ + t ′).

On the other hand, in the case of the trajectory control device D in which the controlled object is constituted of the second support supported by the fixed support D in a freely vibrating manner, the trajectory operation is an external force applied to the second support. Yes, the control signal is expressed by (Formula 4) as an external force function F _III (t ₀ + t ′) of the dimensionless time t with the natural period of the vibrator made of the second support being 2π. Thereby, the trajectory of the second support changes in accordance with the trajectory function x ₁ (t ₀ + t ′) shown in (Equation 39). These functions hold in the range of t '= 0 to Δt.

For example, a specific example of the track control device D is the same as the schematic view of FIG. 10, and the second support 1 d is a single vibrator connected to the fixed support D 7 d by a spring 2 d. Yes. The second support 1d is made of a soft magnetic material having a high magnetic permeability, and an external force is applied by an electromagnetic force generated from a coil 15d or the like disposed around the second support 1d. Further, the position and the velocity of the second support 1d are measured at each operation time by the sensor 11db, and an external force is applied from the power supply 16d according to the external force function F _III (t ₀ + t ′) determined from this information. The amount of current flowing through the coil 15d is controlled by the controller 10d.

On the other hand, in the case of the track control device E in which the controlled object is constituted by the second support movably supported by the fixed support E, the track operation is an external force applied to the second support The control signal is an external force function F _IV (t ₀ + t ′) of a dimensionless time t with the natural period of the vibrator made of the second support being 2π (Equation 5). Thereby, the trajectory of the second support changes in accordance with the trajectory function x ₁ (t ₀ + t ′) shown in (Equation 39). These functions hold in the range of t ′ = 0 to Δt.

For example, a specific example of the track control device E is a free object movably supported by the fixed support E, as shown in the schematic view of FIG. . The second support 1e is made of a soft magnetic material having a high magnetic permeability, and an external force is applied by an electromagnetic force generated from a coil 16e or the like disposed around the second support 1e. Furthermore, the position and the velocity of the second support 1e are measured at each operation time by the sensor 11eb, and an external force is applied according to the function F _IV (t ₀ + t ′) determined from this information, the coil 16 from the power supply 16e The amount of current flowing through 16e is controlled by the controller 10e.

The position and speed of the first support and the second support in the present invention are measured by using a position sensor or a speed sensor, an acceleration sensor, an image processing apparatus, or the like that is attached to each support itself or measured in a non-contact manner. .

The vibrator comprising the second support in the present invention may be a single vibrator comprising a spring and a weight, or a pendulum comprising a weight suspended by a wire. In addition, even in a continuum such as a cantilever, when its main vibration is limited to one mode, it can be used as one vibrator.

However, in the case of a pendulum or cantilever beam, the position becomes the rotation angle of the pendulum, so special care must be taken when controlling this by changing the position of the base perpendicular to gravity. In this case, as will be described later, the change in the position of the pendulum or the like that is the second support is a change in angle as a generalized coordinate. It is necessary to use the amount of change in acceleration at the root as the localization coordinates.

When the angle of the pendulum or the cantilever can be directly controlled, the amount of forced displacement of the root which is the first support is the amount of change of the angle.

In the control method of the present invention, even in a complicated structure, when there are a plurality of specific vibration modes consisting of a mode mass and a mode rigidity appearing by modeling the structure as a multi-body vibrator and performing a mode analysis, By using each operation time determined by the natural period of the vibration mode and applying a forced displacement amount or external force determined from the position and speed information of the mode mass of each vibrator to the structure, The vibration of the structure can be feedforward controlled for each vibration mode or sampled for each vibration mode.

The forced displacement of the second support in the present invention is realized by a one-dimensional actuator or a cam mechanism that moves the root in the displacement direction of the vibrator.

The external force applied to the first support and the second support in the present invention is realized by attracting a soft magnetic material attached to each support with a magnetic field generated in an outer coil. At that time, the external force is changed by changing the cross-sectional area in the moving direction of the soft magnetic body or changing the external magnetic field with time. In addition, reciprocating motion is given to each support by using multiple coils or using the restoring force of a spring.

The amount of movement of the one-dimensional actuator, which is a forced displacement, and the magnetic field of the coil, which is an external force, is a forced displacement function X determined by Δx = x _en -x _in and Δ v = v _en -v _in which is the amount of change in position and velocity. It is generated by moving the controller between t '= ₀ and Δt according to (t ₀ + t') and external force function F _I (t ₀ + t ').

At that time, the sample value is controlled by feeding back the position and speed of the second support obtained from the sensor at every Δt that is the operation time so as to become a target value.

The external force applied to the first support or the second support in the present invention need not be an electromagnetic force, and may be an external force applied by other methods.

Since flexible structures such as robot arms and hard disk arms have their own flexibility, residual vibration occurs when the movement stops. Similarly, pendulums such as overhead cranes generate residual vibration when the movement of the pendulum root stops. In addition, the semiconductor exposure equipment (stepper) is also affected by slight residual vibration, so it is necessary to suppress this. In these devices, it takes time for the residual vibration to stop for accurate positioning, and this leads to a drop in work efficiency in transport operations using a robot or crane, read / write speeds of hard disks, and semiconductor exposure steps.

Although feedback control is mainly used to reduce residual vibration, oscillation occurs in reverse depending on the size of feedback gain, making high-speed position control difficult. Therefore, research has been carried out on residual vibration reduction by feedforward control and optimal trajectory planning using genetic algorithms etc. (Kojima Kojima, Kenichi Habuchi, optimal trajectory planning for rectilinear crane using genetic algorithm) And the residual vibration suppression control experiment, Vol. 69, no. 682, 2003-6, pp. 1479-1485), most of them are trajectories for moving from the initial position to the target position. Since it is necessary to determine the optimal trajectory every time the design parameters of the system change, it has not been possible to cope with unexpected disturbances during movement or at work sites where the parameters change depending on the situation.

The trajectory control device A according to the present invention changes the predetermined integral vibration system by changing the forced displacement of the root in accordance with a forced displacement function X (t ₀ + t ′) determined by setting the target position and the target velocity to 0. The vibration control operation can be completely stopped in the operation time. Here, in order to explain an embodiment of the track control device A in the present invention, this damping operation is applied to damping control of a flexible structure.

Although flexible structures such as cantilever beams have multiple eigenmodes, the primary mode tends to stand as the fundamental vibration. In addition, when the displacement is small, the nonlinearity is not so large, and its behavior can be expressed approximately by a linear vibration system consisting of spring-mass. Therefore, here, the vibration control of the flexible structure such as the robot arm, the hard disk sensor arm, and the precision stage mounting portion of the exposure apparatus is performed by the trajectory control device A as shown in FIG.

The forced displacement function X (t ₀ + t ') in the integral vibration system of (Equation 1) is applied to the movement of the flexible structure. Assuming that the flexible structure which is a cantilever is a robot arm shown in FIG. 13, the change of the position of the mode mass of the integrated vibration system is the change of the position of the robot hand 18 at the tip of the arm, and the position of the root of the integrated vibration system The change in corresponds to the change in acceleration at the arm base.

In this case, the mass of the integral vibration system is the modal mass of the cantilever, and the spring constant of the integral vibration system is the equivalent spring constant of the cantilever.

If the vibration of the robot arm is rotation due to a low rotational spring constant of a reduction gear mainly at the joint, the mass of the integrated vibration system is the moment of inertia of the robot arm around the joint, and the spring constant of the integrated vibration system is , The amount of increase in moment per unit angle.

If the flexible structure that is a cantilever is a cantilever 20 at the tip of an arm that supports the magnetic head 21 of the hard disk shown in FIG. 14, the change in the position of the modal mass of the integrated vibration system is supported by the cantilever. The change in the position of the magnetic head is equivalent to the change in the position of the tip of the relatively rigid arm 19 that supports the cantilever.

Further, when the flexible structure that is a cantilever is the entire semiconductor exposure apparatus including the vibration isolation table, the change in the position of the modal mass of the integrated vibration system has been placed on the optical system composed of a large number of lens systems 28. This is a change in the position of the light source 27. The change in the position of the base of the integrated vibration system is a change in the horizontal position of the entire semiconductor exposure apparatus including the vibration isolation table 32 due to the reaction force of the movement of the wafer stage 30 and the reticle stage 29. Corresponds to change. FIG. 15 shows a schematic view of the positional change of the light source excited by the change of the horizontal position of the entire semiconductor exposure apparatus including the vibration isolation table.

Here, the angular frequency parameter is α ₁ = 1 and α _{p ≠ 1} = 0, the reference time which is the time to start the operation is t ₀ = 20, and the operation time of the flexible structure to be operated is equal to the natural period Δt = 2π, X _in = X (t ₀ ) = 0.0, and V _in = V (t ₀ ) = 0.0. The original position of the modal mass of the flexible structure is x _in = x ₁ (t ₀ ) =-1.5, the original velocity is v _in = x ₁ (t ₀ ) = v ₁ (t ₀ ) = 0.0, the target position Is x _en = x ₁ (t ₀ + Δt) = 0.0, and the target speed is v _en = x ₁ (t ₀ + Δt) = v ₁ (t ₀ + Δt) = 0.0. A numerical result in the case where the forced displacement is given using the function X (t ₀ + t ') in the range of 20 <t <20 + Δt and the amount of forced displacement is 0 in the range of t <20, t> 20 + Δt Fig. 16 shows the change in the position of the arm tip, and Fig. 17 shows the change in the position of the arm base.

From FIG. 16, it can be seen that the mass of the vibrator continues to be free until t = 20 where the forced displacement is applied, and after being subjected to the forced displacement for one period, it becomes completely stationary. Also, at that time, the amount of forced displacement given to the movable body is as shown in FIG. 17, and is in the form of what is generally called a Bang-bang function. In other words, the present invention formulates a Bang-bang function that has not been analytically shown so far, and enables quantification and generalization. By using this function, it becomes possible to operate at any given position and velocity, and at any given position and velocity, with a predetermined operation time.

When the data position is close to the head, such as a hard disk, it is necessary to move the head at a short distance, and seek control that moves from a stationary state and stops immediately. Next, let us consider a control that moves from a stationary state to a stationary state after one cycle of operation time.

In the integrated vibration system, if the forced displacement at the root and the change in the position of the vibrator at the tip are the same, the potential energy of the spring is 0, and if there is no kinetic energy, the system is stationary.

In the forced displacement function X (t ₀ + t ') of (Equation 1), when the change in the position of the root before and after the position operation and the change in the position of the oscillator are the same, from the stationary state at a certain position This is an operation to stand still at another position.

The angular frequency parameters are α ₁ = 1 and α _{p ≠ 1} = 0, X _in = X (t ₀ ) = -d / 2, V _in = V (t ₀ ) = 0.0, and the amount of change in position as the transport distance When d, the original speed is v _in = 0, the target speed is v _en = 0, the original position is x _in = -d / 2, and the target position is x _en = d / 2, (Equation 1) The forced displacement function X (t ₀ + t ′) shown in is rewritten as (Equation 53) below.

The operation time is set equal to the natural period of the oscillator, Δt = 2π, and the operation by the forced displacement function is started at t ₀ = 3Δt. In the range of 3Δt ≦ t ≦ 4Δt, the forcible displacement function X (t ₀ + t ′) represented by (Eq. 53) is given, and in the range of t <3Δt, the forcible displacement is 0, and in the range of t> 4Δt The time change of the mass of the vibrator and the position of the movable body when d is shown in FIG. Here, X _sed represents the time change of the position of the movable body and the time change of the mass position of the x ₁ oscillator. This corresponds to the fastest control in seek control to move the hard disk head for a short distance, centring control to set the position, and following control to keep the same position. It can also be used for intermittent movement with reduced residual vibration in semiconductor exposure equipment (steppers).

In such vibration control, it is necessary to measure the speed, position, rotation amount, rotation speed, etc. of the object corresponding to the first support.

Here, for the forced displacement function X (t ₀ + t ') shown in (Eq. 53), the original position of the mode mass of the flexible structure is x _in = x ₁ (t ₀ ) = 0.0, and the original velocity Let v _in = x ₁ (t ₀ ) = v ₁ (t ₀ ) = 0.0, and set the target velocity v _en = x ₁ (t ₀ + Δt) = v ₁ (t ₀ + Δt) = 0.0. And the transport distance of the mass of the vibrator is d = 2.0. It can be seen that the vibrator in a stationary state receives a forced displacement and becomes stationary at another position.

Next, for the flexible structure, the forced displacement function X (t ₀ + t ') is applied to steady motion control during constant velocity conveyance by using a trajectory control device A as shown in FIG. When the root of the integrated vibration system is moved at a constant speed, the oscillator generates acceleration before the speed is reached, so that the vibrator vibrates after the root reaches the constant speed. Therefore, in the integrated vibration system where the root performs constant velocity translational motion at velocity v ₀ , when damping operation is performed, changes in the mass of the vibrating body and the position of the movable body are shown as shown in FIG. Here, X _sed represents the time change of the position of the movable body and the time change of the mass position of the x ₁ oscillator. This corresponds to changes in the position and velocity of the tip and root of the robot arm moving at a constant velocity.

Here, for the forced displacement function X (t ₀ + t ′) shown in (Expression 1), the angular frequency parameter is α ₁ = 1, α _{p ≠ 1} = 0, and the operation time is the natural period of the oscillator Equally Δt = 2π, the reference time which is the time to start the operation is t ₀ = 5Δt, the constant velocity movement velocity of the root of the oscillator is v ₀ = 1.0, and the initial position and initial velocity of the mass of the oscillator are x ₁ (0) = 1.0, v ₁ (0) = v ₀ , the position of the oscillator mass at the start of operation x _in = x ₁ (t ₀ ) = x ₁ (0) + 5 Δ tv ₀ , the mass of the oscillator The velocity at the start of the operation is v _in = v ₁ (t ₀ ) = v ₀ , the target position of the mass of the oscillator is x _en = x ₁ (t ₀ + Δt) = x ₁ (0) + 6Δtv ₀ , the oscillator The target velocity of the mass of is set as v _en = v ₁ (t ₀ + Δt) = v ₀ . With this vibration control operation, the residual vibration can be extinguished in a predetermined operation time regardless of its magnitude, even in a system where the base is moving at a constant speed.

By considering the flexible structure as an integral vibration system, it is possible to control the vibration within a predetermined operation time as shown above. However, an excessively large force applied to the base during vibration control will cause damage to the drive system such as gears. Therefore, in this case, the vibration control operation of the robot arm is performed in multiple steps, and the change of the acceleration of the root by the number of operations until the stop is observed by numerical calculation.

In the trajectory control device A as shown in FIG. 7, the movement of the mass point of the vibrator in the case of performing multi-step damping operation using the forced displacement function X (t ₀ + t ′) of (Expression 1) It is shown in 20. N is the number of times the operation was performed, and here, it is shown once, three times, and five times. Here, for the forced displacement function X (t ₀ + t ′) shown in (Expression 1), the angular frequency parameters are set to α ₁ = 1 and α _p = 0 ₁ = 0, and the reference time that is the time to start the operation is Let t ₀ = 0, equal to the natural period of the flexible structure operating the operation time, let Δt = 2π, and let X _in = X (t ₀ ) = 0.0, V _in = V (t ₀ ) = 0.0. The original position of the modal mass of the flexible structure is x _in = x ₁ (t ₀ ) = 1.0, the original speed is v _in = v ₁ (t ₀ ) = 0.0, and the target position after N times is x _en = x ₁ (t ₀ + Δt) = 0.0, and the target speed was set to v _en = v ₁ (t ₀ + Δt) = 0.0.

When performing damping operation, the total number of operations to standstill is N times, and in the Mth operation, the original position x _in , so that the position and velocity are (NM) / N times the initial value respectively. The original velocity v _in , the target position x _en , and the target velocity v _in were set each time for operation. Figure 20 shows the change in the acceleration of the mass of the vibrator. From the calculation results, as the number of operations until stationary increases, the acceleration applied to the root decreases and the load is reduced.

On the other hand, when the movement distance of the robot arm is long, the time T required for this is generally longer than the natural period τ of the robot arm. In this case, a forced displacement function X (t ₀ + t ′) can be determined for each predetermined operation time Δt so that the robot arm remains stationary at any trajectory position without residual vibration.

Next, Fig. 21 shows a forced displacement curve created by connecting the forced displacement function X (t ₀ + t ') shown in (Equation 1) so as to stop at the position of 1.0 after 5τ without residual vibration. The trajectory of the follower mechanism driven by this and the cycloid curve are shown in Fig.22. It is the cycloid curve that rises smoothly, and the trajectory of the follower mechanism that rises while shaking. It can be seen that the follower mechanism can be controlled to pass through the cycloid curve without residual vibration at every predetermined operating time Δt. This makes it possible to operate a robot hand that moves on any trajectory without residual vibration.

In the articulated robot hand, if the rigidity of the tip is low and the rigidity of the root is high, design changes in the position and angle of the highly rigid joint with the above-mentioned forced displacement function or forced angular displacement function shown below, The robot hand can be moved while suppressing the residual vibration of the part with low rigidity at the tip.

On the other hand, in the articulated robot arm for industrial use, although the arm has high rigidity, the joint has low rigidity because a high speed reducer such as Harmonic Drive (registered trademark) is used. Therefore, the residual vibration of the industrial articulated robot arm occurs exclusively as rotational vibration of the joint.

Since a one-joint robot arm can be modeled by an integral rotational oscillator as shown in FIG. 90, the robot arm is operated using a forced angular displacement function Θ (t ₀ + t ′) shown in (Expression 58) described later By doing so, residual vibration of rotation can be suppressed.

As shown in FIG. 90, the joint of the robot arm has a speed reducer such as a harmonic drive (registered trademark), which is rotated by an actuator 154 such as a motor. The rotation angle θm of the actuator is transmitted through the rotation spring 156 of the speed reducer to rotate the robot arm 157 by the angle θa. The rotation angle and rotation angular velocity of the robot arm are measured by the encoder 158, and the rotation angle and rotation angular velocity of the actuator are measured by the encoder 154, so that the forced angular displacement function Θ (t ₀ + that suppresses the residual vibration of the rotation after the operation time Δt. t ') is determined.

The effect of reducing the residual vibration of the robot arm by the forced angular displacement function Θ (t ₀ + t ') is the same as other technologies.

These techniques can be applied to seek control of a hard disk, and since the same technique can be used not only for seek control of a hard disk but also for settling control and following control, it is similar to the conventional hard disk It is possible to overcome control instability due to mode switching and inaccuracies in the target position appearing in the control system with two degrees of freedom.

In addition, since servo information representing the position of the head is written discretely on the disk only at equal intervals, there is a problem that the position and speed information of the head can be obtained only at regular time intervals. There was a control failure caused by the estimation of these values. However, according to the present invention, by setting the time interval for obtaining servo information representing the position of the head to be a natural number of a predetermined operation time Δt for controlling the cantilever supporting the magnetic head, residual vibration passing through any trajectory is obtained. It is possible to control sample value with reduced (Figure 22).

Above all, the sample control method itself of the present invention naturally includes feedforward control during a predetermined operation time Δt of the controlled vibration system and feedback control for each operation time of the controlled vibration system. It is a big merit that is different from the control system by complex combination such as two degree of freedom control system.

On the other hand, when applying these techniques to the drive control of a semiconductor exposure apparatus, the operation time is made to be the wafer stage drive time for each step. As a result, the light source and the device body can be accurately positioned without residual vibration.

Further, even if residual vibration remains after one step of movement, by controlling the sample, the shaking of the semiconductor exposure apparatus can dynamically reduce the residual vibration after a predetermined operation time.

The amount of movement of the semiconductor exposure apparatus in the horizontal direction is the reaction due to the reaction of the driving force of the wafer stage, and the driving force of the wafer stage is adjusted so that the amount of movement becomes the derived forced displacement function X (t ₀ + t '). Must.

On the other hand, the semiconductor exposure system is mounted on a vibration isolation table, and this vibration isolation table is connected to the foundation base by a spring. Therefore, the base is the fixed support, the vibration isolation table is the first support, and the conductor exposure device loaded with lenses and reticles swings like a cantilever beam. Is possible.

Set a sensor to measure vibration near the light source of the semiconductor exposure equipment so that the position and speed of the shaking of the exposure equipment can be measured, and also attach a sensor on the vibration isolation equipment to adjust the position and speed of the vibration isolation table. Make it measurable. Thereby, the information of the position and speed of the first support and the second support can be obtained. Thus, it can be seen that the shaking of the semiconductor exposure apparatus can be controlled by the structure of the trajectory control apparatus C.

The force generated by the stage is the product of the acceleration of the wafer stage and the mass of the wafer stage. For this reason, in order to make the force by the wafer stage into the external force function F ' _IIp (t ₀ + t'), the acceleration of the wafer stage is the quotient of the external force function F ' _IIp (t ₀ + t') and the mass of the wafer stage. It can be seen that the control should be such that

In addition, an image sensor is installed at the same height as the wafer stage and separated from the stage, and it is necessary to devise measures such as sensing the position and speed of the reticle and the light source from the movement of the reticle image and changes in the edge. (FIG. 15).

Next, the application of the derived displacement function X (t ₀ + t ′) to damping of an overhead crane will be described as one of the embodiments of the track control device A as shown in FIG. 7 in the present invention. A schematic view of an apparatus in which the present invention is applied to an overhead crane is shown in FIG. The overhead crane is a machine that drives the base of a vibrator comprising a load 37 suspended by a wire 36 by moving the club trolley 34 etc. of the ceiling in the horizontal direction, and the acceleration of the club trolley 34 etc. is the first support. That the deflection angle θ (t ₀ + t ') from the vertical direction of the wire 36 corresponds to the orbit function x ₁ (t ₀ + t'), which is a forced displacement function X (t ₀ + t ') which is a position change of Therefore, the position and speed of the overhead crane can be controlled by the movement of the club trolley.

On the other hand, since the overhead crane is a pendulum, it has non-linear vibration and the natural period depends on the amplitude. Therefore, it is necessary to cope with the change of natural period. However, since it can be treated in the same way as a linear oscillator approximately, by changing the position and speed of the load of the overhead crane, not only suppression of residual vibration after carrying the load but also when starting to carry the load The generated vibration and the vibration generated by the acceleration operation during transportation can be suppressed as well.

In the present invention, it is necessary to know the swing angle θ (t ₀ + t ') and the swing angular velocity dθ (t ₀ + t') / dt at the moment of starting operation, and the position and speed of the club trolley. For overhead cranes, these quantities can be calculated from the position and speed of the suspended luggage and the position and speed of the club trolley. In recent years, low-cost rangefinders and speedometers using lasers have been sold, but it is difficult to keep the laser light from these sensors continuously striking overhead cranes that move frequently in the factory.

On the other hand, overhead cranes are suspended by wire, so if the natural cycle is known, the wire length can be calculated. In addition, since a small three-dimensional acceleration sensor attached to the package is also sold in recent years, the moment when the package passes through the lowest point and the centrifugal force at that time can be determined, and the location and speed of the package are calculated from this can do. Information from the acceleration sensor can be obtained sequentially by skipping it with radio waves such as Bluetooth (registered trademark). Information on the horizontal position and speed of the club trolley 34 is also acquired using a sensor or the like as appropriate.

On the other hand, since the overhead crane has a motor in the transport direction, it is possible to change the transport direction and speed at the calculated timing. A communication unit that receives information from the acceleration sensor near the motor, and an arithmetic output unit that calculates and outputs a forced displacement function X (t ₀ + t ') in response to this, and an amplifier that sends electricity to the motor according to this output A new controller consisting of units will be provided. The schematic diagram of the overhead crane designed in this way is the same as FIG. In the case of a two-dimensional overhead crane, arrange these on each axis.

Since the present invention can arbitrarily change the position and speed of the vibrator after a predetermined operation time, not only damping of swinging when the overhead crane stops but also swinging when the load moves at the start of movement You can stop. If the non-linearity of the overhead crane is ignored, FIG. 19 is equivalent to the trajectory of the load moved at a constant speed after controlling the shaking at the start of movement.

On the other hand, ignoring the non-linearity of the overhead crane as well, FIG. 18 is equivalent to an operation in which the residual vibration of the overhead crane arrived at the target position is damped by forced displacement.

The residual vibration of the load can be detected by the acceleration sensor, so the crane can be constantly monitored for shaking and automated to stop.

In addition, since it is costly to introduce the controller into an existing crane, a follower notch operation is performed to the overhead crane operator as an indicator that notifies the controller output by sound or the length of the bar on the display board. It is also possible to teach the timing and amount of. In this case, since the indicator can be made compact, it can be incorporated into the control panel of the overhead crane or be held together.

Next, the equation of motion is derived from the simplified model of the overhead crane. The mass of the pendulum is m, the length is l, the deflection angle that is the inclination of the wire from the vertical direction is θ, the gravitational acceleration is g, and the forced displacement amount X _tr (t) at the base of the pendulum by the horizontal movement of the trolley The equation of motion of the system when given is expressed as (Eq. 54) below. If Eq. (54) is made dimensionless with a representative time T _r = √ (l / g) and unit length l, the following Eq. 55 is obtained. When the deflection angle θ is small, (Equation 55) is rewritten as (Equation 56) by linear approximation.

Here, the generalized coordinate x (t ₀ + t ′) of the second support is the rotation angle θ (t ₀ + t ′) of the rotary vibrating body, and the generalized coordinate X (t ₀ + t of the first support is By setting ') as the forced displacement angle Θ (t ₀ + t') of the rotating body, the equation of motion (Equation 37) in the orbit control device A is rewritten to the equation of motion of the following rotation (Equation 57).

From the comparison of (Equation 37) and (Equation 57), the forced angular displacement function Θ (t ₀ + t ′) for manipulating the angle and angular velocity with respect to the integral rotational oscillator is the forced displacement function X (t _{0 of} (Equation 1) By transforming + t '), the following equation (58) is derived. Here, the First support reference generalized coordinates X _in the forcible displacement angle of the wire at the reference time _{Θ (t 0) = Θ in} , wires in the first support reference generalized velocity V _in the reference time Of the second support-based generalized coordinates x _{in at the} deflection angle θ (t ₀ ) = θ _in of the wire at the reference time, and the second support based on the forced displacement angular velocity Θ (t ₀ ) = Θ _in The reference generalized velocity v _in is replaced by the swing angular velocity dθ (t ₀ ) / dt = dθ _in / dt of the wire at the reference time.

By comparing the equation of motion of the overhead crane linearly (Equation 56) with the equation of motion of rotation in the trajectory controller A (Equation 57), the amount of forced displacement X _tr (t) due to the horizontal movement of the trolley The relationship of (Equation 59) is established between the forced angular displacement function Θ (t ₀ + t ′) for manipulating the angle and angular velocity with respect to the integral rotating vibrator.

That is, since the forced angular displacement function Θ (t ₀ + t ′) which is negative is equal to the second time derivative of the forced displacement amount X _tr (t) by the horizontal movement of the trolley, the horizontal direction of the trolley It turns out that it is better to make the negative acceleration as (Equation 58). From this, the horizontal acceleration (Equation 60) of the trolley necessary to arbitrarily manipulate the deflection angle and the deflection angular velocity of the wire of the overhead crane can be obtained.

On the other hand, the actual overhead crane wire has a non-linearity due to the pendulum represented by (Equation 55), so even if the horizontal acceleration of the trolley is determined according to (Equation 60), The deflection angle and the deflection angular velocity will deviate from the target values.

In particular, in the case of an overhead crane, acceleration occurs in the horizontal direction of the trolley by starting and stopping, etc., so that an excitation operation for turning the wire to a certain swing angle from a state where the wire is not shaken, and a wire being fixed The luggage can be carried without any residual vibration by combining two of the vibration reduction operations in which the swing angle is set to the swing angle and the swing angle is not shaken.

The simulation of the excitation operation was carried out while variously changing the operation time and the target shake angle (target shake angle). The change in the target shake angle is as shown in FIG. Here, the vertical axis is the ratio of the shake angle after the operation time to the target shake angle, and the operation time is made dimensionless as a representative time in which the natural period of the shake angle is 2π.

When the operation time is Δt = 0.9π and Δt = 1.5π, the ordinate takes a value of 1 regardless of the value of the target shake angle, so that Δt = 0.9π or Δt = 1.5π. It was found that the swing angle of the overhead crane can be controlled to the target swing angle by performing the vibration operation according to the operation time. That is, in the excitation operation in which the swing angle is increased from 0 to a predetermined angle during the operation time, the operation time is set to be 0.45 times or 0.75 times the natural period. Highly accurate operation is possible.

Similarly, when simulation of the vibration reduction operation was performed while variously changing the shake angle (reference shake angle) of the operation time and the reference time, the change of the target shake angle is as shown in FIG. Therefore, it was found that the target shake angle can be controlled to be close to 0 regardless of the value of the reference shake angle by the vibration reduction operation with the operation time Δt = 1.23π. That is, in the vibration reduction operation in which the swing angle is decreased from a predetermined angle to 0 during the operation time, a more accurate operation is possible by setting the operation time to 0.615 times the natural period. It becomes.

However, when the reference deflection angle is large, the target deflection angle still does not become zero, so a device for eliminating the non-linearity effect due to the vibration of the pendulum is still required.

It is thought that the effect of the non-linearity of the wire swaying to the left and right was just offset by this operation time as the reason why the appropriate operation of the overhead crane was able to be performed at these operation times.

FIG. 89 shows an overhead crane operated by suppressing the residual vibration by performing the vibration operation with Δt = 0.9π and then immediately performing the vibration reduction operation with Δt = 1.23π. The simulation result of the orbit is shown. The deflection angle of the wire due to the trolley's acceleration / deceleration for 3 times was suppressed each time, and it was found that it moved at a constant speed after operation.

Since the trajectory of the trolley can be calculated from the horizontal acceleration of the trolley shown in (Equation 60), by using the present invention, it becomes possible to control the sample value of an automatic crane that can carry a load while suppressing shaking. You can see

Next, the angular frequency parameters are α ₁ = 1 and α _{p ≠ 1} = 0, the reference time that is the operation start time is t ₀ = 20, and the operation time Δt is the natural period 2π of the load hung on the wire. By making them equal, Δt = 2π, the original deflection angle is θ _in = θ (t ₀ ), the original angular velocity is dθ _in / dt = dθ (t ₀ ) /dt=0.0, and the target deflection angle is θ _en = θ (t ₀ + Δt) = 0, and the target angular velocity is dθ _en / dt = dθ (t ₀ + Δt) / dt = 0.0. In the range of 20 <t <20 + Δt in dimensionless time, the drive body is given a forced displacement according to (Formula 58), and in the range of t <20 and t> 20 + Δt, the forced displacement amount of the drive body is set to 0. For the case, the following numerical calculation was performed.

When the initial deflection angle is relatively small, θ _in = π / 20, as shown in FIG. 24, the pendulum almost stationary after stationary operation. On the other hand, as shown in FIG. 25, in the case where the initial deflection angle is relatively large such as θ _in = π / 4, although the deflection angle is slightly reduced after the stationary operation, it did not reach to stand still. This is considered to be because the pendulum nonlinearity becomes more prominent as the deflection angle increases, and the natural period of the pendulum deviates from Δt.

Then the deflection angle of the pendulum after damping operation and theta _{end The,} shows the initial deflection angle theta damping ratio _{in η} = θ _end / θ _in Figure 26. It can be seen that the damping effect is lost as the initial deflection angle increases.

Next, Fig. 27 shows the numerical calculation results when damping operation is performed twice continuously under the same conditions. Here, the initial value is θ _in = π / 4.0, dθ _in /dt=0.0, the original deflection angle in the first damping operation is θ _in = θ (t ₀ ), and the original angular velocity is dθ _in / dt = dθ (t ₀ ) / dt, the original deflection angle in the second damping operation is θ _in = θ (t ₀ + Δt), and the original angular velocity is dθ _in / dt = dθ (t ₀ + Δt) / dt . It can be seen that in FIG. 27 where two stationary operations were performed, it can be sufficiently stationary, as opposed to FIG. 25 which could not be stationary in one damping operation.

Next, when performing damping operation, the behavior of the system is numerically calculated using the case where the control side at the start of the operation deviates from the original swing angle θ _in assumed from the actual swing angle θ (t ₀ ) Observe. The attenuation ratio η = θ _en / θ (t ₀ ) when the initial shake angle which is the actual shake angle is θ (t ₀ ) and the appropriate shake angle which is the original shake angle assumed is θ _in The relationship is shown in FIG.

It can be seen that when the proper deflection angle and the initial deflection angle have the same magnitude, it is most attenuated. It can also be seen that even if the initial deflection angle is slightly more or less than the appropriate deflection angle, the attenuation ratio is small and it is sufficiently attenuated. On the other hand, when the initial deflection angle is sufficiently larger than the appropriate deflection angle, a sufficient damping effect can not be obtained, but at least it does not become larger than the initial deflection angle. However, it can be seen that the initial deflection angle may be larger than the initial deflection angle if the initial deflection angle is sufficiently smaller than the appropriate deflection angle.

On the other hand, in the pendulum, it has long been known that the change of the natural period due to the amplitude that appears due to its non-linearity is expressed as a function using perfect elliptic integral. The natural period of a pendulum having a natural period of 2π at a small amplitude is expressed by the following (Equation 61) as a series solution (Morikazu Toda, Introduction to Elliptic Function, Nippon Critics), 5% at θ _max = 50 °, θ _A deviation of 18% appears at _max = 90 °.

Therefore, the natural period 2π in the equation (58) is corrected by T (θ _av ) in the equation (61), and the forced angular displacement function (′ (t ₀ + t ′, Redefine θ _av ). Here omega ₊ 'and omega _-' is (Equation 63) and as shown in (Equation 64), the two bodies coupled vibration system of two of when the deflection angle of the average time of operation is an theta _av natural angular frequency of ω ₊ and ω _- which is the correction value.

When the crane swinging at θ _max = 57 ° was stopped using the equation shown in (Equation 62), the pendulum stopped without residual vibration.

On the other hand, cranes are often operated while changing the length l of the wire. By substituting the length of the wire at each time into (Equation 61), the natural period of the pendulum at that time can be determined, and the forced angular displacement function Θ '(t ₀ + t) of (Equation 62) determined by this Residual vibration can be suppressed by operating the crane using the acceleration of the trolley determined by ', θ _av ).

If you lower the position of the load and operate while making the wire longer, the shaking will be more settled because the Coriolis force acts as a viscous damping. However, if you operate while raising the position of the load and shortening the wire, the Coriolis force acts as an excitation, so it is difficult to settle the shake. For this reason, this function needs further ingenuity.

As described above, the vibration control operation is performed with the operation time set to Δt = 0.9π, and immediately after that, the vibration control operation is performed with the operation time set to Δt = 1.23π to reduce the swing angle to 0. Is possible. If the wire does not touch, the Coriolis force does not affect it, so if you want to change the length of the wire, you can perform more accurate overhead crane operation by inserting a damping operation before that.

In the case of a pendulum, the above-described damping operation with a limited operation time or correction using a solution of the natural period is also useful in other vibration control functions.

On the other hand, if the swing amplitude of the load is fixed to a certain extent in a factory flow operation etc., a forced displacement to be applied to the root of the wire can be created by a two-dimensional plate cam. Below, the Example which performed vibration control by track | orbit control apparatus A as shown in FIG. 8 is shown.

In this device, a specific position is detected from the signal from the acceleration sensor to activate the cam. An example of the cam shape calculated from the current forced displacement function X (t ₀ + t ') is shown in FIG.

Here, the angular frequency parameters are α ₁ = 1 and α _{p ≠ 1} = 0, X _in = X (t ₀ ) = 0.0, and V _in = V (t ₀ ) = 0.0. The original deflection angle is θ _in = θ (t ₀ ) = 1.0, the original angular velocity is dθ _in / dt = dθ (t ₀ ) /dt=0.0, and the target deflection angle is θ _en = θ (t ₀ + Δt) = 0, and the target angular velocity was dθ _en / dt = dθ (t ₀ + Δt) /dt=0.0. The black points in FIG. 29 indicate the rotation center of the cam, and the x points indicate the position at the start of the stationary operation of the cam. One rotation of this cam causes a forced displacement of (Equation 58) on the cam follower. Forced displacement can reduce the vibration by synchronizing the rotation start angle of the cam and the phase of the vibration and matching the rotation period of the cam and the operation time of the load suspended on the wire.

By attaching this cam to the base of a conventional flexible structure or to an overhead crane, it is possible to expect to realize damping of the system in a predetermined operation time without largely changing the mechanical structure. However, in this vibration control method, the state of the vibration control target is limited. Therefore, when performing damping operation using a cam, make the magnitude of vibration generated in the damping object constant each time, attach multiple cams, perform multiple damping operation patterns with one cam, etc. The device of is needed.

As indicated by the forced angular displacement function Θ for manipulating the angle and angular velocity in (Equation 58), when the moment when the load passes underneath (θ _in = 0) is defined as the operation start time, the displacement of the cam is calculated based on the operation start time. It is proportional to the angular velocity dθ _in / dt. If the displacement amount of the cam can be adjusted with a movable lever using a device as shown in FIG. 9, the swing of various amplitudes is stopped by rotating the cam rotation period in accordance with the operation time of the overhead crane. The mechanism becomes possible. Of course, if a single-axis actuator is used instead of a cam, it can cope with any vibration.

The vibration control technology shown for the track control device A as shown in FIGS. 7 to 9 can be applied to a construction crane, a transport machine for molten steel in a foundry, and a robot arm. Also, in the case of the hard disk arm, since the position and speed at the tip can be detected by the device itself, the residual vibration after seek can be similarly reduced. In addition, it can also be used to reduce the residual vibration of the precision stage mounting part in the exposure apparatus.

In these applications, it is necessary not only to correspond to the second support but also to detect the velocity and position of the object on the first support.

Since it takes time to detect position and velocity, and to calculate the amount of control, etc., the sensor measurement itself analyzes a large number of data at a high sampling rate at a specified operation time or more, and performs model calculations, etc. It is preferable to devise to estimate the speed and position of the reference time in advance.

Next, an example of applying the derived forced displacement function X (t ₀ + t ') to a building vibration control method to describe an embodiment in which vibration control is performed by the trajectory control device A as shown in FIG. Let's talk about In particular, we will explain an example of a high-rise building that generates large tremors due to long-period ground motion or strong winds.

In the present invention, for example, the base and the ground of a high-rise building built on a base-isolated bearing body such as an integrated rubber or a sliding bearing that has already been proposed and examples are forcibly displaced in a horizontal direction by a hydraulic actuator. Equipment that can be used (Osamu Yoshida, Mitsuru Hatakeyama, Takeshi Sano, Fumiaki Endo, Tetsugo Watanabe, Hideo Katsumata, Super Active Vibration Control Laputa 2D, Obayashi Institute of Technology Research Report, No. 74. 2010, pp. 1- 8). By attaching the actuator to each surface around the building, it is possible to apply a forced displacement in response to the shaking from any direction.

At the moment of the earthquake, it is necessary to devise a special device more than the present invention because irregular force is included. However, even at the moment of receiving an earthquake, most of the shaking of the building incorporating the seismic isolation system is the vibration of the primary mode as a cantilever beam accumulated by the earthquake motion, so the present invention is effective to some extent It is believed that there is. In addition, it is considered to be sufficiently effective as a method to eliminate residual vibration remaining after the end of earthquake motions and the like. In addition, since the shaking caused by the strong wind is caused by the accumulation of vibration, the present invention is considered to be equally effective.

In order to implement the present invention, the position and velocity of the building's modal mass at the moment of starting to control the swing must be estimated. Therefore, the sensor uses an acceleration or speed or position sensor 11ab attached to several levels of the building. Also, mount the acceleration or velocity or position sensor 11aa on the seismic isolation bearing of the building. As a result, the vibration damping device is represented as shown in FIG.

Since most of the residual vibration remaining in the building is the primary mode vibration when the building is a cantilever beam, it is better to attach an accelerometer and a high sensitivity position sensor by GPS on the top floor of the building. Alternatively, a system that measures the position change in real time by image processing by projecting the image of the upper part of the building from the outside may be used. Given that the natural period of a building is a few seconds, it would be possible to cope with a system capable of rapid measurement, and it would also be possible to predict accurately since vibrations with the same period are repeated.

When the position and speed of the building as a cantilever in a specific direction at the next time are estimated, the forced displacement function X (t ₀ + t ') is calculated under the condition that the vibration is suppressed by the DSP. The hydraulic actuator 42 is driven along Perform sample control to repeat this every predetermined operation time, and continue until the amplitude becomes zero. Even if the magnitude of the hydraulic pressure is small, the forced displacement by the hydraulic pressure works in the direction to suppress the vibration, so the vibration of the building works in the direction to be settled by repeating every operation time. By doing this in any direction, it is possible to suppress the shaking of the building against earthquakes and strong winds from any direction.

At that time, also about how much the amount of forced displacement and speed of the hydraulic actuator etc. is, for example, a sensor 11aa capable of estimating the position and speed is mounted on the seismic isolation support and measured.

Since the residual vibration of the building is relatively simple, the forced displacement to reduce it can be designed with the same cam curve. Therefore, even if it does not use an advanced computing device such as DSP, it can be manufactured by the mechanical mechanism of cam and forceps (Fig. 8). Forced displacement can reduce vibration by synchronizing the cam rotation start angle and the vibration phase, and matching the cam rotation speed and vibration operation time. On the other hand, by using a ladder, the large displacement of the cam can be reduced and the force can be increased conversely, so that it is possible to suppress the sway of the building even if a general motor or engine is used. . In addition, by fixing the main power supply line that flows the current to the building to the base of the building and changing the magnetic field around the main power supply line, Lorentz force is generated to give a predetermined forced displacement to the base of the building. It is possible to suppress the shaking of the building.

For example, if a high-rise building was modeled with a beam with low attenuation, and the natural period of the main primary mode was 2π, the same shaking as the Great Hanshin Earthquake (Fig. 65) If you simulate the sway of the modal mass of a building, it will look like Figure 66.

Assuming that the hydraulic actuator starts to move after the natural period after the earthquake starts, give the forced displacement function X (t ₀ + t ') directly above the building's seismic isolation bearing, and the operation time is unique so as to suppress the shaking of the building When sample value control is performed so as to become a cycle, it can be seen that the sway mass of the modal mass of the building where the same earthquake has struck becomes smaller as shown in FIG.

At this time, the time taken to measure or estimate the position of the mode mass of the building, which is the second support, and the velocity of the mode mass correspond to the time for calculating the forced displacement function X (t ₀ + t ') and the actuator. It is necessary to start measuring the position and velocity of the modal mass of the building at least before the time lag of the predetermined operation time which starts control each time, taking into consideration the time lag which is the sum of the time until it moves. While the natural period of a normal building is a few seconds, the time lag is considered to be sufficiently small.

In addition, based on the values of the position and velocity thus measured, the target value (the second support is set so that the position of the modal mass of the building after a predetermined operation time is at the balance position and the velocity of the modal mass is zero. Determine the target generalization coordinates and the target generalization speed of the second support), and calculate the forced displacement function X (t ₀ + t '). The vibration is controlled by moving the actuator based on the value obtained in this way and inserting a forced displacement on the seismic isolation bearing of the building.

For each predetermined operation time, measure the position of the modal mass of the building and the velocity of the modal mass, compare this with the target value, and force the building again at the next operation time so as to eliminate the deviation. Perform feedforward control by. By repeating this, the deviation can be gradually reduced. This situation is shown in Fig.68.

Although this control is feedforward control within a predetermined operation time, the forced displacement function X (t ₀ + t ') calculated at each reference time at each operation time is the target value and actually It is feedback control because it is corrected to reduce the deviation of the value of. Since feedback control is performed at a fixed time, which is a kind of sample value control, feedforward control is performed within each time interval, and the vibration operation function is a characteristic of the controlled object (natural period) It is new from the conventional technology.

In this device, it is only necessary to measure the sample value by measuring the shaking of the building without considering the acceleration of the earthquake at each moment, so there is a problem with active vibration suppression that works in the direction to cancel the conventional earthquake motion. There is no need to worry about vibration due to a phase shift.

In addition, the forced displacement function X (t ₀ + t ') works in the direction that suppresses shaking no matter how small, so even if the output of the actuator that gives the forced displacement is small, the damping effect is effective regardless of the magnitude of the earthquake. Is obtained. This is a feature not seen in conventional active vibration control. However, the time required for vibration control is unavoidable.

On the other hand, since the shaking of high-rise buildings, which has recently been a problem, is a large building shaking due to the integration of the weak wind force, the sample value control of this time is always used, so it is slightly forced. The amount of displacement can be kept small, and a comfortable living environment can be provided to the residents.

Even in the case of a large crude oil tank, the horizontal position can be changed by installing the tank base on the seismic isolation bearing 40 such as laminated rubber or sliding bearing. By installing several hydraulic actuators 42 so as to surround the crude oil tank between the foundation of the tank and the ground, the foundation part can be forcibly displaced in any direction (FIG. 31). Alternatively, the above-mentioned cam and insulator mechanical mechanism is also possible.

As described later, the sloshing of crude oil in a large tank is equivalent to the sloshing of liquid in a container and can be approximated to the swing of a pendulum.Therefore, the same forced displacement function X (t ₀ + t ') can be used.

The fluctuation of the liquid level of a large tank may be a level gauge 44 attached to several places around the upper surface of the tank, or a hydraulic pressure attached to several places around the bottom of the tank. In the event of an earthquake, in synchronization with changes in these sensors, the base of the crude oil tank is forcibly displaced in the horizontal direction in accordance with a predetermined forced displacement function X (t ₀ + t '). Liquid sloshing is reduced.

At that time, the position / speed sensor 11 is similarly attached to the bottom surface of the tank to be forcibly displaced, and the position and speed for each predetermined operation time are measured or estimated.

Or, in the event of an earthquake, the foundation of the crude oil tank is forcibly displaced in the horizontal direction in synchronism with changes in these sensors and in accordance with the second-order time integration of a predetermined forced displacement function X (t ₀ + t '). This reduces the sloshing of the liquid inside the tank. The latter is better because it is more accurate.

Furthermore, in accordance with the sloshing amount, like the crane, the natural period is corrected by the nonlinearity of the natural period of the pendulum (Formula 62), and is obtained from the second-order time integration of the forced angular displacement function Θ (t ₀ + t '). The sloshing of the liquid inside the tank is further reduced by forcibly displacing the base of the crude oil tank horizontally according to the acceleration function.

Next, consider the case where the track control device A as shown in FIG. 7 is applied to the prevention of galloping by suppressing the horizontal swing of the overhead transmission line. An elevated transmission line is an overhead cable stretched between two fulcrums, and its shape in a stationary state is a suspension line. If the difference in height between the high-voltage tower connection part of the cable and the bottom of the suspension line is D, the distance between the high-voltage towers is 2l, and the gravitational acceleration is g, the primary natural angular frequency ω _c of the overhead cable is Following (formula 65)
(Kenichi Araki, Inherent flexural vibration of an overhead cable stretched between two struts-1-, Journal of Japan Society of Civil Engineers, vol. 6, 1951-8, pp. 53- 57), can be treated as a pendulum with the same fixed handle length as a crane. Therefore, the cable connection part in the high-voltage pylon that is the base of the pendulum is a movable part suspended by the insulator, and an external force is applied to the cable connection part according to the external force function F _IIp (t ₀ + t ′) in (Equation 3). By giving acceleration of forced displacement according to the forced angular displacement function Θ (t ₀ + t ′) of (Equation 58), the sway of the cable can be damped.

Examples applied to prevent galloping are shown in Figs. In Fig. 32 to Fig. 34, the case where the transmission line applied to each elevated steel tower is fixed by each steel tower will be described.

A connection portion is provided in the vicinity of one insulator 57 or one insulator of each of the power transmission lines 49 hanging on the elevated tower 46. Tension ropes 50 are stretched one by one in each direction from both sides of this connection portion, and fixed to each support column 47 of the elevated steel tower 46. The rope shall be an insulator or insulated through a insulator. At this time, it is better to use a spring that guarantees the fluctuation of tension.

A sensor 11cb for measuring the position and speed of shaking is attached to each of the transmission lines 49 on the elevated tower. If an acceleration sensor etc. is used for a sensor, it is cheap and can also estimate a position and speed. The sensor information sends information to the controller that controls the forced displacement of the connection.

Since information on the position and speed of the forceps 57 which are the first support and connections is also required, it is also necessary to attach a sensor 11ca for estimating these quantities.

The motor 51 connected to the controller 56 is placed on the column 47 of the elevated tower 46. Two pulleys are connected to the motor, and one rope is fixed to each pulley in the opposite direction, and when one length becomes longer by rotation, the other becomes shorter.

Also, in order to measure differences in the position, speed, and mode of the transmission line, a speed sensor or acceleration sensor 11cb is attached at the center of the transmission line and at a 1/4, 3/4 length position. These values are sent wirelessly to the control units in the elevated towers on both sides.

When the control device in both elevated towers senses the fluctuation of the transmission line by the sensor, the connected insulators are forcibly displaced simultaneously according to the forced angular displacement function Θ (t ₀ + t ') shown in (Equation 58). . The amount of change in position is determined by the position and speed of the transmission line from the sensor. The natural frequency of the oscillator is the same as the natural frequency of the transmission line. Forced displacement is performed by pulling the rope on the swinging side and loosening the opposite side. This reduces transmission line fluctuations.

The transmission line is a distributed constant vibration system with a longer span as the high-voltage line increases. In addition to a simple primary mode, a secondary mode can be established depending on the wind. It is important to keep in mind that it is necessary to match the natural frequency to that of each mode and to operate with different phases in both towers in order to stop the oscillation of the transmission line in different modes.

In general, galloping does not occur suddenly, but gradually increases as the roll grows and eventually changes to pitch. With this method, even a slight roll can be reduced at the time of occurrence, so galloping can be prevented. The power of the motor that pulls the rope does not need to be so big, as it cancels the small shaking every time.

Also, unless each transmission line is connected by a spacer, etc., it does not always show the same fluctuation, so it is necessary to control each line. On the other hand, in the case of a transmission line in which three or six are connected by a spacer, etc., it is possible to control them collectively because they show the same fluctuation.

Next, another example in which the present invention is applied to galloping prevention by suppressing horizontal shaking of an elevated transmission line is shown in FIGS. The speed sensor or acceleration sensor attached to measure the difference in the position, speed and mode of the wire is the same as the previous example.

Here, the case where the transmission line applied to each elevated tower is fixed by movable insulators 57 suspended from each tower will be described. Remove the two insulators 57 from the tower and suspend the transmission line. By providing a margin for the transmission lines between Japanese insulators, the amount of change in the horizontal position of the transmission lines between the towers can be controlled independently (Fig. 35).

Each insulator is provided with a connecting portion, and this connecting portion is connected to and driven by a one-dimensional actuator attached to the column of the elevated tower (FIG. 36).

Alternatively, a coil 60 may be attached to the upper and lower portions of the insulator, and an electric current may be supplied to make an electromagnet, and this electric current value may be oscillated by Lorentz force by synchronizing with the electric current of the transmission line and changing at commercial frequency (FIG. 37). At that time, it is necessary to monitor and control the amount of change of the position of the transmission line attached to the insulator by the sensor 11ca.

To properly apply Lorentz force to the AC transmission line, it is necessary to apply an alternating magnetic field of the same commercial frequency with an appropriate phase, but it is necessary to correct the phase of the commercial current taken from the transmission line and to bridge the commercial current. It is necessary to make some efforts to switch at commercial frequency by rectifying with diodes etc.

The control devices on both elevated towers change the external force function F _IIp (t ₀ ) (Equation 3) that changes according to the state of the transmission line for each predetermined operation time when the sensors 11ca and 11cb sense the fluctuation of the transmission line. The suspended insulator 57 is forcibly displaced by modulating the amount of current flowing through the coil 60 according to + t ′). The external force function F _IIp (t ₀ + t ') is determined to reduce vibration according to the position and speed of the transmission line from the sensor. With this method, even a slight roll can be reduced at the time of occurrence, so galloping can be prevented.

In this device, it is sufficient to measure only the fluctuation of the transmission line and control the sampled value without considering the wind force at each moment. Further, since the external force function F _IIp (t ₀ + t ′) works in the direction to suppress the vibration no matter how small, the current of the coil 60 for applying the Lorentz force may be small. However, the time required for vibration control is unavoidable. Therefore, it is conceivable to use a small windmill attached to the steel tower or the output of the solar cell to cover the coil power supply.

On the other hand, with this device, the energy of shaking of the transmission line is converted into electrical energy flowing through the transmission line. In other words, the energy of the wind that shakes the transmission line is converted into electrical energy, which indicates that this device becomes a wind power generator.

Figure 69 shows the principle of the current generator. This generator utilizes the vibration control mechanism by the track control device C, and the first support 3c is vibratably attached to the fixed portion 97 which is the fixed support 7c, and the first support 3c is vibratably An external force receiver 138 which is the second support 1c is attached. Here, the direction of vibration of these supports is determined in one direction, and here it is assumed to be in the vertical direction.

Next, an elongated conductor 135 such as a cable is attached to the first support 3c, and the direction of electricity flow is perpendicular to the direction of the previous vibration, which in this case is perpendicular to the paper. It is installed in the direction, and it is assumed that the current i flows from the front side to the back side of the paper. Furthermore, a coil 60, which is an electromagnet, is attached around the first support 3c, and the direction of the magnetic field is set so as to be both perpendicular to the direction of the previous vibration and the direction of current flow. . In this figure, the direction of the magnetic field of the electromagnet is the left-right direction.

Here, assuming that the vibrator, which is the second support, is made to be susceptible to external forces, for example, assuming that the external force receiver 138 is vibrated in the vertical direction by the force of wind flowing in the vertical direction, Accordingly, the first support 3c to which the conductor 135 is attached also starts to vibrate in the vertical direction.

Now, by multiplying the magnetic flux density B by the conductor through which the current i flows, Lorentz force F _B = i × B is generated according to Fleming's left-hand rule. When this magnetic flux density B is constant, the Lorentz force is also constant. On the other hand, since the direction of the conductor's velocity due to vibration switches between positive and negative at random, it is expected that the generated velocity electromotive force will also change randomly around the natural period. A random alternating voltage different from the commercial frequency is less acceptable because it disturbs the commercial frequency. Also, random alternating voltage different from commercial frequency does not increase electrical energy.

But now, the Lorentz force F _B applied to the conductor is the first support, by changing the current flowing through the coil 60 is an electromagnet, and set to reduce the vibration of the second support element (Equation 3 When the external force function F _IIp (t ₀ + t ') is controlled to be the), the vibration of the second support that is being _{excited by} the external force is suppressed.

Conversely, it is assumed that the conductor 135, which is the first support 3c, moves upward at a velocity v due to the vibration of the external force receiver 138, which is the second support 1c. Furthermore, it is assumed that the magnetic field B is applied from left to right to this conductor. Then, according to Fleming's right-hand rule, a voltage by velocity electromotive force represented by v × B = E is generated from the front side to the back side of the paper. As a result, power of P = iE = ivB is generated per unit time. Since this value is equal to P = vF _B = viB, which is the work generated when the conductor 135 moves at a speed v under Lorentz force, it can be seen that the mechanical work performed by the conductor 135 is used for power generation. As a result, the energy of vibration efficiently changes to electric energy, and the direction of the speed electromotive force flows in the same direction as the current, which makes it possible to generate electricity using this method.

The power generation by this method needs to be smoothed when it takes energy from the excitation by natural waves such as random waves and wind, because it gives time-variation to the transmission network. By attaching a large number of vibration generators along a long conductor, it is expected that the fluctuations in time will be reduced by averaging. Further, since the power generation according to the present method can not generate power when the conductor 135 does not move, energy loss can be prevented by turning off the power supply 92 of the electromagnet that generates a magnetic field when large natural energy can not be expected. Most of the energy loss in this method is the copper loss and iron loss of the electromagnet, so if power generation beyond the power loss here can be expected, wave power generation and wind power generation are possible if this device is started. It becomes.

In order to control the external force function F _IIp (t ₀ + t '), the sensors 11ca and 11cb are respectively attached to the first support and the second support, their positions and velocities are measured, and the data are used to Sample value control can be used for each natural period of the second support. In addition, since the Lorentz force varies depending on the current, a sensor 136 that measures the current flowing through the conductor is also required.

On the other hand, when this principle is applied to the trajectory control device C including the power transmission line shown in FIG. 37, the second support 1c, which is the external force receiver 138, becomes the power transmission line 49 itself connecting the high-voltage tower 46, and the first The support 3c is a part 49 of the transmission line of the area of the coil 60 which is suspended by the insulator 57 and which receives the magnetic field. When a commercial current flows in advance in the conductor 49 like a power transmission line, the working Lorentz force should work on the surrounding magnetic field and current so as to reduce galloping which is vibration of the power transmission line. It can be seen that the transmission line galloping reduction device just described also had the effect of a wind power generator that converts wind energy into electricity. In this case, since the transmission line 49 itself serves as a power transmission mechanism, there is an advantage that the cost can be greatly reduced.

At this time, since the increasing amount of current is equal to the energy of shaking lost, there is a risk that the current is modulated with the natural period of the transmission line. In general, high-voltage transmission lines extend over several hundred kilometers, and the strength of the wind flowing between them is averaged. Therefore, if this device can be installed in a wide area where high-voltage transmission lines are placed, the phase of the applied power The turbulence is not expected to increase.

Further, when the main purpose of the present apparatus is a wind power generator, by setting the current flowing through the transmission line to direct current, the current flowing through the coil does not have to be alternating current, which is simpler. If this is used for DC power transmission lines, it is not necessary to change the magnetic field at commercial frequencies, and it is also expected to efficiently collect wind natural energy across the strait.

In this case, it is possible to use more wind energy by further attaching a wind catch or the like around the power transmission line. This method can be used at low cost because the elevated towers used for existing transmission lines can be used as columns and existing transmission lines can be used for connection to the power grid.

In addition, this method is efficient because it can convert all vibrational energy excited by wind drag into electric power. Furthermore, since the span between high-voltage towers extends to 1 km, it is theoretically possible to receive wind of the same area as a large wind turbine per span by attaching a few cm of wind to the transmission line.

On the other hand, this method can also be applied to wave power generation. Figure 91 shows a conceptual diagram of wave power generation using this device. The ocean wave 160 hits the pendulum wave receiver 159 with a certain period width, and the vibration of the wave receiver shakes the conductor 135. An electromagnet composed of a coil 60 is installed in the vertical direction on the conductor, and by supplying an appropriate current from a power source 92 controlled by the controller 83, the Lorentz force is _converted into an external force function F _IIp (t ₀ + t ′). Give a predetermined magnetic flux density B in the vertical direction, according to. At this time, the external force function F _IIp (t ₀ + t ′) is determined by the information of the position and velocity of the wave receiver and the conductor obtained by the position and velocity sensor 11 ca.

The kinetic energy of the conductor generated by the wave force is converted to electrical energy through the conductor. The wave energy is an average of 7 kW per meter of coastline, so by installing 500 units of this equipment per kilometer of coast, 1 MW of power generation per kilometer of coastline is expected. Since the cost per unit can be about 500,000 yen because the structure is simple without using many mechanical parts in the device itself, the power generation cost is less than 10 yen per 1 kWh, and it is expected that the durability by the wave is also high It is done. Fig. 92 shows an image of the wave power generation system arranged side by side along the coastline.

On the other hand, by utilizing the vibration control mechanism by the track control device D, similar vibration power generation is enabled. Figure 93 shows the principle of the current generator. This generator utilizes the vibration control mechanism by the track control device D, and an external force receiver 138 which is the second support 1d is attached to the fixed portion 97 which is the fixed support 7d so as to be capable of vibrating. Here, the direction of vibration of these supports is determined in one direction, and here it is assumed to be in the vertical direction.

Next, an elongated conductor 135 such as a cable is attached to the second support 1d, and the direction of electricity flow is perpendicular to the direction of the previous vibration, which in this case is perpendicular to the paper. It is installed in the direction, and it is assumed that the current i flows from the front side to the back side of the paper. Furthermore, a coil 60, which is an electromagnet, is attached around the second support 1d, and the direction of the magnetic field is set so as to be both perpendicular to the direction of the previous vibration and the direction of the current flow. . In this figure, the direction of the magnetic field of the electromagnet is the left-right direction.

Here, assuming that the vibrator, which is the second support, is made to be susceptible to external force, for example, if it is excited in the vertical direction by the force of wind flowing in the vertical direction, The conductor 135 also starts to vibrate in the vertical direction.

Now, by multiplying the magnetic flux density B by the conductor through which the current i flows, Lorentz force F _B = i × B is generated according to Fleming's left-hand rule. When this magnetic flux density B is constant, the Lorentz force is also constant. On the other hand, since the direction of the conductor's velocity due to vibration switches between positive and negative at random, it is expected that the generated velocity electromotive force will also change randomly around the natural period. A random alternating voltage different from the commercial frequency is less acceptable because it disturbs the commercial frequency. Also, random alternating voltage different from commercial frequency does not increase electrical energy.

But now, the Lorentz force F _B applied to the conductor is the first support, by changing the current flowing through the coil 60 is an electromagnet, and set to reduce the vibration of the second support element (Equation 5 When the external force function F _IV (t ₀ + t ') is controlled to be the), the vibration of the second support that is being excited by the external force is suppressed.

At this time, the position / speed sensor 137 is attached to the external force receiver 138 which is the second support 1d, and the external force function F _IV (t ₀ + t ') is obtained from these values for each predetermined operation time. By using the calculation, an appropriate external force for damping the external force receiver 138 is determined.

Conversely, it is assumed that the conductor 135 moves upward at a velocity v due to the vibration of the external force receiver 138 which is the second support 1 d. Furthermore, it is assumed that the magnetic field B is applied from left to right to this conductor. Then, according to Fleming's right-hand rule, a voltage by velocity electromotive force represented by v × B = E is generated from the front side to the back side of the paper. As a result, power of P = iE = ivB is generated per unit time. Since this value is equal to P = vF _B = viB, which is the work generated when the conductor 135 moves at a speed v under Lorentz force, it can be seen that the mechanical work performed by the conductor 135 is used for power generation. As a result, the energy of vibration efficiently changes to electric energy, and the direction of the speed electromotive force flows in the same direction as the current, which makes it possible to generate electricity using this method.

Next, an example in which the track control device A as shown in FIG. 8 is applied to a relay for large current is shown. The conventional electromagnetic relay can switch the electrical connection depending on whether the movable electrode plate 71 made of a single vibrator or a cantilever is brought into contact with or separated from the terminal electrode 72 by turning on and off the electromagnet. In recent years, electronic switches based on semiconductor devices exist, but because of their low internal resistance, they are important devices for applications where large current and voltage loss are a concern.

On the other hand, since the conventional electromagnetic relay collides at an excessive speed when the movable electrode plate 71 collides with the terminal electrode 72, it does not easily stand still, and causes chattering of several degrees and stops. As a result, discharge occurs when the electrode is released, and the coating on the electrode, which reduces the contact resistance, is blown off. For this reason, the larger the current relay, the more severe the electrical deterioration due to chattering, and the endurance required for the product cannot be maintained.

Therefore, by moving the root of the electrode plate 71 of the electromagnetic relay with a disk cam, the tip of the electromagnetic plate is used according to the forced displacement function X (t ₀ + t ′) shown by (Expression 1) and (Expression 53) according to the present invention It becomes possible to control the collision position and the collision speed of. A schematic diagram of the high current relay thus produced is shown in FIG. A cam follower 67, which is a movable body corresponding to the first support 3a, is mounted on the uniaxial rail 66, and is pressed against the cam 68 by a compression spring 64. The cam 68 can be rotated by a motor 70, and rotates halfway in response to an external signal. A movable electrode 71 corresponding to the second support 1a is attached to the cam follower 67 via a spring 2a, and the movable electrode 71 located on the upper side is lowered by half rotation of the cam 68, and the two terminals directly below The electrode 72 is connected and turned on. Further, when the cam 68 makes a half rotation, the movable electrode 71 located at the lower part moves to the upper part, and the terminal electrode 72 just below loses the connection, and thus becomes the OFF state. Position / speed sensors 11ab and 11aa are respectively attached to measure the position and speed of the movable electrode and the cam follower. However, in the case of an electromagnetic relay, these movements do not change greatly, and are not necessarily required.

By making the rotation time of the cam 68 necessary for connection to one electrode the same as the movement time of the movable electrode plate 71, the fastest electrode switching is possible. The fastest moving position of the movable electrode 71 realized by making the rotation time of the cam 68 the same as the operation time of the electrode plate is equal to FIG. It can be seen that the movable electrode that was stopped moves and slowly contacts the opposite power at zero speed. Since the speed at the time of contact is 0, chattering due to repulsion at the time of collision does not occur, and it is expected that electrode wear will not occur.

In addition, after the collision, the electrode can be connected with a certain elastic contact force by pushing the spring 2a slightly from the balanced position. At that time, it is preferable to make the rotation angle of the cam 68 set above smaller than π and operate the rest for pushing.

Next, an example in which a trajectory control device A as shown in FIG. 7 is applied to an automatic door is shown. In general, a conventional automatic door has a direct connection between the door and the drive device, with no elastic cushioning material therebetween. Therefore, if the door pinches something, the impact is strong and dangerous.

In the present invention, as shown in the schematic view of FIG. 39, an elastic body such as a spring 2a is interposed between an automatic door 73 which is the second support 1a and a drive unit 76 which is the first support 3a. The door should be hung by connecting it to the ceiling rail 77 with wheels so as to reduce the frictional resistance during movement as much as possible. The drive unit 76 allows any forced displacement to be applied by a signal from the control unit 10a. The door 73 and the spring 2a form a single vibrator, and the driving device 76 rotates the wheel to produce a forced displacement.

By moving the drive unit 76 according to the forced displacement function X (t ₀ + t ′) shown by (Equation 1) and (Eq. 53) according to the present invention, the tip position of the door 73 is arbitrary at each predetermined operation time. Can have a position and velocity of. It can also dampen the vibration generated at the door when moving. As a result, although the door is connected by a spring, the door can be opened and closed at a constant speed, or the door can be stopped without residual vibration. As it is frequently used in recent automatic doors, it is possible to smoothly stop the operation and close it slowly when closing it.

In spite of being connected by the spring 2a, the door can be driven to close slowly at about speed 0 and not generate an impact when it is closed. And above all, by making the spring constant sufficiently small, even if your hand gets caught in the door, you will not get injured and you will realize an automatic door with fail-safe safety function.

After closing once, you can realize a tightly closed door by pushing the spring with the drive part after a while. By making the door opening and closing speed constant, there is no need to detect the speed of the door itself, and a vibration suppression device using a cam becomes possible.

Also in the application of this automatic door, for example, a sensor for measuring the speed and position of the door body and the speed and position of the drive unit is attached, and these values are calculated for each operation time.

Next, an example in which a trajectory control device A as shown in FIGS. 7 and 8 is applied to a collision machine is shown. As an example of a collision machine, consider precision press working. The metal thin plate that is the sample is cut out by being struck by a mold and finished to a specific shape.

Here, in order to realize the present invention, consider a machine having an outline as shown in FIG. In this machine, a hammer or mold 79 is hung on a spring 2a which is an elastic body, and a support base 80 at the base of this spring gives an arbitrary forced displacement to a uniaxial actuator 8a using a power supply 84 or a controller 83. It is made to be. When the support base 80 at the base of the spring is forcibly displaced by the uniaxial actuator 8a, the hammer or the mold 79 vibrates, collides with the workpiece 78, and processing is performed. The position and velocity of the hammer or mold 79 at the time of collision are monitored by the sensor 11ab. The position of the one-dimensional actuator 8a relative to the hammer or the mold 79 may be reversed.

According to the present invention, by moving the support base of the base of the spring according to the forced displacement function X (t ₀ + t ′) shown by (Expression 1) or (Expression 53), the hammer or the mold can be moved to any collision position. It can be made to collide with the sample at a collision speed of. Since the position of the workpiece is displaced with the processing, it can be coped with by changing the forced displacement function X (t ₀ + t ') according to the displacement. Moreover, since the collision velocity can be changed each time by the forced displacement function X (t ₀ + t '), variable collision machining becomes possible.

Since the processing position and the processing amount are variable, the same processing as a servo press is possible with this machine. However, there is no need for a servomotor based on feedback, such as a servo press, and it is just feedforward control, and the machine can be built with an inexpensive system.

If it is desired to repeat the same processing for the metal sheet to be conveyed automatically, a cam can be used instead of the uniaxial actuator 8a.

Also in the application of this processing machine, for example, a sensor 11ab for measuring the velocity and position of a hammer or a mold and a sensor 11aa for measuring the velocity and position of a support are attached, and these values are calculated every predetermined operation time.

Next, an example applied to a display using a vibrator using a trajectory control device A as shown in FIG. 7 will be shown. The display includes a fixed portion 94 using a mounting magnet or the like on the base, a battery box 95, a controller / communication device 93, and a power source 92. A support base 91 and a mounting bracket 88 are mounted on the base. There is a driving unit 90 such as a piezoelectric element between the driving unit fixing unit and the vibrator connecting unit. By replacing the electronic box with the solar battery 95, the display device using the vibrator can be kept moving without worrying about battery replacement (FIG. 41).

The fixed part 94 is an Nd magnet, for example, and is attached to a ferromagnetic material such as iron by a strong magnetic field. The mounting bracket 88 is a phosphor bronze rod having a length of several millimeters to several tens of millimeters and a diameter of about φ submillimeter, and a hook portion that can suspend a pendulum is attached to the tip. The support base 91 is a sufficiently thick rigid body extending from the base, through which the wiring of the drive unit passes. The driving unit 90 is a one-dimensional actuator such as a laminated piezoelectric element fixed to the driving unit fixing unit, for example, and expands and contracts in micron order by applying a voltage from the control circuit to both ends. The other end of the drive unit is elastically compressively stressed on the rod of the mounting bracket, and the displacement of the drive unit causes a forced displacement of the hooking portion at the tip of the mounting bracket.

By fixing the pendulum through the mounting bracket and hanging the sign 86 upside down, it becomes a display device that can shake the sign (FIG. 41). Also, by passing a thin rod through the mounting bracket, it can also be a vibration indicator that shakes the signboard 86 on a vertically erected cantilever (FIG. 42).

There is hysteresis in the piezoelectric element, but since the compressive stress is applied, the reproducibility of the position change is good. By obtaining the relationship between the amount of change in position of the piezoelectric element and the applied voltage in advance, it is possible to give a forced displacement along the desired forced displacement function X (t ₀ + t ′).

In addition, the piezoelectric element generates a voltage in proportion to the applied stress, and thus acts as an acceleration sensor 11ab for the vibrator. By switching the wiring connected to the piezoelectric element with a semiconductor switch, the sensor and the drive system can be switched alternately. By expanding and contracting the piezoelectric element in accordance with the timing of the vibrator thus obtained, it becomes possible to vibrate or damp the vibrator. As a result, the vibrator can be shaken or made stationary with a system that is much smaller than the conventional drive system.

By connecting signal lines from other devices to the communication device 93, the vibrator can be vibrated or stopped in accordance with an external signal. By performing vibration suppression control, vibration of the vibrator due to disturbance can be suppressed immediately, and information errors can be prevented.

On the other hand, by using a wireless circuit capable of receiving a signal such as BlueTooth (registered trademark) in the communication device 93, the vibrator can be vibrated or rested in accordance with the wireless signal from the outside.

For example, if you receive a wireless signal from your cell phone and you have free control over the movement of your cell phone strap, you may be able to signal an incoming call or email with the movement of the strap.

Also, for example, if two pendulums are suspended on both sides of the rearview mirror and the swing of each pendulum can be freely controlled according to the radio signal from the in-vehicle navigation system, the navigation map can be checked without checking the navigation map. You can know the direction of the turn while facing. It can also express the distance to turn by the amplitude of the shaking.

For example, it can be applied to a display panel suspended on the ceiling of a large shopping center sales floor. When a customer inputs a product name from a terminal or on the Web, a radio signal for shaking a specific display board can be given, so that the display board for the place where a specific product is located can be shaken, guiding the customer to an appropriate place. can do.

Also, for example, by attaching an advertisement to the end of a metal wire with good springiness and optionally shaking it, a moving display that can be installed in a small place can be realized.

Furthermore, for example, the pendulum of this display can be used to shake the pendulum at a specific position on the spread out paper and stop it at another position. This makes it possible to create a game that imitates a fortune-telling pendulum called douging.

Also in the application of these moving displays, for example, sensors for measuring the speed and position of the display main body, and the speed and position of the drive unit are attached, and these values are calculated for each predetermined operation time.

Next, an example applied to the derivation of the cam curve using the forced displacement function X (t ₀ + t ') shown in (Equation 1) is shown. In the trajectory control device A as shown in FIG. 8, an example of a cam curve which does not cause a residual vibration when the mass of the vibrator is stopped by changing a fixed distance position from the stationary state and then returned to the same distance again is stopped. FIG. 43 shows the profile of the two-dimensional plate cam designed thereby. The origin in Fig. 44 represents the rotation center of the cam. Here, the angular frequency parameters are α ₁ = 1 and α _{p ≠ 1} = 0, X _in = X (t ₀ ) = 0.0, and V _in = V (t ₀ ) = 0.0. In the first change of position, the mass position of the original oscillator is x _in = x ₁ (t ₀ ) = 0.0, the speed of the original oscillator is x _in = x ₁ (t ₀ ) = 0.0, the target vibration The position of the mass of the child was x _en = x ₁ (t ₀ + Δt) = 1.0, and the velocity of the mass of the target oscillator was x _in = x ₁ (t ₀ + Δt) = 0.0. In the next change in position, the mass position of the original oscillator is x _in = x ₁ (t ₀ + Δt) = 1.0, and the speed of the original oscillator is x _in = x ₁ (t ₀ + Δt) = 0.0, the position of the mass of the target oscillator was x _en = x ₁ (t ₀ + 2 Δt) = 0.0, and the velocity of the mass of the target oscillator was x _in = x ₁ (t ₀ + 2 Δt) = 0.0.

On the other hand, FIG. 45 shows x ₁ (t ₀ + t ′) which is the trajectory of the mass of the vibrator which is a follower mechanism driven by the cam curve of FIG. 43 in the trajectory control device A as shown in FIG. . For comparison, a cycloid curve, which is a general cam curve, is also shown. It can be seen that the follower mechanism trajectory is very close to the conventional cam curve. It can be seen that the cam curve of this time can arbitrarily design the trajectory of the mass of the vibrator driven by it, whereas the cam curve of the past only determined the trajectory of the cam follower.

On the other hand, since the acceleration curve of the cam of FIG. 43 obtained this time is expressed as shown in FIG. 46, it is not the stationary cam but the common sense of the conventional cam design even though the follower mechanism is stopped. It can be seen that is different.

On the other hand, when the base of a vibrator with a different natural angular frequency ω is forcibly displaced using a cam designed to make the vibrator with an angular frequency ω _t stationary without residual vibration, the amplitude of the vibrator obtained Figure 47 shows the relationship between the frequency and the ratio of both angular frequencies. That is, FIG. 47 shows the influence of the ratio of the cam rotation frequency ω _c and the natural angular frequency ω _t of the vibrator on the damping function.

As shown in this figure, it can be seen that when the natural frequency ω of the vibrator is equal to ω _t , the vibrator is stationary without residual vibration. On the other hand, as it deviates from this frequency, residual vibration remains and does not completely stop. If omega / omega _t is smaller than 1, the residual amplitude increases, does not exceed approximately 1. Conversely, when the omega / omega _t is 2 close, the residual amplitude is greater than the rather original. Therefore, although the cam designed this time exhibits damping most efficiently for a vibrator with a specific natural frequency, it can be seen that it does not guarantee this for other than that. If the rotation speed of the cam can be selected arbitrarily, it can be seen that it is desirable to adjust it according to the natural frequency of the vibrator.

The cam introduced in the present invention has a pointed shape because inclination may be discontinuous at the boundary. By increasing the base radius of the cam, these non-smooth points will change unintentionally. However, when using the cam, it will be the first place to be easily worn. , Maintenance should be taken care of.

In the cam introduced in the present invention, the mass is determined for each operation time Δt without residual vibration by dividing the time ΔT required for the movement of the cam into the operation time Δt which can be several different lengths. It can be designed to follow a path with a specific position and speed.

In that case, the cam curve is defined by connecting a forced displacement function X (t ₀ + t ′) designed to have a position and a velocity determined at each predetermined time of operation Δt. When the position of the mass of the vibrator is determined for each operation time Δt in any cam curve, the forced displacement function X (t ₀ + t ′) is used to vibrate at a predetermined position for each operation time Δt. By designing the cam curve so as to make the mass of the element stationary, it is possible to control the mass at any position for each operation time Δt without residual vibration. In other words, it is possible to design a cam with a variable rotation period that suppresses residual vibration by simply determining a cam curve determined from the forced displacement function X (t ₀ + t ') based on an arbitrary cam curve.

Next, using the forced displacement function X (t ₀ + t ') shown in (Equation 1), the displacement curve of the follower mechanism passes through the predetermined position of the cycloid curve at every operation time Δt, and makes a circle at 10 Δt. A design example of a cam curve that does not cause residual vibration is shown in FIG. In this example, the natural period τ of the follower mechanism was set equal to Δt. Fig. 49 shows the trajectory of the follower mechanism driven by this and the cycloid curve. It can be seen that the follower mechanism can be controlled without residual vibration by passing through the cycloid curve for each operation time Δt. The profile of the two-dimensional plate cam designed by this is shown in Fig. 50. The origin in FIG. 50 represents the rotation center of the cam. This plate cam rotates once with a period of 10 Δt.

Next, an example in which the trajectory control device A as shown in FIGS. 7 and 8 is applied to the suppression of the sloshing of the liquid in the container is shown. A model diagram when the liquid in the container is sloshing is shown in FIG. Here, h _s is the height of the liquid in the container, θ is the inclination of the liquid surface from the horizontal surface, g is the gravitational acceleration, and m is the mass of the liquid in the container. Point O is the center position of the liquid level. If the moment of inertia around the O point of the liquid is J, the equivalent pendulum length l of the liquid in the container can be obtained from J = ml ² , but the actual frequency of sloshing is actually calculated from the approximation with the pendulum described below. It is good to decide by measuring.

In the model of FIG. 51, the sloshing of the liquid is approximated by a pendulum of length l and mass m suspended from point O. The control of vibration in the pendulum is equivalent to that described for the overhead crane. Since the hanging position of the pendulum is realized by the movement of the container, the sloshing is suppressed by performing the forced displacement, which is performed to the hanging position in the overhead crane, on the container.

The position and velocity of the controlled object in the liquid in the container are determined by the inclination θ (t ₀ + t ') of the liquid surface from the horizontal surface of the liquid surface in the container and the angular velocity dθ (t ₀ + t') / dt, which corresponds to swing angle and swing angular velocity, which is the inclination of the wire from the vertical direction in the overhead crane.

Therefore, by measuring the liquid surface inclination θ _in and the liquid surface angular velocity dθ _in / dt at the moment of starting control, the target liquid surface inclination and liquid surface angular velocity are set to 0 (formula 58) is given. The sloshing of the liquid level is suppressed by giving the acceleration of the forced displacement amount determined by the forced angular displacement function Θ (t ₀ + t ') that manipulates the angle / angular velocity expressed by (Formula 58) in the horizontal direction of the container. Ru. Since sloshing is equivalent to a pendulum, nonlinearity exists as the inclination of the liquid surface increases, and residual vibration remains even after this control method. Therefore, it is the same as that for overhead cranes that requires several vibration suppression operations, corrects the natural period by amplitude, and limits the operation time to a specific time.

Fig. 52 shows a schematic diagram of the sloshing suppression device according to the present invention. A mounting base 104 on which the container 98 containing the liquid is placed is placed on the uniaxial rail 105. A cam follower 13a is attached to the side surface of the table facing the liquid traveling direction, and the entire table is brought into contact with the cam 12a by a compression spring 64. The cam follower 13a is attached with a sensor 11aa that measures the position and speed of the installation table. An installation table 104 on which a container 98 containing liquid is placed is placed on a movable carriage 102. Further, a liquid level gauge 103 for measuring the angle and angular velocity of the liquid level is attached to the upper part of the container.

The cam 12a is designed on the assumption of a specific liquid surface angle and angular velocity, and when the signal from the liquid level gauge 103 becomes close to this value, the cam 12a is operated and it is decided on the mounting table 104 on which the container is mounted. Enter the forced displacement pattern. The rotation period is also adjusted so that the operation time can be changed according to the natural period of the liquid shaking. By inserting this amount of change every time the sensor detects a predetermined shaking, sloshing of the liquid being transported is suppressed.

This prevents sloshing and the like of the molten steel that occurs when carrying the molten metal from the melting furnace to the mold during casting, thereby preventing an accident in the factory.

Also in the application of this cam, for example, a sensor for measuring the speed and position of the other side receiving the forced displacement, and the speed and position of the cam follower is attached, and these values are calculated for each operation time.

Next, in order to describe an embodiment in which vibration control is performed by the track control device A as shown in FIG. 7, the derived forced displacement function X (t ₀ + t ′) is applied to an active suspension of a train or a car. Here is an example.

For example, in the case of trains on railways, track displacement, which is a change in the track position in the vertical and horizontal directions of the track, gives vibration to the vehicle body, and there is a risk of derailment due to the large growth of the vibration. In addition, vibration of the car body reduces the ride quality of the passengers, so it is necessary to reduce this as much as possible. Similarly, in the case of automobiles, changes in the position of the road surface give vibration to the vehicle body.

Conventionally, many active suspensions for trains and automobiles have been designed and controlled using Skyhook theory, which controls the vehicle body to be damped from a single point on the ceiling.

However, when the change in the position of the road surface is large in a car, using skyhook theory, it is necessary to give the same large change in position to the vehicle height, and the actuator requires a large amount of power. Also in trains, the body is heavy, so a large amount of power is required to change the height of the body even if the position changes slightly. In general, actuators used in active suspensions do not have enough power, so the vehicle body cannot be damped when it passes through sharp irregularities.

On the other hand, if the actuator is slightly corrected by the actuator with respect to changes in the track or road surface, and the forced displacement function X (t ₀ + t ') according to the present invention, the vehicle changes in position similar to changes in the track or road surface. Although it shows, residual vibration of the car body can be suppressed small.

In addition, even when the power of the actuator is not sufficient, the sway can be reduced by applying sample value control for each predetermined operation time of the vibrator composed of a spring and a vehicle body. This will greatly improve the ride comfort of cars and trains.

On the other hand, the conventional active suspension detects the acceleration applied to the vehicle body with a sensor and then cancels it by generating the reverse acceleration with an actuator. There is also a risk of accidents.

However, in the present technology, a forced displacement function X (t ₀ + t ′) for optimally controlling the residual vibration of the vehicle body is feedforwarded by combining the road and track relief information obtained as described later and the speed control technology. Can be determined automatically.

On the other hand, if undulation information on roads and tracks can be obtained, changes in the position of the actuator that arbitrarily manipulates the position and speed of the vehicle body can be calculated with the conventional control technology, although the change in the vibration of the vehicle body can be simulated. It cannot be obtained analytically.

However, in the present invention, since the forced displacement function solves the inverse problem of the dynamics, it becomes possible to control the sample value for each operation time for rapidly reducing the residual vibration of the vehicle body.

In the case of automobiles and trains, the spring constant of the primary spring of the tire or carriage is much larger than the spring constant of the spring on the suspension that rides on it, so it can be ignored as a model. Therefore, the approximate amount of change in position on the trolley or axle can be calculated from the amount of change in the position of the road surface or route (hereinafter, unified with the road surface).

Now, as shown in FIG. 70, an actuator 8a that is driven by hydraulic pressure or the like is mounted on an unsprung mass 145 of a truck or the like directly above the axle. The uniaxial actuator 8a can be arbitrarily moved in the vertical direction by the controller 10a. A suspension spring 2a is mounted on the actuator 8a via a lower seat 151, and a vehicle body 144 having a sprung mass is mounted on the spring 2a. Further, sensors 11ab and 11aa are attached to the vehicle body and the lower seat, respectively, for estimating the position and the velocity with respect to the change direction of the position. A preview sensor 146 for measuring the unevenness in the vertical direction of the road surface is attached.

If the vehicle body 144, the suspension spring 147, and the lower seat 151 constitute an integrated vibrator of the track control apparatus A as shown in FIG. 7, the vehicle body is the second support 1a, the lower seat is the first support 3a, and the suspension spring. Becomes a spring 2a connecting them. The sum of the displacement in the height direction by the uniaxial actuator 8a and the road surface corresponds to the amount of forced displacement given to the first support 3a which is a lower seat.

When the road surface changes significantly to vertical movement, the vehicle body is subject to fluctuation. Now, after obtaining information on the position and velocity in the height direction of the vehicle body 144 and the lower seat 151 at every operation time, the forced displacement function X (t ₀ + is obtained from the target position and velocity determined to stop the vibration of the vehicle body. Determine t '). During the next operation time, the sum (X _d + X _a ) of the road surface change amount X _d in the height direction and the change amount X _a of the uniaxial actuator becomes the forced displacement function X (t ₀ + t ') If the uniaxial actuator 8a is changed, the residual vibration appearing at the position x in the height direction of the vehicle body can be suppressed.

In this case, if it is possible to obtain the height direction of the change amount X _d in the road surface or line that passes to the next operation time from pre sensors and cloud information, advance the variation X _a uniaxial actuator in the next operation time, more It can be decided appropriately and the effect of suppressing residual vibration is enhanced.

However, even if the amount of change X _d in the height direction on the road surface or track passing in the next operation time can not be predicted, the residual in one operation time delayed by using the actual amount of change X _d as noise in sample value control. Vibration suppression control is possible.

For example, when considering a smooth step-like road surface displacement _Xd as shown by a solid line in FIG. 82, in the prior art, the change amount of the actuator needs to be about the same as the road surface displacement.

On the other hand, in the present technology to provide a change in X _a position of slight actuator as shown in broken line in FIG. 82, forced displacement was determined feedforward combined with position change of the axle and bogie function X (t ₀ + t ') can be realized, and the residual vibration of the vehicle body can be suppressed. FIG. 83 shows the time variation x of the vehicle body position at that time. It can be seen that after the vehicle body made a step-like change in vertical motion, the shaking was settled without residual vibration.

In this method, residual vibration of the vehicle body in the left-right direction can be suppressed by installing hydraulically driven actuators on the left and right sides of the carriage and axle. Since many of the track swings are lateral displacements, it can be an effective method for trains.

The natural frequency due to suspension of automobiles and trains is usually designed to be 1.0 to 1.5 Hz. When an automobile or train travels at 90 km / h (= 25 m / s), changes in the track or road surface at this distance are 20 to 25 m per second, so changes in the track or road surface at this distance It greatly affects the vibration (Furukawa Kei, track management for improving riding comfort, RRR, Vol. 65, p. 22-25, 2008). The distance of the road surface that affects the vibration is determined by the speed and takes a constant value from time to time, so it is called the characteristic distance d _s . Displacement of the road surface and track over a distance greater than the characteristic distance can cause vibration of automobiles and trains.

In the case of a train, the track displacement of the track can be measured in advance, and combined with GPS and position information from the surroundings, the horizontal position and vertical position of the carriage at the next characteristic distance or more The time change of can be estimated.

Also, in the case of a car, the information on the road height and swell changes greatly depending on where the wheel passes. For this reason, it is necessary to install a sensor that measures the height and undulation information of the road surface ahead of the vehicle body, and to estimate the time variation of the road height within the next characteristic distance from this information. Also, in recent years, there is a tendency for data on road undulations and undulations to be clouded, so it is possible to calculate the time change in the height direction of the road surface at the next characteristic distance or more from the position information by GPS. It becomes possible.

In this way, it is possible to estimate the time change of the displacement of the axle or the truck in the vertical or lateral direction from the displacement of the road surface or track and the speed of the vehicle body in the future route of the car or train.

Now, if the change of position is a road with unevenness like a cycloid curve, if there is no control and the damping rate is small, a large residual vibration will appear in the vehicle that has passed this road surface.

However, using the position and speed information of the vehicle body, axles, and carriages at the start of the operation for each operation time, the parameter α _p is fitted so as to be as close as possible to the actual position change so as to stop residual vibration. By doing so, the forced displacement function X (t ₀ + t ') of (Equation 1) is determined. By operating the actuator so as to compensate for the difference between this forced displacement function X (t ₀ + t ') and the actual displacement of the axle or carriage, the time change of the position of the lower seat between the actuator and the spring is forced displacement function By making X (t ₀ + t ') closer, the residual vibration can be made zero. In this way, the vehicle body can be controlled by controlling the sample value using the forced displacement function of the actuator determined by measuring the change of the road surface at the next characteristic distance using the position and speed of the vehicle body, axles and carriages for each operation time. It can always be kept free of residual vibration.

In the active suspension of the present invention, although the residual vibration of the vehicle body can be made zero, the vehicle body itself changes its position in the vertical and horizontal directions, so the acceleration applied to the passengers and objects inside the vehicle body reduces these vibrations. Induce. When the change is extremely large, the target position is changed to increase the amount of change in position by the actuator, and control with further reduced acceleration inside the car body becomes possible.

In addition, since the sway of the vehicle body is not limited to the vertical and lateral directions, and also occurs in the rotational direction around the center of gravity, the same control is required in the rotational direction of the vehicle body.

On the other hand, when data on road undulations and undulations are accumulated in the cloud or in-vehicle storage, the amount of change in the position of the axle or carriage due to the road surface height or undulation at the previous characteristic distance from the GPS location information X _d Can be known. If X _d can be selected so as to be close to the forced displacement function X (t ₀ + t ') of (Equation 1) which can suppress this based on the current vehicle shake information, the actuator is not used Both can improve the ride comfort.

In recent years, it has become possible to control the speed by automatic driving and cruise control, so it is possible to select the route and speed so that the amount of change in the position of the axle and carriage is close to the forced displacement function that suppresses shaking. It is expected to be. In this case, changes in road height and undulations work in reverse to suppress vibration, making it the most energy-efficient, active suspension that can be achieved without using an actuator.

The active suspension according to the present invention makes it possible to develop a car or train having a comfortable ride with less vibration.

Next, in order to describe an embodiment in which vibration control is performed by the trajectory control device D as shown in FIG. 10, the external force function F _III (t ₀ + t ′) of (Equation 4) is derived from the spring itself An example of preventing the release of a contact part preloaded by a spring by applying it to suppression of surging which is vibration is described.

Among mechanical parts, there is a mechanism in which a part connected to one end of a spring is subjected to forced displacement by another part and the other end is fixed by a wall (FIG. 71). For example, in a valve mechanism in a car, the tappet at the end of the valve connected to one of the springs is cyclically driven by a cam, and the other end is fixed by the wall of the engine.

In the brushed DC motor, the electrical brush connected to one of the springs is in contact with the commutator, and the other spring is fixed to the motor case. This spring is called a brush presser spring.

Furthermore, in the pantograph used for the electric railway overhead train line system, one end of the restoring spring on the frame is connected to the trolley wire of the overhead line via a sliding material, and the frame on the other end of the restoring spring is the wall It plays a role.

In the following, for the sake of uniform explanation, the machine part connected to the spring on the opposite side of the wall will be represented by a cam follower, and the machine part that will contact this cam follower and give a forced displacement will be represented by a cam.

In these mechanisms, it is known that cam followers that are pressed by spring preload often jump away from the cam during movement. In the case of the engine's valve mechanism, this jump is known as the tappet moving away from the cam, causing engine damage.

In addition, jumping in which a brush for a DC motor with a similar mechanism leaves the commutator by a similar mechanism is called brush dance. Also, due to the same mechanism, the jump of the sliding material in the overhead line system of the electric railway from the trolley line is called pantograph separation. Since the pressing force by a spring in a brushed DC motor or pantograph enables electrical connection, this jump causes arc discharge and causes the electrode to wear out.

Since the consumption of electric brushes and sliding materials requires periodic replacement of these electrodes, it is necessary to reduce this jump to extend the life. In addition, since it determines the limit of engine speed, it is necessary to devise a mechanism that does not generate an up to higher speed in order to obtain a powerful output. However, the mechanism of these phenomena has not been clarified.

Since the cam movement moves the center of gravity of the spring itself, there is a possibility of triggering the surging of the spring. Now _assuming that the mass of the spring itself is m _s and the spring constant of the spring is k _s , surging of the primary mode of the spring itself, one end of which is fixed to the wall and the other end receives a change of the position of Δx, is mass m _s, spring spring constant 2k _s - mass system is modeled by the equation of Ricardo as a single vibration undergoes a change in position of the [Delta] x / 2, natural period Delta] t _s of surging of the spring is expressed by equation (66).
A more precise spring constant can be obtained by Hashikura's equation (Hashikura Katsuharu, Natural frequency calculation equation for a valve, JAS Journal, Vol. 7, No. 60, pp. 143-152 (1940)). There is a mass M cam follower at the base of the spring, which is subjected to a constant forced displacement by the cam.

If the cam is a cycloid curve and the displacement of the cam seen from the natural period of the spring does not become a vibration operation function for growing the vibration of the spring, the change in the position of the center of gravity of the spring is as shown in FIG. Large surging does not occur. Here, x _g is the center of gravity of the spring, S _A is the displacement by the cam, and the difference between the two represents the amplitude of the vibration (surging) at the center of gravity of the spring.

On the other hand, in this cycloid curve, a change in position due to slight unevenness that functions to increase the position and speed of the spring represented by the forced displacement function X (t ₀ + t ′) in (Equation 1) is the vibration of the spring. As shown in FIG. 73, the spring surging grows greatly. Here, S _B is the amount of displacement due to the cam with slight unevenness.

On the other hand, if the preload of the spring is P, the spring constant of the cam spring is k, the cam displacement function is X, the mass of the cam follower is M, and the position of the center of gravity of the spring is x, the contact pressure between the moving cam follower and the cam N is expressed by the following (Equation 67).
As shown in FIG. 74, when the surging of the spring becomes strong, the contact pressure becomes negative, and a phenomenon occurs in which the cam follower and the cam are separated. This is valve dance.

When the surging is large, the contact pressure between the cam and the cam follower fluctuates as shown in FIG. 74, so that a forced displacement occurs which causes the surging due to wear. For example, the wavy wear seen on the trolley wire of the railway overhead line is thought to be caused by pressure fluctuation due to surging of the restoring spring. In addition, cyclic machining flaws that occur on the cam during machining can also be forced displacement that causes surging.

In other words, it is important to prevent surging of the restoring spring attached for the purpose of applying contact pressure to prevent valve jumping, brush dancing, and pantograph separation (Shigeo Kotake, Yuichiro Kawakita, spring vibration) Cycle component of the cam that grows the spring, Proceedings of the Spring and Restoring Force Application Lecture Meeting, November 1, 2013) (Shigeo Kotake, Yuichiro Kawakita, engine valve viewed from the inverse problem of the one-piece collision oscillator Leaping phenomenon and its suppression method, Proceedings of the 24th Symposium of the Japan Society of Mechanical Engineers, November 26-28, 2013).

There are several ways to prevent spring surging. One is an active damping operation, for example, by measuring the position and velocity of the center of gravity of the spring, the movement of the spring is stopped at a predetermined operation time, and the base of the spring is (Equation 1) A change in position is given by the forced displacement function X (t ₀ + t '), or an external force is applied to the center of gravity of the spring according to the external force function F _III (t ₀ + t') of (Equation 4).

In order to apply an external force to the center of gravity of the spring 127, for example, only the center of gravity of the spring 127 is magnetized, a power source is connected to the coil 60 installed around the center, and the external force function F _III (t ₀ + t ′) is followed. Apply electromagnetic force (Fig. 75). At this time, since it is necessary to know the position and speed of the center of gravity of the spring, the sensor 11db is installed near the coil.

Since the surging of the spring is the accumulation of energy given from a slight change in the position of the cam, it can be sufficiently controlled by continuing to give even a slight electromagnetic force by the above device and give an appropriate external force function Therefore, surging is reduced. In this method, the position and speed of the center of gravity of the spring can be estimated from the induced electromotive force of the coil generated by the magnetization of the center of gravity of the spring.

For example, when an external force according to an external force function F _III (t ₀ + t ′) determined according to the position and speed of the center of gravity is applied to the center of gravity of a spring where large surging occurs due to a periodically worn cam. Spring surging can be suppressed.

In this method, it is possible to devise a method in which the magnetization remains more by making a ferromagnetic thin film near the center of gravity of the spring or by nitriding and carbonizing near the center of gravity of the spring.

Furthermore, the same effect can be obtained by halving the spring and sandwiching a ferromagnetic material such as ferrite at the center. In this case, by designing the density of the interposed ferromagnetic material in the length direction of the spring to be the same as that of the spring, it is possible to devise that surging hardly occurs.

On the other hand, in order to prevent the surging of the spring, it is possible to simply apply viscous drag to the movement of the center of gravity of the spring. As described above, when the center of gravity of the spring is magnetized, a voltage is generated in the surrounding coil due to the induced electromotive force caused by the intense vibration of the center of gravity. By connecting a resistance to this coil, the vibrational energy of the center of gravity of the spring is dissipated and surging is prevented. In addition, by regenerating the generated voltage, energy harvesting becomes possible, and the fuel consumption of the car can be improved.

In addition, if the spring is plastically deformed beyond the normal elastic deformation in the absence of a magnetic field, the remanent magnetization of the magnetized spring decreases (Shigeo Kotake, additional plastic deformation indicated by changes in remanent magnetization, inspection Technology, March 2014 issue, pp. 11-17). On the other hand, in the case of elastic-only deformation in a normal spring, if the elongation is restored, the magnetization will also be restored. This is due to the behavior of the domain wall pinned by the dislocation. Although the dislocation does not move in elastic deformation, the residual magnetization does not change, but the domain wall changes in a more stable direction by moving the dislocation depending on plastic deformation. This is due to the fact that

Since the plastic deformation of the spring means the progress of the fatigue phenomenon, the balance position of the spring changes and the restoring force by the spring decreases. Therefore, by monitoring the voltage generated in the coil, it is possible to evaluate the degree of fatigue and the degree of fatigue of the spring.

In these technologies, the remanent magnetization of the magnetized spring deteriorates over time, so the coil must also have a function to magnetize the spring when the operation is stationary.

On the other hand, in the case of a brushed DC motor, in general, in a commutator, a plurality of n commutator pieces are separated by insulating pieces and arranged in a cylindrical shape. As general electric brush do not catch, the edge of the commutator segments are lowered prime, since the center of the commutator are raised, the brush rotating in contact with the commutator, the rotation of the motor rotation period t _c Is subject to forced displacement at a period of t _c / n. From Eq. 22, it is the forced displacement function X (t ₀ + t ') of (Equation 1) which makes the speed of the center of gravity of the spring increase as the repetition of cyclical change in the position of the mountain becomes a commutator shape In itself, there is a risk of inducing surging of the presser spring that applies pressure to the commutator.

Therefore, when the maximum rotation period when using a DC motor with a brush is t _cmax , the natural period τ of the brush presser spring itself that applies pressure to the commutator needs to be designed to satisfy the following (Equation 68). You can see that there is When there is no fraction 2 here, it is just a resonance condition, and the surging grows the most, but by adding 2 to the fraction, it is expected that the surging will be reduced by canceling each other's excitation. .

On the other hand, in the case of the overhead railway system of the electric railway, the trolley wire is suspended at a distance d (usually 5 m) by a hanger and takes the form of a catenary. Therefore, the sliding member is subject to forced displacement downward at d intervals, and this periodical change in position causes surging in the restoring spring. When the maximum speed in train operation is v, the restoring spring is vibrated with a period d / v. Therefore, the natural period τ of the restoring spring is expressed by the following (Equation 69) so that the surging does not grow. It is necessary to design to satisfy.

As a result, the pantograph is not derailed and the life of the sliding material is improved. In the case of pantographs, depending on the speed, it may also be the main spring that resonates with the trolley wire, which may have to be taken into account as well.

Next, in order to describe an embodiment in which vibration control is performed by the trajectory control device D as shown in FIG. 10, an example in which the derived external force function F _III (t ₀ + t ′) is applied to a rolling mill will be described.

In a tandem-type multistage rolling mill, large pitch vibration called chattering occurs during cold rolling of a thin plate at high speed, resulting in periodic nonuniformity in plate thickness. Although the reason for these has not yet been clarified, it is widely recognized that self-excited vibrations occur when the mode resonance frequency of a multi-high rolling mill coincides with periodic plate thickness fluctuations (Kazu Ishino) Naru, Michiya Kazuhisa, Yoshikawa Takao, Transactions of the Japan Society of Mechanical Engineers, 69C, 687 (2003), 2975.).

The occurrence of chattering not only reduces the accuracy of the plate thickness, but also causes a reduction in efficiency, such as the inability to increase the rolling speed to suppress the occurrence of vibration. Therefore, development of technology to suppress chattering has been desired.

For prevention of chattering up to now, lubricant oil at the time of rolling is appropriately selected (Kimura et al., Chatter generation mechanism in cold tandem rolling, NKK technical report, No. 170, (2000), 15.), Although attempts have been made to reduce the rolling speed in order to shift the self-excitation frequency, this is a passive measure to suppress the occurrence of chattering, and a method to suppress chattering once has not been proposed. . As a result, it was impossible to improve the productivity of the rolling process because it was impossible to roll at high speed beyond the self-excited vibration.

By using the orbit control device D according to the present invention, the mode mass position and velocity are measured at each operation time defined in the natural period of each vibration mode by treating the self-excited vibration mode as an integral vibrator. By applying an external force to reduce this amplitude, self-oscillation can be dynamically reduced.

Now, FIG. 53 shows a linear spring model in which the respective rolls of each multistage rolling mill and the springs connecting the respective rolls are modeled. The rolls are a work roll 108, an intermediate roll 107, and a backup roll 106 from the side closer to the material to be rolled 109. Vibration and pressurization are considered to occur in up-and-down symmetry, and the linear spring model of each of the upper and lower N stages has N natural vibration modes. The vibration of mode n of a many-body linear vibration system can be expressed as one independent vibrator consisting of each mode mass m _n and each mode stiffness k _n .

On the other hand, the shaft of the working roll 108 of the multi-stage rolling apparatus is displaced in the vertical direction due to the thickness variation of the material 109 to be rolled during rolling. This working roll shaft displacement h (t) is equivalent to the trajectory control device A shown in FIG. 7 because it is a forced displacement at the root of a specific vibration mode of one multi-high rolling mill. .

Therefore, chattering is expected to occur when the displacement h (t) of the working roll shaft becomes a forced displacement function that has the function of growing a specific vibration mode of the multi-high rolling mill. Therefore, the occurrence of chattering can be examined from the function of the displacement h (t) of the working roll shaft due to the plate thickness variation as a forced displacement function, but it will not be described in detail here.

On the other hand, when an electromagnetic force generator that applies an external force to each roll is attached, the mode external force assigned to each roll at a certain ratio can be applied at a frequency that matches the vibration mode to be generated. This is equivalent to the external force for the modal mass expressed by one oscillator described above.

Assuming that the amplitude of plate pressure fluctuation can be ignored compared to the amplitude of the chattering vibration that has grown, the multistage rolling mill attached with an electromagnetic force generator under chattering vibration is equivalent to the trajectory control device D shown in FIG. is there.

For the generated chattering vibration, the position and velocity of the mode mass are measured every predetermined operation time Δt, and the external force function F _III (formula 4) is determined so that the position and velocity of the mode mass approach zero. By performing sampling control in which an external force is applied to the work roll at intervals of the operation time Δt according to t ₀ + t ′), it is possible to suppress chattering vibration grown as shown in FIG. Fig. 55 shows the state of chattering vibration in which the amplitude of the mode mass is gradually reduced by the external force F _III (t ₀ + t ').

Fig. 56 shows a schematic view of an electromagnetic force generator that applies an external force to each roll in order to suppress chattering vibration in a tandem multi-stage rolling mill. Since chattering vibration is generated in the vertical direction of the roll, by applying electromagnetic force to the bearing 111 connected to the shaft 110 of each roll via the bearing by the coil 112 around the plunger 113 having a high magnetic permeability, Generate an external force according to the external force function F _III (t ₀ + t ') in (Equation 4). As a result, chattering can be dynamically avoided, and rolling can be performed at a higher speed beyond the vibration mode of the multistage rolling mill.

Also in the application of this rolling machine, for example, a sensor 11da for measuring the speed and position of a rolling roll, and a sensor 11db for measuring the displacement of a drive unit are attached, and these values for each operation time are calculated.

Next, in order to describe an embodiment in which vibration control is performed by the trajectory control device D as shown in FIG. 10, an example in which the derived external force function F _III (t ₀ + t ′) is applied to a removal processing device will be described. .

There are many types of removal processing devices, such as lathes, milling machines, NC machines, and grinding machines. These are machining methods in which a part of a workpiece is scraped by contacting each other while rotating the tool or workpiece.

In these removal processes, if the processing speed is increased or the rigidity of the work or shank is insufficient, chatter vibration is generated between the tool and the work due to large self-excitation, and a trace of periodic unevenness is generated on the work. It is known.

Chatter vibration not only reduces machining accuracy, but also reduces efficiency, such as not being able to increase the machining speed in order to suppress vibrations. Therefore, the development of technology to suppress chatter vibration has been desired.

For example, when cutting the side of a round bar, if the round bar is supported only by a chuck and the round bar itself has low rigidity, the round bar itself vibrates as a cantilever. The specific vibration mode in this cantilever can be treated as a single oscillator with a specific mode mass and a specific mode stiffness. When the stiffness of the shank itself is low, the following discussion is a technique for the vibration of the shank as a cantilever.

Now, assuming that the radius d of the side surface of the round bar which is the work material is shifted due to deviation from a true circle, the work in contact with the shank is forced to be displaced by h (t).

Now, assuming that the bending stiffness of the work is small and a specific vibration mode occurs due to its own displacement, the forcible displacement amount h (t) of the work becomes a forced displacement of the root relative to its own vibration mode, The chatter vibration generated in the workpiece is equivalent to the trajectory control device A shown in FIG.

Therefore, chatter vibration is expected to occur when h (t), which is a deviation from the perfect circle of the workpiece, becomes a forced displacement function that has the function of growing a specific vibration mode of the workpiece itself. Therefore, the occurrence of chatter vibration can be examined from the function of h (t), which is the deviation of the workpiece from the perfect circle, as a forced displacement function, but it will not be described in detail here.

On the other hand, as shown in FIG. 57, when the plunger 113, which is an electromagnetic force generator for applying an external force to the work 119, and the chuck 116 with the coil 112 as a fulcrum are separately attached, the mode external force is canceled to cancel the generated vibration mode. Can be given. This is equivalent to the external force for the modal mass expressed by one oscillator described above. Determine the external force function F _III (t ₀ + t ') of (Equation 4) so as to suppress the vibration of the workpiece from the information on the position and velocity of the workpiece captured by the sensor 11 db, and apply the electromagnetic force to the workpiece accordingly Therefore, a removal processing apparatus (FIG. 57) that can prevent chatter vibration can be obtained. Assuming that the amplitude of the workpiece radius variation is negligible compared to the amplitude of the chatter vibration that has grown, the removal processing device attached with the electromagnetic force generator under chatter vibration is equivalent to the trajectory control device D shown in FIG. Is.

With respect to frequent vibration, the position and velocity of the mode mass in the work are measured every predetermined operation time Δt, and it is determined that the position and velocity of the mode mass approach 0 (Equation 4) external force function F Chatter vibration can be suppressed by performing sampling control in which an external force is applied to the work at each operation time Δt in accordance with _III (t ₀ + t ′). The mode mass chatter vibration amplitude is gradually reduced by the external force as in Fig. 55. As a result, chatter vibration due to self-excitation can be dynamically avoided, and cutting can be performed at higher speed beyond the vibration mode of the workpiece.

Also in the application of these cutting machines, for example, a sensor for measuring the speed and position of the workpiece and the driving force of the driving unit is attached, and these values are calculated for each operation time Δt.

Next, the external force function F _III (t ₀ + t ′) of (Equation 4) derived is applied to a wind turbine to describe an embodiment in which vibration control is performed by the trajectory control device D as shown in FIG. Here is an example.

A windmill that rotates in response to wind is subject not only to fluctuations in the wind but also to fluctuations in external force due to rotation even under constant wind speed. This is because the wind weakens every time the blades of the wind turbine pass through the column, and in the case of an N-blade wind turbine with a rotational speed f, the force of the cycle of t _b = N f is subject to fluctuations in the external force.

Wind turbine struts are getting higher as the blades get larger, so the natural period of the struts is getting lower. The rotation speed of the normal wind turbine blades is controlled not to match the natural frequency of the support, but in the case of a large-sized wind turbine, when the wind becomes strong, the blades are rotated beyond a certain natural mode Therefore, it is inevitable to operate at resonance. For this reason, there are problems such as large vibrations of the struts.

In recent years, accidents such as breakage of a wind turbine support after 10 years have occurred, and fatigue destruction of the support due to shaking has become a problem. In order to suppress fatigue failure, it is necessary to suppress the amplitude due to vibration of the struts so that the generated stress is below the fatigue limit.

The column 120 of the wind turbine, which receives fluctuations in external force due to the rotation of the blades, uses a column fixed to the ground as a cantilever beam, and handles the self-oscillating mode as an integral vibrator, thereby the trajectory control device D of the present invention. Is modeled as By setting the rotation period of the blades / the number of blades as the operation time Δt, the position and velocity of the mode mass of the wind turbine are measured at each operation time, and the rotation phase of the blades is controlled to reduce this amplitude. By changing, self-excited vibration can be reduced dynamically. Fig. 58 shows a schematic view of the windmill modeled in this way.

The fluctuation component (ΔF) of the external force due to the rotation of the blades of the wind turbine is the external force that generates a specific vibration mode in the column of the wind turbine. Since this is equivalent to the external force on the mode mass represented by one vibrator, the vibration of the support of the wind turbine due to the wind is equivalent to the trajectory control device D shown in FIG. The generation of the vibration of the strut can be understood from the fact that the fluctuation component of the external force due to the rotation of the blades of the windmill works to increase the vibration as the external force function F _III (t ₀ + t '), but it will not be described in detail here .

Since the rotation of the blades of the wind turbine has a period of 1 / Nf, the fluctuation of the external force resulting from this is equivalent to the trajectory operation by the operation time of Δt = 1 / Nf. Therefore, the position and velocity of the mode mass in the vibration of the column are measured by the sensor 11 db at every operation time Δt = 1 / Nf with respect to the column vibration generated, and the position and the velocity of the mode mass are determined to approach zero. By controlling the position of the blade during the operation time Δt according to the external force function F _III (t ₀ + t ′) of (Expression 4), it is possible to suppress the vibration of the support.

For example, from the external force function F _III (t ₀ + t ′) in (Equation 4), when the speed of the swing of the support is maximum in the leeward direction at the position of the support, the blade phase θ is π / 2. Controlling the speed of the blades to reduce the swing of the struts. On the other hand, when the speed of the sway of the support is maximum in the upwind direction at the position of the support, the speed of the wing is controlled so that the phase θ of the wing becomes 3π / 2, as shown in FIG. In addition, the swing of the support can be reduced. Even when the natural period of the support is different from the operation time Δt, control is possible by using the external force function F _III (t ₀ + t ′) of (Expression 4).

Generally, when the vibration of the column becomes large, the wind is strong and the wind turbine must be operated with reduced efficiency. Therefore, although the control of changing the phase of the blade to suppress the vibration results in slightly reducing the power generation efficiency, it can be said to be more desirable because it prevents fatigue failure and prolongs the life of the wind turbine.

In these wind power generation applications, for example, a sensor that measures the speed and position of the nacelle and the amount of wind power that is a driving unit is attached, and these values are calculated for each operation time.

On the other hand, if the wind turbine is an offshore wind power generator floating on the ocean, the floating body is greatly shaken by the wind and waves, and if the inclination of the offshore wind power generator reaches a critical value, it will overturn. When a storm approaches, technology that suppresses shaking is necessary. Because the offshore wind power generator slowly rotates around the center of gravity due to the couple generated by the deviation between the center of gravity and the center of floating when the floating body is inclined, the natural period of the vibration to be controlled is Will also be slow. Therefore, the phase shift of the rotation of the blade, which is a short cycle, does not affect the swing around the center of gravity of the floating body.

In addition, the wind turbine changes the thrust force due to the wind because the direction of the blade pitch is controlled so that the amount of torque caused by the wind is constant at wind speeds above the rating. Since the wind power near the hub changes periodically due to the pitch rotation of the entire floating body, the operation of changing the blade pitch of each blade of the wind turbine corresponding to this changes the thrust force of the wind at a pitch period. It has the most influence on the shaking of the.

Generally, the operation of the blade pitch of each blade is performed to keep the rotational speed of the wind turbine constant, but when the pitching vibration of the floating body becomes large, the control to make the rotational speed constant is stopped and this method is used. Measures such as giving top priority to preventing floating bodies of offshore wind turbines are required.

The center of gravity of the floating body fluctuates in six degrees of freedom consisting of vertical movement and rotation under the influence of waves etc. However, each rotation and vibration in a certain direction can be handled independently if the influence is small. In addition, when the change of wind is slower than the swing cycle of the floating body and the wind per cycle can be regarded as constant, the thrust force of the wind applied to the wind turbine is changed by rotating the blade pitch of the blades at the swing cycle. Therefore, the rotational vibration in the pitching direction can be mainly suppressed.

Now, if the rotation angle and angular velocity of the floating body around the pitching for each predetermined operation time can be measured, F _III (t ₀ ) of the moment function (Equation 4) is used to suppress the swing around the pitching of the floating body. + t ') can be determined. Furthermore, if the flow rate of the wind is measured and the rotation of the blade pitch is controlled so that the moment due to the wind force applied to the windmill becomes the function F _III (t ₀ + t '), the floating body can be prevented from shaking around the pitching of the floating body. The sample value can be controlled by the period of fluctuation of.

In addition, if the rotation angle and angular velocity of the floating body around the rolling for each period can be measured, the moment function F _III (t ₀ + t ') can be determined so as to suppress the swing around the floating body. By controlling the rotation of the blade pitch of each blade so that the moment due to the difference in the force of the wind applied to the left and right of the wind turbine becomes a function F _III (t ₀ + t '), the suppression of the swing around the rolling of the floating body is suppressed. The sample value can be controlled by the period of shaking.

In this device, no matter how small the wind force is, it works in the direction of suppressing the shaking caused by the rotation of the offshore wind power generator. However, it is necessary to design the size of the wind turbine to obtain sufficient wind strength to match the size of the wave shake so that the time taken for damping is too long and it does not overturn.

Moreover, although the force of the wind that is optimal for damping deviates from the external force function F _III (t ₀ + t ') due to the force of the waves that strike the offshore structure, the per-rotational energy of a huge offshore wind power generator Because the wave force of is small, ignoring it as an error does not affect the control.

On the other hand, this device operates the blade pitch of the blade to exert a greater force when the swing moves in the opposite direction to the wind, so the rotational energy becomes the kinetic energy of the blade, and finally It is absorbed as energy of a wind power generator.

On the other hand, the swaying of offshore wind turbines is caused not only by wind but also by ocean waves. Among these, this device that suppresses the shaking due to the rotation by the force of the wind converts the wave power once to the rotational energy of the offshore wind power generator, and this becomes the kinetic energy of the blades, and finally it becomes the energy of the wind power generator and absorbs It can be understood that it works as a kind of wave power generation.

In particular, the waves in the offshore excite the gravity center of the offshore wind power generator up and down in the heave direction, so if the wave period is twice the rotational period of the floating body, the wave vibration and the rotational vibration of the floating body Works as an autoparametric resonance, and the fluctuation of the rotation of the floating body is increased by the waves. In particular, the rotation period around the pitching of the offshore wind turbine that is easy to control by the present technology is designed to be half the average period of the waves, and with this method, the fluctuation around the pitching of the offshore wind turbine is sufficiently suppressed. If it is possible, it becomes a more efficient wave power generator (FIG. 76).

Also in the application of this offshore wind power generator, it is necessary to attach, for example, 11 da which is a sensor which measures the amount of horizontal movement of the floating body itself, and 11 db which is a sensor which measures the swing and rotational angle and their angular velocity in each rotational direction. . In addition, a sensor 136 for measuring the change in wind power as the driving force is attached, and these values are calculated by sampling higher than a predetermined operation time.

An angle and an angular velocity of the pitching rotation of the floating body 141 are obtained every predetermined operation time Δt, and F _III (t ₀ + t ′) in (Expression 4) is determined so that the pitching rotation is settled. The 140 blade pitch rotating device is controlled so that the thrust force applied to the wind turbine by the wind force becomes this function. Thereby, the pitching shake of an offshore wind power generator can be suppressed. Since the period of pitching rotation is about 30s in a 2 MW class offshore wind turbine, the rotation of the blade pitch is sufficiently operable.

Next, an external force function F _IV (formula 5) derived to explain an embodiment in which vibration control is performed by a trajectory control device E as shown in FIG. 12 and a trajectory control device D as shown in FIG. An example of applying t ₀ + t ') and F _III (t ₀ + t') in (Equation 4) to an electromagnetically driven valve of an engine is described.

The valve mechanism of the engine is a system that controls the injection of fuel and the emission of exhaust gas, and greatly affects the combustion efficiency of the engine. However, since the conventional valve mechanism is driven by receiving the force of the piston with the timing belt, the opening / closing speed must depend on the engine speed, and the valve is opened / closed at an appropriate timing, speed, and opening / closing amount. Could not. As a result, the engine could not be operated most efficiently at each rotational speed.

In order to overcome these problems, in recent years, the cam mechanism for moving the valve has been devised to change the valve opening / closing timing and the opening / closing amount. It was not possible to control the valve in which all conditions were optimized (“The next generation engine Part 2 Variable engine technology of the engine,” Nikkei Automotive Technology, Nikkei Inc., (2006) No. 4, pp. 130-135) .).

In addition, the valve mechanism of the conventional engine has a valve jump due to the natural vibration of the mechanism at high speed rotation, so it is necessary to set the valve spring higher. However, this conversely causes a large dynamic friction in the cam at low speed operation, which reduces fuel consumption. As described above, in the conventional valve mechanism, the increase in friction loss and the increase in engine speed are in a trade-off relationship, which causes the inability to design a high-speed engine. Variable technology could not be overcome.

Therefore, an electromagnetically driven valve that drives the valve with the electromagnetic force from the circuit, regardless of the engine, has been proposed, and this development has been actively studied. This makes it possible to open and close the valve at the most efficient and free timing. In addition, the friction loss can be reduced because the cam is not required, and the engine may be expected to rotate at high speed.

However, since a large electromagnetic force is required to drive and stop the valve at high speed, an electromagnetically driven valve requires a large amount of electrical energy. When the valve speed is high at the valve open / close position, not only large kinetic energy is lost due to collision but also the valve dances by bounce back, so the valve needs to approach the speed to 0 without limit Therefore, it is necessary to find the function of the driving force by the optimum electromagnetic field.

Various studies have been conducted on the optimal driving force function in an electromagnetic field valve. For example, a feedforward function using a compensator such as Uchida has been proposed. And the residual vibration could not be suppressed (Matsuta Muta, Hideyuki Hasegawa, Yoshifumi Morita, Takao Tadami, "Positioning Control of an Electromagnetic Drive Valve for a Car Engine by Sliding Mode Control: Valve by Feedforward Compensation "Improvement of control performance at the time of opening", Japan AEM Journal, Vol. 18, No. 1 (2010), pp. 48-53.) (Matsuta Uta, Masaya Takemura, Yoshifumi Morita, Hisashi Kamito, Takao Tadami, "Design of movable magnet type linear vibration actuator for electromagnetically driven valve for automobile engine", Journal of AEM Society of Japan, Vol.14, No.4 (2006), pp.394-399.

It is extremely difficult to reduce the speed of the valve, which has been rapidly accelerated by the electromagnetic force, to 0 and close it rapidly, and these studies have not solved these problems, and the electromagnetically driven valve is still Not practical.

On the other hand, according to the present invention, the electromagnetically driven valve can be manufactured by the orbit control device E as shown in FIG. Fig. 60 shows a schematic diagram of the electromagnetic drive valve mechanism designed by this mechanism. A plunger 131, which is a movable iron core made of a soft magnetic material having a high magnetic permeability, which is the second support 1e, is connected to a valve 126, and is fixed by a guide so as to freely move in the valve opening / closing direction. In order to apply an external force in the valve opening and closing direction to the plunger by electromagnetic force, a solenoid 129 is arranged around the plunger. The solenoid is connected to the power supply 132 and the controller 133. As described later, when it is necessary to control the sample value so as to eliminate the valve dance of the electromagnetic drive valve, it is necessary to measure the position and speed of the plunger after a predetermined operation time Δt. Install the sensor and speed sensor 11eb.

In the electromagnetically driven valve shown in FIG. 60, a plurality of plungers 131 and solenoids 129 are arranged in the moving direction of the valve. By devising the amount of current flowing through each solenoid and the timing, the electromagnetic force can be changed and the valve lift can be changed.

In this electromagnetically driven valve device, the valve 126 as the controlled body is the second support body 1e that is free to move. Therefore, by giving the external force function F _IV (t ₀ + t ′) shown in (Equation 5). From the state of being stationary at the closed position, the valve which is stationary at the opened position after Δt and then stationary at the opened position can be stationary at the closed position after Δt.

FIG. 61 shows the time change of the external force function F _IV (t ₀ + t ′) required when the electromagnetically driven valve is opened over Δt = 4 ms and then closed again over 4 ms. The different curves are 10 mm, 5 mm, and 2 mm, respectively, from the larger one. At this time, the trajectory drawn by the valve is shown in FIG.

On the other hand, in the electromagnetically driven valve device shown in FIG. 60, since the electromagnetically driven valve is a free object, fail-safe does not work if it is out of control. Therefore, a device that moves the electromagnetically driven valve by connecting it with a weak spring is also conceivable.

Therefore, the plunger 131 can be limited by connecting the plunger 131 to the frame 128 via the spring 2d. Figure 63 shows a schematic of the electromagnetically driven valve designed in this way. This electromagnetically driven valve becomes a trajectory control device D as shown in FIG. 10, and promotes the opening and closing by applying an external force function F _III (t ₀ + t ′) represented by (Expression 4) to the plunger.

In a device in which the valve is connected using a spring (k '= 0.05) of 5% of the spring constant necessary when the operation time Δt is the natural period of the vibrator whose mass is the valve, the valve is the same as FIG. Fig. 64 shows the external force required when drawing a trajectory. The different curves are the electromagnetic forces required at the same different valve lifts as before.

On the other hand, instead of the plunger in the device of FIG. 60, as shown in FIG. 77, it is connected to the valve 126 by using a permanent magnet 152 made of hard magnetic material with alternating poles, as shown in FIG. A linear motor can be formed by arranging the electromagnetic coils 15e connected to the power source, and an electromagnetically driven valve can be similarly manufactured using this. In the linear motor, since it is necessary to match the polarity of the permanent magnet and the electromagnet coil, the sensor 11eb for detecting the position of the operating permanent magnet is necessary, but by using this, it is necessary for sample value control The position and velocity of the valve after the operation time Δt can be estimated.

When a linear motor is used in the drive system of the electromagnetic drive valve, the electromagnetic force is proportional to the current flow, which has the advantage of facilitating the design of the voltage signal applied to the motor. For example, since the electromagnetic force applied to the valve is determined by the external force function F _IV (t ₀ + t ′) in (Equation 5), if the thrust coefficient (counterelectromotive force coefficient) is κ _t , the current flowing through the electromagnetic coil is It is expressed as (Equation 70).

On the other hand, since the electromagnet of the linear motor can be modeled by a coil and a resistance, when the voltage applied to the coil is E (t ₀ + t ′), (Equation 71) holds.
As a result, the voltage applied to the coil can be designed. Now, 3.85MH the inductance L of the coil, the resistance R 2.0Omu, When the thrust coefficient kappa _t 10.0, voltage for realizing the external force of the valve lift 10mm in FIG. 64 FIG. 78, the current Is represented as shown in FIG. In a high-speed engine, the voltage applied to the electromagnetically driven valve after opening the lift amount of 10 mm over Δt = 4 ms and then closing again over 4 ms is about 250 V, which can be sufficiently realized in electric vehicles and hybrid vehicles. It turns out that it becomes.

Also in the application of these electromagnetically driven valves, by attaching a sensor that detects the position and speed of the valve, it is possible to control the sample value to prevent the valve dance etc. from the deviation of these values, and realize a faster engine. can do.

This vibration control function can obtain not only the trajectory but also the function of the driving force and the voltage and current applied to the motor that gives the driving force, so that the feedforward control of the motor itself becomes possible, and In combination, simple DC motors and linear motors may be able to produce a positionable motor mainly based on feedforward.

This technology is expected to contribute to the industry as a new and inexpensive positioning device because it can achieve the same effect as an expensive technology such as a servo motor by improving an inexpensive DC motor.

Finally, in each trajectory control device, we will describe how to determine the parameters of each forced displacement function and each external force function required to control vibration. The discussion will be made using a non-dimensionalization time t where the natural period is 2π in the case where the oscillator consisting of the second support is a single oscillator. For simplicity, in the following, the inertial system is assumed to be a stationary coordinate system, and the velocity of the inertial system is v ₀ = 0. One of the solid supports in the stationary coordinate system is placed at the origin of the stationary coordinate system, and control is performed every predetermined operation time from time 0, and the position and speed of each support in the Nth operation , N in the subscript.

In the following description, since a plurality of coordinate systems having different origins are handled, the coordinates of the center of gravity of each support in a fixed coordinate system stationary in the inertial system are called “positions”. In each N-th operation, the position of each support when the entire three-body vibration system to be placed is in a balanced state is called the “balance position” of each support, and the balance position of the fixed support in the fixed coordinate system O _{, N} , the balance position of the first support in the fixed coordinate system is O _{X, N} , the balance position of the second support in the fixed coordinate system is O _{x1, N} , and the balance position of the third support in the fixed coordinate system _Are called O _{x2 and N.}

Also, since the speed of each support does not depend on how to set the origin of the coordinate system, the speed of the first support is V _{, N} , the speed of the second support is v _{1, N} , and the speed of the third support is Express the velocity as v _{2, N.} The speed of the fixed support is always zero.

In addition, in order to make it easier to compare with the real problems, the distance between the centers of gravity of each support was determined when the entire three-body vibration system was in balance. This corresponds to the length of the spring when each mass in the mass-spring model is considered as the mass point. Therefore, it is easy to understand here and expresses it as the length of a spring. This time, the length of the spring between the fixed support and the first support is L, the length of the spring between the first support and the second support is L ₁ , the spring between the first support and the third support of the length it was L _2.

Thereby, the relationship of (Formula 72-1)-(Formula 72-3) is established between the positions of the respective supports.

Also place the position of the first support in the fixed coordinate system of the operation of the N-th _{Y, N,} and the position of the second support element y _{1, N,} the position of the third supporting member y _{2, N.} The position of the fixed support in the fixed coordinate system in each Nth operation is equal to OO _{, N.}

The position of each support in the N-th operation is also expressed by a coordinate system in which each balance position is set as the origin, and “displacement of fixed support”, “displacement of first support”, “second support”. We call it "displacement of the body" and "displacement of the third support". Respectively, the displacement of the first support _{X, N,} a displacement of the second support element x _{1, N,} the displacement of the third supporting member is expressed as x _{2, N.} The displacement of the fixed support is always zero. From the definitions so far, the relationships represented by (Expression 73-1) to (Expression 75-3) hold.

The position of each support when viewed from the fixed coordinate system when the whole is in a balanced state is represented as shown in the upper part of FIG. The positions of the supports of the three-body vibration system out of the balanced state are represented as shown in the lower part of FIG.

The following describes how to determine various parameters and changes in the position and velocity of each support in general trajectory operation continued for each predetermined operation time Δt that can be of various lengths, separately for each trajectory control device. Show. It is assumed that each support is placed in order from the negative support to the positive support, the fixed support, the first support, and the second support, and these supports are to be moved in the positive direction.

Before that, we show the relational expressions that hold in common for each trajectory control device of the present invention.

The displacement and velocity of the second support for each operation time Δt _{N which} can be of various lengths subjected to the present track operation are in any case the relationship of (Expression 74-1) to (Expression 74-4) Satisfy the expression

Since the second support is always present in each track control device this time, the displacement x _{1, N} of the second support at the reference time t = t _N which is the operation start time in the N-th operation is the target value It is defined as

On the other hand, the increase amount (d _{1, N} ) of the displacement of the second support in the Nth operation is expressed by the equation (Equation 75).

The second support is always present in each track control device this time, so the position y _{1, N} of the second support at the reference time t = t _N which is the operation start time in the N-th operation is The relational expression of (Expression 76) is satisfied.

In the discrete dynamical system at each operation time Δt, the interaction between the second support and the third support and the movement of the first support are separated, so that the controlled object has a forced displacement function X (t ₀ + When subjected to vibration control by t ′), the displacement and speed of the first support satisfy the relational expressions (Expression 77-1 and Expression 177-2).

Since the value of the forced displacement function X (t ₀ + t ') is the displacement of the first support, the relational expression (Equation 78) always holds for the displacement of the first support.

On the other hand, the velocity of the second support is always v _{1, N} since the velocity of each support does not depend on the origin of the coordinate system. The velocity of the second support V _{, N} = (-1) ^NV _{, 0} . As mentioned above, the speed of the fixed support is always zero. Since this is the same for all trajectory controllers, we will not discuss speed below.

Next, we discuss the individual trajectory control devices.

In the case of the trajectory control device A, since the first support is real in addition to the second support, the position of the first support at the reference time t = t _N which is the operation start time in the Nth operation is It is expressed by continuous physical quantities Y 1 _{and N 2} . Position Y of the first support member at each reference time in the fixed coordinate _system, showing the time variation of the _N position y _{1, N} of the second support element in FIG. 81. By defining the increase (D 1 _{, N 2} ) of the displacement of the first support in the N-th operation, the relational expression (Expression 79) holds.

In the case of the track control device A, the controlled object is composed of a first support movably supported by the fixed support and a second support oscillatably supported by the first support. Yes. Therefore in addition to the second support member, since the first support is a real, reference time t = position Y of the first support member at t _N, the _N and position y _{1, N} of the second support member, first Is set as the target value.

From the relational expression (Formula 78) regarding the displacement of the first support, the displacement of the first support is expressed by (Expression 80).

The balanced position of the first support in the fixed coordinate system is expressed by (Equation 81).
Thus, forced displacement function X (t ₀ + t ') is balanced position O _X of the first support in the fixed coordinate system represented by the equation _(81), as the origin of the _{N, X (t 0 + t} ') It can be seen that the forced displacement of is applied to the first support.

On the other hand, since the length of the spring between the second support and the first support in the balanced state is L ₁ , the balanced position of the second support is expressed by (Expression 82).
Thus, the second support element of the track function _{x 1 (t 0 + t '} ) as origin balanced position O _{x1, N} of the second support member in a fixed coordinate system represented by the equation (82), x ₁ ( It can be seen that the orbit of t ₀ + t ') is drawn.

On the other hand, since the length of the spring between the first support and the fixed support in the balanced state is L, the balanced position of the fixed support is expressed by (Equation 83).

In the trajectory control apparatus A, although the fixed support is virtual, it is always present at the balanced position of the fixed support expressed by (Equation 83) due to the conditions of the fixed support.

Next, in the case of the track control device C, since the first support vibratably attached to the fixed support and the second support vibratably attached to the first support, the second support Besides, the first support and the fixed support are real.

First, since the position of the fixed support at the reference time t = t _N is always fixed, by taking this as the origin of the fixed coordinate system. O _{, N} = 0.

On the other hand, since the position of the fixed support is the origin, the balance position of the first support is always L. Since the position of the first support at the reference time t = 0 is given, Y 1 _{, 0} is determined. Furthermore, since the balance position of the first support is always L, the balance position of the second support is always L + L ₁ .

Since the displacement of the first support body by the vibration operation function represented by the external force function F ′ _IIp (t ₀ + t ′) satisfies the relational expression (Expression 78), the first support at the reference time t = t _N The relation of (Equation 84) holds for the position of the body.

Since the displacement of the second support body by the vibration operation function represented by the external force function F ′ _IIp (t ₀ + t ′) satisfies the relational expression (Expression 74-1), the second support at the reference time t = t _N The relational expression of (Equation 85) holds for the position of the two supports.

Next, in the case of the track control device E, only the second support is real because it is composed of the movably supported second support. Thus, the position y _{1, N} of the second support member at the reference time t = t _N is initially set as a target value.

On the other hand, the increase amount (d _{1, N} ) of the displacement of the second support in the Nth operation is expressed by the equation (Equation 75).

The second support is always present in each track control device this time, so the position y _{1, N} of the second support at the reference time t = t _N which is the operation start time in the N-th operation is The relational expression of (Expression 76) is satisfied.

Therefore, the balanced position of the second support in the fixed coordinate system is expressed by (Equation 86).

On the other hand, since the length of the spring between the second support and the first support in the equilibrium state is L _1, balanced position of the first support is represented by (Equation 87).

In the trajectory control device E, the first support is virtual, so the position (Y 1 _{, N} ) of the first support in the Nth operation is arbitrarily determined.

On the other hand, the increase amount (D 1 _{, N 2} ) of the displacement of the first support from the position and the balance position of the first support in the Nth operation is expressed by (Equation 88).

However, since the relational expression of (Equation 80) always holds for the displacement of the first support, the first support that has moved a certain distance after the operation time has a. It can be seen that the position changes discontinuously.

On the other hand, since the length of the spring between the first support and the fixed support in the balanced state is L, the balanced position of the fixed support is expressed by (Equation 89).

In the trajectory control device E, although the fixed support is virtual, it is always present at the balanced position of the fixed support expressed by (Equation 89) due to the conditions of the fixed support.

Next, in the case of the track control device D, the second support supported by the fixed support D vibratably, the second support alone is present. Thus, the position y _{1, N} of the second support member at the reference time t = t _N is initially set as a target value.

On the other hand, the increase amount (d _{1, N} ) of the displacement of the second support in the Nth operation is expressed by the equation (Equation 75).

Since the second support always exists in each orbit control device this time, the position y _{1, N} of the second support at the reference time t = t _N that is the operation start time in the N-th operation is The relation of (Eq. 76) is satisfied.

Therefore, the balanced position of the second support in the fixed coordinate system is expressed by (Equation 86).

On the other hand, since the length of the spring between the second support and the first support in the equilibrium state is L _1, balanced position of the first support is represented by (Equation 87).

In the trajectory control device D, since the balance position of the first support is fixed, when the origin is taken at the balance position of the first support, O _{x, N} = 0, and (Equation 90) holds.

The balance position of the first support is the origin, and since the relationship of (Equation 80) holds for the displacement of the first support, (Equation 91) holds for the position of the first support.

In the trajectory control device D, since the first support is virtual, the amount of increase (D 1 _{, N 2} ) of the displacement of the first support is arbitrarily determined in each operation, so that it is not possible at each reference time. It becomes continuous.

On the other hand, since the length of the spring between the first support and the fixed support in the balanced state is L, the balanced position of the fixed support is expressed by (Equation 92).
Since the fixed support is fixed at the balanced position, the position of the fixed support is also
It exists in the balance position of the fixed support body represented by (Formula 89).

[Invention 13]
The present invention provides a trajectory control device according to any one of inventions 3 to 5 for controlling a trajectory of a magnetic head in a hard disk,
The first support is an arm having an arm rotation axis provided in the hard disk,
The second support is the magnetic head supported by the arm via a cantilever.
The target function is a target function of forced displacement of the rotation angle of the arm rotation axis to be given to the arm,
The control means performs the feedforward control of the magnetic head by giving a forced displacement of the rotation angle to the arm during the operation time from the reference time based on the target function.
It may be a track control device.

[Invention 14]
The present invention is the trajectory control device according to the sixth or seventh invention for controlling a trajectory of a light source for semiconductor exposure provided in a semiconductor exposure apparatus mounted on a vibration isolation table,
The fixed support is a foundation on which the vibration isolation table is placed,
The first support is the vibration isolation table mounted on a foundation via a spring,
The second support is the semiconductor exposure light source supported by the vibration isolation table via a cantilever consisting of the entire frame of the semiconductor exposure apparatus,
The target function is a target function of a horizontal external force applied to the vibration isolation table,
The control means gives the horizontal acceleration to a wafer stage placed on the vibration isolation table inside the semiconductor exposure apparatus, and thus the horizontal direction given by the product of the acceleration and the mass of the wafer stage. The external exposure force is applied to the vibration isolation table, and the semiconductor exposure is performed by applying the horizontal external force to the vibration isolation table from the reference time until the operation time elapses based on the target function. Perform the feedforward control in the horizontal direction of the
It may be a track control device.

[Invention 15]
The present invention is a track control device according to any one of inventions 3 to 5 for controlling a track of a high voltage transmission line attached to an elevated steel tower,
The first support is a ladder that connects the elevated steel tower and the high voltage transmission line,
The second support is the high-voltage power transmission line supported by the insulator,
The target function is a target function of acceleration of a forced displacement in a horizontal direction perpendicular to the high-voltage power transmission line applied to the insulator,
The control means performs the feedforward control of the high-voltage power transmission line by applying forced displacement in the horizontal direction to the forceps during the operation time from the reference time based on the target function.
It may be a track control device.

[Invention 16]
The present invention is the track control device according to the invention 6 or the invention 7 for controlling the track of the high-voltage power transmission line attached to the elevated tower,
The fixed support is the elevated steel tower,
The first support is an insulator that suspends the high-voltage power transmission line attached to the elevated tower.
The second support is the high-voltage power transmission line supported by the insulator,
The target function is a target function of external force in the horizontal direction perpendicular to the high voltage transmission line given to the high voltage transmission line,
The control means performs the feedforward control of the high-voltage power transmission line by applying the external force in the horizontal direction to the high-voltage power transmission line from the reference time to the elapse of the operation time based on the target function. ,
It may be a track control device.

[Invention 18]
The present invention is the wind power generator according to the invention 17, which converts vibration energy caused by wind force of the conductive wire attached to the elevated tower to electric energy,
The fixed support is the elevated steel tower,
The first support is a ladder that suspends the conductive wire attached to the elevated tower;
The second support and the conductor are the conductive wire supported by the insulator,
The magnetic field generating means is an electromagnet that applies a magnetic field in a vertical direction to the conductive wire,
The magnetic field control device is a variable power supply device attached to the electromagnet,
The reference information acquisition means is a measuring device capable of measuring the position and velocity of the conductive wire and the forceps,
The power transmission means is a transformer attached to an end of the conductive wire,
By suspending the conductive wire between the plurality of elevated steel towers,
It is good also as a wind power generator which utilizes the wind force concerning the said conductive wire for electric power generation via the vibration of a high voltage | pressure transmission line.

[Invention 19-2]
The present invention relates to the trajectory control device according to any one of inventions 3 to 5 that suppresses vibration of an arm tip portion in a robot arm, wherein the arm tip portion and the robot arm as the second support body. The cantilever made of the above-mentioned controlled body, the base of the robot arm as the first support, the target function is a target function of forced displacement in the rotational direction applied to the base, and the base of the robot arm is The drive mechanism to be moved may be the track operation actuator.

[Invention 20]
The present invention is the trajectory control device according to any one of inventions 3 to 5 for controlling vibrations in a collision machine, comprising a mold that is the second support and a spring connected to the mold. The vibrating body is the controlled body, the mold drive unit that is moved via a spring is the first support body, the target function is a target function of a forced displacement in the vertical direction applied to the mold drive unit, and the mold A trajectory control device for a mold in a collision machine, wherein the trajectory operation actuator is a drive mechanism that moves the mold drive unit.

[Invention 21]
The present invention is the track control device according to any one of inventions 3 to 5 for preventing chattering in a DC relay, comprising a moving electrode as the second support and a spring connected to the moving electrode. A movable cam that moves the cam follower, wherein the vibration body is the controlled body, the cam follower connected to the base of the spring is the first support, the target function is a target function of forced displacement in the displacement direction applied to the cam follower The track operating actuator may be used as the chattering preventing device in the DC relay.

[Invention 22]
The present invention is the trajectory control device according to any one of inventions 3 to 5 having a fail-safe function of a drive device in an automatic door, wherein the door is the second support and a spring connected to the door. The driven body connected to the root of the spring as the first support, and the target function as the target function of forced displacement in the horizontal direction given to the driven body; It is good also as a fail safe mechanism of the drive device in the automatic door characterized by using the trajectory operation actuator as a motor for moving the body.

[Invention 23]
The present invention is the track control device according to any one of the inventions 3 to 5 for suppressing the sloshing of the liquid in the container, wherein the liquid is the controlled object, and the container is the first support. A sloshing suppression device for liquid in a container, wherein the target function is a target function of acceleration due to a forced displacement in a horizontal direction applied to the container, and a moving mechanism for moving the container is the trajectory operation actuator It may be

[Invention 24]
The present invention is a track control device according to any one of inventions 3 to 5 for suppressing vibration of a building built on a base isolation support, wherein the building is a second support. The cantilever beam is the controlled body, the seismic isolation bearing body on which the building is placed is the first support, and the target function is a target function of a horizontal forced displacement given to the seismic isolation bearing body. Further, an actuator for moving the vicinity of the seismic isolation bearing body of the building may be the trajectory operation actuator.

[Invention 25]
The present invention relates to a trajectory control device according to any one of inventions 3 to 5 for vibrating or damping a display object which is the mass of a vibrator, wherein the display device is a vibrator which is a second support. Is the controlled body, the connecting device at the base of the vibrator is the first support, the target function is a target function of acceleration due to a forced displacement in the horizontal direction applied to the connecting device, and an actuator that moves the connecting device The trajectory operation actuator may be used as a display device using a vibrator.

[Invention 29]
The present invention is the track control device according to the invention 8 or 9, wherein, in the valve mechanism of the engine, the surging of the valve spring subjected to forced displacement via the tappet by the cam attached to the engine wall is suppressed. (2) The vibration of the center of gravity of the valve spring itself, which is the two supports, is the controlled body, the engine wall is the fixed support B, and the target function is the target function of the external force in the vibration direction applied to the center of gravity of the valve spring itself. The device for applying an external force to the center of gravity of the valve spring is the orbital operation actuator, and by applying an external force to the center of gravity of the valve spring by the orbital operation actuator, vibration of the center of gravity of the valve spring is suppressed, and the valve spring It may be a valve jump prevention device in the valve mechanism of an engine characterized by preventing valve jump caused by vibration of the center of gravity of the engine.

[Invention 30]
The present invention relates to the trajectory control device according to invention 8 or D9, wherein in the brushed DC motor, the surging of the brush holding spring that is forcedly displaced via the electric brush by the commutator attached to the outer wall of the motor is suppressed. The vibration of the center of gravity of the brush presser spring itself as the second support is the controlled body, the outer wall of the motor is the fixed support B, and the target function is a vibration direction applied to the center of gravity of the presser spring itself. A device that applies an external force to the center of gravity of the brush presser spring as a target function of the external force is the trajectory operation actuator, and by applying an external force to the center of gravity of the brush presser spring by the trajectory operation actuator, D with brush that suppresses vibration and prevents brush jumping caused by vibration of the center of gravity of the brush presser spring It is good also as a brush jump prevention device in C motor.

[Invention 31]
The present invention is described in Invention 8 or Invention 9, which suppresses surging of a restoring spring that receives a forced displacement through a sliding material by a trolley wire in a pantograph attached to a vehicle body wall used in an electric railway overhead train line system. The trajectory control apparatus, wherein the vibration of the center of gravity of the restoration spring itself which is the second support body is the controlled object, the body wall is the fixed support D, and the target function is the restoration spring itself A device that applies an external force to the center of gravity of the restoring spring as the target function of the external force in the vibration direction applied to the center of gravity is the trajectory operation actuator, and the external force is applied to the center of gravity of the restoring spring by the orbital operation actuator, Vibration of the center of gravity of the spring, and separation of the sliding material generated by the vibration of the center of gravity of the restoring spring is prevented. It is also possible to use as a line separation prevention device for

[Invention 32]
The present invention provides the trajectory control device according to any one of inventions 29 to 31 that suppresses surging of a spring, magnetizes the vicinity of the center of gravity of the spring including a ferromagnetic material, and controls the center of gravity of the spring. By installing a coil around the periphery, vibration energy of the spring may be converted into electrical energy by an induced electromotive force generated by surging of the spring, and an energy harvesting apparatus may be used in surging of the spring.

[Invention 33]
The present invention provides the trajectory control device according to any one of inventions 29 to 31 that suppresses surging of a spring, magnetizes the vicinity of the center of gravity of the spring including a ferromagnetic material, and controls the center of gravity of the spring. By installing a coil around, the degree of residual magnetization in the vicinity of the center of gravity of the spring is estimated by an induced electromotive force generated by surging of the spring, and the fatigue degree of the spring is inspected. It is good also as a fatigue degree inspection device of the spring.

[Invention 34]
The present invention is a spring for suppressing surging according to the invention 30 or invention 31, wherein the natural period of the oscillation of the surging of said spring is shorter than the shortest time of passing through one commutator piece or one hanger interval in use. It is also possible to design a spring characterized by shortening.

[Invention 35]
The present invention is the orbit control device according to the invention 8 or the invention 9 for preventing chattering of the multi-stage rolling roll attached to the frame in the multi-stage rolling apparatus so as to freely vibrate, wherein the multi-stage rolling roll as the second support is provided. A vibration body having a mode rigidity composed of a spring connecting the mode mass and the multi-stage rolling roll is the controlled body, the work roll in the multi-stage rolling roll is the second support, and the frame is the fixed support D. The target function is a target function of the external force in the vibration direction applied to the work roll, the device that applies the external force to the shaft of the multi-stage rolling roll is the track operation actuator, and the mode of the multi-stage rolling roll is determined by the track operation actuator. Multistage pressure characterized by suppressing vibration of the multistage rolling roll by applying mode external force to the mass It is good also as a chattering prevention device in an extension device.

[Invention 36]
The present invention is the track control device according to the eighth or ninth aspect of the present invention for preventing chatter vibration of a work (shank) attached to a chuck in a processing and removal apparatus, wherein the work is a second support (shank) A vibrating body having a mode mass and mode rigidity of the work (shank) is the controlled body, a chuck of the processing and removal apparatus is the fixed support D, and the target function is an external force in the vibration direction applied to the work. A device that applies an external force to the work (shank) as a target function is the trajectory operation actuator, and the mode operation force is applied to the mode mass of the work (shank) by the trajectory operation actuator, thereby vibrating the work (shank). It is good also as a chatter vibration prevention apparatus in the said process removal apparatus characterized by suppressing.

[Invention 37]
The present invention relates to the trajectory control device according to the invention 8 or the invention 9, which prevents the vibration of the column in the wind turbine attached to the base, and the mode mass of the column that is the second support and the mode rigidity of the column. The vibration body comprising the controlled body, the base of the windmill as the fixed support D, the target function of the external force in the vibration direction applied to the mode mass, and the wind turbine blades connected to the support By using an external force as the trajectory operation actuator and controlling the phase of rotation of the blades of the windmill, a mode external force due to the external force of the wind is applied to the mode mass of the prop to suppress vibration of the prop. The vibration prevention device in the wind turbine may be used.

[Invention 38]
The present invention provides the trajectory control device according to the invention 8 or the invention 9 that prevents the swing around the floating body in the offshore wind power generator, and the rotation around the center of gravity of the floating body in the offshore wind power generator as the second support. Is the controlled body, the center of gravity of the floating body is the solid support A, and the target function is a target function of an external force around the center of gravity applied to the floating body, and is a part of the offshore wind turbine generator The external force of the wind received by the blades of the windmill is used as the trajectory operation actuator, and by controlling the blade pitch of the blades of the offshore wind power generator, a rotational moment due to the external force of the wind is applied to the floating body, thereby In the above-described offshore wind turbine generator, the vibration suppressor may be used to suppress the shaking caused by the rotation of the above.

[Invention 39]
The present invention is a power generation device using the vibration suppressing device according to the invention 38 for preventing a swing around a floating body in an offshore wind power generation device, wherein the natural frequency around the pitching of the floating body in the offshore wind power generation device The vibration energy in the heave direction of the floating body generated by the vertical movement of the waves on the ocean is changed to vibration energy around the pitching of the floating body by parametric resonance by reducing the average frequency of the waves to half, and the blades of the offshore wind power generator By controlling the blade pitch of the floating body, a rotational moment due to the external force of the wind is given to the floating body, and the rotational energy around the pitching of the floating body is converted into the kinetic energy of the blades of the offshore wind power generator, which is used for power generation It is good also as a wave power generator using the said vibration suppression apparatus characterized by being able to carry out.

[Invention 40]
The present invention provides the trajectory control device according to the tenth or eleventh aspect of the present invention, wherein the trajectory of the valve in the engine is controlled by electromagnetic drive, wherein the valve that is the second support is the controlled body, and the engine valve An electromagnetic actuator that applies an external force may be the track operation actuator, and an external force may be applied to the valve by the track operation actuator to control an orbit of the valve.

[Invention 41]
The present invention
The control means
In the case where a real vibrator included in the controlled object is different from a virtual vibrator corresponding to the real vibrator of the three-body vibration system of which the controlled body is a part, the virtual vibrator Forced displacement of generalized coordinates or generalized external force applied to at least a part of the controlled body during the operation time so that the motion of the real oscillator coincides with the motion of the virtual oscillator during the natural period Based on the modified target function by adding a correction to the target function of
The feedforward control is performed by applying a forced displacement of the generalized coordinates or the generalized external force to at least a part of the controlled object during the operation time elapses from the reference time.
The trajectory control device according to any one of Inventions 3 to 9 and D12 to 39 may be used.

[Invention 42]
In the present invention, the control means comprises the second support-based generalized coordinates and the second support-based generalized velocity, the first support-based generalized coordinates, and the first support-based generalized velocity. From the reference time, which is determined based on the free movement of the three-body vibration system during the operation time determined from the second support target generalized coordinates and the second support target generalized velocity. The first support reaching generalized coordinates and the first support reaching generalized speed, which are the generalized coordinates and generalized speed of the first support after the operation time, can be derived,
The difference between the second support target generalized coordinates and the first support reaching generalized coordinates is reduced to zero from the difference between the second support based generalized coordinates and the first support based generalized coordinates The second support target generalized coordinates and the second support target generalized coordinates and so as to reduce vibrational energy by bringing the second support target generalized velocity and the first support attainment generalized velocity closer to the same speed. Determining the second support target generalized speed, and performing the feedforward control based on the determined second support target generalized coordinates and the determined second support target generalized speed, To suppress the vibrational energy of two supports,
The trajectory control device according to any one of Inventions 3 to 9, D 12 to 39, and 41 may be used.

[Invention 43]
The present invention is the trajectory control device according to any one of inventions 1 to 42,
Acceleration information acquisition means for acquiring acceleration information from which the fixed support in the three-body vibration system including the controlled body as a part of a dynamic system can derive an acceleration of a reference object that is a reference of the inertial system. Prepared,
When the target function is the generalized external force, the control means performs the trajectory manipulation function according to the trajectory manipulation function corrected so as to cancel an apparent force due to an acceleration generated on the reference object derived based on the acceleration information. The feedback control is performed by applying a generalized external force, and when the target function is a forced displacement of the generalized coordinates, correction is made so as to cancel the deviation of the trajectory of the second support caused by the apparent force. A trajectory control device that performs the feedback control by giving a forced displacement amount of the generalized coordinates according to the trajectory operation function.

  It should be noted that the present invention is not limited to the above-described embodiment, and it goes without saying that the present invention can be implemented in various modes as long as it belongs to the technical scope of the present invention.

In the figure, reference numeral 1 denotes a second support (mass of the small oscillator 1), 2 denotes a spring of the second support (spring of the small oscillator 1), and 3 denotes a first support (mass of the large oscillator). , 4 is the spring of the first support (the spring of the large oscillator), 5 is the third support (the mass of the small oscillator 2), 6 is the spring of the third support (spring of the small oscillator 2) ), 7 is a fixed support, 8 is a uniaxial actuator, 9 is a motor, 10 is a controller, 11 is a speed / position sensor, 12 is a cam, 13 is a cam follower, 14 is an insulator, 15 is a coil, 16 is a bipolar power supply, 17 is a rod, 18 is a robot hand, 19 is an arm, 20 is a cantilever, 21 is a magnetic head, 22 is servo information, 23 is recording information Disc, 24 is a position / speed information calculator, 25 is an Reference numeral 26 denotes a semiconductor exposure apparatus, 27 denotes a light source, 28 denotes a lens, 29 denotes a reticle, 30 denotes a wafer stage, 31 denotes an image sensor, 32 denotes a vibration isolation table, 33 denotes a controller, and 34 is a moving mechanism (club trolley), 35 is a rail, 36 is a wire, 37 is a transported object, 38 is a high-rise building, 39 is a controller, 40 is a seismic isolation bearing, 40 is a rod, Reference numeral 42 is a hydraulic actuator, 43 is a base, 44 is a liquid level sensor, 45 is a crude oil tank, 46 is a steel tower, 47 is a support, 48 is a ladder, 49 is a transmission line, 50 is a rope, Reference numeral 51 denotes a motor, reference numeral 52 denotes an insulator, reference numeral 53 denotes a spring, reference numeral 54 denotes a rope, reference numeral 55 denotes a pulley, reference numeral 56 denotes a control device and a power source, reference numeral 57 denotes an insulator, reference numeral 58 Reference numeral 59 is a mounting base, reference numeral 60 is a coil, reference numeral 61 is a mounting base, reference numeral 62 is a power source, reference numeral 63 is a controller, reference numeral 64 is a compression spring, reference numeral 65 is a case, reference numeral 66 is 1 Shaft rail, reference numeral 67 is a cam follower, reference numeral 68 is a cam, reference numeral 69 is a shaft, reference numeral 70 is a motor, reference numeral 71 is a movable electrode plate, reference numeral 72 is a terminal electrode, reference numeral 73 is a door, reference numeral 74 is a wall, reference numeral 75 is attached Reference numeral 76 denotes a drive unit (trolley), 77 denotes a rail, 78 denotes a workpiece, 79 denotes a hammer or a mold, 80 denotes a support, 81 denotes a frame, 82 denotes a rod, 83 denotes a rod, and 83 denotes a rod. Reference numeral 84 indicates a case, reference numeral 86 indicates a signboard, reference numeral 87 indicates a string, reference numeral 88 indicates a mounting bracket, reference numeral 89 indicates an elastic plate, reference numeral 90 indicates a piezoelectric element, reference numeral 90 indicates a support, and reference numeral 91 indicates a support. Is a power supply, 93 is a controller and communication device, 94 is a fixed part (attachment magnet), 95 is a solar cell (battery box), 96 is an elastic beam, 97 is a fixed part, 98 is a container, 99 is the mass (virtual) of a pendulum equivalent to the mass of the liquid in the container, 100 is a wire of an equivalent pendulum length (virtual), 101 is a liquid, 102 is a carriage, 103 is a level gauge, 104 Reference numeral 105 indicates a single axis rail, reference numeral 106 indicates a backup roll, reference numeral 107 indicates an intermediate roll, reference numeral 108 indicates a work roll, reference numeral 109 indicates a material to be rolled, reference numeral 110 indicates a shaft, reference numeral 111 indicates a bearing, and reference numeral 112 indicates a coil. Reference numeral 113 is a plunger, reference numeral 114 is a power source, reference numeral 115 is a removal processing apparatus, reference numeral 116 is a chuck, reference numeral 117 is a shank, reference numeral 118 is a tool, reference numeral 119 Workpiece, reference numeral 120 is a support, reference numeral 121 is a nacelle, reference numeral 122 is a windmill blade, reference numeral 123 is wind, reference numeral 124 is a shaft, reference numeral 125 is an engine wall, reference numeral 126 is a valve, reference numeral 127 is a spring, reference numeral 128 is a frame, The numeral 129 is a solenoid, the numeral 130 is an iron core, the numeral 131 is a plunger, the numeral 132 is a power supply, the numeral 133 is a controller, the numeral 134 is a spring, the numeral 135 is a conductor, the numeral 136 is a current sensor, the numeral 137 is a magnet and Position and velocity sensor, numeral 138 is external force, numeral 139 is external force, numeral 140 is a blade pitch rotating device, numeral 141 is a floating body, numeral 142 is an ocean, numeral 143 is an acceleration sensor, and numeral 144 is a car body (sprung body Mass), 145 is the unsprung mass, 146 is the preview sensor, and 147 is the suspension. Reference numeral 148 is a road surface, reference numeral 149 is a wheel, reference numeral 150 is a wheel at a reference time, reference numeral 151 is a lower seat, reference numeral 152 is a permanent magnet, reference numeral 153 is a positioner, reference numeral 154 is an actuator with an encoder, and reference numeral 155 is a reduction gear. Reference numeral 156 is a rotating spring of the reduction gear, reference numeral 157 is a robot arm, reference numeral 158 is an encoder of the robot arm, reference numeral 159 is a pendulum type wave force receiving member, reference numeral 160 is a sea wave, and reference numeral 161 is a fixed tower. Note that the suffixes of the letters suffixed below the numbers have the same name in the case of the same number.

  INDUSTRIAL APPLICABILITY The present invention is applicable to the field of control devices that control the trajectory of a controlled object and control or suppress vibration.

1 Second support (mass of small oscillator 1)
2 Spring of second support (spring of small oscillator 1)
3 First support (mass of large vibrator)
4 Spring of first support (large oscillator spring)
5 Third support (mass of small oscillator 2)
6 Three support springs (spring of small oscillator 2)
7 Fixed support 8 Single axis actuator 9 Motor 10 Controller 11 Speed / position sensor 12 Cam 13 Cam follower 14 Insulator 15 Coil 16 Bipolar power supply

Claims (5)

A trajectory control device for controlling a trajectory of at least the second support in a controlled object including at least a first support and a second support vibratably supported by the first support,
The second support reference generalized coordinates and the second support reference generalized speed, which are generalized coordinates and a generalized speed at a predetermined reference time of at least the second support among the controlled bodies, and the first support Reference information acquisition means for acquiring reference information capable of deriving a first support reference generalized coordinate and a first support reference generalized speed which are generalized coordinates and a generalized speed at a predetermined reference time of the body;
The natural period is the same when the controlled body is supported by a fixed support in an inertial system so as to be able to vibrate, and is supported in parallel by the first support so as to be able to vibrate and is a single vibrator. Two unique features of a two-body coupled vibration system comprising the second support and the third support, and comprising the center of gravity of the second support and the third support and the first support When the product of the absolute value of the difference in angular frequency and a predetermined operation time is regarded as a dynamic system that is a part of a three-body vibration system set to be a natural number multiple of 2π, said second support member reference generalized coordinates and the second support member reference generalized velocity is derived based, the first support reference generalized coordinates and the first support element is derived based on the reference information A reference generalization speed, and the second support at a time after the operation time from the reference time Determined based on the free motion of the three-body vibration system within the operation time determined from the second support target generalized coordinate and the second support target generalized speed, which are generalized coordinates and the generalized speed , based on the forced displacement of the objective function of the generalized coordinates given to said first support member in said operating time,
Between from the reference time to elapse the operating time, the first support to provide a forced displacement of the generalized coordinates, the second support generalized coordinates and generalized velocity feedforward control to control means When,
Equipped with
When the generalized coordinates of the first support when the entire three-body vibration system is in the balanced state are set as the origin of the generalized coordinates of the first support, and the entire three-body vibration system is in the balanced state The generalized coordinate of the second support is the origin of the generalized coordinate of the second support, and the generalized coordinate of the first support is forced to the generalized coordinate represented by the following (formula 1) Trajectory control device which controls to become displacement function X (t ₀ + t ').
However, Δt is the operation time,
Among the two natural angular frequencies of the two-body coupled vibration system, the large natural angular frequency is ω ₊ = (2p + 1) π / Δt, the small natural angular frequency is ω ₋ = π / Δt, and p is a natural number Do.
Further, the second support reference generalized coordinate is x _in , the second support reference generalized speed is v _in , the first support reference generalized coordinate is X _in , and the first support reference generalized speed is Is V _in , the second support target generalized coordinate is x _en , and the second support target generalized speed is v _en .
Further, (Equation 1) is a non-dimensionalization function with the characteristic period of the single oscillator consisting of the second support as 2π and a representative time, and the generalized mass of the second support as a representative mass, It holds in the range of t '= 0 to Δt. Α _p is any real number that satisfies (Equation 2).
The controlled body includes the first support body that is movably supported by a fixed support body A, and the second support body that is supported by the first support body so as to vibrate freely.
The fixed support A is a support fixed at an arbitrary stationary position as viewed from the fixed support, and the reference information acquisition means includes the second support reference generalized coordinates, the second support reference generalized Obtaining the reference information capable of deriving a speed, the first support reference generalized coordinates, and the first support reference generalized speed;
The target function is the second support reference generalized coordinates derived from the reference information when the controlled body is regarded as a dynamic system that is a part of the three-body vibration system, the second Support reference generalized speed, the first support reference generalized coordinates, and the first support reference generalized speed, the second support target generalized coordinates and the second support target generalized speed, A target function of the forced displacement of the generalized coordinates expressed by (Equation 1) given to the first support during the operation time, which is determined based on the free motion of the three-body vibration system determined from before SL control means, on the basis of the objective function, while from the reference time to elapse the operating time, by giving forced displacement of the generalized coordinates in the first support, performing the feedforward control,
The trajectory control device according to claim 1 . A trajectory control device that controls at least a trajectory of the second support in a controlled body including at least a first support and a second support that is supported by the first support in a freely vibrating manner,
The second support reference generalized coordinates and the second support reference generalized speed, which are generalized coordinates and a generalized speed at a predetermined reference time of at least the second support among the controlled bodies, and the first support Reference information acquisition means for acquiring reference information capable of deriving a first support reference generalized coordinate and a first support reference generalized speed which are generalized coordinates and a generalized speed at a predetermined reference time of the body;
The natural period is the same when the controlled body is supported by a fixed support in an inertial system so as to be able to vibrate, and is supported in parallel by the first support so as to be able to vibrate and is a single vibrator. Two unique features of a two-body coupled vibration system comprising the second support and the third support, and comprising the center of gravity of the second support and the third support and the first support When the product of the absolute value of the difference in angular frequency and a predetermined operation time is regarded as a dynamic system that is a part of a three-body vibration system set to be a natural number multiple of 2π, The second support reference generalized coordinates and the second support reference generalized speed derived based on the first support reference generalized coordinates and the first support derived based on the reference information A reference generalization speed, and the second support at a time after the operation time from the reference time Determined based on the free motion of the three-body vibration system within the operation time determined from the second support target generalized coordinate and the second support target generalized speed, which are generalized coordinates and the generalized speed , Based on a generalized external force target function of generalized coordinates applied to the first support within the operation time,
Control means for feedforward controlling the generalized coordinates and generalized speed of the second support by applying a generalized external force of generalized coordinates to the first support from the reference time to the operation time elapse When,
With
The target function is that the generalized coordinates of the first support when the entire three-body vibration system is in a balanced state is the origin of the generalized coordinates of the first support, and the entire three-body vibration system is balanced. The generalized external force function F _IIp (t ₀ + t) expressed by the following (Equation 3), where the generalized coordinates of the second support in the state are the origin of the generalized coordinates of the second support Trajectory control device to control to become ' ) .
However, Δt is the operation time,
Among the two natural angular frequencies of the two-body coupled vibration system, the large natural angular frequency is ω ₊ = (2p + 1) π / Δt, the small natural angular frequency is ω ₋ = π / Δt, and p is a natural number Do.
Further, the second support reference generalized coordinate is x _in , the second support reference generalized speed is v _in , the first support reference generalized coordinate is X _in , and the first support reference generalized speed is Is V _in , the second support target generalized coordinate is x _en , and the second support target generalized speed is v _en .
Further, (Equation 3) is a dimensionless function in which the natural period is 2π and the generalized mass of the second support is a representative mass, and holds in the range of t ′ = 0 to Δt.
In addition, γ is any positive real number. The reference information acquisition means repeatedly acquires the reference information for each of the operation times of various lengths that are sequentially determined, with the new reference time after the operation time has elapsed from the reference time,
The control means is configured such that the generalized coordinates and the generalized speed of the second support after the operation time has elapsed from the reference time are the second support target generalized coordinates and the second support target generalized speed. approaches manner, performs the feed-forward control, as a new reference time to after the operation time from the reference time, the trajectory control device according to claim 1 or 3 repeated the feedforward control. The track control device according to claim 3, wherein
A magnetic field control unit capable of controlling a magnetic field of the magnetic field generation means, a magnetic field generation means attached to the periphery of the first support body, the first support integrated with a conductor; The reference information acquisition means capable of acquiring the position and speed of the vibration direction of the two support bodies and the first support body, and a power transmission means for transmitting electricity from the conductor to the outside,
The second support is devised so that vibrations are excited by external forces,
The conductor is arranged so that it can be energized in a direction perpendicular to the vibration direction of the first support,
The magnetic field generating means is arranged to be able to apply a magnetic field perpendicular to both the vibration direction and the energization direction,
Lorentz force acting on the current flowing in the conductor, which vibrates integrally with the first support,
A generalized external force function F _IIp (defined) to reduce the position and velocity of the vibrating second support based on the position and velocity of the second support and the first support in the direction of vibration. t ₀ + t '),
By controlling the magnetic field of the magnetic field generating means to be equal,
Suppressing vibration of the second support, and
The electric conductor can generate a voltage by a speed electromotive force to increase a transmission voltage.
A trajectory control device that converts vibration energy of the second support into electrical energy flowing through the conductor.