JP6453750B2 - Orbit control device - Google Patents

Description

The present invention controls the vibration operation actuator based on the detected mass position and speed of the controlled object so that the controlled object position and speed at a certain period become a target value. The present invention relates to a trajectory control apparatus and a trajectory control method for performing feedforward control of the trajectory of the body and using this to further control the sample value.

The present invention controls the vibration operation actuator based on the detected mass position and speed of the controlled vibrating body so that the position and speed of the controlled vibrating body at a predetermined period become the target values. The present invention relates to a vibration control apparatus and a vibration control method for feedforward control or sample value control of the trajectory of a controlled vibration body.

Since the controlled body often has a vibrator inside, it is also called a controlled oscillator. The trajectory control device and trajectory control method of the controlled body are also called the vibration control device and the vibration control method because they operate the vibration when the controlled body 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 it 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, it is an inverse problem to give an external force or forced displacement that is a non-conservative force that determines the mass position and velocity of each vibrator constituting an integral or multi-body vibrator to an arbitrary target value after an arbitrary time. In general, it cannot be determined unless specific conditions and closed systems are defined (Non-patent Document 1).

In addition, there are an infinite number of oscillator trajectories that set the mass position and velocity of each oscillator constituting an integral or multibody oscillator to an arbitrary value at the start and end points of a fixed time. How to determine the route is related to what is used as the variation, and how to determine the variation has not yet been determined (Non-patent Document 2).

Recently, in order to suppress the residual vibration of the vibrator, an optimal trajectory based on a kinematic model composed of kinematic information such as minimizing the square integral of the jerk of the vibrator mass has been proposed. (Non-Patent Document 3), however, it was not always possible to suppress residual vibration.

In addition to this, a standard such as the minimum error variance model of the end point has been proposed as a method for determining the optimal trajectory of the vibrating body, but the principle of determining the trajectory was not clear.

In the principle of determining the trajectory, 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. Had a lack of grounds to satisfy many,

For this reason, in conventional vibration control, the controlled vibrator is regarded as a black box without any particular model, and the mass position and velocity of the vibrator are measured at each moment. Feedback control for determining external force and forced displacement has been performed (Patent Document 1, Patent Document 2, Patent Document 3, Patent Document 4, Patent Document 5).

In addition, when the measurement signal is fed back, various measures such as spectral separation and filtering have been made on the measurement signal so as to cancel out the natural period of the controlled vibrator (Patent Document 6, Patent Document 7).

Many of these feedback controls have a control method centered on analog feedback for continuous signals (Patent Document 8, Patent Document 9, and Patent Document 10), or samples that digitally feed back discrete signals Although value control has been proposed (Patent Documents 11 and 12), the sampling period is set to half the natural period of the controlled vibrator, 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, 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. Has been proposed and various attempts have been made (Non-Patent Document 4).

On the other hand, energy transfer between different oscillators can be formulated and analyzed by defining the system and discussing the mode vibration under natural vibration.

A typical system that controls a model is a 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 for the damper (Patent Document 13), the energy transfer between the vibrators constituting the system and the position and speed of the vibrator are controlled. No method has been sought.

In addition, the motion of a multi-body vibration system over two-body vibration system is generally complicated because chaos and the like occur due to the three-body problem even in a linear vibration system. I could not do it until now.

On the other hand, research on quantum algorithms that run on quantum computers is progressing with recent advances in quantum information theory. The quantum algorithm expresses the entire wave as a state vector, and expresses the operation as an operator that is a matrix that represents the operation. Quantum algorithms can be applied to classical wave phenomena where entanglement between particles and focusing of wave packets due to observations do not hold, so even in phenomena such as vibration, state vectors are expressed discretely by matrix operators. Thus, a series of operations of the vibration system can be expressed as a wave algorithm.

For example, A. Patel reports that, in a specially designed three-body collision vibration system in which two transducers are connected in parallel to one transducer, the energy transfer between the two transducers inside is equivalent to the Grover algorithm. (Non-patent document 6).

Takada et al. Analyzed the conditions under which the Grover algorithm holds for the three-body collision vibration system in detail and formulated the operator. The Grover algorithm between two oscillators It is reported that it is a periodic vibration (Non-patent Document 7).

Takada et al. Also reported that the Graze bifurcation in a collision oscillator is a transition between different collision modes (Non-patent Document 8). Furthermore, Kotake et al. Reported that the energy transfer between two oscillators can be controlled arbitrarily by changing the order of collision calculations (Non-patent Document 9).

Therefore, Yagi et al. Derived an external force function and a forced displacement function that enable steady collision in 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). ). Yagi et al. Proved that the steady-state vibration of the three-body collision vibration system is a stable vibration that draws a limit cycle (Non-Patent Document 11).

Furthermore, Yagi et al. Studied the application to a collision processing machine using an external force function and a forced displacement function that enable steady collision in the two-body collision oscillator and the one-piece collision oscillator (Non-patent Document 12). , Non-Patent Document 13).

Kotake is also studying the chattering mechanism in rolling mills using an external force function and a forced displacement function that enable steady collisions in this two-body collision vibrator and one-piece collision vibrator (non-patent literature). 14).

In addition, the following are mentioned as related prior art (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 Laid-Open No. 7-337055 JP-A-6-137371 JP-A-5-340443 JP-A-5-240295 JP-A-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), pp815-825. 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 Japan Society of Mechanical Engineers, Volume C, 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, “Non-harmonious external force that enables constant and variable impact machining” The 20th Mechanical Materials and Materials Processing Technology Lecture Meeting (M & P2012). Kazunori Yagi, Shigeo Kotake, “Intermittent forced displacement function enabling variable steady semi-open loop press working” Proceedings of the 25th JSAP Spring Meeting. 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”, Transactions of the Japan Society of Mechanical Engineers, C, 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 . Ono Kyoo, “Optimum high-speed trajectory control of vibration mechanism system (1st report, analysis of one-degree-of-freedom vibration system model)”, Transactions of the Japan Society of Mechanical Engineers, 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.

In the conventional vibration control technology, the vibrator control method using feedback needs to calculate the deviation from the target value using a high-speed sensor. The actuator was also necessary. 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, a conventional model using a dynamic vibration absorber is generally a two-body vibration system, and the motion of the mass of one oscillator is affected by two different natural vibrations, and it is necessary to consider the entire vibration. there were. In the conventional model, it is difficult to arbitrarily manipulate the motion of the vibrator under external force, and it is difficult to analytically guide the manipulation that gives any position and velocity to the mass of the vibrator.

Furthermore, in the conventional vibration damping method, the residual vibration remaining in the system after control cannot 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).

In addition, the conventional sampling value damping method is mainly digitized by discretizing analog control, and the optimum sampling period has not been determined even though the control is affected by the difference in sampling period. (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 optimal trajectory was found, the choice was not exempted. (Non-patent document 20).

The problem with these controls is that there is no target feedforward function, and an optimal trajectory cannot be obtained using an ambiguous evaluation function (Non-patent Document 18).

The control method using the input shaping function enables open-loop feedforward control. However, the input parameters require information such as the frequency, amplitude, and attenuation rate of the vibrator, and the input function depends on conditions. There is no strict formulation. In addition, the control tends to diverge due to the deviation of the 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 frequency of the system. (Non-patent Document 4).

Until now, various methods for determining the optimal trajectory of a vibrating body have been proposed in feedforward control, but no method that satisfies the dynamic variational principle has been proposed (Non-Patent Document 1, Non-Patent Document 1). Reference 2). Therefore, the external force and the forced displacement that can arbitrarily determine the position and speed of the vibrating body after a certain period have not been formulated.

Here, the external force is a force applied to at least a part of the system from the outside of the system. When the position is expressed in generalized coordinates as described later, it becomes a generalized external force. The forced displacement is the amount of forced position change that the system receives from the outside. Similarly, when the position is expressed in generalized coordinates, it is the amount of change in generalized coordinates.

On the other hand, the external force function and forced displacement function that enable steady collisions in the two-body collision oscillator and the one-piece collision oscillator shown by Yagi et al. Often deviated, and this function could not correct it. Further, since special vibration conditions such as steady collision are required, it is difficult to find a general application destination other than steady collision machining (Non-Patent Document 10, Non-Patent Document 11, Non-Patent Document 12). , Non-Patent Document 13).

  The present invention has been made to solve the above-described problems. The generalized coordinates and the generalized speed of the second support, which is the control target of the controlled bodies, are simply set from the second support. The main purpose is to accurately change the target generalized coordinates and generalized speed after the natural period of the vibrator.

[Invention D1]
The trajectory control device of the present invention is
A trajectory control device for controlling a trajectory of at least the second support in a controlled body provided with at least a second support,
A reference that can derive a second support reference generalized coordinate and a 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. Reference information acquisition means for acquiring information;
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 the natural period 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, based on the reference information Generalization at the reference time of the first support derived or virtually determined based on the reference information, the second support reference generalized coordinates and the second support reference generalized speed derived First support reference generalized coordinates and first support, which are coordinates and generalized speed A reference generalized speed, a second support target generalized coordinate and a second support target generalized speed, which are a generalized coordinate and a generalized speed of the second support at a time after the natural period from the reference time; Is determined based on the free motion of the three-body vibration system during the natural period determined from the above, based on the forced displacement of generalized coordinates given to the controlled body during the natural period or the target function of the generalized external force ,
From the reference time to the elapse of the natural period, the generalized coordinate and the generalized velocity of the second support are obtained by applying a generalized coordinate forced displacement or generalized external force to at least a part of the controlled body. Control means for feedforward control;
Is provided.

  This trajectory control device is applied to at least a part of the controlled object from the reference time to the elapse of the natural period based on the forced displacement of the generalized coordinates given to the controlled object during the natural period or the target function of generalized external force By applying a forced displacement of the generalized coordinates or a generalized external force, the generalized coordinates and the generalized speed of the second support are feedforward controlled. This target function is the second derived from the reference information when the controlled body including at least the second support is regarded as a dynamic system that is a part of the three-body vibration system set as described above. The first support reference generalized coordinates and the first support reference generalized speed derived from the reference information or virtually determined from the reference information, the second support reference generalized coordinates, and the second support reference generalized speed, the second support It is determined based on the free motion of the three-body vibration system during the natural period determined from the target generalized coordinates and the second support target generalized speed. By applying generalized coordinates or generalized external force to the controlled body based on this target function, the trajectory of the second support is controlled, and the generalized coordinates and generalized speed of the second support are unique from the reference time. After the cycle, the target generalized coordinates and the target generalized speed can be accurately changed. This reason will be described in detail later.

  Here, the reference information may be information that can derive the second support reference generalized coordinates and the second support reference generalized speed. That is, the reference information may be information indicating the second support reference generalized coordinate or the second support reference generalized speed itself, or the second support reference generalized coordinate or the second support reference generalized speed. May be indirect information that can be derived. The control means may perform the derivation of the second support reference generalized coordinates and the second support reference generalized speed based on the reference information. The control means may also perform the derivation of the first support reference generalized coordinates and the first support reference generalized speed or the setting of virtual values. The control means may set the second support target generalized coordinates and the second support target generalized speed.

Further, the reference information acquisition unit 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 generalized speed of the second support at the reference time”, the time to be acquired may be a time before the reference time, for example. 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. In consideration of the time required for derivation, the reference information acquisition unit may 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 reference generalized coordinates and the second support reference generalized speed is a fixed value, the reference information acquisition unit may read and acquire a prestored fixed value. Good. The reference information acquisition unit 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, or the second support target generalized coordinate. , Software determined in advance to perform output based on the input variable (a value representing the forced displacement of the generalized coordinates or the generalized external force) with the second support target generalized speed and time as variables, It may be configured as hardware.

[Invention D2]
In the trajectory control device of the present invention, the reference information acquisition means repeatedly acquires the reference information for each natural period, with the elapse of the natural period from the reference time as a new reference time, and the control means includes the The feed so that the generalized coordinates and generalized speed of the second support after the elapse of the natural period from a reference time approach the second support target generalized coordinates and the second support target generalized speed. Forward control may be performed, and the feedforward control may be repeatedly performed with a new reference time after the elapse of the natural period from the reference time. If it carries out like this, the track | orbit of a 2nd support body can be controlled over several continuous natural periods by repeating feedforward control between natural periods. Here, the second support target generalized coordinates may be reset for each control during each natural period, or may be the same value over the control during a plurality of natural periods. Alternatively, the second support target generalized coordinates for each control during each natural period may be set so that the second support target generalized coordinates gradually approach the final target value. The same applies to the second support target generalization speed.

[Invention D3]
In the trajectory control device of the present invention, the controlled body includes the first support body that is movable, and the second support body that is supported by the first support body so as to be capable of vibration, The reference information acquisition means includes the second support reference generalized coordinates, the second support reference generalized speed, the first support reference generalized coordinates, and the first support reference generalized speed. The derivable reference information is acquired, and the target function is derived based on the reference information when the controlled body is regarded as a dynamic system that is a part of the three-body vibration system. Support reference generalized coordinates, second support reference generalized speed, first support reference generalized coordinates, first support reference generalized speed, second support target generalized coordinates and The second support target generalization speed, and the freedom of the three-body vibration system determined from A target function of forced displacement of generalized coordinates given to the first support during the natural period determined based on movement, and the control means, based on the target function, passes the natural period from the reference time. In the meantime, the feedforward control may be performed by giving a forced displacement of the generalized coordinates to the first support.

[Invention D4]
In this case, the target function is the three-body vibration with the generalized coordinates of the first support when the whole three-body vibration system is in a balanced state as the origin of the generalized coordinates of the first support. The generalized coordinate of the second support when the entire system is in a balanced state is set as the origin of the generalized coordinate of the second support, and the third vibration system when the entire three-body vibration system is in a balanced state A generalized coordinate forced displacement function X (t ₀ + t ′) represented by the following equation 32a may be used with the generalized coordinate of one support as the origin.


Where ω _t is the natural angular frequency of a single oscillator comprising the second support,
Of the two natural angular frequencies of the two-body coupled vibration system, the large natural angular frequency is ω _{+ −} = (p + 1/2) ω _t , and the small natural angular frequency is ω ₋ = ω _t / 2, p. Is a natural number.
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 (t ₀ ), the first support reference The generalized speed is V (t ₀ ), the second support target generalized coordinate is x _en , and the second support target generalized speed is v _en .
Equation 32a is a dimensionless function in which the natural period of the second support is 2π as a representative time, the generalized mass of the second support is a representative mass, and t ′ = 0 to 2π. It holds in the range. Α _p is an arbitrary real number satisfying Equation 33.

[Invention D5]
In the trajectory control device according to the present invention in which control is performed using (Equation 32a) described above, the control means is such that the first support and the second support are both stationary in a stationary coordinate system. In this case, the generalized coordinates of the second support are moved by d, the first support reference generalized coordinates are set to -d / 2, and the second support target generalized speed is set 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 D6]
In the trajectory control device of the present invention, the controlled body is supported by the fixed support, the first support supported by the fixed support so as to vibrate, and supported by the first support so as to vibrate. 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, Obtaining the reference information from which the first support reference generalized speed can be derived, and when the target function regards the controlled body as a dynamic system that is part of the three-body vibration system, The second support reference generalized coordinates, the second support reference generalized speed, the first support reference generalized coordinates, and the first support reference generalized speed derived based on the reference information; The second support target generalized coordinates and the second support target generalized speed; A target function of a generalized external force applied to the first support during the natural period, which is determined based on the free motion of the three-body vibration system determined from: 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 during the period from the reference time to the elapse of the natural period.

[Invention D7]
In this case, the target function is the three-body vibration with the generalized coordinates of the first support when the whole three-body vibration system is in a balanced state as the origin of the generalized coordinates of the first support. A generalized external force function F _IIp (t ₀₎ represented by the following formula 51, 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. + t ').


Where ω _t is the natural angular frequency of a single oscillator comprising the second support,
Of the two natural angular frequencies of the two-body coupled vibration system, the large natural angular frequency is ω _{+ −} = (p + 1/2) ω _t , and the small natural angular frequency is ω ₋ = ω _t / 2, p. Is a natural number.
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 (t ₀ ), the first support reference The generalized speed is V (t ₀ ), the second support target generalized coordinate is x _en , and the second support target generalized speed is v _en .
Equation 51 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 2π.
Further, γ is an arbitrary real number.

[Invention D8]
In the trajectory control device according to the present invention, the controlled body includes a fixed support A and the second support that is supported by the fixed support A so as to be able to vibrate. The reference information from which the second support reference generalized coordinates and the second support reference generalized speed can be derived is obtained, and the target function is the first support defined as the second support and the virtual When the fixed support A is placed on the generalized coordinates of the first support when the entire three-body vibration system is in a balanced state, it is regarded as a dynamic system that is a part of the three-body vibration system. The second support reference generalized coordinates and the second support reference generalized speed derived based on the reference information, the first support reference generalized coordinates and the first support reference generalized speed, The second support target generalized coordinates and the second support eye A target function of a generalized external force applied to the second support during the natural period, which is determined based on a free motion of the three-body vibration system determined from a generalized speed, and the control means includes the reference The feedforward control may be performed by applying the generalized external force to the second support based on the target function from the time until the natural period elapses.

[Invention D9]
In this case, the target function is the three-body vibration with the generalized coordinates of the first support when the entire three-body vibration system is in a balanced state as the origin of the generalized coordinates of the first support. A generalized external force function F _III (t ₀₎ expressed by the following equation 60, 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. + t ').


Where ω _t is the natural angular frequency of a single oscillator comprising the second support,
Of the two natural angular frequencies of the two-body coupled vibration system, the large natural angular frequency is ω _{+ −} = (p + 1/2) ω _t , and the small natural angular frequency is ω ₋ = ω _t / 2, p. Is a natural number.
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 (t ₀ ), the first support reference The generalized speed is V (t ₀ ), the second support target generalized coordinate is x _en , and the second support target generalized speed is v _en .
Equation 60 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 2π. Further, α _p is an arbitrary real number satisfying Expression 33.

[Invention D10]
In the trajectory control device of the present invention, the controlled body is the movable second support body,
The reference information acquisition means acquires the reference information from which the second support reference generalized coordinates and the second support reference generalized speed can be derived, and the target function sets the controlled body to the three bodies The second support reference generalized coordinates and the second support reference generalized speed derived based on the reference information, when considered as a dynamic system that is a part of the vibration system, and the three-body vibration system Determined from 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 virtually determined in FIG. A target function of a generalized external force applied to the second support during the natural period, which is determined based on the free motion of the three-body vibration system, and the control means is based on the target function and the reference Between the time and the elapse of the natural period By providing the generalized external force to the second support member may be subjected to the feedforward control.

[Invention D11]
In this case, the target function is the three-body vibration with the generalized coordinates of the first support when the entire three-body vibration system is in a balanced state as the origin of the generalized coordinates of the first support. The generalized external force function F _IV (t ₀₎ expressed by the following equation 66, 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. + t ').


Where ω _t is the natural angular frequency of a single oscillator comprising the second support,
Of the two natural angular frequencies of the two-body coupled vibration system, the large natural angular frequency is ω _{+ −} = (p + 1/2) ω _t , and the small natural angular frequency is ω ₋ = ω _t / 2, p. Is a natural number.
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 (t ₀ ), the first support reference The generalized speed is V (t ₀ ), the second support target generalized coordinate is x _en , and the second support target generalized speed is v _en .
Equation 66 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 2π. Further, α _p is an arbitrary real number satisfying Expression 33.

  Hereinafter, the controlled body may be referred to as a controlled vibrating body. 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 referred to as 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 a controlled vibration body. The trajectory of the controlled vibrator is determined based on the free motion of the vibration system.

Since the trajectory of the controlled oscillator is determined by the Hamiltonian principle of the dynamical system in the free motion of the three-body vibration system, the principle is clear and mechanically natural.

The three-body vibration system is designed so that Grover's wave algorithm can be established so that energy transfer occurs only between two specific oscillators with the same natural period. By dividing into a child and the remaining one-body oscillator, the three-body problem does not occur and the motion 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, the position and velocity vector of the multi-body vibrator can be freely manipulated (Non-Patent Document 9).

By making the controlled vibrator one of the two specific vibrators, the vibration energy of the controlled vibrator can be freely moved to the other specific vibrator after the natural period. The position and speed of the controlled vibrator can be freely determined for each.

Further, the three-body vibration system includes a controlled vibrator including one of the specific two vibrators, and a controlled vibrator including the other of the two specific vibrators, which is a part other than the controlled vibrator. By dividing into two, the vibration energy can be freely moved between the controlled vibrator and the controlled vibrator after the natural period.

Further, by making the controlled vibration body real and making the control vibration body virtual, the action and reaction of the force at the boundary between the controlled vibration body and the control vibration body can be externally applied to the controlled vibration body. The applied external force and the force applied to the outside from the controlled vibrator. The change in the mass position at the boundary between the controlled vibrator and the controlled vibrator is a forced displacement from the outside of the controlled vibrator.

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

The three-body vibration system according to the present invention includes a first support that is supported by a stationary support in an inertial system so as to be capable of vibration, and a second support that is supported by the first support so as to be capable of vibrating in parallel and has an equal natural period. A vibration system designed to move kinetic energy only between the second support and the third support for each natural period.

Characteristic of this three-body vibration system by considering a controlled vibration body having a second support supported by the first support as a part of a three-body vibration system that freely moves in a conserving force field In the vibration system under various constraints, the position and speed of the second support can be changed arbitrarily after the natural period of the single oscillator consisting of the second support in the vibration system under various constraints. The control function for the external force and forced displacement that can be generated is analytically derived.

As a result, the control function of the external force and forced displacement that controls the controlled vibrator is 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 mechanical condition consisting of.

In the present invention, as will be described later, since discrete mechanical energy transfer is limited to a part of two systems of a three-body vibration system, and a condition for separating speed and position control is used, a sample for applying a control function is provided. The optimal period of value control is determined by the natural period of a single oscillator consisting of two supports.

By limiting the discrete mechanical energy transfer in the present invention to a part of two systems of the three-body vibration system, the three-body vibration system designed to satisfy the Grover algorithm is supported by a fixed support so as to freely vibrate. A three-body vibration system comprising a first support, a second support supported in parallel with the first support and a third support, 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 . At that time, using the natural number p, the two coupled natural frequencies ω ₊ and ω ₋ in the two-body vibration system composed of the center of gravity of the first support and the second and third supports are expressed by Design the three-body vibration system to satisfy 1). In this case, p is a natural number, ω _+> ω _- is established. The period in the discrete mechanics is the natural period Δt of the single oscillator composed of the second support, and ω _t = 2π / Δt.


The three-body vibration system satisfying (Expression 1) may have various cases. As a special case, the three-body vibration system satisfies the following (Expression 2-1 and Expression 2-2). There exists a design of.

When the three-body vibration system satisfies (Equation 2-1 and Equation 2-2), the mass position and velocity can be determined independently in the operation of the mass position and velocity of the vibrator, as will be described later. Is possible. In the following, this special case will be discussed and discussed.

A schematic diagram of the three-body vibration system designed in this way is shown in Fig. 1. The vibrator composed of the first support that is supported at one end by a fixed support is called a large vibrator, and its mass is M and its spring constant is K. Of the two vibrators attached to the first support so as to freely vibrate in parallel, the vibrator made of the second support is a small vibrator 1, the mass of which is m ₁ , and the spring constant thereof is k _1. Let's say. Also an oscillator consisting of said third support is small vibrator 2, the mass m _2, to the spring constant and k _2.

Since the two small vibrators have the same natural angular frequency and are expressed by the following (Equation 3),


You can set m ₂ = γm ₁ and k ₂ = γk ₁ . Where 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. This Delta] t is a natural period of the small vibrator by is dimensionless and _{Δt = 1 / ω t = 2π} .

From the above-described conditional expression of the coupled natural frequency, the mass and spring constant of the dimensionless large vibrator are expressed by the following (Expression 4) and (Expression 5).

The position obtained from the balance position of the large oscillator is X, the position obtained from the balance position of the small oscillator 1 is x ₁ , and the position obtained from the balance position of the small oscillator 2 is x ₂ , The equation of motion of the free vibration in the dimensionless three-body vibrator is expressed as (Formula 6-1, Formula 6-2, Formula 6-3) below.

Since X, x ₁ , x ₂ which are the amounts of the positions of the vibrators appearing here and V, v ₁ , v ₂ which are the amounts of velocity are collectively explained at the end using FIG. Please refer to it. Note that the origins of the coordinates of each position are different because X, x ₁ , and x ₂ , which are the amounts of the positions of each transducer, have origins at different locations such as the balance position of each transducer. I want to be done.

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

Solving this equation gives (Equation 7) below.

Here, (Equation 8) is a state vector of the position of each mass point of the three-body vibrator at time t ₀ ,


(Equation 9) is the velocity state vector of each mass point of the three-body vibrator when time is t ₀ .


Here, V is the speed of the large vibrator, and v ₁ and v ₂ are the speeds of the small vibrator 1 and the small vibrator 2, respectively. Furthermore, by arranging these vectors, the state vector of the position and velocity of each mass point of the three-body transducer when the time shown in (Equation 10) is t ₀ is obtained.

Furthermore, A, B, and C are 3 × 3 matrices, and each component of the matrices A and B is shown below (Formula 11-1 to Formula 11-10) and (Formula 12-1 to Formula 12-10). Is represented by This time, the components of matrix C are omitted because they are not directly related to the explanation.

Furthermore, by setting the time evolution time t ′ as the natural period of the small oscillator shown in the following (Equation 13),


The matrix B (t '= Δt) and the matrix C (t' = Δt) are zero matrices. Since the matrix A (t ′ = Δt) is expressed as the following (Expression 14), (Expression 15) and (Expression 16) are obtained.

As described above, the position state vector and the velocity state vector show independent time development under the conditions of (Expression 2-1 and Expression 2-2) and (Expression 13), and the interaction between the small oscillators Can be separated from the large oscillator. As a result, the coupled vibration of the two small oscillators becomes a two-body problem under discrete mechanics, and simple time evolution appears. On the contrary, if it deviates from this condition, the vibration becomes a three-body problem consisting of the two small oscillators and one large oscillator, and the position and velocity are mixed with each other in a discrete mechanical manner, and complex chaotic vibrations may appear. This condition prevents this.

In addition to the time evolution operator of this time, we define a collision operator that elastically collides one of the small oscillators, and by operating these alternately on the state vector | φ _v (t ₀ )>, the Grover algorithm is established. Almost periodic motion is generated in the system (Non-Patent Document 7), but in the present invention, a collision operator is not necessarily required, so it is not mentioned.

Next, from the previous (Expression 16), the speeds of both small vibrators around Δt time satisfy the following (Expression 17).


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 (18).

Similarly, from the previous (Expression 15), the positions of both small vibrators around Δt time satisfy the following (Expression 19).


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 that satisfies the following (Equation 20).

On the other hand, from (Expression 7), the position of the large vibrator after time t ₀ + t ′ is expressed as (Expression 21) 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 -1 to Expression 11-10), and the coefficients defined in (Expression 12-1 to Expression 12-10) and (Expression 18) and (Expression 20) are substituted, so that the position of the vibrator 1 is x The forced displacement function ((Equation 22)) of the large oscillator that can change the speed of the oscillator 1 from _in to x _en and v _in to v _en is obtained. Since this forced displacement function is a function of ω ₊ = p + 1/2, it becomes a function that jumps differently depending on the parameter p that is a natural number. In the following, the forced displacement function when ω ₊ = p + 1/2 is expressed as X _p (t ₀ + t ').

Next, in the three-body vibration system, the position of the small vibrator 1 after time t ₀ + t ′ is expressed as (Expression 23) below from (Expression 7).

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 -1 to Expression 11-10), and the coefficients defined in (Expression 12-1 to Expression 12-10) and (Expression 18) and (Expression 20) are substituted, so that the position of the vibrator 1 is x The orbit function ((Equation 24)) of the small oscillator 1 is obtained from _in to x _en and the speed of the oscillator 1 from v _in to v _en . Since the orbital function of the small oscillator 1 is also a function of ω ₊ = p + 1/2, it becomes a function that varies depending on the parameter p which is a natural number. Below, the orbital function of the small oscillator 1 when ω ₊ = p + 1/2 is expressed as x _1p (t ₀ + t ').

As shown by the dotted line A in FIG. 1, when the vibrator 1 is taken out from the three-body vibration system to be an integral vibrator, the position of the large vibrator X _p (t ₀ + t ′) is This is equivalent to the forced displacement function at the root of the integrated oscillator. Figure 2 shows an outline of an integrated vibrator that forcibly displaces the root.

The integrated vibrator thus taken out is a vibrating body composed of a first support body movably supported by a fixed support body and a second support body movably supported by the first support body. .

By forcibly displacing the first support with X _p (t ₀ + t ′) between t ′ = ₀ and 2π, the trajectory of the second support becomes x _1p (t ₀ + t ′), 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 subject to forced displacement is expressed by the following (Equation 25).

In this differential equation, by taking the linear sum of each parameter p, a differential equation represented by the following (Equation 26) is obtained, whereby the second support has a trajectory function represented by (Equation 31a). The forced displacement function X (t ₀ + t ') of (Equation 32a) that draws x ₁ (t ₀ + t') is defined.





Where X (t ₀ + t ′) is a dimensionless function in which the natural period of the single oscillator made of the second support is 2π and the mass of the second support is the representative mass, and t ′ = It holds in the range of 0 to 2π. In the natural number p, ω ₊ = p + 1/2 and ω ₋ = 1/2, and α _p is an arbitrary real number satisfying the following (Equation 27).

On the other hand, since the discussion is the same for the coordinates of the inertial system, a differential equation is established as in (Equation 28) below.


Therefore, when the first support is subjected to the forced displacement shown in the following (Equation 29):


The second support body draws a trajectory function x ₁ (t ₀ + t ′) represented by the following (Equation 30).


By applying a forced displacement represented by (Equation 29) to the first support during the natural period Δt of the integral vibrator, the position of the second support is changed from x _in to x _en + 2πv ₀ , and The speed of the second support can be changed from v _in + v ₀ to v _en + v ₀ .

In summary, the forced displacement function X (t ₀ + t ′) given to the first support in order for the second support to draw the orbit function x ₁ (t ₀ + t ′) shown in (Equation 31) is: It is expressed as (Equation 32) below.



(Formula 32)


Where X (t ₀ + t ′) is a dimensionless function in which the natural period of the single oscillator made of the second support is 2π and the mass of the second support is the representative mass, and t ′ = It holds in the range of 0 to 2π. Also, in the natural number p, ω ₊ = p + 1/2 and ω ₋ = 1/2, v ₀ is an arbitrary constant that is the velocity of the inertial system, and α _p is an arbitrary real number that satisfies (Equation 33). is there.

On the other hand, for the integrated oscillator for forced displacement of the root shown in Fig. 2, the coordinate system of the non-inertial system fixed to the root is rewritten. Thereby, the trajectory function y _1p (t ₀ + t ′) drawn by the second support is expressed by the following (formula 34).


As a result, the differential equation shown in (Equation 35) below is obtained, and inertial force is generated. As a result, an equation of motion is obtained when an external force acts on the mass of the integrated vibrator with its root fixed as shown in Fig. 3.

The integrated vibrator taken out in this way is a vibrating body composed of a second support that is supported by a fixed first support so as to vibrate freely, and an external force is applied to the second support.

In this case, the external force function F _I (t ₀ + t ′) applied to the second support is expressed by the following (formula 36).


Here, F _Ip (t ₀ + t ′) is an external force function ((Equation 37)) applied to the second support when ω ₊ = p + 1/2.


Therefore, the external force function F _I (t ₀ + t ′) applied to the second support is expressed by the following (formula 38).


Thereby, the orbital function y ₁ (t ₀ + t ′) drawn by the second support is expressed as shown in (Equation 39) below.

(Formula 39)
Therefore, the trajectory function y ₁ (t ₀ + t ′) drawn by the second support is expressed by (Equation 40) shown below.

Thus, by applying an external force along F _I (t ₀ + t ′) represented by (Equation 38) between t ′ = 0 and 2π to the second support, v _yen trajectory becomes y ₁ represented by formula _{(39) (t 0 + t '} ), the position of the second support from y _in the y _en, and the speed of the second support from v _yin Can be changed to

Here, from (Expression 34), the following relational expressions (Expression 41) to (Expression 44) hold.

In a system with a fixed root, X _p (t ₀ ) and V _p (t ₀ ) are virtual positions and velocities, and X _p (t ₀ ) = -X _p (t ₀ + 2π) and V _p ( Since t ₀ ) = -V _p (t ₀ + 2π) holds, X _p (t ₀ ) = X _p (t ₀ + 2π) = 0 and V _p (t ₀ ) = V _p (t ₀ + 2π) ) = 0, the relational expressions shown in (Equation 45) to (Equation 48) hold, and it can be seen that the amount of increase in position and velocity does not change due to coordinate transformation. Therefore, for the sake of simplicity, the parameter coordinate x is rewritten with the coordinate y and displayed.

In summary, the external force function F _I (t ₀ + t ′) given to the second support in order for the second support to draw the orbital function y ₁ (t ₀ + t ′) shown in (Equation 40) is , (Equation 38).
Where F _I (t ₀ + t ′) is a dimensionless function in which the natural period of the single oscillator composed of the second support is 2π and the mass of the second support is the representative mass, and t ′ It holds in the range of 0 to 2π. Also, ω ₊ = p + 1/2 and ω ₋ = 1/2, and α _p is an arbitrary real number that satisfies (Equation 33). Furthermore, v ₀ is an arbitrary constant that is the velocity of the inertial system, and X (t ₀ ) and V (t ₀ ) are parameters of an arbitrary constant.

Next, in the three-body vibration system, the position of the small vibrator 2 after time t ₀ + t ′ is expressed by (Expression 7) as follows (Expression 49).

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 −1 to Equation 11-10), and the coefficients defined in (Equation 12-1 to Equation 12-10) and (Equation 18) and (Equation 20) are substituted into x _in , The orbital function ((Equation 50)) of the small oscillator 2 that changes from v _in to x _en and v _en is obtained. Since the orbital function of the small oscillator 2 is also a function of ω ₊ = p + 1/2, it becomes a function that varies with the parameter p which is a natural number. Below, the orbital function of the small oscillator 2 when ω ₊ = p + 1/2 is represented as x _2p (t ₀ + t ').

Further, by multiplying the difference between the position of the large oscillator shown in (Expression 22) and the position of the small oscillator 2 shown in (Expression 50) by a spring constant γ, ω ₊ = The external force function F _IIp (t ₀ + t ') _applied to the large oscillator in the case of p + 1/2 is obtained.

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

The equation of motion of the two-body oscillator using F _IIp (t ₀ + t ′) as the excitation force of the large oscillator is expressed as (Formula 52-1 and Formula 52-2) below.

The two-body vibrator taken out in this way is a vibrating body composed of a first support that is supported by a fixed support so as to be able to vibrate, and a second support that is supported by the first support so as to be able to vibrate. Yes, an external force is applied to the first support.

By applying an external force F _IIp (t ₀ + t ′) expressed by (Equation 51) to the first support during t ′ = _{0 to 2π} , the trajectory of the second support is expressed by (Equation 24). X _1p (t ₀ + t ′) as shown, and 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 .

Next, this equation of motion can be transformed as shown in the following (Formula 53-1, Formula 53-2) by newly setting the spring constant of the large oscillator as K ′.

Thus, by newly expressing the external force function as shown in (Equation 54),


It can be seen that the spring constant of the large oscillator can be arbitrarily selected as K '. Conversely, it can be seen that the external force can be changed to an appropriate function by appropriately selecting the spring constant K '.

In the two-body vibrator thus taken out, the spring constant of the first support supported by the fixed support in a freely oscillating manner is set to K ′ by appropriately applying an external force applied to the first support. You can choose arbitrarily.

By applying an external force to the first support along the external force function F ′ _IIp (t ₀ + t ′) expressed by (Equation 54) between t ′ = _{0 and 2π} , the trajectory of the second support _Becomes x _1p (t ₀ + t ′) shown in (Equation 24), the position of the second support from x _in to x _en , and the speed of the second support from v _in to v _en Can be changed.

In summary, the external force function F ′ _IIp (t ₀ + t ′) given to the second support in order for the second support to draw the orbit function x _1p (t ₀ + t ′) shown in (Equation 24) is Is expressed as (Equation 55) below.


Where F ′ _IIp (t ₀ + t ′) is a function of the dimensionless time t with the natural period of the single oscillator made of the second support being 2π, and in the range of t ′ = 0 to 2π. It holds. In p is a natural _{number, ω + = p + 1/} 2, ω - = 1/2, K = (γ + 1) (2p + 1) 2 / {3 (2p + 3) (2p-1)} in Yes, γ and K 'are arbitrary real numbers.

On the other hand, the second term on the right-hand side of (Equation 25), which is the force generated by the forced displacement of the root, with respect to (Equation 25) in the integrated vibrator forcibly displacing the root shown in FIG. By using the external force function F _IIIp (t ₀ + t ′), (Equation 56) holds.

(Equation 56) is an equation of motion that holds for a vibrating body composed of a second support that is supported by the fixed first support shown in FIG. 5 so as to be able to vibrate. F _IIIp (t ₀ + t ′) Since = X _p (t ₀ + t ′), the external force function F _IIIp (t ₀ + t ′) for the second support is expressed as (Equation 57).


Here, since the first support has no substance, X (t ₀ ) and V (t ₀ ) are just parameters.

Even when the first support shown in FIG. 5 is an unfixed movable body, if the acceleration is sufficiently smaller than the external force function F _IIIp (t ₀ + t ′), the external force function F _IIIp (t ₀ + t ') is rarely changed.

Similarly, the second term on the right-hand side of (Equation 26), which is the force generated by the forced displacement of the root, is expressed by By using the external force function F _III (t ₀ + t ′) for the second support shown, (Equation 59) holds.




Here, α _p is an arbitrary real number satisfying (Equation 27).

(Equation 59) is an equation of motion that holds for a vibrating body composed of a second support that is oscillated on a fixed first support shown in FIG. 60) The external force F _III (t ₀ + t ′) represented by 60) is applied.


Here, since the first support has no substance, X (t ₀ ) and V (t ₀ ) are just parameters as well.

By applying the external force F _III (t ₀ + t ′) shown in (Equation 60) to the second support during t ′ = 0 to 2π, the fixed first support is equal in speed v ₀ and so on. When moving fast, the trajectory drawn by the second support is the trajectory function x ₁ (t ₀ + t ′) shown in (Equation 31), and the position of the second support is changed from x _in to x _en , In addition, the speed of the second support can be changed from v _in + v ₀ to v _en + v ₀ .

Next, the equation of motion of (Equation 59) can be modified as shown in the following (Equation 61) by newly setting the spring constant of the second support as k ′.

Thus, it can be seen that the spring constant of the second support can be arbitrarily selected as k ′ by newly expressing the external force function as shown in (Equation 62). Conversely, it can be seen that the external force can be changed to an appropriate function by appropriately selecting the spring constant k '.

In the integrated vibrator thus taken out, by appropriately applying an external force applied to the second support, the spring constant of the second support supported by the fixed support so as to freely vibrate is arbitrarily set to k ′. You can choose

By applying an external force to the second support along the external force function F ′ _III (t ₀ + t ′) represented by (Equation 61) between t ′ = 0 and 2π, the trajectory of the second support _Becomes x _1p (t ₀ + t ′) shown in (Equation 24), the position of the second support from x _in to x _en , and the speed of the second support from v _in to v _en Can be changed.

In summary, the external force function F ′ _III (t ₀ + t ′) given to the second support in order for the second support to draw the trajectory function x ₁ (t ₀ + t ′) shown in Equation 31 is This is expressed as Equation 63.


However, F ′ _III (t ₀ + t ′) is a value in which the natural period of the single oscillator composed of the second support in the case of k ′ = 1 is 2π and the mass of the second support is the representative mass. A dimensionalization function, which holds in the range of t '= 0 to 2π. In the natural number p, ω ₊ = p + 1/2 and ω ₋ = 1/2, and α _p is an arbitrary real number satisfying (Equation 33). v ₀ is an arbitrary constant that is the velocity of the inertial system. Furthermore, k 'is the spring constant of the single oscillator consisting of the second support, and X (t ₀ ) and V (t ₀ ) are parameters of arbitrary constants.

On the other hand, as shown by the dotted line C in FIG. 5, the position and speed of the second support are arbitrarily manipulated by taking out the second support as a free object that is movably supported by the fixed support. An external force function applied to the second support that makes it possible is obtained. An outline of the second support is shown in FIG.

By setting the right side of (Equation 25) to the external force function F _IVp (t ₀ + t ′) = − x _1p (t ₀ + t ′) + X _p (t ₀ + t ′) for the second support, The equation of motion for the second support holds.

Similarly, by setting the right side of (Equation 26) as the external force function F _IV (t ₀ + t ′) for the second support shown in (Equation 64), the equation of motion for the second support is obtained (Equation 65 ) Holds.




Here, α _p is an arbitrary real number satisfying (Equation 27).

Thus, the trajectory drawn by the second support is the trajectory function x ₁ (t ₀ + t ′) shown in (Equation 31).

By applying the external force F _IV (t ₀ + t ′) shown in (Expression 64) to the second support during t ′ = 0 to 2π, the trajectory drawn by the second support is expressed by (Expression 31). Orbital function x ₁ (t ₀ + t ′) shown in FIG. 2), the position of the second support from x _in to x _en and the speed of the second support from v _in + v ₀ to v _en + v can be changed to ₀ .

In summary, the external force function F _IV (t ₀ + t ′) given to the second support in order for the second support to draw the orbital function x ₁ (t ₀ + t ′) shown in (Equation 31) is: It is expressed as (Equation 66) below.


However, F _IV (t ₀ + t ′) is a dimensionless function in which the natural period of the single oscillator composed of the second support is 2π and the mass of the second support is the representative mass, and t ′ It holds in the range of 0 to 2π. In the natural number p, ω ₊ = p + 1/2 and ω ₋ = 1/2, and α _p is an arbitrary real number satisfying (Equation 33). v ₀ is an arbitrary constant that is the velocity of the inertial system, and X (t ₀ ) and V (t ₀ ) are parameters of an arbitrary constant.

The group of functions representing forced displacement and external force that can arbitrarily manipulate the position and speed of the second support after the natural period, as described above, can be collectively referred to as “integrated oscillator operation function” or “vibration operation”. We will call it "function". In some cases, it is also called an “objective function” because it fulfills the purpose of the vibration operation.

Since the three-body vibration system is a Hamilton system in which energy is conserved during the natural period, Hamiltonian and Lagrangian are defined. Therefore, generalized momentum and generalized external force are defined as partial differentials of Hamiltonian and Lagrangian when generalized coordinates are obtained by generalizing the conventional one-dimensional linear coordinate position and displacement. 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 generalized momentum and general acceleration.

Since the three-body vibration system satisfies the Lagrangian equation of motion during the natural period, 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 related to the control of the trajectory defined by the position and velocity discussed so far is that the position is generalized coordinates, the velocity is generalized velocity, the acceleration is generalized acceleration, and the jerk is generalized jerk. The same holds true when the force is a generalized external force and the mass is a generalized mass.

For example, when the generalized coordinate is taken as the angle of rotation, the generalized external force becomes the moment of force, the generalized mass becomes the moment of inertia, and the present invention also holds in the vibration of rotation based on the equation of motion of rotation. Of course, it can be applied to physical quantities defined by other generalized coordinates.

According to the present invention, in the various vibrators described above, the position of the second support is set to Δx = x after Δt by applying a forced displacement or an external force during the natural period Δt of one vibrator made of the second support. _en + 2πv ₀ -x _in , and feedforward control that changes the speed to Δv = v _en -v _in is possible.

As a result, the motion of the oscillator of interest is determined as an open-box model, and the mass trajectory is determined analytically, so highly reliable feedforward control is realized. This is because the base three-body vibration system can manipulate the position and speed between the small oscillators independently and freely in a discrete mechanical manner for each natural period without depending on the state of the large oscillator. This is an advantage not seen in the conventional dynamic vibration absorber model based on the two-body vibration system. Furthermore, because the forced displacement is given by a fixed function, it is possible to use an inexpensive and high-speed control method such as a cam mechanism. Furthermore, since the external force is given by a fixed function, the output of the device that applies the external force can be minimized and energy loss can be reduced.

Further, according to the present invention, in the above-described various vibrating bodies, information on the position x _in and velocity v _in + v ₀ of the second support is obtained for each natural period Δt, and the forced displacement obtained this time during Δt. Alternatively, by applying an external force, it is possible to control the sample value by changing the position of the second support to x _en + 2πv ₀ and the speed of the second support to v _en + v ₀ after Δt.

As a result, even when the position and speed of the second support are different from the intended purpose, it can be corrected during the next natural period. As a result, even when the natural period is deviated, the robustness of the external force function and the forced displacement function can be improved, and the target value can be approached.

Furthermore, this method performs feed-forward control between natural periods, and enables feedback control that compares and corrects the target position and speed and their actual values at the boundary of each period. And both feedback control and high-speed and accurate positioning and trajectory control.

In addition, the sample period is determined by the natural period of the oscillator, eliminating the need for faster sample control 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 it can be controlled to gradually approach the target value at each natural period, it is not necessary to prepare a high-power actuator. In addition, it becomes possible to control the vibrator without residual vibration after the natural period, and the fastest vibration control is possible.

Since the sample period is determined by the natural period of the oscillator, it works effectively in the situation where feedback information can only be obtained in discrete time. For example, in hard disk seek control, the head position can only be obtained by reading the position information written on the disk at regular intervals, but the time interval at which the position information is obtained and the natural period of the arm are the same. By designing the system in this way, seek control with the fastest and less residual vibration becomes possible by using the sample control of the present invention.

Basic three-body vibration system, integrated vibration system (A) and two-body vibration system (B) Controlled vibrator comprising a first support that is movable and a second support that is supported by the first support. A controlled vibration body composed of a fixed first support body and a second support body supported by the first support body so as to vibrate freely, and an arbitrary external force is applied to the second support body A fixed support, a first support that is supported by the fixed support in a freely oscillating manner, and a second support that is supported by the fixed support in a freely oscillating manner, to which an external force is applied to the first support. Control vibrator A controlled vibration body composed of a second support that is supported by a fixed support A so as to vibrate, and to which an arbitrary external force is applied to the second support Controlled vibrator that is composed of a movable second support and that allows any external force to be applied to the second support Measures the position and speed of the first and second supports with a controlled vibrator composed of a first support movably supported by an actuator and a second support movably supported by the actuator. The vibration control device A for controlling the amount of movement of the first support from the result It has a controlled vibrating body composed of a first support that is movably supported by a cam mechanism and a second support that is movably supported by the cam mechanism, and the position and speed of the first and second supports are determined. Vibration control device A for measuring and controlling cam mechanism from the result It has a controlled vibrator composed of a first support that is movably supported by a cam and lever mechanism, and a second support that is supported so as to be able to vibrate. Vibration control device A that measures the speed and controls the cam and lever mechanism from the result It has a controlled vibrating body composed of a fixed first support and a second support supported so as to be able to vibrate. The position and speed of the second support are measured. Vibration control device B or vibration control device D for controlling external force to the support The first and second supports have a controlled vibrating body composed of a fixed support, a first support that is supported by the fixed support in a freely vibrating manner, and a second support that is supported by the fixed support in a freely swingable manner. Vibration control device C that measures the position and velocity of the body and controls the external force on the first support from the result Consists of a second support that is movably supported, and has a controlled vibrator that can apply any external force to the second support. The position and speed of the second support are measured, and the results are used to determine the second support. Vibration control device E for controlling external force on the body Conceptual diagram of vibration control device A consisting of a robot arm attached to a uniaxial movable body that can be arbitrarily moved Conceptual diagram of vibration control device A consisting of a cantilever with a magnetic head attached to an arbitrarily rotatable arm in a hard disk. Conceptual diagram of vibration control device A consisting of the entire semiconductor exposure device including the vibration isolation table Changes in the position of the modal mass of a flexible structure when the residual vibration is removed from the flexible structure that has been subjected to residual vibration by the vibration controller A Changes in the position of the roots when residual vibration removal operation is applied to a flexible structure by vibration control device A Changes in modal mass and root position of flexible structure when moving from stop position to another stop position by vibration controller A Change in modal mass and root position when removing residual vibration of a flexible structure moving at a constant speed by using vibration control device A Changes in the acceleration at the base of a flexible structure that was gradually stopped in several steps Changes in the base position of a flexible structure when a stop operation is performed while moving the modal mass of the flexible structure every natural period Changes in the position of the modal mass of the flexible structure and the cycloid curve used as the trajectory when the stop operation was performed while moving each natural period Conceptual diagram of overhead crane 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 deflection angle and residual oscillation angle in overhead crane In an overhead crane with an initial deflection angle of π / 4, the time change of the angle when removing residual vibration in two stages 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 the vibration control mechanism of a building built on a seismic isolation bearing Conceptual diagram of the damping mechanism for sloshing in large tanks built on seismic isolation bearings Front view of elevated transmission line tower with galloping prevention mechanism Side view of elevated transmission line tower with galloping prevention mechanism Conceptual diagram of the galloping prevention mechanism installed on the column of the elevated transmission line tower Side view of elevated transmission line tower with suspension-type galloping prevention mechanism Enlarged view of galloping prevention mechanism by hanging type Enlarged view of the galloping prevention mechanism that is suspended and works without contact Conceptual diagram of a relay for high current that does not cause chattering Conceptual diagram of an automatic door with fail-safe safety features Conceptual diagram of high-speed press with variable impact position and impact speed Conceptual diagram of a display device with a pendulum Conceptual diagram of a cantilever display device 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 Changes in the position of the follower mechanism moved by a cam that allows movement over a certain distance without causing residual vibration, and the reference cycloid curve 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 Cam curve that allows a certain distance to move by performing a stop operation at each natural period The trajectory of the follower mechanism and the reference cycloid curve with a cam curve that allows a fixed distance of movement by performing a stop operation at each natural period Example of a disc cam that allows a certain distance to move by performing a stop operation for each natural period Relationship between sloshing of liquid in container and virtual pendulum Slot Thing suppression device attached to the transporter of the entering liquid in the container 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 vibration (chattering) of multi-stage rolling mill by external force Chattering suppression device attached to each roll of multi-stage rolling mill Chatter vibration suppression device attached to processing removal device Side view of wind turbine strut vibration suppression device by controlling wind turbine blade phase Front view of vibration suppression device for wind turbine struts by controlling the phase of the blades of the wind turbine Conceptual diagram of an electromagnetically driven valve comprising a vibration control device E Time variation of external force applied to electromagnetically driven valve consisting of vibration 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 an electromagnetically driven valve consisting of vibration control device D Temporal change of external force applied to electromagnetically driven valve consisting of vibration 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 variation of the shaking of a building subjected to a large earthquake with a seismic intensity of 5 classes when the vibration suppression sample value control is performed by the vibration suppression device using the vibration control device A Flow chart of sample value control for each natural period Vibration power generator using vibration control device C Schematic of active suspension of automobile using vibration 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 vibration control device D Pitching vibration suppression device for offshore wind turbine generator using vibration control device D by blade pitch operation Conceptual diagram of an electromagnetically driven valve using a linear motor 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 The position of each support in the fixed coordinate system

The present invention relates to a vibration comprising the second support according to a control signal created by detecting the positions and speeds of the masses of the first support and the second support constituting the controlled vibrator at the operation start time. It is a vibration control device that performs feedforward control or sample value control of the position and speed of the second support by performing the following vibration operation during the natural period of the child.

The vibration control device A includes a first support body that is movably supported by a fixed support body, and a second support body that is movably supported by the first support body. In this case, the vibration operation is a forced displacement applied to the second support, and the control signal is a forced displacement function X () of a dimensionless time t with the natural period of the vibrator made of the second support being 2π. t ₀ + t ′) (Expression 32). Thereby, the trajectory of the second support changes in accordance with the trajectory function x ₁ (t ₀ + t ′) shown in (Equation 31). These functions hold in the range t '= 0 to 2π.

For example, in a specific example of the vibration control device A, as shown in the schematic diagram of FIG. 7, the first support is connected to the fixed support via a one-dimensional actuator, and the second support is a spring. The single vibrator is connected to the first support. Further, the position and speed of the first support and the second support are measured for each natural period by the sensor, and the first support is determined according to the forced displacement function X (t ₀ + t ′) determined from this information. The one-dimensional actuator is moved by the controller.

The first support can be forcibly displaced by a planar cam mechanism composed of a cam and a cam follower according to a forced displacement function X (t ₀ + t ′) (FIG. 8). Alternatively, the first support may be forcibly displaced by a mechanism in which the amount of displacement of the planar cam constituted by the cam and the cam follower is enlarged or reduced by an insulator or the like according to the forced displacement function X (t ₀ + t ′). (Fig. 9).

On the other hand, in the case of the vibration control device B in which the controlled vibrator is composed of a fixed first support and a second support that is supported by the first support so as to freely vibrate, The vibration operation is an external force applied to the second support, and the control signal is an external force function F _I (t ₀ + t ′) of a dimensionless time t with the natural period of the vibrator made of the second support being 2π. (Expression 38). As a result, the trajectory of the second support changes according to the trajectory function y ₁ (t ₀ + t ′) shown in (Equation 40). These functions hold in the range t '= 0 to 2π.

For example, in a specific example of the vibration control device B, as shown in the schematic diagram of FIG. 10, the first support is the fixed support itself, and the second support is attached to the fixed support with a spring. It is a connected single oscillator. The second support 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. Further, the position and speed of the second support are measured by the sensor at each natural period, and current flows from the power source to the coil according to the external force function F _I (t ₀ + t ′) determined from this information. It is controlled by the controller.

On the other hand, the controlled vibration body is composed of a first support body that is supported by a fixed support body so as to freely vibrate, and a second support body that is supported by the first support body so as to vibrate freely. In the case of C, the vibration operation is an external force applied to the first support, and the control signal is an external force function F ′ _IIp of the dimensionless time t with the natural period of the vibrator made of the second support being 2π. It is represented by (Equation 51) which is (t ₀ + t ′). Thereby, the trajectory of the second support changes in accordance with the trajectory function x _1p (t ₀ + t ′) shown in (Equation 24). These functions hold in the range t '= 0 to 2π.

For example, as shown in the schematic diagram of FIG. 11, a specific example of the vibration control device C is such that the first support is connected to the fixed support via a spring, and the second support is a spring. By connecting to the first support, it becomes a two-body vibrator connected in series. The first support is made of soft magnetic material with high magnetic permeability, and external force is applied by the electromagnetic force generated from the surrounding coil. Further, the position and velocity of the first support and the second support are measured at each natural period by the sensor, and an external force is applied according to a function F ′ _IIp (t ₀ + t ′) determined from this information. Current flows from the power source to the coil, and the amount of current is controlled by the controller.

On the other hand, in the case of the vibration control device D in which the controlled vibration body is constituted by the second support body supported by the fixed body A so as to freely vibrate, the vibration operation is performed by an external force applied to the second support body. The control signal is expressed by the 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 (Equation 60). Thereby, the trajectory of the second support changes in accordance with the trajectory function x ₁ (t ₀ + t ′) shown in (Equation 31). These functions hold in the range t '= 0 to 2π.

On the other hand, in the case of the vibration control device D in which the controlled vibrating body is composed of the second support body that is supported by the fixed support body so as to freely vibrate, the spring constant of the elastic body that supports the second support body. When k ′ is k ′, the vibration operation is an external force applied to the second support, and the control signal is a dimensionless with a natural period of 2π when k ′ = 1 in the vibrator composed of the second support. The external force function F ′ _III (t ₀ + t ′) of the conversion time t is expressed by (Equation 63). Thereby, the trajectory of the second support changes in accordance with the trajectory function x ₁ (t ₀ + t ′) shown in (Equation 31). These functions hold in the range t '= 0 to 2π.

For example, a specific example of the vibration control device D is the same as the schematic diagram of FIG. 10, the first support is the fixed support itself, and the second support is connected to the fixed support with a spring. It is a single oscillator. The second support 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. Furthermore, the sensor measures the position and velocity of the second support for each natural period, and current is applied from the power source to the coil so that an external force is applied according to the external force function F _III (t ₀ + t ') determined from this information. The flow and the amount of current are controlled by the controller.

On the other hand, in the case of the vibration control device E in which the controlled vibration body is constituted by a second support body that is movably supported, the track operation is an external force applied to the second support body, and the control signal is The external force function F _IV (t ₀ + t ′) of the dimensionless time t with the natural period of the vibrator made of the second support being 2π is expressed by (Equation 66). Thereby, the trajectory of the second support changes in accordance with the trajectory function x ₁ (t ₀ + t ′) shown in (Equation 31). These functions hold in the range t '= 0 to 2π.

For example, in a specific example of the vibration control device E, the second support is a free object that is movably supported by a fixed support, as shown in the schematic diagram of FIG. The second support 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. Further, the sensor measures the position and velocity of the second support at each natural period, and current flows from the power source to the coil so that an external force is applied according to the function F _IV (t ₀ + t ') determined from this information. The amount of current is controlled by the controller.

The positions and speeds 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 device, 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. A continuous body such as a cantilever can also be used as a single oscillator if its main vibration is limited to one mode.

However, in the case of a pendulum or cantilever, the position is 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 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, and the forced displacement of the root that is the first support is It is necessary to use the amount of change in the acceleration at the base as the normalized coordinates.

If the angle of the pendulum or cantilever can be directly controlled, the amount of forced displacement at the base of the first support is the amount of change in angle.

In the control method of the present invention, even in a complex structure, when the structure is modeled as a multi-body vibrator, and a specific vibration mode consisting of a mode mass and a mode stiffness appearing by mode analysis is the main vibration. By applying a forced displacement amount or an external force determined from the position and speed information of the mode mass of the vibrator to the structure, the vibration of the structure is similarly controlled by feedforward control or sample value control for each mode period. Is possible.

The forced displacement of the second support in the present invention is realized by a one-dimensional actuator or 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 material 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 displacement of the one-dimensional actuator, which is a forced displacement, and the magnetic field of the coil, which is an external force, are determined by the displacements of position and velocity, which are determined by Δx = x _en + 2πv ₀ -x _in and Δv = v _en -v _in . It is generated by moving the controller between t '= 0 and 2π according to the displacement function X (t ₀ + t') and the external force function F _I (t ₀ + t ').

At that time, the sample value control is performed by feeding back the position and speed of the second support obtained from the sensor at every Δt which is the natural period of the vibrator made of the second support so as to become a target value. Do.

Because of the flexibility of flexible structures such as robot arms and hard disk arms, residual vibration occurs when the movement stops. Similarly, a pendulum such as an overhead crane causes residual vibration when the movement of the pendulum root stops. Furthermore, the semiconductor exposure equipment (stepper) is 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, which leads to a decrease in work efficiency in transportation work using a robot or crane, hard disk read / write speed, and semiconductor exposure process.

Feedback control is mainly used to reduce residual vibration, but depending on the magnitude of the feedback gain, it oscillates conversely, making high-speed position control difficult. Therefore, research on residual vibration reduction has been carried out by optimal trajectory planning using feedforward control and genetic algorithms (Hiroyuki Kojima, Kenichi Hakui, optimal trajectory planning for straight-crane cranes using genetic algorithm) And the residual vibration suppression control experiment, Proceedings of the Japan Society of Mechanical Engineers, C, vol. 69, no. 682, 2003-6, pp. 1479-1485), many of which are trajectories when moving from the initial position to the target position Therefore, it is necessary to find the optimal trajectory whenever the design parameters of the system change, and it was not possible to cope with unexpected disturbances during movement or work sites where the parameters changed depending on the situation.

The vibration control apparatus A according to the present invention changes the integral vibration system to the natural period by changing the forced displacement at the base according to the forced displacement function X (t ₀ + t ′) determined by setting the target position and the target speed to 0. The vibration control operation can be completely stopped with. Here, in order to explain an embodiment of the vibration control apparatus A according to the present invention, this damping operation is applied to damping control of a flexible structure.

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

The forced displacement function X (t ₀ + t ') in the integral vibration system of (Equation 32a) is applied to the movement of the flexible structure. If the flexible structure which is a cantilever is a robot arm shown in FIG. 13, the change in the position of the modal mass of the integrated vibration system is the change in the position of the arm tip, and the change in the position of the root of the integrated vibration system is This 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 beam, and the spring constant of the integral vibration system is the equivalent spring constant of the cantilever beam.

If the vibration of the robot arm is mainly due to rotation with a low rotational spring constant of a reduction gear or the like 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 moment increase per unit angle.

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

In addition, when the flexible structure, which is a cantilever, is used as the entire semiconductor exposure apparatus including the vibration isolation table, the change in the position of the modal mass of the integrated vibration system is caused by a light source mounted on an optical system consisting of a number of lens systems. The change in the position of the base of the integrated vibration system corresponds to the change in the horizontal position of the entire semiconductor exposure apparatus including the vibration isolation table due to the reaction force of the movement of the wafer stage and the reticle stage. FIG. 15 shows a schematic diagram of the position change of the light source excited by the change in the horizontal position of the entire semiconductor exposure apparatus including the vibration isolation table.

Here, 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, the natural period of the flexible structure to be operated is Δt = 2π, and the inertia Let the speed of the system be v ₀ = 0, X (t ₀ ) = 0.0, and 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. Numerical results when force 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 oscillator continues free vibration until t = 20 where the forced displacement is applied, and after being subjected to the forced displacement for one period, it becomes completely stationary. At that time, the amount of forced displacement given to the movable body is as shown in Fig. 17, which is generally called the Bang-bang function. In other words, the present invention formulates the Bang-bang function, which has not been shown analytically so far, and enables quantification and generalization. By using this function, it is possible to operate from an arbitrary position and velocity state to another arbitrary position and velocity state with a natural period.

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

In the integrated vibration system, when 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 when there is no kinetic energy, the system is stationary.

In the forced displacement function X (t ₀ + t ′) of (Equation 32a), if the change in the root position before and after the position operation is the same as the change in the position of the vibrator, , It becomes the operation to the rest state in another position.

The angular frequency parameters are α ₁ = 1, α _{p ≠ 1} = 0, the velocity of the inertial system is v ₀ = 0, X (t ₀ ) = -d / 2, V (t ₀ ) = 0.0, position change The quantity is the transport distance d, the original speed is v _in = 0, the target speed is v _en = 0, the original position is x _in = -d / 2, the target position is x _en = d / 2, and the inertial system When the velocity is v ₀ = 0, the forced displacement function X (t ₀ + t ′) shown in (Equation 32a) is rewritten as follows.

The natural period of the vibrator is set to Δt = 2π, and the operation using the forced displacement function is started at t ₀ = 3Δt. In the range of 3Δt ≦ t ≦ 4Δt, the forced displacement function X (t ₀ + t ') expressed by (Equation 67) is given, the forced displacement is 0 in the range of t <3Δt, and the forced displacement is in the range of t> 4Δt. Figure 18 shows the time variation of the mass of the transducer and the position of the movable body when d is set. Here, X _sed indicates 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).

For such vibration control, it is also necessary to measure the speed, position, rotation amount, rotation speed, etc. of the object corresponding to the first support, so it is advisable to install sensors to measure these amounts.

Here, for the forced displacement function X (t ₀ + t ') shown in (Equation 67), the original position of the modal mass of the flexible structure is x _in = x ₁ (t ₀ ) = 0.0, and the original velocity is v _in = x ₁ (t ₀ ) = v ₁ (t ₀ ) = 0.0, the target speed is v _en = x ₁ (t ₀ + Δt) = v ₁ (t ₀ + Δt) = 0.0, and the root of the oscillator 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. In addition, when carrying by this method, the root position needs to be moved by the natural period of the vibrator, so the one-time carrying distance is limited.

Next, for the flexible structure, the forced displacement function X (t ₀ + t ') is applied to steady-state control during constant speed conveyance by using the vibration 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. Therefore, the oscillator vibrates after the root reaches the constant speed. Therefore, when the vibration control operation was performed in an integrated vibration system with a constant velocity translation of ₀ at the root, the change in the mass of the vibrating body and the position of the movable body as shown in Fig. 19 was shown. Here, X _sed indicates 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 speed of the tip and root of a robot arm that moves at a constant speed.

Here, for the forced displacement function X (t ₀ + t ′) shown in (Equation 32a), the angular frequency parameter is α ₁ = 1, α _{p ≠ 1} = 0, and the natural period of the transducer is Δt = 2π. , T ₀ = 5Δt, the reference time, which is the time to start the operation, v ₀ = 1.0 for the constant velocity motion at the base of the vibrator, and x ₁ (0) = 1.0 for the initial position and initial speed of the vibrator mass. , V ₁ (0) = v ₀ , the starting position of the oscillator mass x _in = x ₁ (t ₀ ) = x ₁ (0) + 5Δtv ₀ , the oscillator mass starting speed V _in = v ₁ (t ₀ ) = v ₀ , the target position of the oscillator mass is x _en = x ₁ (t ₀ + Δt) = x ₁ (0) + 6Δtv ₀ , the target speed of the oscillator mass V _en = v ₁ (t ₀ + Δt) = v ₀ . With this vibration control operation, the residual vibration can be extinguished with a natural period regardless of its magnitude, even in a system whose base is moving at a constant speed.

By considering the flexible structure as an integral vibration system, it is possible to control the vibration with the natural period as shown above. However, an excessively large force applied to the base during vibration suppression causes damage to the drive system such as gears. Therefore, here, the vibration control operation of the robot arm is performed in multiple stages, and the change in the acceleration at the base due to the number of operations until stationary is observed by numerical calculation.

In the vibration control apparatus A as shown in FIG. 7, the motion of the mass point of the vibrator when the multistage vibration damping operation is performed using the forced displacement function X (t ₀ + t ′) of (Equation 32) is shown. 20 shows. N is the number of times the operation has been performed, and here, it indicates 1, 3, and 5 times. Here, for the forced displacement function X (t ₀ + t ′) shown in (Equation 32), the angular frequency parameters are α ₁ = 1 and α _{p ≠ 1} = 0, and the reference time that is the time to start the operation is Let t ₀ = 0, the natural period of the flexible structure to be operated is Δt = 2π, the velocity of the inertial system is v ₀ = 0, X (t ₀ ) = 0.0, and V (t ₀ ) = 0.0. Also, the original position of the modal mass of the flexible structure is x _in = x ₁ (t ₀ ) = 1.0, the original velocity is v _in = x ₁ (t ₀ ) = v ₁ (t ₀ ) = 0.0, and after N times 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.

When performing vibration control operation, the total number of operations until stationary is N, and the original position x _in , so that the position and speed are (NM) / N times the initial value in the Mth operation. The original speed v _in , target position x _en and target speed v _in were set every time. 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 period Δt of the robot arm. In this case, a forced displacement function X (t ₀ + t ') can be determined for each period of 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 32) to stop without residual vibration at 1.0 after 5 Δt. The trajectory of the follower mechanism driven by this is shown in FIG. 22 together with the cycloid curve. The cycloid curve rises smoothly, and the orbit of the follower mechanism rises while shaking. It can be seen that the follower mechanism can be controlled to pass through the cycloid curve without residual vibration every period Δt. This makes it possible to operate a robot hand that moves on any trajectory without residual vibration.

In the multi-joint robot hand, when the rigidity of the tip is low and the rigidity of the root is high, the change in position and angle of the joint with high rigidity is designed with the above-mentioned forced displacement function and the 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.

These techniques can also be applied to the seek control of the hard disk, the same technology is not only the seek control of the hard disk, such as the fact that you can also be used for settling control and following control are performed in a conventional hard disk Therefore, it is possible to overcome the instability of control due to mode switching and the inaccuracy of the target position appearing in the two-degree-of-freedom control system.

In addition, since the servo information indicating the head position is written on the disk only at regular intervals, there is a problem that the head position and speed information can be obtained only at regular intervals. There were control obstacles caused by the estimation of these values. However, according to the present invention, by setting the time interval for obtaining the servo information representing the head position to a natural number multiple of natural period Δt of the cantilever beam supporting the magnetic head or a fraction of the natural number, residual vibration passing through an arbitrary trajectory is obtained. The sample value can be controlled while suppressing (FIG. 22).

Above all, the sample control method itself of the present invention naturally includes feedforward control during the period Δt of the controlled vibration system and feedback control for each period of the controlled vibration system. It is a big merit that is different from the control system by complicated combination.

On the other hand, when these techniques are applied to the drive control of a semiconductor exposure apparatus, the integral multiple of the natural period of shaking of the semiconductor exposure apparatus is set 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.

Even if residual vibration remains after one step of movement, the residual vibration can be reduced dynamically after the natural period of shaking of the semiconductor exposure apparatus by controlling the sample.

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

On the other hand, the semiconductor exposure system is mounted on a vibration isolation table, which is connected to the foundation of the foundation with a spring. For this reason, the base is a fixed support, the vibration isolation table is the first support, and the conductor exposure device loaded with a lens and a reticle 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 shake of the exposure equipment can be measured, and also attach a sensor on the vibration isolation equipment to change the position and speed of the vibration isolation table. Make it measurable. As a result, information on the position and speed of the first and second supports can be obtained. Thus, it can be seen that the shaking of the semiconductor exposure apparatus can be controlled by the structure of the vibration control apparatus C.

The force generated by the stage is the product of the wafer stage acceleration and the wafer stage mass. Therefore, in order to set the force due to the wafer stage to the external force function F ′ _IIp (t ₀ + t ′), the acceleration of the wafer stage is a 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 on the main body side 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, as an example of the vibration control apparatus A as shown in FIG. 7 in the present invention, the application of the derived forced displacement function X (t ₀ + t ′) to vibration suppression of an overhead crane will be described. Figure 23 shows a schematic diagram of an apparatus in which the present invention is applied to an overhead crane. An overhead crane is a machine that drives the base of a vibrator consisting of a load suspended by a wire by moving a club trolley or the like on the ceiling in the horizontal direction, and the amount of movement of the club trolley or the like depends on the forced displacement function X (t ₀ + t '), the position of the overhead crane load corresponds to the trajectory function x ₁ (t ₀ + t'), so the position and speed of the overhead crane load can be controlled by the movement of the club trolley.

On the other hand, since the overhead crane is a pendulum, the vibration is nonlinear and the natural period depends on the amplitude. Therefore, it is necessary to deal with changes in the natural period. However, since it can be handled in the same way as a linear vibrator, the position and speed of the overhead crane load can be changed arbitrarily, not only to suppress residual vibration after the load has been transported, but also to start transporting 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 position and speed of the mass of the vibrator and the position and speed of the driving body at the moment of starting the operation. In an overhead crane, it is suspended and corresponds to the position and speed of the load. In recent years, inexpensive rangefinders and speedometers using lasers have been sold, but it is difficult to keep laser light from these sensors on overhead cranes that move frequently in factories.

On the other hand, since the overhead crane is suspended by a wire, the length of the wire can be calculated if the period is known. In recent years, small three-dimensional accelerometers that can be attached to packages have been sold, so the moment the package passes through the lowest point and the centrifugal force at that moment can be calculated, and the position and speed of the package are calculated from this. can do. Information from the accelerometer can be obtained sequentially by using Bluetooth (registered trademark) or other radio waves. 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, an arithmetic output unit that calculates and outputs the forced displacement function X (t ₀ + t '), and an amplifier that sends electricity to the motor in accordance with this output A new controller consisting of units will be provided. GENERAL schematic representation of an overhead crane, which is designed in this way is the same as FIG. 23. In the case of 2D overhead cranes, these are arranged on each axis.

Since the position and speed of the vibrator can be arbitrarily changed after one cycle, the present invention not only attenuates the shaking when stopping the overhead crane, but also stops the shaking when moving the load at the start of movement. Is possible. Neglecting the non-linearity of the overhead crane, 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 controlled by forced displacement.

Since the residual vibration of the load can be detected by an acceleration sensor, the crane can always be automated to monitor and stop shaking.

In addition, since it is costly to introduce a 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 small, it can be built into the operation panel of an overhead crane or can be held together.

Next, the equation of motion is derived from a simple model of an overhead crane. Equation of motion of the system when the pendulum mass is m, the length is l, the deflection angle of the wire from the vertical direction is θ, the gravitational acceleration is g, and the forced displacement X (t) is given to the base of the pendulum Is expressed as (Equation 68) below.

When (Equation 68) is made dimensionless with the representative time T _r = √ (l / g) and the unit length l, the following (Equation 69) is obtained.

Here, the original position x _in and the original speed v _in in the forced displacement function X (t ₀ + t ′) in (Equation 67) are the original swing width sin θ _in and the original swing speed θ _in cos. Rewriting each with θ _in and setting the target position and velocity to 0, the forced angular displacement function X _θ (t ₀ + t ') for manipulating the angle and angular velocity with respect to the pendulum is as follows (Equation 70).

When the second term on the right side in (Equation 69) becomes equal to (Equation 70), it becomes the same form as (Equation 25) except for the weak nonlinearity due to the sine function. It is expected that the shaking will be reduced by forcibly displacing the root so that (Equation 70a) holds.

In other words, it can be seen that the acceleration due to the forced displacement at the base of the crane should be expressed as (Equation 70).

On the other hand, since the forced angular displacement function X _θ (t ₀ + t ′) expressed in (Equation 70) is mainly a simple trigonometric function, its second-order integral is greatly different from the original function although the sign is reversed. Does not change. Therefore, (Equation 70a) can also be approximated as (Equation 70b) below, and control can also be performed by making the change in position due to the forced displacement at the base of the crane as shown in (Equation 70). I understand that. However, this is an approximate expression, and the root position of the crane should be forcibly displaced using a function obtained by integrating the forced angular displacement function X _θ (t ₀ + t ′) with the second order over time according to (Equation 70a). .

The angular frequency parameters are α ₁ = 1, α _{p ≠ 1} = 0, the reference time, which is the operation start time, is t ₀ = 20, the natural period of the load hung on the wire is Δt = 2π, and the original swing The angle is θ _in = θ (t ₀ ), the original angular velocity is θ ′ _in = θ ′ (t ₀ ) = 0.0, the target deflection angle is θ _en = θ (t ₀ + Δt) = 0, and the target angular velocity is θ ′ _en = θ ′ (t ₀ + Δt) = 0.0. In the range of 20 <t <20 + Δt in dimensionless time, the driver is given a forced displacement according to (Equation 70), and in the range of t <20, t> 20 + Δt, the forced displacement of the driver is set to 0. For the case, the following numerical calculation was performed. It should be noted that the time derivative of θ, that is, the angular velocity, is expressed by “θ ′” in the sentence as described above (Lagrange notation), and is expressed by “•” above θ in the formula (Newton notation).

When the initial deflection angle was relatively small, θ _in = π / 20, the pendulum was almost stationary after the stationary operation as shown in FIG. On the other hand, as shown in FIG. 25, when the initial deflection angle was relatively large as θ _in = π / 4, the deflection angle decreased somewhat after the stationary operation, but did not reach rest. This is considered to be because the pendulum nonlinearity becomes more prominent as the swing angle increases, and the pendulum period deviates from Δt.

Next, let θ _{end be} the swing angle of the pendulum after damping operation, and Fig. 26 shows the damping ratio η = θ _end / θ _in with respect to the initial swing angle θ _in . 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 the vibration control operation is performed twice in succession under the same conditions. Here, the initial values are θ _in = π / 4.0, θ ′ _in = 0.0, the original deflection angle in the first damping operation is θ _in = θ (t ₀ ), and the original angular velocity is θ ′ _in = θ ′ ( t ₀ ), the original deflection angle in the second damping operation was θ _in = θ (t ₀ + Δt), and the original angular velocity was θ ′ _in = θ ′ (t ₀ + Δt). It can be seen that in FIG. 27 where the stationary operation was performed twice, it was sufficiently stationary in FIG. 27 where the stationary operation was performed twice.

Next, when performing a vibration suppression operation, the system behavior is calculated numerically when the original deflection angle θ _in assumed by the control side at the start of the operation deviates from the actual deflection angle θ (t ₀ ). Observe. The initial deflection angle, which is the actual deflection angle, is θ (t ₀ ), and the damping ratio η = θ _en / θ (t ₀ ) when the appropriate deflection angle, which is the assumed original deflection angle, is θ _in Figure 28 shows the relationship.

It can be seen that when the appropriate deflection angle and the initial deflection angle are the same size, they are damped most. It can also be seen that even if the initial deflection angle is slightly more or less than the appropriate deflection angle, the damping ratio is small and it is sufficiently attenuated. On the other hand, if the initial deflection angle is sufficiently larger than the appropriate deflection angle, sufficient damping effect cannot be obtained, but at least it will not be larger than the initial deflection angle. However, it can be seen that if the initial deflection angle is sufficiently smaller than the appropriate deflection angle, it may be larger than the initial deflection angle.

On the other hand, in pendulums, it has been known for a long time that the change in period due to the amplitude that appears due to its nonlinearity is expressed by a function using a complete elliptic integral. The period of a pendulum with a period of 2π at a small amplitude is expressed by the following (Equation 70b) as a series solution (Morikazu Toda, Introduction to Elliptic Function, Nippon Critics), 5% at θ _max = 50 °, θ _max = At 90 °, a deviation of 18% appears.

Therefore, the period 2π in the expression (Expression 70) is corrected by T (θ _max ) in (Expression 70b), and the forced angular displacement function X _θ (t ₀ + t ′, θ is expressed as (Expression 70c) below. redefine _max ). Where α is the correction coefficient.

When the crane swinging at θ _max = 57 ° was stopped using the equation shown in (Equation 70c), the pendulum stopped with the least residual vibration when α = 0.7. The optimal α is a function of θ _max , and its value can be obtained by numerical calculation.

However, in the vibration of θ _max > 60 °, even if the equation shown in (Equation 70c) is used, the residual vibration cannot be kept small at one time. As shown in FIG. Vibration control by operation became necessary. This is probably because cosθ was ignored in linear approximation of the previous pendulum swing.

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 70b), the period of the pendulum at that time is obtained, and the forced angular displacement function X _θ (t ₀ + t ′) of (Equation 70c) determined thereby is obtained. , θ _max ) can be used to control the residual vibration.

When driving while lowering the position of the load and lengthening the wire, the Coriolis force acts as a viscous damping, so the shaking is more subdued. However, when driving while raising the position of the load and shortening the wire, the Coriolis force acts as an excitation, so the shaking is less likely to settle. For this reason, this function needs further ingenuity.

In the case of a pendulum, the correction using the periodic solution as described above is also useful for other vibration manipulation functions.

On the other hand, if the amplitude of the swing of the load is fixed to some extent due to factory flow work etc., the forced displacement applied to the base of the wire can be created with a two-dimensional plate cam. In the following, an embodiment is shown in which vibration control is performed by the vibration control device A as shown in FIG.

In this device, the cam is activated by detecting a specific position from the signal from the acceleration sensor. 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, α _{p ≠ 1} = 0, and the velocity of the inertial system is v ₀ = 0, X (t ₀ ) = 0.0, V (t ₀ ) = 0.0. The original deflection angle is θ _in = θ (t ₀ ) = 1.0, the original angular velocity is θ ′ _in = θ ′ (t ₀ ) = 0.0, and the target deflection angle is θ _en = θ (t ₀ + Δt) = 0 The target angular velocity was set to θ ′ _en = θ ′ (t ₀ + Δt) = 0.0. In FIG. 29, the black point indicates the center of rotation of the cam, and the x point indicates the position at the start of the cam stationary operation. One rotation of this cam causes a forced displacement of (Equation 70) in the cam follower. Forced displacement can reduce vibration by synchronizing the cam rotation start angle and the phase of vibration and matching the rotation period of the cam with the period of the load hung on the wire.

By attaching this cam to the base of a conventional flexible structure or an overhead crane, it is possible to expect vibration suppression of the system in the natural period without greatly changing the mechanical structure. However, with this damping method, the state of the damping object is limited. Therefore, when performing vibration control using a cam, make sure that the amount of vibration generated in the vibration control object is constant each time, install multiple cams, perform multiple vibration control patterns with one cam, etc. The idea of is necessary.

Angle and forced angular displacement function X _theta is as shown for angular operating the equation (70), if the package is to the pass (theta _in = 0) instantaneous operation start time beneath the displacement of the cam, the operation starting time Is proportional to the angular velocity θ ′ _in . If the amount of displacement of the cam can be adjusted with a movable lever using the device shown in FIG. 9, a mechanism that stops the swing of various amplitudes by rotating the cam rotation period in accordance with the period of the overhead crane. Is possible. Of course, if a single-axis actuator is used instead of a cam, it can handle any vibration.

The vibration control technology shown for the vibration control device A as shown in FIGS. 7 to 9 can be applied to a construction crane, a molten metal transport machine in a foundry, and a robot arm. In addition, the position and speed of the hard disk arm can be detected by the device itself, so the residual vibration after seeking can be reduced as well. It can also be used in exposure equipment to reduce the residual vibration of the precision stage mounting part.

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

Since it takes time to detect the position and speed, and to calculate the control amount, the sensor itself performs a model calculation by analyzing a large number of data at a sampling rate higher than the natural period. It is preferable to devise a method for estimating the speed and position of the reference time in advance.

Next, in order to explain an embodiment in which vibration control is performed by the vibration control device A as shown in FIG. 7, an example in which the derived forced displacement function X (t ₀ + t ′) is applied to a building vibration control method. Is described. 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 such as an integrated rubber or a sliding bearing, which have been proposed as examples, are forcibly displaced in a horizontal direction by a hydraulic actuator. (Hiroshi 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 becomes possible to apply a forced displacement in response to the shaking from any direction.

At the moment of the earthquake, there is an irregular force, so a special contrivance is required beyond the present invention. However, even at the moment of receiving an earthquake, the majority of the shaking of a building incorporating a seismic isolation device is the vibration of the first mode as a cantilever beam accumulated by the seismic motion. It is believed that there is. It is also considered to be effective as a method of eliminating residual vibrations remaining after the earthquake motion. 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.

To carry out the present invention, the position and velocity of the building's modal mass at the moment of starting to control the shaking must be estimated. Therefore, the sensor uses acceleration or velocity or position sensors attached to several levels of the building. As a result, the vibration damping device is represented as shown in FIG.

Since most of the residual vibration that remains in the building is vibration in the primary mode when the building is cantilevered, it is recommended to install an accelerometer or a highly sensitive position sensor using 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. Since the period is a few seconds, a system that can measure quickly will be able to handle it, and the same period is repeated, so it can be predicted accurately.

When the position and velocity 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 is driven along Repeat the sample control every cycle and continue until the amplitude becomes zero. Even if the hydraulic pressure is small, forced displacement due to hydraulic pressure works in a direction that suppresses vibrations, so that it repeats every cycle and works in a direction where the vibrations of the building are contained. 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, the amount of forced displacement or speed of the hydraulic actuator or the like is measured by attaching a sensor capable of estimating the position and speed, for example.

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, it is possible to manufacture with the mechanical mechanism of the cam and insulator without using an advanced computing device such as DSP (Fig. 8). Forced displacement can reduce the vibration by synchronizing the cam rotation start angle and the vibration phase and matching the cam rotation speed and vibration period. On the other hand, by using a lever, the large displacement of the cam can be reduced and the forcible force can be increased on the contrary. Therefore, even if a general motor or engine is used, the shaking of the building can be suppressed. .

For example, if a high-rise building is modeled with a beam with low attenuation, and the natural period of the main first-order mode is 2π, the same shaking as the Great Hanshin Earthquake (Fig. 65) Figure 66 shows the simulation of the fluctuation of the modal mass of the building.

Assuming that the hydraulic actuator starts to move 2π seconds after the earthquake starts, the forced displacement function X (t ₀ + t ') is given directly above the building's seismic isolation bearing, and the sample value is controlled to suppress the shaking of the building. As a result, it can be seen that the fluctuation of the modal mass of the building hit by the same earthquake becomes smaller as shown in FIG.

At this time, the actuator corresponds to the time required to measure or estimate the modal mass position and the modal mass velocity of the second support, the time required to calculate the forced displacement function X (t ₀ + t '). In consideration of the time lag, which is the sum of the time to move, it is necessary to start measuring the position and velocity of the modal mass of the building before the time lag of the natural period at which each control starts. While the normal building cycle is a few seconds, the time lag is considered to be sufficiently small.

Also, based on the position and velocity values measured in this way, the target value (target general target of the second support is set so that the modal mass position of the building after the natural period is in a balanced position and the modal mass velocity is zero. The forced displacement function X (t ₀ + t ') is calculated. Based on the value obtained in this way, the actuator is moved and forced displacement is put on the seismic isolation bearing of the building to control the vibration.

At each natural period, the position of the modal mass of the building and the velocity of the modal mass are measured, compared with the target value, and feedforward due to forced displacement is again applied to the building in the next natural period so as to eliminate the deviation. Control. By repeating this, the deviation can be gradually reduced. This situation is shown in Fig.68.

Although this control is feedforward control within the natural period, the forced displacement function X (t ₀ + t ') calculated at each reference time of the natural period shows a difference between the target value and the actual value. Since it is corrected so as to be small, it is a feedback control. Since feedback control is performed at a fixed time, it is a kind of sample value control, but it is possible to perform feedforward control within each time interval, and the sampling time is based on the characteristics (natural period) of the controlled object. What is determined is not new to the conventional technology.

With this system, it is only necessary to measure the sample value and control the sample value without taking into account the acceleration of the earthquake at each moment, so there is a problem with active vibration suppression that works in the direction of canceling 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 the vibration 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, the recent high-rise building shake caused by the wind is a large building shake due to the integration of the weak wind force. The amount of displacement can be kept small to provide a comfortable living environment for residents.

Even in large crude oil tanks, the horizontal position can be changed by installing the tank foundation on a base-isolated bearing such as laminated rubber or sliding bearings. By installing several hydraulic actuators between the tank foundation and the ground so as to surround the crude oil tank, it is possible to forcibly displace the foundation 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 liquid level of the large tank may be shaken with several liquid level gauges installed around the top of the tank, or with several liquid pressure gauges installed 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 '). slot Thing liquid is reduced.

At that time, a sensor is also attached to the bottom of the tank to be forcibly displaced, and the position and velocity for each natural period are measured or estimated.

Alternatively, 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 in accordance with the second-order time integration of the prescribed forced displacement function X (t ₀ + t '). it makes slot Thing tank internal liquid is reduced. The latter is more accurate and gives better results.

Furthermore, in accordance with the sloshing amount, the foundation of the crude oil tank is forcibly displaced in the horizontal direction in accordance with the second-order time integration of the function (Equation 70c) with the natural period corrected by the non-linearity of the pendulum period in accordance with the sloshing amount. by, slot Thing liquid inside the tank is further reduced.

Next, let us consider the case where the vibration control device A as shown in Fig. 7 is applied to prevent galloping by suppressing horizontal shaking 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. Assuming that the height difference between the high-voltage tower connection 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


(Kenichi Araki, On the inherent flexural vibration of an aerial cable straddled between two struts-1-, Journal of Japan Society of Civil Engineers, vol. 6, 1951-8, pp. 53- 57), can be handled as a pendulum with the same pattern length as a crane. Therefore, the cable connection part in the high-voltage tower that is the base of the pendulum is made 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 51). By accelerating the forced displacement according to the forced angular displacement function X _θ (t ₀ + t ') in (Equation 70), the vibration of the cable can be suppressed.

Examples applied to prevent galloping are shown in Figs. Figures 32 to 34 describe the case where the transmission lines for each elevated tower are fixed at each tower.

A connecting part will be provided in the vicinity of each insulator or near each insulator on the elevated tower. Extend one tension rope in each direction from both sides of this connection, and fix it to each column of the elevated tower. The rope should be an insulator or insulated through an insulator. At this time, it is better to use a spring that guarantees the fluctuation of tension.

A sensor that measures the position and speed of shaking is attached to each insulator of each transmission line on the elevated tower. If an accelerometer or the like is used for the sensor, it is inexpensive and the position and velocity can be estimated. The sensor information is sent to the controller that controls the forced displacement of the connection.

Since information on the position and speed of the insulator and connection part as the first support is also necessary, it is necessary to install a sensor that estimates these quantities.

Place the motor connected to the controller on the pillar of the elevated tower. Two pulleys are connected to the motor, and one rope is fixed to each pulley in the opposite direction. When one length is increased by rotation, the other is shortened.

In addition, in order to measure the difference in the position, speed, and mode of the transmission line, a speed sensor or an acceleration sensor is installed at the center of the transmission line and at 1/4/4/3/4 length. These values are sent wirelessly to the control units in the elevated towers on both sides.

When the control devices on both elevated towers sense the fluctuation of the transmission line by the sensor, the connected insulators are simultaneously forced to be displaced according to the forced angular displacement function X _θ (t ₀ + t ') shown in (Equation 70). Let 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 for higher voltage lines. In addition to a simple primary mode, a secondary mode can occur depending on the wind. In order to stop the fluctuation of transmission lines with different modes, it is necessary to make the natural frequency coincide with that of each mode and to operate with different phases in both towers.

In general, galloping does not occur abruptly, but rolls that gradually increase grow and eventually change to pitch. By this method, even a slight roll can be reduced at the time of occurrence, so galloping can be prevented. Since the small shaking is eliminated every time, the output of the motor that pulls the rope does not need to be so large.

Also, unless each transmission line is connected by a spacer, etc., it does not necessarily 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 spacers, etc., the same fluctuation will be shown, so it will be possible to control them collectively.

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 installed to measure the difference in the position, speed, and mode of the wire is the same as the previous example.

Here, we describe the case where the transmission lines that run on each elevated tower are fixed by a movable insulator suspended from each tower. Remove the two insulators from the tower and suspend the transmission line. By providing a margin for transmission lines between insulators in Japan, the amount of change in the horizontal position of the transmission line between each tower can be controlled independently (Fig. 35).

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

Alternatively, coils can be attached to the top and bottom of the insulator, and current can be passed through it to make an electromagnet. By changing this current value at the commercial frequency in synchronization with the current of the transmission line, it can be vibrated with Lorentz force ( FIG. 37). At that time, it is necessary to monitor and control the amount of change in the position of the transmission line attached to the insulator.

In order to properly apply Lorentz force to a transmission line carrying alternating current, it is necessary to apply an alternating magnetic field of the same commercial frequency in an appropriate phase. However, the phase of the commercial current taken from the transmission line is corrected, and the commercial current is bridged. It needs to be rectified with a diode, etc., and to switch at the commercial frequency.

When the control devices in both elevated towers sense the fluctuation of the transmission line by the sensor, the current flowing through the coil according to the external force function F _IIp (t ₀ + t ') of (Equation 51) that changes according to the period of the transmission line. The suspended insulator is forcibly displaced by modulating the quantity. 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. By this method, even a slight roll can be reduced at the time of occurrence, so galloping can be prevented.

In this equipment, it is only necessary to measure the fluctuation of the transmission line and control the sample value without considering the wind force at each moment. The external force function F _IIp (t ₀ + t ') works in the direction to suppress the swing no matter how small, so the coil current that gives 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.

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 fluctuates the transmission line is converted to electrical energy, which indicates that this device becomes a wind power generator.

Figure 69 shows the principle of the current generator. This generator uses a vibration control mechanism by the vibration control device C, and a first support body that can vibrate is attached to a fixed support body, and a second support body that is vibrated to the first support body. . Here, the direction of vibration of these supports is determined in one direction, and here it is assumed to be the vertical direction.

Next, an elongated conductor such as a cable is attached to the first support, and the direction of electricity flow is perpendicular to the direction of vibration, and in this case, it is perpendicular to the paper. is set up. In addition, an electromagnet is installed around the first support, and the direction of the magnetic field is set to be perpendicular to the direction of 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 as the second support body is easily made to receive the force from the outside world. For example, if the vibrator is vibrated in the vertical direction under the force of the wind flowing in the vertical direction, The first support, which is a conductor, also starts to vibrate in the vertical direction.

Suppose that the force F received by the conductor, which is the first support, is applied upward by vibration. Furthermore, it is assumed that the magnetic field B is applied to this conductor from left to right. Then, according to Fleming's right-hand rule, a current represented by F × B = I is generated in the direction from the front side to the back side of the page.

On the contrary, this current generates Lorentz force F _B according to Fleming's left-hand rule. This force is opposite to the force applied by vibration, and is applied in the direction to cancel the vibration. However, the direction of the force applied to the conductor due to the vibration changes near the natural period of the vibration, and the vertical direction is switched. Therefore, the generated current is expected to be an alternating current that changes randomly near the natural period of the vibration. Random alternating current is less acceptable because it disrupts the commercial frequency. Vibration energy cannot be efficiently converted into electrical energy.

However, now, the Lorentz force F _B applied to the first support member, by varying the current applied to the electromagnet B, the external force function F _IIp (t of to reduce the vibration of the first support (Formula 51) ₀ + t ') is controlled. Then, the energy of vibration efficiently changes to electrical energy, and the direction of the current flows in a certain direction from the front to the back of the paper, enabling DC power generation.

To control the external force function F _IIp (t ₀ + t '), sensors are attached to the first support and the second support, their positions and velocities are measured, and the second support is determined based on the data. Sample value control can be used for each natural period of. Also, since the Lorentz force varies with the current, a sensor that measures the current is also required if no current is passed through the conductor in advance.

On the other hand, when this principle is applied to the vibration control device C including the transmission line shown in FIG. 37, the second support is the transmission line itself connecting the high-voltage towers, and the first support is suspended by the insulator. In addition, it becomes part of the transmission line in the region that receives the magnetic field of the electromagnet.

When a commercial current flows in advance like a power transmission line, the Lorentz force that acts on the surrounding magnetic field and current should work so as to reduce galloping, which is vibration of the transmission line, It can be seen that the transmission line galloping reduction device just described has the effect of a wind power generator that converts wind energy into electricity. In this case, since the transmission line itself bears the 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 period of the transmission line. In general, high-voltage transmission lines extend over several hundred km, 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.

When the main purpose of this device is a wind power generator, the current flowing through the transmission line is changed to direct current, so that the current flowing through the coil does not need to be changed to alternating current. If this is used for a DC transmission line, it is not necessary to change the magnetic field at commercial frequencies, and it is expected that the natural energy of the wind across the strait will be collected efficiently.

In this case, it is possible to use more wind energy by installing a wind receiver around the transmission line. This method can use the elevated tower used for the existing transmission line as a support, and can use the existing transmission line for connection with the power grid, so installation is also cheap.

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

Next, an example in which the vibration control device A as shown in FIG. 8 is applied to a relay for high current is shown. In conventional electromagnetic relays, the electrical connection can be switched depending on whether the movable electrode plate consisting of a single oscillator or cantilever is in contact with or separated from the terminal by turning the electromagnet on and off. In recent years, electronic switches based on semiconductor devices also exist, but their internal resistance is small, so they are important devices for applications where large current and voltage losses are a concern.

On the other hand, the conventional electromagnetic relay does not stop easily because it collides with an excessive speed when the movable electrode plate collides with the terminal, and stops with several chattering. As a result, discharge occurs when the electrode is released, and the electrode coating that reduces the contact resistance is skipped. Therefore, the larger current relays, the more electrical deterioration due to chattering, and the longer the durability required for the product cannot be maintained.

Therefore, by moving the base of the electrode plate of the electromagnetic relay with the disc cam, the tip of the electromagnetic plate is moved according to the forced displacement function X (t ₀ + t ′) expressed by (Equation 32) or (Equation 67) according to the present invention. The collision position and collision speed can be controlled arbitrarily. The approximate schematic diagram of the relay for a large current can thus shown in Figure 38. The movable body rides on a single-axis rail and is pressed against the cam by a compression spring. The cam can be rotated by a motor, and rotates halfway in response to an external signal. An electrode is attached to the movable body via a spring, and when the cam rotates halfway, the upper electrode is lowered and the two electrodes underneath are connected and turned on. Furthermore, when the cam is further rotated halfway, the electrode at the bottom moves to the top and the electrode just below loses connection, so it is turned off.

By making the cam rotation time required to connect to one electrode the same as the natural period of the electrode plate, the fastest electrode switching is possible. The fastest electrode position movement achieved by setting the cam rotation time to be the same as the natural period of the electrode plate is the same as in FIG. It can be seen that the stopped electrode 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 electrode wear is not expected.

Moreover, after the collision, the electrode can be connected with a certain elastic contact force by pushing the spring a little from the balanced position. At this time, the cam rotation angle set above should be smaller than π, and the rest should be operated for pushing.

Next, an example in which the vibration control device A as shown in FIG. 7 is applied to an automatic door is shown. In general, conventional automatic doors are directly connected to the door and drive unit, and there is no elastic cushioning material between them. Therefore, if something is caught between the doors, the impact is strong and dangerous.

In the present invention, it is connected across the elastic body such as a spring between the automatic door and the drive device as shown in the outline schematic of Figure 39. The door should be hung by connecting it to the rail of the ceiling with wheels so as to reduce the frictional resistance when moving as much as possible. The drive unit is designed to be subjected to arbitrary forced displacement by the signal from the control unit. The door and spring form a single vibrator, and the drive unit rotates the wheel to produce forced displacement.

By moving the driving device according to the forced displacement function X (t ₀ + t ′) shown in (Equation 32) or (Equation 67) according to the present invention, the position of the front end of the door can be set to an arbitrary position and speed in each cycle. Can have. It can also attenuate the vibration generated in the door when moving. This makes it possible to open and close the door at a constant speed, or to stop the door without residual vibration, even though the door is connected by a spring. As is often used in recent automatic doors, when closing, it can be stopped smoothly and then closed slowly.

Despite being connected by a spring, the door closes slowly at almost zero speed and can be driven so as not to produce an impact when closed. Above all, by making the spring constant small enough, even if a hand is caught in the door, there will be no injury and an automatic door with a fail-safe safety function will be realized.

After closing once, the door can be closed tightly by pushing the spring in the drive unit. 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.

In this automatic door application, for example, a sensor that measures 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 natural period.

Next, an example in which the vibration 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 and finished in a specific shape by being struck by a die.

Here, in order to realize the present invention, a machine having an outline as shown in FIG. 40 is considered. This machine is hung on a spring whose mold is an elastic body, and the base plate of this spring is made so that any forced displacement can be given to the uniaxial actuator using a controller. When the plate at the base of the spring is forcibly displaced by the uniaxial actuator, the mold vibrates and collides with the sample, and machining is performed. The position and speed of the mold at the time of collision are monitored by sensors. The position of the one-dimensional actuator relative to the mold may be upside down.

By moving the base plate of the spring according to the forced displacement function X (t ₀ + t ′) expressed by (Equation 32) or (Equation 67) according to the present invention, the mold can be moved to any collision position and any collision speed. Can be made to collide with the sample. Since the position of the sample is displaced during processing, it can be dealt with by changing the forced displacement function X (t ₀ + t ') according to the displacement. In addition, since the impact velocity can be changed every time by the forced displacement function X (t ₀ + t '), variable impact machining becomes possible.

Since the machining position and machining amount are variable, this machine can perform the same machining as a servo press. However, there is no need for a servo motor such as a servo press that assumes feedback, and it is feed-forward control, and a machine can be built with an inexpensive system.

If you want to repeat the same processing on a metal plate that is automatically conveyed, you can use a cam instead of a single-axis actuator.

In the application of this processing machine, for example, a sensor that measures the speed and position of the mold and the speed and position of the drive unit is attached, and these values are calculated for each natural period.

Next, an example of application to a display using a vibrator using a vibration control device A as shown in FIG. The display has a fixed part, battery box, control circuit, and external connection circuit on the base, and the drive fixed part and the transducer connection part are on the base. There is a drive unit between the fixed unit and the transducer connection. By replacing the electronic box with a solar cell, the display device using the vibrator can continue to operate without worrying about battery replacement (Fig. 41).

The fixed part is, for example, an Nd magnet, which is attached to a ferromagnetic material such as iron by a strong magnetic field. The vibrator connection part is a phosphor bronze rod with a length of several millimeters to a few dozen millimeters and a diameter of about φ sub millimeters, and a hook that can hang a pendulum is attached to the tip. The driving unit fixing part is a sufficiently thick rigid body extending from the base, and the wiring of the driving unit passes through it. The driving unit is a one-dimensional actuator, such as a laminated piezoelectric element, fixed to the driving unit fixing unit, and expands and contracts on the order of microns by applying a voltage from the control circuit to both ends. At the other end of the drive unit, compressive stress is elastically applied to the rod of the vibrator connection part, and the hook part at the tip of the vibrator connection part undergoes forced displacement due to the displacement of the drive part.

A pendulum string is fixed to the hook part, and the fixed part is hung upside down, so that the display device can control the vibration of the pendulum with the weight suspended (Fig. 41). In addition, by passing a thin rod through the hook, the vertical cantilever can swing and become a vibration display (Figure 42).

The piezoelectric element has hysteresis, but the reproducibility of the position change is good because of the compressive stress. By obtaining the relationship between the change in the position of the piezoelectric element and the additional voltage in advance, the forced displacement along the desired forced displacement function X (t ₀ + t ') can be given.

In addition, the piezoelectric element generates a voltage in proportion to the applied stress, and thus acts as an acceleration sensor for the vibrator. By switching the wiring connected to the piezoelectric element with a semiconductor switch, the sensor and drive system can be switched alternately. If the piezoelectric element is expanded and contracted in accordance with the timing of the vibrator obtained in this way, the vibrator can be vibrated or damped. 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 external connection circuit, the vibrator can be vibrated or stationary depending on the signal from the outside. 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 that can receive signals such as an antenna or BlueTooth as the external connection circuit, the vibrator can be vibrated or stationary depending on the external wireless signal.

For example, if a mobile phone strap can be freely controlled by receiving a wireless signal from a mobile phone, the swing of the strap can inform you of incoming calls and emails.

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 board suspended from the ceiling of a large shopping center. When a customer inputs a product name from a terminal or on the Web and outputs a wireless signal that shakes a specific display board, the display board where the specific product is located can be shaken, and the customer is guided to an appropriate location. can do.

Also, for example, if you attach an advertisement to the tip of a metal wire with good springiness and swing it arbitrarily, you can realize a moving display that can be installed in a small place.

For example, if you use the pendulum of this display, you can swing the pendulum greatly at a specific position on the spread paper and stop it at another position. This makes it possible to create a game that mimics a fortune-telling pendulum called dowsing.

In these moving display applications, for example, a sensor that measures the speed and position of the display body and the speed and position of the drive unit is attached, and these values are calculated for each natural period.

Next, an example applied to the derivation of the cam curve using the forced displacement function X (t ₀ + t ') shown in (Equation 32) is shown. In the vibration control apparatus A as shown in FIG. 8, an example of a cam curve that does not cause residual vibration when the mass of the vibrator is made stationary by changing the position of a certain distance from the stationary state and then returning again by the same distance. Fig. 43 shows the profile of the two-dimensional plate cam designed in this way. The origin in Fig. 44 represents the rotation center of the cam. Here, the angular frequency parameters are α ₁ = 1, α _{p ≠ 1} = 0, and the velocity of the inertial system is v ₀ = 0, X (t ₀ ) = 0.0, and 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 child mass is x _en = x ₁ (t ₀ + Δt) = 1.0, and the mass velocity of the target oscillator is 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) = The target oscillator mass position is x _en = x ₁ (t ₀ + 2Δt) = 0.0, and the target oscillator mass velocity is x _in = x ₁ (t ₀ + 2Δt) = 0.0.

On the other hand, in the vibration control apparatus A as shown in FIG. 8, x ₁ (t ₀ + t ′) which is the mass trajectory of the vibrator which is the follower mechanism driven by the cam curve of FIG. 43 is shown in FIG. . For comparison, a cycloid curve, which is a general cam curve, is also shown. It can be seen that the trajectory of the follower mechanism is very close to the conventional cam curve. This cam curve until the, contrary to was only had decided the orbit of cam follower A, this time the cam curve it can be seen that any design mass of the trajectory of the vibrator is driven by it.

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 common sense of conventional cam design, not a stationary cam, even though the follower mechanism is stationary. Can be seen to be different.

On the other hand, when the root 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 _t and the natural angular frequency ω 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, it can be seen that the cam designed this time exhibits the most efficient vibration suppression for a vibrator with a specific natural frequency, but this is not guaranteed otherwise. If the rotation speed of the cam can be selected arbitrarily, it can be seen that it is desirable to adjust to the natural frequency of the vibrator.

The cam introduced in the present invention has a sharp shape because the slope may be discontinuous at the boundary. By increasing the radius of the cam base circle, these non-smooth points change unintentionally. However, when using the cam, it becomes a point where it tends to wear out first. , You should pay attention to maintenance.

In the cam introduced in the present invention, the time ΔT required for the cam movement is unlikely to be equal to the period of the follower mechanism. In that case, by setting ΔT to an integral multiple of the period Δt of the vibrator, the mass can be designed to pass through a path with a position and speed determined for each period Δt without residual vibration.

In that case, the cam curve is defined by connecting a forced displacement function X (t ₀ + t ') designed to have a position and velocity determined at each time every period Δt. If the position of the mass of the oscillator for each period Δt is determined in an arbitrary cam curve, the mass of the oscillator is determined at a predetermined position for each period Δt using the forced displacement function X (t ₀ + t '). By designing the cam curve to be stationary, the mass can be controlled without any residual vibration at any position for each period Δt. 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 32), the displacement curve of the follower mechanism passes through a predetermined position of the cycloid curve every cycle Δt and makes a residual vibration that makes a round at 10Δt. Fig. 48 shows an example of a cam curve design that does not cause the. The trajectory of the follower mechanism driven by this is shown in Fig. 49 together with the cycloid curve. It can be seen that the follower mechanism can be controlled without residual vibration through the cycloid curve for each period 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 10Δt.

Next, an example in which the vibration control device A as shown in FIGS. 7 and 8 is applied to suppress 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. Where h _s is the height of the liquid in the container, θ is the inclination of the liquid surface from the horizontal plane, g is the acceleration of gravity, 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 shaking due to 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 explained for the overhead crane. Since the pendulum suspension position is realized by moving the container, sloshing can be suppressed by applying the forced displacement of the overhead crane to the suspension position.

The position and velocity of the control object in the liquid in the container are expressed by the inclination θ (t ₀ + t ') of the liquid level from the horizontal plane of the liquid in the container and the angular velocity θ ′ (t ₀ + t') of the liquid level. This corresponds to the swing angle and swing angular velocity, which are the inclination of the wire from the vertical direction in an overhead crane.

Therefore, by measuring the liquid surface inclination θ _in and the liquid surface angular velocity θ ′ _in at the moment of starting control, the target liquid surface inclination and the liquid surface angular velocity are set to 0 (Equation 70). ) Is given. Sloshing of the liquid level is suppressed by applying the acceleration of the forced displacement amount determined by the forced angular displacement function X _θ (t ₀ + t ') that manipulates the angle and angular velocity represented by (Equation 70) in the horizontal direction of the container. It is done. Ro since Tsu Thing is equivalent to a pendulum, non-linearity is present the greater the inclination of the liquid surface, also the residual vibration remained after the control method. Therefore, it is necessary to give vibration suppression operation several times in the same way as an overhead crane.

Fig. 52 shows a schematic diagram of the sloshing suppression device according to the present invention. Place the platform on which the container containing the liquid is placed on the linear motion rail. A cam follower is attached to the side of the pedestal facing the direction of liquid movement, and the pedestal is brought into contact with the cam by a compression spring. A table with a container containing liquid is placed on a movable transporter. In addition, a sensor that measures the angle and angular velocity of the liquid level is attached to the top of the container.

The cam is designed assuming a specific liquid level angle and angular velocity, and when the sensor is close to this value, the cam is activated and a fixed displacement pattern is placed on the base on which the container is placed. In addition, the rotation period should be adjusted according to the period of liquid shaking. By inserting this amount of change every time the sensor detects a predetermined shake, sloshing of the liquid being transported is suppressed.

       This prevents sloshing of the molten metal that occurs when the molten metal during casting is transported from the melting furnace to the mold, preventing accidents in the factory.

In this cam application, for example, sensors for measuring the speed and position of the other side subject to forced displacement and the speed and position of the cam follower are attached, and these values are calculated for each natural period.

Next, in order to explain an embodiment in which vibration control is performed by the vibration 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. An example is described.

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, the vibration of the car body reduces the ride comfort for passengers, so it is necessary to reduce it 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, if the change in the position of the road surface is large in an automobile, using Skyhook theory, it is necessary to give the same large position change to the vehicle height, and the actuator requires a large amount of power. Also in trains, the vehicle body is heavy, so a large amount of power is required to change the vehicle height even with a slight change in position. 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, when the actuator is slightly corrected for changes in the track and road surface to obtain the forced displacement function X (t ₀ + t ') according to the present invention, the vehicle body changes in position in the same way as the track and road surface changes. However, the residual vibration of the vehicle body can be kept small.

Even when the power of the actuator is not sufficient, the shaking can be reduced by applying sample value control for each period of the vibrator consisting of the spring and the car body. This will greatly improve the ride comfort of cars and trains.

On the other hand, in the conventional active suspension, the acceleration applied to the vehicle body is detected by the sensor, and then the reverse acceleration is generated by the actuator and canceled out. Therefore, the rapid change cannot be followed and the vibration suppression is rejected. There is also a risk of accidents.

In this technology, however, the forced displacement function X (t ₀ + t ') that optimally controls the residual vibration of the vehicle body is fed forward by combining the road and rail undulation 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 can arbitrarily control the position and speed of the vehicle body can be calculated, although the conventional control technology can simulate changes in vehicle body vibration. It cannot be obtained analytically.

However, in the present invention, since the forced displacement function solves the inverse problem of dynamics, it is possible to control the sample value for each natural period that rapidly reduces the residual vibration of the vehicle body.

In the case of automobiles and trains, the spring constants of the primary springs of tires and trolleys are much larger than the spring constants of the springs that ride on them, so it can be safely ignored as a model. Therefore, the approximate amount of change in the position of the bogie and axle can be calculated from the amount of change in the position of the road surface and route (hereinafter unified with the road surface).

Now, an actuator that is driven by hydraulic pressure, etc., is installed directly above the carriage or axle. This actuator can be arbitrarily moved up and down by computer control. A spring is mounted on the actuator via a lower seat, and a vehicle body is mounted on the spring. In addition, sensors for estimating the position and speed in the direction of change of these positions are attached to the car body, the axle and the cart (FIG. 70).

Assuming that the vehicle body and the spring are integral vibrators of the vibration control device A as shown in FIG. 7, a forced displacement function determined from the position and speed in the height direction of the vehicle body for each natural period of the vibrator. If the sum (X _d + X _a ) of the change amount X _d of the position of the axle or carriage and the change amount X _a of the actuator position X a is changed according to X (t ₀ + t ′), the position x in the height direction of the vehicle body It is possible to suppress the residual vibration appearing in.

By attaching hydraulically driven actuators on the left and right sides of the carriage and axle, it is possible to suppress residual vibration of the vehicle body in the left-right direction.

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), it travels 20 to 25 m per second, so the change in the track or road surface at this distance is It has a great influence on vibration (Furukawa Hajime, Track Management for Riding Comfort Improvement, RRR, Vol.65, p.22-25, 2008). The distance of the road surface that affects the vibration is determined by the speed, and since it takes a constant value from time to time, it is called the characteristic distance d _s .

In the case of a train, the track displacement of the track can be measured in advance, and the amount of change in the position of the carriage at the next characteristic distance can be estimated by combining it with GPS and position information from the surroundings. .

In the case of automobiles, road height and swell information varies greatly depending on where the wheels pass. 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 measure changes in the height of the road surface within the next characteristic distance from this information. In recent years, data on road undulations and undulations are in the direction of cloud computing, so it is possible to calculate the change in the height direction of the road surface at the next characteristic distance from GPS location information.

Suppose that at the characteristic distance d, the position of the axle or carriage changes up and down or left and right by h depending on the road surface and track. If the speed of the vehicle body at this time is v, the time for the position change is equal to the natural period Δt = d / v.

Suppose that the change in position is a road with unevenness like a cycloid curve. When nothing is controlled and the damping rate is small, a large residual vibration appears in the vehicle that has passed this road surface.

However, by using the position and speed information of the vehicle body, axle, and bogie for each natural period, the parameter α _p is fitted so as to be as close as possible to the actual position change so as to stop the residual vibration (Equation 32). ) Forced displacement function X (t ₀ + t ') is determined. Residual vibration can be reduced to zero by adding a slight position change with the actuator. In this way, by using the position and speed of the vehicle body, axle, and carriage for each natural period, the sample value is controlled by the forced displacement function of the actuator determined by measuring the change in the road surface of the next characteristic distance. It can be kept without residual vibration.

In the active suspension of the present invention, the residual vibration of the vehicle body can be reduced to zero, but the position of the vehicle body changes in the vertical and horizontal directions, so the acceleration applied to passengers and objects inside the vehicle body reduces these vibrations. Induce. When the change is extremely large, the amount of change in the position by the actuator is increased by changing the target position, and control closer to the Skyhook theory is also possible.

In addition, the vehicle body swings not only in the vertical and horizontal directions, but also in the rotational direction around the center of gravity, so the same control is required for the rotational direction of the vehicle body.

On the other hand, when data on road undulations and undulations are accumulated in the cloud and in-vehicle storage, the amount of change in the position of the axle and carriage due to the road surface height and undulations at the previous characteristic distance from the GPS location information X _d Can be known. If _Xd can be selected so as to be close to the forced displacement function X (t ₀ + t ′) in (Equation 32), which can be suppressed based on the current vehicle shake information, an actuator is not used. Both can improve the ride comfort.

In recent years, speed control by automatic driving and cruise control has become possible, 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, it serves to change or waviness height of the road reduce vibration Conversely, can be the most energy-efficient active suspension can be made without using an actuator.

The active suspension according to the present invention makes it possible to develop cars and trains with less vibration and good ride comfort.

Next, in order to explain an embodiment in which vibration control is performed by the vibration control device D as shown in FIG. 10, the derived external force function F _III (t ₀ + t ′) of (Equation 60) 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 forcedly displaced by another part and the other end is fixed by a wall (Fig. 71). For example, in a valve mechanism in an automobile, the tappet at the tip of the valve connected to one of the springs is periodically driven by a cam, and the other end is fixed by the engine wall.

In a brushed DC motor, the electric 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 panda graph used for the electric railway overhead train line system, one end of the restoring spring on the frame is connected to the trolley line of the overhead wire via a sliding material, and the frame on the other end of the restoring spring is the wall. It plays the role of

In the following, in order to explain in a unified manner, 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 pressed by spring preload often jump away from the cam during movement. In the case of an engine valve mechanism, this jump is called a valve jump that tappets away from the cam and causes 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, the jumping of the sliding material away from the trolley line in the electric railway overhead train line system by the same mechanism is called the panda graph separation line. The spring force in brushed DC motors and panda graphs allows electrical connection, so this jump causes arcing and wears the electrodes.

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 service life. In addition, since the valve jump determines the limit of the engine speed, in order to obtain a powerful output, it is necessary to devise a mechanism that does not cause the valve jump to a higher speed. 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. Assuming that the mass of the spring itself is m _s and the spring constant of the spring is k _s , the surging of the first mode of the spring itself, where one end is fixed to the wall and the other end is subjected to the change of the position Δx, is the mass m The spring-mass system with _s and spring constant 2k _s is modeled by Ricardo's equation as a simple vibration that undergoes a change in position of Δx / 2, and the natural period Δt _s of the spring surging is expressed by (Equation 70e).


A more accurate spring constant can be obtained by Hashikura's formula (Katsuharu Hashikura, formula for calculating natural frequency of valving, Japan Aeronautical Society, 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 natural period of the spring is greatly deviated from the rotational period of the cam, the change in the position of the center of gravity of the spring is as shown in FIG. 72, and no significant surging occurs. Where x _g is the position of the center of gravity of the spring, S _A is the amount of displacement by the cam, and the difference between them represents the amplitude of the vibration (surging) of the position of the center of gravity of the spring.

On the other hand, in the cycloid curve, a change in position due to slight unevenness that increases the position and speed of the spring represented by the forced displacement function X (t ₀ + t ′) in (Equation 32) is inherent to the spring itself. When it is applied every period, the surging of the spring grows greatly as shown in FIG. Here, S _B is the 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 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 70f).


As shown in FIG. 74, when the spring surging becomes intense, this contact pressure becomes negative, and the phenomenon that the cam follower and the cam are separated occurs. This is valve dance.

When the surging is increased, the contact pressure between the cam and the cam follower fluctuates as shown in FIG. 74, so that a forced displacement that causes surging occurs due to wear. For example, the wavy wear seen on the trolley wire of the railway overhead line is thought to be due to pressure fluctuations due to surging of the restoring spring. Periodic machining flaws that occur in the cam during machining can also be forced displacements that generate 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 panda graph separation (Shigeo Kotake, Yuichiro Kawakita, Approximate periodic component of cam that grows vibration, Proceedings of Spring and Restoring Force Application Lecture Meeting, Spring Society of Japan, November 1, 2013), Shigeo Kotake, Yuichiro Kawakita (Valuation 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 vibration suppression operation. For example, the position and speed of the center of gravity of the spring is measured, and at the root of the spring so that the movement of the spring stops at each natural period of the spring (Equation 32) The position is changed by the forced displacement function X (t ₀ + t '), and 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 60).

To apply an external force to the center of gravity of the spring, for example, magnetize only the center of gravity of the spring, connect a power source to the coil installed around the center, and apply an electromagnetic force according to the external force function F _III (t ₀ + t ') (FIG. 75).

The surging of the spring is the accumulation of energy given from the slight change of the cam position, so that it can be sufficiently controlled by applying 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 the external force function F _III (t ₀ + t ') determined according to the position and speed of the center of gravity is given to the center of gravity of the spring in which large surging occurs due to the periodically worn cam, Spring surging can be suppressed.

In this method, it is possible to create 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 so that the magnetization remains more.

The same effect can be obtained by halving the spring and sandwiching a ferromagnetic material such as ferrite in the center. In this case, by designing the sandwiched ferromagnetic material to have the same length density as the spring, surging is less likely to occur.

On the other hand, to prevent spring surging, it is possible to simply apply viscous resistance to the motion 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 due to the intense vibration of the center of gravity. By connecting a resistor to this coil, the vibration energy at the center of gravity of the spring is dissipated and surging is prevented. Also, by regenerating the generated voltage, energy harvesting becomes possible, and the fuel efficiency of the car can be improved.

In addition, when 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 the remanent magnetization change, inspection Technology, March 2014, pp. 11-17). On the other hand, in an elastic-only deformation of a normal spring, if the elongation returns, the magnetization returns. This is due to the behavior of the domain wall pinned by the dislocation. Although the dislocation does not move due to elastic deformation, the residual magnetization does not change, but the dislocation moves due to plastic deformation, and the domain wall changes in a more stable direction. 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, the degree of fatigue and sag of the spring can be evaluated.

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, the commutator is generally arranged in a cylindrical shape with n pieces of commutator pieces separated by insulating pieces. 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 the equation (22), the repetition of the cyclic change in the position of the peak is the forced displacement function X (t ₀ + t ′) of (Equation 32) that increases the speed of the center of gravity of the spring. 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 brushed DC motor is t _cmax , the natural period Δt of the brush presser spring itself that applies pressure to the commutator must be designed to satisfy the following (formula 70g): You can see that Here when 2 is not in the denominator is just the resonance condition, most surge grows large, but by placing a 2 in the denominator, just expected to surging cancel the excitation of each other is reduced It is done.

On the other hand, in the case of the electric railway overhead train line system, the trolley line is suspended by a hanger at d intervals (usually 5 m) and takes the form of a catenary. For this reason, the sliding material is subjected to a forced displacement downward at d intervals, and this periodic 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 Δt of the restoring spring is as follows (Equation 70h) so that this does not grow surging: It is necessary to design to satisfy.

As a result, the panda graph is not derailed and the life of the sliding material is improved. In the case of pandagraphs, it is added that depending on the speed, it may be the main spring that resonates with the trolley wire, and the design of this may have to be considered as well.

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

A tandem type multi-high rolling mill generates large pitch vibration called chattering when cold rolling a thin sheet at high speed, causing periodic unevenness in the sheet 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-stage rolling mill coincides with periodic plate thickness fluctuations (Kazu Ishino) Naru, Kazuhisa Kabe and Takao Yoshikawa, 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.

To prevent chattering so far, the lubricating oil during rolling can be selected appropriately (Yukio Kimura et al., Chattering generation mechanism in cold tandem rolling, NKK Technical Report, No.170, (2000), 15.) Although measures such as reducing the rolling speed to shift the self-excited frequency have been devised, it is a passive countermeasure to suppress chattering, and no method has been proposed to dynamically suppress chattering once generated. . As a result, it was impossible to improve the rolling process productivity because it was impossible to roll at high speed beyond the self-excited vibration.

By using the vibration control device D according to the present invention, the self-excited vibration mode is handled as an integral vibrator, and the position and speed of the mode mass for each vibration period are measured, and the external force is reduced so as to reduce this amplitude. By adding, self-excited vibration can be reduced dynamically.

Fig. 53 shows a linear spring model that models each roll of each multi-high rolling mill and the spring connecting each roll. Rolls are the work roll, intermediate roll, and backup roll from the side closer to the plate. Vibration and pressurization are thought to occur symmetrically, and the N-stage linear spring model has N natural vibration modes. The vibration of mode n in a many-body linear vibration system can be expressed as an independent oscillator consisting of each mode mass m _n and each mode stiffness k _n .

On the other hand, at the intermediate position under the working roll pressure of the multi-stage rolling mill, the thickness d of the rolled material is divided into the average plate pressure (d ₀ ) and the plate pressure fluctuation component (Δd) (d = d ₀ + Δd). If the plate pressure fluctuation component fluctuates periodically at the wavelength λ, assuming that the rolling speed at the intermediate position is v _r , the working roll is subjected to a forced displacement at a frequency f = v _r / λ due to rolling. When the frequency f is equal to the vibration mode of the multi-high rolling mill, mode resonance occurs in the multi-high rolling mill due to the periodic forced displacement at the root.

On the other hand, a static pressure P _s is applied to the backup roll, which is used for rolling the plate. In addition to static pressure, the plate generates dynamic pressure fluctuation P _d due to self-excited vibration of the roll. However, since static pressure is independent of dynamic pressure fluctuation and is balanced, it can be ignored. it can.

As a result, a specific vibration mode of one multi-high rolling mill when chattering occurs is expressed as a one-body vibration system that receives a forced displacement at the root with a period Δt = 1 / f under pressure, and the vibration mode shown in FIG. Equivalent to controller A.

Now, the forced displacement of the period Δt due to the plate pressure fluctuation component of the rolled material is an approximate period with a Fourier component (Δd _f ) having an angular frequency of ω = 2πpf and an angular frequency of ω = 2π (p + 1/2) f. _Suppose that it is divided into components (Δd _a ) (Δd = Δd _f + Δd _a ). Where p is a natural number. The former is caused by smooth plate thickness fluctuations, and the latter is caused by non-smooth plate thickness fluctuations that are continuous but have discrete coefficients.

The Fourier component periodically vibrates a specific vibration mode at the frequency f of the multi-high rolling mill, but the amplitude of the mode mass is constant and does not change. In general, when the plate thickness variation is small, the mode mass variation due to this component is small and can be ignored.

On the other hand, the approximate periodic component of the forced displacement at the root of the vibrator can be expressed by a linear sum of the forced displacement function X _p (t ₀ + t ′) expressed by Expression 22 ((Expression 71)).


If the sum of the angular frequency parameter in the linear sum was xi] ((Equation 72)), position and speed of the modal mass for each one period, respectively _{ξ (x en -x in),} ξ (v en - v _in ) changes.

Therefore, if the same periodic component continues periodically in the forced displacement, the amplitude of the mode mass gradually increases and chattering oscillation occurs as shown in FIG. Thus, it can be seen that the almost periodic component of the plate pressure fluctuation accumulates the vibration energy of the multi-high rolling mill, which has already been explained as an effect of the forced displacement function X (t ₀ + t ′) in the present invention. . With the above model, the plate pressure variation due to P _d and this dynamic pressure fluctuations by chattering can argue the effect to be promoted and will not mention details.

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

If the amplitude of the plate pressure fluctuation is negligible compared with the amplitude of the chattering vibration that has grown, the multi-stage rolling device attached with the electromagnetic force generator under chattering vibration is equivalent to the vibration control device D shown in FIG. is there.

For the generated chattering vibration, the position and speed of the mode mass are measured every period Δt, and the external force function F _III (t ₀ +) determined to approximate the position and speed of the mode mass to 0 (equation 60). By controlling the sampling to apply external force to the work roll for period Δt according to t '), chattering vibration can be suppressed. 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 diagram of an electromagnetic force generator that applies external force to each roll in order to suppress chattering vibration in a tandem type multi-high rolling mill. Chattering vibrations occur in the vertical direction of the rolls. Therefore, by applying electromagnetic force to the bearings connected to the shafts of the rolls via bearings by means of coils around the plunger with high permeability, (Equation 60) Generates an external force according to the external force function F _III (t ₀ + t '). As a result, chattering can be avoided dynamically and rolling can be performed at a higher speed beyond the vibration mode of the multi-high rolling mill.

In this rolling mill application, for example, sensors for measuring the speed and position of the rolling roll and the force of the drive unit are attached, and these values are calculated for each natural period.

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

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

In these removal processes, when the processing speed is increased or the rigidity of the workpiece or shank is insufficient, chatter vibration due to large self-excitation occurs between the tool and the workpiece, and traces of periodic irregularities are generated on the workpiece. 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 specific mode mass and specific mode stiffness. If the rigidity of the shank itself is low, the following discussion is a technique for vibration of the shank as a cantilever.

Assuming that the radius d of the side surface periodically fluctuates by Δd for every angle Δθ radians, the tool that contacts the workpiece rotating at the rotation frequency f ₀ has the root of the cantilever at f = 2πf ₀ / Δθ. It will be forcibly displaced with frequency.

The forced displacement of the period Δt = Δθ / 2πf ₀ due to the workpiece radius fluctuation component is roughly a Fourier component (Δd _f ) with an angular frequency of ω = 2πpf and a frequency of ω = 2π (p + 1/2) f. _Suppose that it is divided into periodic components (Δd _a ) (Δd = Δd _f + Δd _a ). Where p is a natural number. The former is caused by a smooth radius variation, and the latter is caused by a non-smooth radius variation which is continuous but has a discontinuous derivative.

The Fourier component periodically vibrates the vibration mode of the workpiece with frequency f, but the amplitude of the modal mass of the workpiece as a cantilever is constant and does not change. In general, when the radius variation is small, the modal mass variation due to this component is small and can be ignored.

On the other hand, the approximate periodic component of the forced displacement at the root of the vibrator can be expressed by a linear sum of the forced displacement function X _p (t ₀ + t ′) expressed by (Expression 22) ((Expression 71)). . If the sum of the angular frequency parameter in the linear sum was xi] (Equation 72), position and speed of the modal mass of the workpiece in each cycle, respectively _{ξ (x en -x in),} ξ (v en - v _in ) changes. Therefore, when the same periodic component continues periodically in the forced displacement, the amplitude of the mode mass gradually increases and chatter vibration occurs as shown in FIG.

On the other hand, when an electromagnetic force generator that applies external force to the workpiece is installed separately from the chuck as a fulcrum, the mode external force can be applied at a frequency that matches the generated vibration mode. This is equivalent to the external force for the modal mass expressed by one oscillator described above. As a result, 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 vibration control device D shown in FIG. It is.

With respect to the generated chatter vibration, the position and speed of the modal mass in the work are measured every period Δt, and the external force function F _III (t _By controlling the sampling to apply external force to the workpiece for a period of Δt according to ₀ + t '), chatter vibration can be suppressed. The mode mass chatter vibration amplitude is gradually reduced by the external force as in Fig. 55. This makes it possible to avoid chatter vibration caused by self-excitation and to cut the workpiece at a higher speed than the workpiece vibration mode.

In these cutting machine applications, for example, a sensor that measures the speed and position of the workpiece and the driving force of the drive unit is attached, and these values are calculated for each natural period.

Next, in order to describe an embodiment in which vibration control is performed by the vibration control device D as shown in FIG. 10, the derived external force function F _III (t ₀ + t ′) of (Equation 60) is applied to a wind turbine. An example is described.

A windmill that rotates in response to wind receives not only fluctuations in the wind but also fluctuations in the external force due to the rotation under constant wind speed. This is because the wind weakens each time the blade of the windmill passes through the support column. In the case of an N-blade windmill with a rotation speed f, the wind force at the frequency of Nf causes fluctuations in external force.

Wind turbine struts are getting higher as the blades become larger, so the natural period of the struts is getting lower. The rotation speed of the blades of a normal wind turbine is controlled so as not to coincide with the natural frequency of the struts. However, when the wind becomes strong, the blades must be rotated beyond a certain natural mode. It is inevitable to drive in a state. For this reason, there are problems such as large vibrations of the struts.

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

As a vibration control device D according to the present invention, a wind turbine column that receives fluctuations in external force due to blade rotation is treated as a cantilever with a column fixed to the ground, and the self-excited vibration mode is handled as an integrated vibrator. Modeled. The self-excited vibration is dynamically reduced by changing the external force by measuring the position and speed of the modal mass of the windmill for each vibration period and controlling the blade rotation phase to reduce this amplitude. Is possible. Fig. 58 shows a schematic diagram of the wind turbine modeled in this way.

The fluctuation component (ΔF) of the external force due to the rotation of the wind turbine blades is a Fourier component (ΔF _f ) with an angular frequency of ω = 2πpNf and an almost periodic component with a frequency of ω = 2π (p + 1/2) Nf (ΔF _a )) (ΔF = ΔF _f + ΔF _a ). Where p is a natural number. The former is caused by smooth external force fluctuations, and the latter is caused by non-smooth external force fluctuations that are continuous but have discrete coefficients.

The Fourier component of the external force vibrates the column periodically, but the amplitude of the modal mass of the column is constant and does not change. On the other hand, the approximate periodic component of the external force can be expressed by a linear sum of the external force function F _IIIp (t ₀ + t ′) expressed by (Expression 57) ((Expression 73)).


When the sum of the angular frequency parameters in the linear sum is ξ ((Equation 72)), the position and speed of the workpiece modal mass for each period are ξ (x _en -x _in ) and ξ (v _en -v _in ). Therefore, if the same periodic component continues periodically in the forced displacement, the amplitude of the mode mass gradually increases as shown in Fig. 54, and the vibration of the column increases.

On the other hand, the generation of external force due to the position of the blade is the smallest when the blade is directly below and is in equilibrium with the support. For this reason, the external force applied to the upper blades becomes stronger, and a moment is generated in the direction of tilting the column downwind. On the other hand, when the angle between the blades is parallel to the column, no moment is generated. Therefore, the direction of the periodic external force can be expressed by setting the phase θ when the blades are directed downward to 0 and the phase θ when the next blade is directed downwards to 2π (FIG. 59).

For the generated vibration of the column, the position and speed of the modal mass are measured every period Δt = 1 / Nf, and the external force function F of (Equation 60) determined to bring the position and speed of the modal mass close to zero. It is possible to suppress the vibration of the strut by sampling the position of the blade during the period Δt with external force according to _III (t ₀ + t ').

For example, from the external force function F _III (t ₀ + t ′) in (Equation 60), when the speed of the support swing is maximum in the leeward direction at the support balance position, the blade phase θ is π / 2. Controlling the speed of the blades can reduce the swing of the support. 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 blade phase θ is 3π / 2, as shown in FIG. In addition, the swing of the support can be reduced. Even when the natural period of the strut is different from Δt, control is possible by using the external force function F ′ _III (t ₀ + t ′) in (Equation 63).

In general, when the vibration of the column becomes large, the wind is strong and the windmill must be operated with reduced efficiency. Therefore, these controls that change the phase of the blades to suppress vibrations are more desirable because they prevent the fatigue failure and prolong the life of the windmill, although they result in a slight reduction in power generation efficiency.

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 as the drive unit is attached, and these values are calculated for each natural period.

On the other hand, if the wind turbine is an offshore wind power generator floating on the ocean, the floating body will be greatly shaken by 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. The offshore wind power generator rotates slowly around the center of gravity due to the couple generated by the deviation between the center of gravity and buoyancy when the floating body is tilted, so the period of vibration to be controlled is less than the period of wind turbine blades passing through the column. It will be slow. Therefore, the phase shift of the blade rotation, which is a short period, does not affect the swing around the center of gravity of the floating body.

In addition, since the windmill changes the direction of the nacelle so that it receives the wind from the front, the operation of changing the blade pitch of each blade greatly changes the drag of the wind, and the rotation around the pitching has the most influence on the swing of the floating body.

In general, the blade pitch operation of each blade is performed to keep the rotation speed of the wind turbine most efficient. However, when the storm approaches, the wind speed is sufficient, so the blade pitch operation is performed to maintain the rotation speed. It is not necessary to use it for the first time, and even if it is operated with a little lower efficiency, priority is given to preventing the floating body of the offshore wind power generator from shaking.

The center of gravity of the floating body swings in various degrees of freedom, consisting of vertical movement and rotation, due to the influence of waves, etc., but each rotation and vibration in a certain direction can be used independently if the influence is small. Also, if the wind changes more slowly than the swinging period of the floating body and the wind per period can be considered constant, the wind force applied to the windmill can be changed by rotating the blade pitch of the blades at the swinging period. Is possible.

Now, if the rotation angle and angular velocity of the floating body around the pitching for each period can be measured, F _III (t ₀ + t ' ) Can be determined. Furthermore, if the flow rate of the wind is measured and the blade pitch rotation is controlled so that the moment due to the wind force applied to the wind turbine becomes the function F _III (t ₀ + t '), the floating body can be restrained from swinging around the pitching. The sample value can be controlled by the period of fluctuation of.

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. If the rotation of the blade pitch of each blade is controlled so that the moment due to the difference in wind force applied to the left and right of the windmill becomes the function F _III (t ₀ + t '), the swinging around the rolling of the floating body can be 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 to suppress the shaking caused by the rotation of the offshore wind power generator. However, the size of the wind turbine must be designed to obtain sufficient wind strength to match the magnitude of the sway caused by the waves so that the time required for vibration suppression is not too long.

In addition, although the optimal wind force for vibration control deviates from the external force function F _III (t ₀ + t ') due to the wave force hitting the offshore structure, the rotation force of a huge offshore wind power generator Since the wave force is small, it can be ignored as an error without affecting the control.

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

On the other hand, the shaking of offshore wind turbines is caused not only by the wind but also by ocean waves. Of these, this device that suppresses the shaking caused by the rotation with the force of the wind once converts the wave force into the rotational energy of the offshore wind power generator, which becomes the kinetic energy of the blades and finally the energy of the wind power generator. Therefore, it can be seen that it works as a kind of wave power generation.

In particular, offshore waves vibrate the center of gravity of offshore wind power generators up and down in the heave direction, so if the wave period is twice the rotation period of the floating body, the vibration of the wave 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 power generator, which is easy to control with this technology, is designed to be half of the average period of the waves, and this method can sufficiently suppress the swing around the pitching of the offshore wind power generator. If it is possible, it will be a more efficient wave power generator (Fig. 76).

In the application of this offshore wind turbine generator, for example, a sensor is installed to measure the vibration and rotation angle of each floating body, the rotation angle and their speed, the change in wind power as driving force, and the vibration due to disturbance. These values are calculated by sampling higher than the natural period.

Next, in order to describe an embodiment in which vibration control is performed by the vibration control device E as shown in FIG. 12 or the vibration control device D as shown in FIG. 10, an external force function F _IV ( An example of applying t ₀ + t ') and F' _III (t ₀ + t ') in (Equation 63) to an electromagnetically driven valve of an engine is described.

The valve mechanism of the engine is a system that controls fuel injection and exhaust gas emission, which greatly affects the combustion efficiency of the engine. However, since the conventional valve mechanism is driven by receiving the piston force with a timing belt, the opening and closing speed must be dependent on the engine speed, and the valve is opened and 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.

To overcome these problems, in recent years, and devised a cam mechanism for moving the valve, variable technologies timing and closing amount of the opening and closing of the valve, has been proposed from the car companies companies each rotational speed It was not possible to control the valve with all the conditions optimized ("The next-generation engine that can be seen Part2 Engine variable technology", Nikkei Automotive Technology, Nihon Keizai Shimbun, (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, so it is necessary to set the valve spring higher. However, this causes a large dynamic friction on the cam during 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 has caused a problem that a high-speed engine cannot be designed. 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, since a cam is not required, friction loss can be reduced, and high-speed engine rotation may be desired.

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. In addition, when the valve speed is high at the valve opening / closing position, not only a large kinetic energy is lost due to a collision, but also valve dancing occurs due to rebounding. Therefore, the valve needs to approach the speed as much as possible at the opening / closing position. Therefore, it is necessary to find the function of the driving force by the optimal electromagnetic field.

Various studies have been conducted on the optimal driving force function in electromagnetic field valves. For example, a feedforward function using a compensator such as Uchida has been proposed. (Masaki Uchida, Hideyuki Hasegawa, Yoshifumi Morita, Takao Kusumi, “Positioning control of electromagnetically driven valves for automobile engines by sliding mode control: Valves by feed-forward compensation”) ”Improvement of control performance at the time of opening”, Journal of AEM Society of Japan, Vol.18, No.1 (2010), pp.48-53.) (Masaki Uchida, Masaya Takemura, Yoshifumi Morita, Hisashi Kamito, Takao Shiomi, "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 close the valve, which has received rapid acceleration due to electromagnetic force, to zero, and it has been difficult to close the valve. So far, these problems have not been solved, and electromagnetically driven valves are still not available. Not practical.

On the other hand, according to the present invention, an electromagnetically driven valve can be manufactured by a vibration control device E as shown in FIG. The plunger, which is a movable iron core made of a soft magnetic material having a high magnetic permeability, is connected to the valve, and is fixed by a guide so that it can move freely in the valve opening and closing direction. In order to give the plunger an external force in the valve opening and closing direction by electromagnetic force, a solenoid is placed around the plunger. The solenoid is connected to the power source. As will be described later, when it is desired to control the sample value so as to eliminate the valve dance of the electromagnetically driven valve, it is necessary to measure the position and speed of the plunger after the natural period Δt. Install the speed sensor. A schematic diagram of the electromagnetically driven valve mechanism designed in this way is shown in FIG.

In the electromagnetically driven valve shown in FIG. 60, a plurality of plungers and solenoids 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, by applying the external force function F _IV (t ₀ + t ′) shown in Equation 66 to the valve that is the controlled vibrating body, the position opened after Δt from the closed position The valve that is stationary at, and then stationary at the open position, can rest 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. In the different curves, the valve lifts are 10 mm, 5 mm, and 2 mm, respectively, from the largest. At this time, the orbit drawn by the valve is shown in Fig.62.

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 can be limited by connecting the plunger to the fixed part via a spring. Fig. 63 shows a schematic diagram of the electromagnetically driven valve thus designed. This electromagnetically driven valve is a vibration control device D as shown in FIG. 10, and is urged to open and close by applying an external force function F ′ _III (t ₀ + t ′) represented by (Equation 63) to the plunger. .

In a device in which a valve is connected using a spring (k '= 0.05) of 5% of the spring constant required when the natural period of the vibrator with the valve as mass is Δt, the valve follows the same trajectory as FIG. Figure 64 shows the external force required in this case. The different curves are the electromagnetic forces required for the same different valve lifts as above.

On the other hand, instead of the plunger in the apparatus of FIG. 60, a permanent magnet made of a hard magnetic material that alternately changes poles is connected to a valve, and an electromagnetic coil connected to a power source around each permanent magnet is connected. By arranging them, a linear motor can be formed, and an electromagnetically driven valve can be similarly manufactured using this. In linear motors, it is necessary to match the polarities of the permanent magnet and the electromagnetic coil. Therefore, a sensor that detects the position of the operating permanent magnet is required. The position and speed of the valve after the period Δt can be estimated. A schematic diagram of the electromagnetically driven valve mechanism designed in this way is shown in FIG.

When a linear motor is used for the drive system of the electromagnetically driven valve, the electromagnetic force is proportional to the energizing current, so there is an advantage that it is easy to design 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 66), if the thrust coefficient (counterelectromotive force coefficient) is κ _t , the current flowing through the electromagnetic coil is It is expressed as (Equation 73a).

On the other hand, since the electromagnet of a linear motor can be modeled by a coil and a resistance, if the voltage applied to the coil is E (t ₀ + t ′), (Equation 73b) holds.


As a result, the voltage applied to the coil can be designed. Now, assuming that the inductance L of the coil is 3.85 mH, the resistance R is 2.0Ω, and the thrust coefficient κ _t is 10.0, the voltage for realizing the external force with a valve lift of 10 mm in FIG. Is expressed as in Figure 79. In an engine running at high speed, 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. You can see that

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

Since this vibration operation function can obtain not only the trajectory but also its driving force and functions such as the voltage and current applied to the motor that provides that driving force, the feedforward control of the motor itself becomes possible, and sample value control and By combining them, even simple DC motors and linear motors may be capable of positioning motors that are mainly 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 the inexpensive DC motor.

Finally, how to determine the parameters of each forced displacement function and each external force function necessary to control vibration in each vibration control device is described. The discussion will be made using a dimensionless time t with a natural period of 2π when the oscillator made of the second support is a single oscillator. For simplicity, in the following, the inertial system is taken as a stationary coordinate system and v ₀ = 0. One of the substantial supports in the stationary coordinate system is placed at the origin of the stationary coordinate system, and control is performed for each natural period from time 0. For the position and speed of each support in the Nth operation, N This is indicated by the subscript.

In the following explanation, since multiple coordinate systems with 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 _Is called O _{x2, N.}

Also, the speed of each support does not depend on the origin of the coordinate system, so 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 order to make it easier to compare with the actual problem, the distance between the centers of gravity of each support was determined when the entire three-body vibration system was in a balanced state. 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 expressed here as the length of the 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 , and the spring between the first support and the third support of the length it was L _2.

Thereby, the relationship of (Formula 74-1 to Formula 73-3) 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.}

In addition, the position of each support in the Nth operation is also expressed by a coordinate system in which the respective balanced positions are set as the origin, and “displacement of the fixed support”, “displacement of the first support”, and “second support”, respectively. This is called "body displacement" or "third support displacement". 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 definition so far, the relationship represented by (Expression 75-1 to 75-3) holds.

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. Also, the positions of the support members of the three-body vibration system that are out of balance are represented as shown in the lower part of FIG.

The following describes how to determine various parameters and changes in the position and speed of each support in the general vibration operation that is continued for each natural period for each vibration control device. Each support shall be placed in the order from negative to positive, fixed support, first support, and second support, and these support will be moved in the positive direction.

Before that, the relational expressions that hold in common are shown for each vibration control device of the present invention.

The displacement and speed of the second support for each natural period τ subjected to the vibration operation this time (every 2π in the dimensionless time) are, in each case, the relational expressions of (Expression 76-1 to Expression 76-4) Is satisfied.

Since the second support always exists in each vibration control device this time, the displacement x _{1, N} of the second support at the reference time t = t _N = 2πN, which is the operation start time in the Nth operation _, is It is 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 77).

Since the second support always exists in each vibration control device this time, the position y _{1, N} of the second support at the reference time t = t _N = 2πN, which is the operation start time in the Nth operation. Satisfies the relation of (Equation 78).

On the other hand, the motion of this three-body vibration system is based on the interaction between the second support and the third support in the discrete dynamic system for each natural period τ of the second support (every 2π in dimensionless time). Since it is separated from the motion of the first support, when the controlled body is subjected to vibration control by the forced displacement function X (t ₀ + t ′), the displacement and speed of the first support are expressed by (Equation 79− 1, the relational expression 79-2) is satisfied.

Since the value of the forced displacement function X (t ₀ + t ′) is the displacement of the first support, the relational expression (Equation 80) always holds for the displacement of the first support.

On the other hand, since the speed of each support does not depend on the origin of the coordinate system, the speed of the second support is always v _{1, N.} 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 vibration control devices, we will not discuss speed below.

Next, we discuss each vibration control device.

In the case of the vibration control device A, in addition to the second support, the first support is actually present, and therefore the first support at the reference time t = t _N = 2πN, which is the operation start time in the Nth operation. The position is represented by continuous physical quantities Y 1 _{, N} , and by defining the amount of increase (D 1 _{, N 2} ) in displacement of the first support in the Nth operation, the relational expression (Equation 81) holds.

In the case of the vibration control apparatus A, the controlled vibration body is composed of a first support body that is movably supported by a fixed support body, and a second support body that is supported by the first support body in a freely oscillating manner. ing. 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 of (Expression 80) regarding the displacement of the first support, the displacement of the first support is expressed by (Expression 82).

The balanced position of the first support in the fixed coordinate system is expressed by (Equation 83).

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 _(83), 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 equilibrium state is L _1, balanced position of the second support element is represented by (Equation 84).

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 (84), x ₁ ( You can see the trajectory of t ₀ + t ').

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 85).

In the vibration control apparatus A, although the fixed support is virtual, it always exists at the balanced position of the fixed support expressed by (Equation 85) due to the conditions of the fixed support.

Next, in the case of the vibration control device C, the first support body that is attached to the fixed support body so as to vibrate and the second support body that is attached to the first support body so as to vibrate are attached. In addition, 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, this should be taken 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 80), the first support at the reference time t = t _N The relational expression (Equation 86) holds for the position of the body.

Since the displacement of the second support body by the vibration operation function expressed by the external force function F ′ _IIp (t ₀ + t ′) satisfies the relational expression (Expression 76-1), the displacement at the reference time t = t _N The relational expression (Equation 87) holds for the position of the two supports.

Next, in the case of the vibration control device E, since it is composed of a second support that is movably supported, only the second support is real. 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 77).

Since the second support always exists in each vibration control device this time, the position y _{1, N} of the second support at the reference time t = t _N = 2πN, which is the operation start time in the Nth operation. Satisfies the relation of (Equation 78).

Therefore, the balanced position of the second support in the fixed coordinate system is expressed by (Equation 88).

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 89).

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

On the other hand, from the position and balance position of the first support in the Nth operation, the amount of increase (D 1 _{, N} ) in displacement of the first support is expressed by (Equation 90).

However, since the relational expression (Equation 82) always holds for the displacement of the first support, the first support that has moved a certain distance after the natural period is at each reference time. 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 91).

In the vibration control apparatus E, although the fixed support is virtual, it always exists at the balanced position of the fixed support expressed by (Equation 91) due to the conditions of the fixed support.

Next, in the case of the vibration control device D, since it is composed of a second support that is supported by the fixed body A so as to freely vibrate, only the second support is actual. 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 77).

Since the second support always exists in each vibration control device this time, the position y _{1, N} of the second support at the reference time t = t _N = 2πN, which is the operation start time in the Nth operation. Satisfies the relation of (Equation 78).

Therefore, the balanced position of the second support in the fixed coordinate system is expressed by (Equation 88).

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 89).

In the vibration 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 92) holds.

The balance position of the first support is the origin, and the relationship of (Equation 82) holds for the displacement of the first support, so that the position of the first support holds (Equation 93).

In the vibration control device D, since the first support is virtual, the increase amount (D 1 _{, N 2} ) of the displacement of the first support is arbitrarily determined in each operation. 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 94).

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 91).

[Invention A1]
The present invention
A vibration control device that detects a position and speed of a mass of a controlled vibrating body and controls a vibration operation actuator to operate the position and speed of the controlled vibrating body, wherein the controlled vibrating body is attached to a fixed support body. A first support that is movably supported; and a second support that is supported by the first support so as to be able to vibrate. In order to detect the position x ^* _1in , the speed v ^* _1in , the position X ^* (0) and the speed V ^* (0) of the first support, and set the displacement amount of the first support to a predetermined value, When the controlled vibration body is a non-collision vibrator (Equation 113), and when the controlled vibration body collides and vibrates with an object having a restitution coefficient a, the controlled vibration body obtained from the Grover algorithm determined from (Equation 114) A control signal is created from the function of the dimensionless time t ^* with the natural period of 2π The dynamic operation actuator changes the displacement amount of the first support to the control signal value, so that the position x ^* _1in and the speed v ^* _1in of the second support are positioned after the natural period of the controlled vibrating body. Vibration control device characterized by suppressing vibration by changing to x ^* _1en and speed v ^* _1en ,
It is good.






(Formula 113)
_{However, ω - = 1/2,} ω + = p + 1/2 (p: natural number)







(Formula 114)
_{However, ω - = 1/2,} ω + = p + 1/2 (p: natural number)

[Invention A2]
The present invention detects the position and speed of the mass of the controlled vibrating body used in the vibration control device of invention A1, and controls the vibration operation actuator to control the vibration by controlling the position and speed of the controlled vibrating body. It is good also as a vibration control method characterized by these.

[Invention A3]
In the present invention, the vibration control device for operating the position and speed of the controlled vibrating body in the invention A1 is supported by the cam follower movably supported by the fixed support body, the cam in contact with the cam follower, and the cam follower. When the position of the cam follower at the operation start time is X ^* (0) and the speed is V ^* (0), the position of the second support x ^* _1in and the speed v ^* _1in is changed to a position x ^* _1en and a speed v ^* _1en after the natural period of the controlled vibrating body, when the controlled vibrating body is a non-collision vibrator (Equation 113), When the control vibrating body vibrates and collides with an object having a coefficient of restitution a, a cam having a cam curve obtained by the above (formula 114) may be used.

[Invention B3]
According to the present invention, the vibration control device for operating the position and speed of the controlled vibration body in the invention A1 is indirectly connected to the cam follower via the cam follower that is movably supported by the fixed support and the cam follower or the lever. And a second support that is supported by the cam follower so as to vibrate freely. The position of the cam follower at the operation start time is X ^* (0) and the speed is V ^* (0). in, wherein the changing to the second support position x ^* _1in the velocity v ^* _1in the position after the natural period of the controlled vibrator _x ^* 1en and velocity v ^{_* 1en,} said controlled vibrator When the non-collisional vibrator is a non-collision vibrator, a cam having a cam curve obtained by the above (Formula 114) is used when the controlled vibrating body collides and vibrates with an object having a coefficient of restitution a. In invention A1 It is good also as a vibration suppression apparatus of description.

[Invention C1]
The present invention
A first support that is supported by a stationary support in an inertial system so as to vibrate;
A second support and a third support having the same natural period supported in parallel on the first support so as to vibrate freely; and
From a three-body vibration system designed so that kinetic energy moves only between the second support and the third support for each natural period, the position and speed of the second support after the natural period By defining the initial conditions of the three-body vibration system for each natural period so as to be the target value,
Determining the trajectory of the second support during the natural period from the free motion of the three-body vibration system during the natural period;
By taking out the controlled vibration body from the three-body vibration system so as to include the second support body, and making the control vibration body, which is the remaining part from which the controlled vibration body is removed, virtual, In accordance with a control signal obtained by freely determining the initial condition of the controlled vibrating body, a forced displacement or external force is applied to the controlled vibrating body by an actuator so that the position of the second support body after the natural period And a vibration control device or trajectory control device characterized by feedforward control or sample value control characterized by bringing the speed close to a target value,
It is good.

[Invention C2]
The present invention relates to a vibration control device that detects the position and speed of the mass of a controlled vibrating body and controls a vibration operation actuator to operate the position and speed of the mass of the controlled vibrating body, wherein the controlled vibration The body includes a first support body that is movably supported by a fixed support body, and a second support body that is supported by the first support body in a freely oscillating manner, and the vibration control device operates at an operation start time. Control signal X (t ₀ + t) from the values of the position x _in and velocity v _in + v ₀ of the second support, the position X (t ₀ ) and velocity V (t ₀ ) of the first support detected in ') (Formula 32) is created, and the vibration operating actuator changes the displacement amount of the first support to the control signal value during t' = 0 to 2π, so that the second support position x _in the velocity v _in + v ₀ is varied at the position x _en + 2πv ₀ and velocity v _en + v ₀ after the natural period of a single vibrator consisting of the second support member, the Two trajectories of the support _{x 1 (t 0 + t '} ) or as a vibration control apparatus shown in invention C1, characterized in that controlling the feed forward control or sample values such that (Equation 31).

(Formula 31)

(Formula 32)
However, X _p (t ₀ + t ′) is a dimensionless function in which the natural period of the single oscillator made of the second support is 2π and the mass of the second support is the representative mass, and t ′ It holds in the range of 0 to 2π. In the natural number p, ω ₊ = p + 1/2 and ω ₋ = 1/2, and α _p is an arbitrary real number satisfying Equation 33. In addition, v ₀ is an arbitrary constant that is the velocity of the inertial system.

[Invention C3]
The present invention relates to a vibration control device that detects the position and speed of the mass of a controlled vibrating body and controls a vibration operation actuator to operate the position and speed of the mass of the controlled vibrating body, wherein the controlled vibration The body is composed of a second support body supported by a fixed first support body so as to vibrate freely, and the position x _in and speed v of the second support body detected at the operation start time by the vibration control device. _A control signal F _I (t ₀ + t ′) (formula 38) is created from the value of _in + v ₀ , and the vibration operation actuator applies an external force applied to the first support during t ′ = 0 to 2π. By changing to the control signal value, the position x _in and velocity v _in + v ₀ of the second support are changed to the position x _en + 2πv ₀ and velocity v after the natural period of the single vibrator made of the second support. _en + v ₀ to changing, the second support member orbits y ₁ of (t ₀ + t ') is also a feed forward control so that (equation 40) Ku may be a vibration control apparatus shown in invention C1 which is characterized in that the control sample value.

(Formula 40)

(Formula 38)
Where F _I (t ₀ + t ′) is a dimensionless function in which the natural period of the single oscillator composed of the second support is 2π and the mass of the second support is the representative mass, and t ′ It holds in the range of 0 to 2π. In the natural number p, ω ₊ = p + 1/2 and ω ₋ = 1/2, and α _p is an arbitrary real number satisfying Equation 33. Furthermore, v ₀ is an arbitrary constant that is the velocity of the inertial system, and X (t ₀ ) and V (t ₀ ) are parameters of an arbitrary constant.

[Invention C4]
The present invention relates to a vibration control device that detects the position and speed of the mass of a controlled vibrating body and controls a vibration operation actuator to operate the position and speed of the mass of the controlled vibrating body, wherein the controlled vibration The body is composed of a first support that is supported by a fixed support so as to vibrate and a second support that is supported by the first support so as to vibrate, and the vibration control device operates at an operation start time. Control signal F ′ _IIp (t ₀ ) from the values of the second support position x _in , the speed v _in + v ₀ , the first support position X (t ₀ ), and the speed V (t ₀ ) detected in + t ′) (Formula 55) is created, and the second operation is performed by changing the external force applied to the first support by the vibration operation actuator to the control signal value during t ′ = 0 to 2π. change of the position x _in the velocity v _in + v ₀ position after the natural period of a single vibrator consisting of the second support member x _en + 2πv ₀ and velocity v _en + v ₀ of the body It may be vibration control apparatus shown in invention C1, characterized in that controlling the feed forward control or sample values so that the trajectory of the second support becomes _{x 1p (t 0 + t '} ) ( Equation 24) .

(Formula 24)

(Formula 55)
Where F ′ _IIp (t ₀ + t ′) is a dimensionless function in which the natural period of the single oscillator composed of the second support is 2π and the mass of the second support is the representative mass, and t It holds in the range of '= 0 to 2π. In p is a natural _{number, ω + = p + 1/} 2, ω - = 1/2, K = (γ + 1) (2p + 1) 2 / {3 (2p + 3) in the (2p-1)) Yes, γ and K 'are arbitrary real numbers. v ₀ is an arbitrary constant that is the velocity of the inertial system.

[Invention C5]
The present invention relates to a vibration control device that detects the position and speed of the mass of a controlled vibrating body and controls a vibration operation actuator to operate the position and speed of the mass of the controlled vibrating body, wherein the controlled vibration The body is composed of a second support that is supported by the fixed support so as to freely vibrate, and the position x _in and speed v _in + v _{0 of} the second support detected by the vibration control device at the operation start time. A control signal F ′ _III (t ₀ + t ′) (formula 63) is created from the value of the control signal, and an external force applied to the second support by the vibration operation actuator between t ′ = 0 and 2π is generated as the control signal. By changing the value to the value, the position x _in and the speed v _in + v ₀ of the second support are changed to the position x after the natural period when the spring constant of the single oscillator made of the second support is k ′ = 1. _en + 2πv ₀ and velocity v _en + v ₀ , and the feed forward so that the trajectory of the second support becomes x ₁ (t ₀ + t ′) (Equation 31). The vibration control device shown in the invention C1 may be configured to perform the code control or the sample value control.

(Formula 63)
However, F ′ _III (t ₀ + t ′) is a single oscillator composed of the second support, and the natural period when the spring constant k ′ = 1 is 2π, and the mass of the second support is the representative mass. Is a dimensionless function and holds in the range t '= 0 to 2π. In the natural number p, ω ₊ = p + 1/2 and ω ₋ = 1/2, and α _p is an arbitrary real number satisfying Equation 33. v ₀ is an arbitrary constant that is the velocity of the inertial system, and X (t ₀ ) and V (t ₀ ) are parameters of an arbitrary constant.

[Invention C6]
The present invention relates to a trajectory control device that detects the position and speed of the mass of a controlled moving body and controls a vibration operation actuator to control the position and speed of the mass of the controlled moving body. The body is composed of a second support that is movably supported by a fixed support, and the position x _in and speed v _in + v _{0 of} the second support detected by the trajectory control device at the operation start time. A control signal F _IV (t ₀ + t ′) (formula 66) is created from the value of the control signal value, and the external force applied to the second support by the vibration operating actuator during t ′ = 0 to 2π is the control signal value. To change the position x _in and the velocity v _in + v ₀ of the second support to a position x _en + 2πv ₀ and a velocity v _en + v ₀ after a certain period, and the trajectory of the second support Feedforward control or sample value control so that x ₁ (t ₀ + t ') (Equation 31) The trajectory control device indicated by M1 may be used.

(Formula 66)
However, F _IV (t ₀ + t ′) is a dimensionless function in which the natural period of the single oscillator composed of the second support is 2π and the mass of the second support is the representative mass, and t ′ It holds in the range of 0 to 2π. In the natural number p, ω ₊ = p + 1/2 and ω ₋ = 1/2, and α _p is an arbitrary real number satisfying Equation 33. v ₀ is an arbitrary constant that is the velocity of the inertial system, and X (t ₀ ) and V (t ₀ ) are parameters of an arbitrary constant.

[Invention D12]
The present invention is a track control device according to any one of the inventions D3 to D5 for controlling a track of a transported object in a crane,
The first support is a wire suspension of the crane;
The second support is the transported object supported by the wire hanging part via a wire,
The target function is a target function of acceleration due to a forced displacement in the horizontal direction given to the wire suspension part,
The control means performs the feedforward control of the transported object by giving the horizontal displacement to the wire suspension part from the reference time to the elapse of the natural period based on the target function. Do,
A trajectory control device may be used.

[Invention D13]
The present invention is a trajectory control device according to any one of the inventions D3 to D5 for controlling the 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 beam,
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 from the reference time to the elapse of the natural period based on the target function.
A trajectory control device may be used.

[Invention D14]
The present invention is the trajectory control device according to the invention D6 or D7 for controlling the trajectory of the light source for semiconductor exposure provided in the semiconductor exposure apparatus mounted on the 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 placed 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 between the reference time and the elapse of the natural period based on the target function. Performing the feedforward control of the light source for the horizontal direction,
A trajectory control device may be used.

[Invention D15]
The present invention is a track control device according to any one of the inventions D3 to D5 for controlling the track of a high-voltage power transmission line attached to an elevated tower,
The first support is an insulator that connects the elevated tower and the high-voltage power 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 giving the horizontal forced displacement to the insulator from the reference time to the elapse of the natural period based on the target function.
A trajectory control device may be used.

[Invention D16]
The present invention is the track control device according to the invention D6 or D7 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 an external force in a horizontal direction perpendicular to the high-voltage transmission line applied to the high-voltage transmission line,
The control means performs the feedforward control of the high-voltage power transmission line by applying an external force in the horizontal direction to the high-voltage power transmission line from the reference time to the elapse of the natural period based on the target function. ,
A trajectory control device may be used.

[Invention D17]
The present invention is a power generation device for converting vibration energy into electrical energy, comprising the orbit control device of the invention D7,
The first support integrated with the conductor, the magnetic field generating means attached around the first support, the magnetic field control device capable of controlling the magnetic field of the magnetic field generating means, and the first at the reference time Two reference bodies, the reference information acquisition means capable of acquiring the position and speed of the first support body in the vibration direction, 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 a virtual or real current flowing in one direction of the conductor, which vibrates integrally with the first support,
Based on the position and speed of the second support and the first support in the vibration direction, a generalized external force function F _IIp (determined to reduce the position and speed of the second support that vibrates is reduced. t ₀ + t '),
By controlling the magnetic field of the magnetic field generating means to be equal,
Suppress vibrations of the second support, and
The current can be transmitted to the conductor by generating or increasing the current.
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.

[Invention D18]
The present invention is the wind power generator according to the invention D17 for converting 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 an insulator for hanging the conductive wire attached to the elevated tower,
The second support and the conductor are the conductive wires 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 instrument capable of measuring the position and speed of the conductive wire and the insulator,
The power transmission means is a transformer attached to an end of the conductive wire;
By suspending the conductive wire between a plurality of the elevated towers,
It is good also as a wind power generator which utilizes the wind force applied to the said conductive wire for electric power generation via the vibration of a high voltage power transmission line.

[Invention D19]
The present invention is the trajectory control device according to any one of the inventions D3 to D5 for suppressing vibration of an arm tip portion in a robot arm, wherein the arm tip portion serving as the second support and the robot arm The cantilever is the controlled body, the base of the robot arm is 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 moved. A vibration suppressing device for a robot arm tip may be used, wherein the drive mechanism is the vibration operation actuator.

[Invention D20]
The present invention is the trajectory control device according to any one of the inventions D3 to D5 for controlling vibration in a collision machine, wherein the vibration is a mold that is the second support and a spring that is connected to the mold. The 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 drive mechanism for moving the drive unit may be the vibration operation actuator, and may be a mold vibration control device for a collision machine.

[Invention D21]
The present invention is the trajectory control device according to any one of the inventions D3 to D5 for preventing chattering in a DC relay, the vibration comprising a moving electrode as the second support and a spring connected to the moving electrode. The body is the controlled body, the cam follower connected to the base of the spring is the first support body, the target function is a target function of forced displacement in the displacement direction applied to the cam follower, and a movable cam that moves the cam follower is provided. It is good also as a chattering prevention apparatus in DC relay characterized by setting it as the said vibration operation actuator.

[Invention D22]
The present invention is the trajectory control device according to any one of the inventions D3 to D5 having a fail-safe function of a driving device in an automatic door, wherein the door is a second support body and a spring connected to the door. The vibrating body is the controlled body, the driving body connected to the base of the spring is the first support body, the target function is a target function of a forced displacement in the horizontal direction applied to the driving body, and the driving body It is good also as a fail safe mechanism of the drive device in the automatic door characterized by making the motor which moves the said vibration operation actuator into.

[Invention D23]
The present invention is the trajectory control device according to any one of the inventions D3 to D5 for suppressing sloshing of the liquid in the container, wherein the liquid is the controlled body, and the container is the first support body. The target function is a target function of acceleration caused by a horizontal forced displacement applied to the container, and the moving mechanism for moving the container is the vibration operation actuator. Also good.

[Invention D24]
This invention is a track control apparatus as described in any one of invention D3-D5 which suppresses the vibration of the building built on the seismic isolation bearing body, Comprising: The building which is a 2nd support body The cantilever is the controlled body, the seismic isolation bearing on which the building is mounted is the first support, and the target function is a target function of a horizontal forced displacement given to the seismic isolation bearing, It is good also as a vibration suppression apparatus of the building characterized by making the actuator which moves the said seismic isolation bearing body vicinity of the said building into the said vibration operation actuator.

[Invention D25]
The present invention relates to a trajectory control device according to any one of the inventions D3 to D5 for vibrating or damping a display object that is the mass of a vibrator, the display device using a vibrator being a second support. The controlled body, the connecting device at the base of the vibrator is a first support, the target function is a target function of acceleration caused by a horizontal forced displacement applied to the connecting device, and an actuator that moves the connecting device A display device using a vibrator may be used as the vibration operation actuator.

[Invention D26]
The present invention may be a cam curve design method characterized by defining a curve using the forced displacement function X (t ₀ + t ′) described in the invention D4 or D5.

[Invention D27]
The present invention is the cam mechanism device according to any one of the inventions D3 to D5 for suppressing vibration of a follower vibrator connected to a cam follower, wherein the follower vibrator including a second support is As a controlled body, the cam follower on which the building is placed is a first support, the target function is a target function of forced displacement in a displacement direction given to the cam follower, and a cam attached to a motor for moving the cam follower and the cam It is good also as a cam mechanism apparatus characterized by using the connected insulator as a vibration operation actuator.

[Invention D28]
The present invention is the track control device according to any one of the inventions D3 to D5 for suppressing vibration of a car body of a car or a train that is vibrated due to a displacement of a road surface or a track, and is an up / down or left / right of an axle or a carriage. An actuator is mounted in the direction, a spring is then mounted via a lower seat, and then a vehicle body is mounted. The vibrating body including the vehicle body and the spring as a second support is the controlled body, The lower seat is a first support, and the target function is a target function of vertical or horizontal forced displacement given to the lower seat, and the sum of the displacement amount of the actuator and the displacement amount of the road surface or track is The suspension may be an active suspension of a car body or a train body.

[Invention D29]
The present invention relates to the trajectory control device according to invention D8 or invention D9, wherein in the valve mechanism of the engine, the surging of the valve spring that receives forced displacement via the tappet by a cam attached to the engine wall is provided. The vibration of the center of gravity of the valve spring itself, which is a two-supported body, is the controlled body, the engine wall is the fixed support A, and the target function is a 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 vibration operation actuator, and the vibration operation actuator applies an external force to the center of gravity of the valve spring, thereby suppressing the vibration of the center of gravity of the valve spring. Further, a valve jump prevention device in a valve mechanism of an engine, which is characterized by preventing valve jump generated by vibration of the center of gravity of the engine, may be used.

[Invention D30]
The present invention relates to the trajectory control device according to the invention D8 or D9, which suppresses surging of a brush holding spring that is subjected to forced displacement via an electric brush by a commutator attached to a motor outer wall in a brushed DC motor. , 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 A, and the target function is a vibration direction applied to the center of gravity of the presser spring itself. A device for applying an external force to the center of gravity of the brush presser spring as a target function of external force is the vibration operation actuator, and by applying an external force to the center of gravity of the brush presser spring by the vibration operation actuator, With brush that suppresses vibration and prevents brush jump caused by vibration of the center of gravity of the brush presser spring It may be a brush dance prevention device in the DC motor.

[Invention D31]
The present invention is described in Invention D8 or D9, which suppresses surging of a restoring spring that receives a forced displacement through a sliding material by a trolley wire in a panda graph attached to a vehicle body wall used in an electric railway overhead train line system. The trajectory control device of the present invention, wherein the vibration of the center of gravity of the restoration spring itself as the second support is the controlled body, the vehicle body wall is the fixed support A, and the target function is that of the restoration spring itself. A device for applying an external force to the center of gravity of the restoring spring as the target function of an external force in the vibration direction applied to the center of gravity is the vibration operating actuator, and the external force is applied to the center of gravity of the restoring spring by the vibration operating actuator. The electric railway overhead train line system is characterized in that the vibration of the center of gravity of the rail is suppressed and the separation of the sliding material caused by the vibration of the center of gravity of the restoring spring is prevented. It is also possible to use a panda graph separation prevention device.

[Invention D32]
The present invention is the vibration control device according to any one of the inventions D29 to D31 for suppressing surging of a spring, magnetizing the vicinity of the center of gravity of the spring including a ferromagnetic material, and surrounding the center of gravity of the spring By installing a coil in the spring, an energy harvesting device in spring surging may be used, in which vibration energy of the spring is converted into electric energy by an induced electromotive force generated by the spring surging.

[Invention D33]
The present invention is the vibration control device according to any one of the inventions D29 to D31 for suppressing surging of a spring, magnetizing the vicinity of the center of gravity of the spring including a ferromagnetic material, and surrounding the center of gravity of the spring The degree of residual magnetization in the vicinity of the center of gravity of the spring is estimated based on the induced electromotive force generated by surging of the spring, and the degree of fatigue of the spring is inspected. A spring fatigue level inspection device may be used.

[Invention D34]
The invention provides a spring for suppressing surging according to invention D30 or invention D31, wherein the natural period of the surging vibration of the spring is shorter than the shortest time of passing one commutator piece or one hanger interval in use. It may be a spring design method characterized by shortening.

[Invention D35]
The present invention is the orbit control device according to invention D8 or D9 for preventing chattering of a multi-stage rolling roll attached to a frame in a multi-stage rolling apparatus so as to vibrate freely, and the mode of the multi-stage rolling roll as the second support. A vibrating body having a mode rigidity composed of a mass and a spring connected to 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 A. The target function is a target function of an external force in a vibration direction applied to the work roll, a device that applies an external force to the shaft of the multi-stage rolling roll is the vibration operation actuator, and the mode mass of the multi-stage rolling roll is determined by the vibration operation actuator. A multi-stage pressure characterized by suppressing vibration of the multi-stage rolling roll by applying a mode external force to It is good also as a chattering prevention apparatus in a rolling device.

[Invention D36]
The present invention is the trajectory control device according to the invention D8 or D9 for preventing chatter vibrations of a work (shank) attached to a chuck in a machining removal apparatus, wherein the mode of the work (shank) is the second support. The vibrating body having the mass and the mode rigidity of the workpiece (shank) is the controlled body, the chuck of the processing removal apparatus is the fixed support A, and the target function is a target of the external force in the vibration direction applied to the workpiece. As a function, a device for applying an external force to the work (shank) is the vibration operation actuator, and by applying a mode external force to the mode mass of the work (shank) by the vibration operation actuator, the vibration of the work (shank) is reduced. It is good also as a chatter vibration prevention apparatus in the said process removal apparatus characterized by suppressing.

[Invention D37]
The present invention relates to the trajectory control device according to the invention D8 or D9 for preventing vibration of a column in a windmill attached to a base, from the mode mass of the column that is the second support and the mode rigidity of the column. The vibration body to be controlled is the controlled body, the base of the windmill is the fixed support A, the target function of the external force in the vibration direction applied to the mode mass, and the wind external force received by the blades of the windmill connected to the column The vibration operation actuator is used, and by controlling the phase of rotation of the blades of the windmill, the mode mass of the column is given a mode external force due to the external force of the wind, thereby suppressing the vibration of the column. It is good also as a vibration preventing device in the windmill.

[Invention D38]
The present invention provides the orbit control device according to the invention D8 or D9, which prevents the swinging 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. The controlled body, the center of gravity of the floating body is the solid support A, the target function is a target function of external force in the rotational direction around the center of gravity applied to the floating body, and a windmill that is a part of the offshore wind turbine generator The external force of the wind received by the blades is used as the vibration 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. It is good also as a vibration suppression apparatus in the said offshore wind power generator characterized by suppressing the shake by rotation.

[Invention D39]
The present invention is a power generation device using the vibration suppressing device according to the invention D38 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 By halving the average frequency of the wave, the vibration energy in the heave direction of the floating body generated by the vertical motion of the wave on the ocean is changed to vibration energy around the pitching of the floating body by parametric resonance, 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 the above-mentioned.

[Invention D40]
The present invention provides the track control device according to the invention D10 or D11 for controlling the valve track in the engine by electromagnetic drive, wherein the valve that is the second support is the controlled body, and an external force is applied to the engine valve. By using the vibration actuator as the electromagnetic actuator that provides the control signal, an external force may be applied to the valve by the vibration actuator to control the orbit of the valve.

[Invention D41]
The present invention
The control means includes
In the case where the real vibrator included in the controlled body is different from the virtual vibrator corresponding to the real vibrator of the three-body vibration system including the controlled body as a part thereof, the virtual vibrator Forced displacement of generalized coordinates given to at least a part of the controlled object during the natural period of the virtual oscillator so that the movement of the real oscillator coincides with the movement of the virtual oscillator during the natural period Or, based on the modified target function by adding correction to the target function of generalized external force,
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 body from the reference time to the elapse of the natural period.
The trajectory control device according to any one of the inventions D3 to D9 and D12 to D39 may be used.

[Invention D42]
In the present invention, the control means includes the second support reference generalized coordinates and 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 are determined based on free motion of the three-body vibration system during the natural period determined from the natural time from the reference time. It is possible to derive generalized coordinates and generalized speed of the first support that are generalized coordinates and generalized speed of the first support after the period,
Rather than the difference between the second support reference generalized coordinate and the first support reference generalized coordinate, the difference between the second support target generalized coordinate and the first support arrival generalized coordinate is zero. The second support target generalized coordinates and the second support target generalized speed and the first support target generalized speed and the first support arrival generalized speed are both close to the same speed to reduce vibration energy. 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, Suppresses vibration energy of two supports,
It is good also as a track control device given in any 1 of invention D3-D9, D12-D39, and D41.

[Invention D43]
The present invention is the trajectory control device according to any one of the inventions D1 to D42,
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,
Wherein if the target function is said generalized force in accordance trajectory manipulation functions corrected so as to cancel the force apparent by the acceleration generated in the reference object to be derived based on the acceleration information performs feedback control by giving the generalized external force, so that if the target function is a forced displacement of the generalized coordinate, cancel the deviation of the trajectory of the second support member caused by the force of the apparent A trajectory control apparatus that performs the feedback control by giving a forced displacement amount of the generalized coordinates according to the corrected trajectory operation function may be used.

  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 (the mass of the small oscillator 1), reference numeral 2 denotes a spring of the second support (the spring of the small oscillator 1), and reference numeral 3 denotes a first support (the mass of the large oscillator). ), 4 is a spring of the first support (large oscillator spring), 5 is a third support (mass of the small oscillator 2), and 6 is a spring of 3 supports (the 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 Disk, code 24 is position / speed information calculator, code 25 is Reference numeral 26 is a semiconductor exposure apparatus, reference numeral 27 is a light source, reference numeral 28 is a lens, reference numeral 29 is a reticle, reference numeral 30 is a wafer stage, reference numeral 31 is an image sensor, reference numeral 32 is a vibration isolator, reference numeral 33 is a controller, reference numeral 34 is a moving mechanism (club trolley), 35 is a rail, 36 is a wire, 37 is a carrying object, 38 is a high-rise building, 39 is a controller, 40 is a seismic isolation bearing, 41 is a rod, Reference numeral 42 is a hydraulic actuator, reference numeral 43 is a base, reference numeral 44 is a liquid level sensor, reference numeral 45 is a crude oil tank, reference numeral 46 is a steel tower, reference numeral 47 is a support, reference numeral 48 is an insulator, reference numeral 49 is a transmission line, reference numeral 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 denotes a mounting base, reference numeral 60 denotes a coil, reference numeral 61 denotes a mounting base, reference numeral 62 denotes a power source, reference numeral 63 denotes a controller, reference numeral 64 denotes a spring, reference numeral 65 denotes a case, and reference numeral 66 denotes a single-axis 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 an electrode, reference numeral 72 is an electrode, reference numeral 73 is a door, reference numeral 74 is a wall, reference numeral 75 is a mounting portion, reference numeral 76 is Moving mechanism (trolley), reference numeral 77 is rail, reference numeral 78 is workpiece, reference numeral 79 is hammer, reference numeral 80 is support base, reference numeral 81 is frame, reference numeral 82 is rod, reference numeral 83 is controller, reference numeral 84 is power supply, Reference numeral 85 is a case, reference numeral 86 is a signboard, reference numeral 87 is a string, reference numeral 88 is a mounting bracket, reference numeral 89 is an elastic plate, reference numeral 90 is a piezoelectric element, reference numeral 91 is a support base, reference numeral 92 is a power supply, reference numeral 93 is a controller Yo , A reference numeral 94 is a mounting magnet, a reference numeral 95 is a solar cell, a reference numeral 96 is an elastic beam, a reference numeral 97 is a fixed part, a reference numeral 98 is a container, and a reference numeral 99 is a pendulum mass equivalent to the liquid mass in the container (virtual ), 100 is a wire with an equivalent pendulum length (virtual), 101 is a liquid, 102 is a carriage, 103 is a level gauge, 104 is an installation table, 105 is a single-axis rail, 106 is a backup roll , 107 is an intermediate roll, 108 is a work roll, 109 is a material to be rolled, 110 is a shaft, 111 is a bearing, 112 is a coil, 112 is a plunger, 113 is a plunger, 114 is a power supply, 115 is removed Machining device, 116 is a chuck, 117 is a shank, 118 is a tool, 118 is a work, 120 is a support, 121 is a nacelle, 1 Reference numeral 2 is a windmill blade, reference numeral 123 is wind, reference numeral 124 is an axis, 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, reference numeral 129 is a coil, reference numeral 130 is an iron core, reference numeral 131 Is a plunger, 132 is a power supply, 133 is a controller, 134 is a spring, 135 is a conductor, 136 is a position and speed sensor, 137 is a magnetic and position and speed sensor, 138 is an external force receiver, Reference numeral 139 is an external force from the outside, reference numeral 140 is a blade pitch rotation device, reference numeral 141 is a float, reference numeral 142 is an ocean, reference numeral 143 is an acceleration sensor, reference numeral 144 is a vehicle body, reference numeral 145 is an actuator controller, and reference numeral 146 is an actuator. Suspension 147 is a suspension spring, 148 is a road surface, Issue 149 wheel, reference numeral 150 is a wheel at the reference time, reference numeral 151 is a traveling direction, reference numeral 152 is a permanent magnet, reference numeral 153 is a Stator.

  The present invention can be used in the field of control devices that control the trajectory of a controlled body or control or suppress vibration.

Claims (15)

A trajectory control device for controlling a trajectory of at least the second support in a controlled body provided with at least a second support,
A reference that can derive a second support reference generalized coordinate and a 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. Reference information acquisition means for acquiring information;
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 the natural period 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, based on the reference information Generalization at the reference time of the first support derived or virtually determined based on the reference information, the second support reference generalized coordinates and the second support reference generalized speed derived First support reference generalized coordinates and first support, which are coordinates and generalized speed A reference generalized speed, a second support target generalized coordinate and a second support target generalized speed, which are a generalized coordinate and a generalized speed of the second support at a time after the natural period from the reference time; Is determined based on the free motion of the three-body vibration system during the natural period determined from the above, based on the forced displacement of generalized coordinates given to the controlled body during the natural period or the target function of the generalized external force ,
From the reference time to the elapse of the natural period, the generalized coordinate and the generalized velocity of the second support are obtained by applying a generalized coordinate forced displacement or generalized external force to at least a part of the controlled body. Control means for feedforward control;
A trajectory control device comprising: The reference information acquisition unit repeatedly acquires the reference information for each natural period, after the elapse of the natural period from the reference time as a new reference time,
The control means is configured such that the generalized coordinates and generalized speed of the second support after the elapse of the natural period from the reference time become the second support target generalized coordinates and the second support target generalized speed. The trajectory control device according to claim 1, wherein the feedforward control is performed so as to approach, and the feedforward control is repeatedly performed with a new reference time after the elapse of the natural period from the reference time. The controlled body includes the first support body that is movable, and the second support body that is supported by the first support body so as to freely vibrate.
The reference information acquisition means includes the second support reference generalized coordinates, the second support reference generalized speed, the first support reference generalized coordinates, the first support reference generalized speed, Obtaining the reference information from which
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 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 forced displacement of generalized coordinates given to the first support during the natural period, which is determined based on the free motion of the three-body vibration system determined from
The control means performs the feedforward control by giving a forced displacement of the generalized coordinates to the first support during the period from the reference time to the elapse of the natural period based on the target function.
The trajectory control device according to claim 1 or 2. 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 coordinate forced displacement function X (t ₀ + t) expressed by the following equation 32a, where the generalized coordinate of the second support in the state is the origin of the generalized coordinate of the second support. ')
The trajectory control device according to claim 3.

Where ω _t is the natural angular frequency of a single oscillator comprising the second support,
Of the two natural angular frequencies of the two-body coupled vibration system, ω ₊ = (p + 1/2) ω _{t for} the large natural angular frequency, and ω ₋ = ω _t / 2, p for the small natural angular frequency. A natural number.
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 (t ₀ ), the first support reference The generalized speed is V (t ₀ ), the second support target generalized coordinate is x _en , and the second support target generalized speed is v _en .
Equation 32a is a dimensionless function in which the natural period of the second support is 2π as a representative time, the generalized mass of the second support is a representative mass, and t ′ = 0 to 2π. It holds in the range. Α _p is an arbitrary real number satisfying Equation 33.
The control means is means for moving the generalized coordinates of the second support by d when both the first support and the second support are stationary in a stationary coordinate system, One support standard generalized coordinate is -d / 2,
Set the second support target generalization speed to 0,
Setting the second support target generalized coordinate to d / 2;
Performing the feedforward control based on the forced displacement function X (t ₀ + t ′),
The trajectory control device according to claim 4. The controlled body includes the fixed support, the first support supported by the fixed support in a freely vibrating manner, and the second support supported by the first support in a freely swingable manner. Including
The reference information acquisition means includes the second support reference generalized coordinates, the second support reference generalized speed, the first support reference generalized coordinates, and the first support reference generalized speed. , Obtain the reference information from which derivation is possible,
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 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 a generalized external force applied to the first support during the natural period, which is determined based on the free motion of the three-body vibration system determined from
The control means performs the feedforward control by applying the generalized external force to the first support during the period from the reference time to the elapse of the natural period based on the target function.
The trajectory control device according to claim 1 or 2. 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 ′) represented by the following formula 51, where the generalized coordinates of the second support in the state are the origin of the generalized coordinates of the second support Is,
The trajectory control device according to claim 6.

Where ω _t is the natural angular frequency of a single oscillator comprising the second support,
Of the two natural angular frequencies of the two-body coupled vibration system, ω ₊ = (p + 1/2) ω _{t for} the large natural angular frequency, and ω ₋ = ω _t / 2, p for the small natural angular frequency. A natural number.
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 (t ₀ ), the first support reference The generalized speed is V (t ₀ ), the second support target generalized coordinate is x _en , and the second support target generalized speed is v _en .
Equation 51 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 2π.
Further, γ is an arbitrary real number. The controlled body includes a fixed support A, and the second support that is supported by the fixed support A so as to be able to vibrate,
The reference information acquisition means acquires the reference information from which the second support reference generalized coordinates and the second support reference generalized speed can be derived,
The target function regards the second support and the first support defined as virtual as a dynamical system that is a part of the three-body vibration system, and the fixed support A as a whole of the three-body vibration system. The second support reference generalized coordinates and the second support reference generalized speed derived based on the reference information when placed in the generalized coordinates of the first support when in a balanced state; The three bodies determined from 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 a generalized external force applied to the second support during the natural period, which is determined based on a free motion of a vibration system;
The control means performs the feedforward control by applying the generalized external force to the second support based on the target function from the reference time to the elapse of the natural period.
The trajectory control device according to claim 1 or 2. The target function is such 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 _III (t ₀ + t ′) represented by the following equation 60, where the generalized coordinates of the second support in the state are the origin of the generalized coordinates of the second support Is,
The trajectory control device according to claim 8.

Where ω _t is the natural angular frequency of a single oscillator comprising the second support,
Of the two natural angular frequencies of the two-body coupled vibration system, ω ₊ = (p + 1/2) ω _{t for} the large natural angular frequency, and ω ₋ = ω _t / 2, p for the small natural angular frequency. A natural number.
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 (t ₀ ), the first support reference The generalized speed is V (t ₀ ), the second support target generalized coordinate is x _en , and the second support target generalized speed is v _en .
Equation 60 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 2π. Further, α _p is an arbitrary real number satisfying Expression 33.
The controlled body is the movable second support body,
The reference information acquisition means acquires the reference information from which the second support reference generalized coordinates and the second support reference generalized speed can be derived,
The target function includes 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, and the second Support reference generalized speed, the first support reference generalized coordinates and the first support reference generalized speed virtually determined in the three-body vibration system, the second support target generalized coordinates, A target function of a generalized external force applied to the second support during the natural period, which is determined based on the free motion of the three-body vibration system determined from the second support target generalized speed,
The control means performs the feedforward control by applying the generalized external force to the second support during the period from the reference time to the elapse of the natural period based on the target function.
The trajectory control device according to claim 1 or 2. The target function is such 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 _IV (t ₀ + t ′) expressed by the following formula 66, where the generalized coordinates of the second support in the state are the origin of the generalized coordinates of the second support Is,
The trajectory control device according to claim 10.

Where ω _t is the natural angular frequency of a single oscillator comprising the second support,
Of the two natural angular frequencies of the two-body coupled vibration system, ω ₊ = (p + 1/2) ω _{t for} the large natural angular frequency, and ω ₋ = ω _t / 2, p for the small natural angular frequency. A natural number.
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 (t ₀ ), the first support reference The generalized speed is V (t ₀ ), the second support target generalized coordinate is x _en , and the second support target generalized speed is v _en .
Equation 66 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 2π. Further, α _p is an arbitrary real number satisfying Expression 33.
The trajectory control device according to claim 7,
The first support integrated with the conductor, the magnetic field generating means attached around the first support, the magnetic field control device capable of controlling the magnetic field of the magnetic field generating means, and the first at the reference time Two reference bodies, the reference information acquisition means capable of acquiring the position and speed of the first support body in the vibration direction, 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 a virtual or real current flowing in one direction of the conductor, which vibrates integrally with the first support,
Based on the position and speed of the second support and the first support in the vibration direction, a generalized external force function F _IIp (determined to reduce the position and speed of the second support that vibrates is reduced. t ₀ + t '),
By controlling the magnetic field of the magnetic field generating means to be equal,
Suppress vibrations of the second support, and
The current can be transmitted to the conductor by generating or increasing the current.
A trajectory control device configured as a power generator that converts vibration energy of the second support into electrical energy flowing through the conductor. The control means includes
In the case where the real vibrator included in the controlled body is different from the virtual vibrator corresponding to the real vibrator of the three-body vibration system including the controlled body as a part thereof, the virtual vibrator Forced displacement of generalized coordinates given to at least a part of the controlled object during the natural period of the virtual oscillator so that the movement of the real oscillator coincides with the movement of the virtual oscillator during the natural period Or, based on the modified target function by adding correction to the target function of generalized external force,
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 body from the reference time to the elapse of the natural period.
The trajectory control device according to any one of claims 3 to 9, 12 . The control means includes the second support reference generalized coordinates and the second support reference generalized speed, the first support reference generalized coordinates and the first support reference generalized speed, and the second support reference generalized coordinates. Determined based on the free motion of the three-body vibration system between the natural periods determined from the support target generalized coordinates and the second support target generalized speed, and after the natural period from the reference time The first support reaching generalized coordinates and the first support reaching generalized speed, which are generalized coordinates and generalized speed of the first support, can be derived,
Rather than the difference between the second support reference generalized coordinate and the first support reference generalized coordinate, the difference between the second support target generalized coordinate and the first support arrival generalized coordinate is zero. The second support target generalized coordinates and the second support target generalized speed and the first support target generalized speed and the first support arrival generalized speed are both close to the same speed to reduce vibration energy. 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, Suppresses vibration energy of two supports,
The trajectory control device according to any one of claims 3 to 9, 12 , and 13 . The trajectory control device according to any one of claims 1 to 14,
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,
Wherein if the target function is said generalized force in accordance trajectory manipulation functions corrected so as to cancel the force apparent by the acceleration generated in the reference object to be derived based on the acceleration information performs feedback control by giving the generalized external force, so that if the target function is a forced displacement of the generalized coordinate, cancel the deviation of the trajectory of the second support member caused by the force of the apparent The feedback control is performed by giving a forced displacement amount of the generalized coordinates according to the corrected trajectory operation function.
Orbit control device.