JPH086492B2 - Control method of vibration suppression device - Google Patents

Description

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for controlling a vibration damping device for a structure, and more particularly, to prevent a structure from being shaken by an earthquake or wind and to provide a higher-rise structure. The present invention relates to a method of controlling a vibration damping device installed in a structure in order to enable the construction of the building and to realize comfortable habitability with less shaking.

(Prior art) Buildings, steel towers, and other structures generally have only small damping elements, and the structures resonate due to dynamic disturbances such as wind and earthquakes, and low-frequency vibrations easily occur. Has become.
Especially in middle and high-rise buildings, there is a problem of livability due to vibrations caused by winds, earthquakes and the like.

In order to suppress the vibration of the structure described above, there has been a method of adding a damping element to the structure to reduce the response magnification at the time of resonance.

In this method, a passive damping element is attached to the structure and the vibration energy of the structure is absorbed to reduce the vibration, and the structure is equipped with a control device for vibration suppression. There is an active vibration control device that positively reduces vibration of a structure by supplying damping energy from the outside.

The active type is a disadvantage of the passive type. (1) It is difficult to simultaneously suppress the vibration modes of a plurality of structures. (2) The damping effect is reduced when the characteristics of the structure change. (3) It is difficult to obtain a large vibration reduction effect. It is attracting attention in terms of improving things.

 A conventional active vibration control device is shown in FIG.

An additional mass 2 that can move linearly is installed on the upper part of the structure 1, and the additional mass 2 is moved by an actuator 3 fixed to the structure 1.

When an external force is applied to the structure 1, the vibration sensor 5 installed in the structure 1 detects the structure acceleration and inputs it to the controller z. The additional mass velocity detected by the sensor is also input to the controller z. In the controller z, the speed of the structure is determined by the integrator 1 / s from the acceleration of the structure, the deviation of the speed of the additional mass and the speed of the additional mass is obtained, this signal is amplified by the power amplifier a, and output as the actuator current, Exercise 2 That is, the actuator 3 moves the additional mass 2 in accordance with the amount of vibration of the structure 1 which is resonated by receiving an external force, and the reaction force of the additional mass 2 at this time cancels the external force of the structure 1 to cause vibration. Suppress.

Further, when vibration control is not being executed (when the vibration of the structure 1 is below a predetermined level), the additional mass may deviate from the neutral position due to the zero adjustment deviation of the actuator. The deviation from the neutral position of the additional mass 2 may reach the stroke end of the operation allowable range of the additional mass 2 immediately depending on the swing direction of the structure when the structure 1 starts to swing and moves the additional mass 2. Not able to exert sufficient vibration damping effect. Therefore, the support spring 4 is interposed between the additional mass 2 and the actuator 3, and the additional mass 2
Was trying to maintain a neutral position.

Alternatively, the displacement of the additional mass 2 is detected, and when the displacement is deviated from the neutral position, the actuator is controlled.

(Problems to be solved by the invention) However, according to the conventional example, when the additional mass is largely deviated from the neutral position, the additional mass is returned to the neutral position by the position control, and the reaction force when the additional mass moves There was a problem that the structure was vibrated.

On the other hand, if a spring is provided, the structure becomes complicated and it is necessary to increase the operating force of the actuator by the spring force.

The present invention has been made in view of the above problems of the conventional example,
An object of the present invention is to provide a control method for a vibration damping device that moves an additional mass to a neutral position without applying vibration to a structure.

(Means for Solving the Problems) In order to achieve the above object, the present invention has an additional mass movable in a vibration direction of a structure and a means for moving the additional mass, and the movement of the additional mass In the control method of the vibration damping device for suppressing the vibration of the structure by controlling the above, there is a control stop state in which the vibration damping device does not need to move the additional mass, and the additional mass deviates from the neutral position of the operating range. At this time, the hydraulic cylinder is controlled so that the additional mass is returned to the neutral position.

At that time, the variables related to the velocity of the additional mass, the displacement from the neutral position, and other vibrations of the structure are obtained, and various state variables are set to be the state variable vector indicating the state of the system in the multivariable control. A control input signal for controlling the supply flow rate to the hydraulic cylinder is calculated by an arithmetic expression composed of an inner product of the set optimum feedback vector and the state variable vector.

Then, the optimal feedback vector is expressed by the state equation and the output equation that describe the dynamic characteristics of the system,
The output variable of interest is selected from the state variables of the system, and the integral type evaluation function defined based on this output variable is set to be the minimum by the optimal control theory.

Therefore, by making the control input signal of the arithmetic expression the optimum input, the hydraulic cylinder has a characteristic that the supply flow rate to the hydraulic cylinder with respect to the control input signal has a linear approximation characteristic, and the hydraulic cylinder is returned so as to return the additional mass to the neutral position. It is designed to be controlled.

That is, the state variable vector , The optimal feedback vector In this case, if the control input signal is u, Given in. Also, the optimal feedback vector Is set to minimize the defined integral type evaluation function, Is given by the general formula of.

here Satisfy the Riccati matrix equation of

Is a weight matrix for the control input u, which prevents reaching an unrealizable solution such that the power of the input becomes infinite.

Is a weighting matrix for the state variables, and by increasing the weight corresponding to the state variable to be controlled with high precision, it is possible to design optimal feed vectors with different damping effects.

Is a matrix obtained from the characteristics of the structure and the mass of the additional mass, the spring constant, the damping constant, and the like.

(Operation) When the additional mass deviates from the neutral position of the operating range in a control stop state in which it is not necessary to move the additional mass, the displacement of the additional mass is detected and the additional mass is returned to the neutral position.
At this time, a signal is detected from the state variable detection means installed in the structure and the additional mass, and a control input that minimizes the evaluation function is obtained by the optimal regulator theory. The additional mass is moved to the neutral position while preventing the swaying of the structure.

(Example) An example of the present invention will be described with reference to the drawings.

FIG. 5 shows a side view of the vibration damping device installed above the structure, and FIG. 6 shows a plan view thereof.

A rectangular parallelepiped additional mass 2 is placed at the top of the structure 1.
Cylinders 6 are mounted on the peripheral surfaces of the additional masses 2, and one ends of rod rods 7 of the cylinders 6 are connected to a wall 8 standing on the structure 1 so as to surround the additional masses 2. A hydraulic unit 9 that supplies oil to the cylinder 6 is installed at the center of the additional mass 2. Wheel 10 is attached to the bottom of additional mass 2,
The additional mass 2 can freely move on a horizontal plane surrounded by the wall 8 depending on the way of supplying oil to the four cylinders. In addition, the horizontal plane surrounded by the wall 8 reduces the frictional force and makes the wheel 10 easy to move.

FIG. 2 shows a model diagram of a vibration damping device controlled by the method of the present invention.

An additional mass 2 which can be moved by a cylinder 6 is attached to the upper part of the structure 1. In FIG. 2, the additional mass 2 is moved by one cylinder for simplification. Further, in the actual device, the structure 1 and the additional mass 2 sway horizontally, but in the model diagram, they oscillate vertically.

The structure 1 and the additional mass 2 are provided with displacement detecting means 11 and 12 as state variable detecting means, and the structure 1 is used as a state quantity.
Displacement x ₁ and displacement x ₂ of the additional mass ₂ are detected. Displacement x ₁ , x ₂
Is set to 0 when the structure 1 and the additional mass 2 do not vibrate and are stationary at the neutral position, and the positive and negative ground is taken.

The signals from the displacement detecting means 11 and 12 are input to a controller z including a state variable setting unit w and a calculation unit y. In the state variable setting unit w, the relative displacement ▲ x ^′ ₂ ▼ (x ₂ −x ₁ ) of the structure 1 and the additional mass 2 from the displacements x ₁ and x ₂ of the structure and the additional mass 2.
And by passing x ₁ ▲ x ^' ₂ ▼ through the differentiator s,
Speed ₁ and the relative velocity of the structure ▲ _^'2 ▼ seek state variable. Further, the speed of the structure 1 can be directly obtained by providing the structure 1 with a speed detecting means or a speed signal generator.

These signals are input to the arithmetic unit y, the state variable vector x is the state quantities x ₁ of ^{_{(x 1 ▲ x '2 ▼}} 1 ▲' 2 ▼), ▲ x
Optimal field back vector determined in advance for ^′ ₂ ▼, ₁ , ▲ ^′ ₂ ▼ F ₁ , f ₂ , f ₃ and f ₄ are multiplied respectively and the respective values are added, and the control input u = f ₁ x ₁ + f ₂ ▲ x ^′ ₂ ▼ + f _{3 1} + f ₄ ▲
^′ ₂ ▼ is obtained.

A control input u output from the controller z is configured to energize a solenoid 15 that slides a spool 14 of the servo valve 13. Of the three ports provided on the hydraulic pressure supply side of the servo valve 13, the central port 16 communicates with the pump P (not shown), and the left and right ports 17 and 18 are the tank T respectively.
(Not shown). The two ports 19 and 20 provided in the servo valve 13 communicate with the chamber of the cylinder 6 respectively.

In the model diagram shown in FIG. 2, oil leakage from the seal portion of the cylinder 6 is taken into consideration, and a model of how oil flows out using the throttles R ₁ R ₂ and the tank is modeled. Further, in the model diagram, a spring (spring constant K2) is present between the structure and the additional mass, but this spring does not have sufficient elastic force to return the additional mass to the neutral position. .
That is, even when the structure is installed on a structure via a spring without providing a means for positively moving the additional mass, the additional mass moves due to the vibration of the structure by adjusting the spring constant. It is known to exert a damping effect (passive damping device). The above-mentioned spring (spring constant
K2) is equivalent to this spring, and by installing this spring, it is possible to promote the vibration damping action and reduce the size of the hydraulic cylinder in the system.

FIG. 1 shows a flowchart of the method of the present invention. The control input u is 0 in the control stop state in which there is no external vibration and it is not necessary to operate the additional mass 2. The hydraulic unit 9 is turned on so that hydraulic pressure can be supplied to the cylinder 6.
Next, load the relief valve and load the servo valve 13 with the pump Ps.
Connect standby and turn on. The state variable relating to the vibration of the structure 1 is detected by the state variable detecting means, read as a state variable vector x, and this signal is converted from analog to digital.

Optimal feedback vector stored in the controller z in advance in the state variable vector x Control input To get Digital-analog conversion of the control input is performed, the oil flowing through the servo valve 13 is controlled by the control input u, and the operation of the additional mass 2 is performed. Relative displacement of displacement x ₂ from the neutral position of additional mass 2 and displacement x ₁ of structure 1 ▲ x ^′ ₂ ▼
However, if it is larger than the value δ stored in advance, the above-mentioned flow is repeated, and if it is smaller than δ, the additional mass 2 is returned to the neutral position and the additional mass control is stopped. After that, when the structure 1 starts to sway, the additional mass 2 is near the neutral position, the additional mass 2 does not reach the stroke end of the operating range immediately, and sufficient vibration is suppressed even when the structure 1 starts to sway. It can exert its effect.

Further, as shown in FIG. 3, a concave portion 2a is formed in the lower portion of the additional mass 2.
The additional mass 2 can be fixed at the neutral position by providing the concave portion 2a with a fixing means formed so as to fit the hook 30 that is vertically expandable and contractable in the floor surface 1a of the structure 1 in the concave portion 2a. You can When the structure 1 vibrates, the vibration is detected, the hook 30 is removed from the recess 2a, and the additional mass 2 is movable. Expansion and contraction of the hook 30 is performed by using a solenoid, a spring, a motor, a hydraulic cylinder, or the like.

Further, the hook 30 may be provided on the bottom surface side of the additional mass 2 and the concave portion may be provided on the floor surface of the structure. Further, fixing means composed of hooks and recesses may be provided on the upper surface side of the additional mass.

When the additional mass 2 is deviated from the neutral position due to a disturbance or a zero adjustment deviation of the servo valve, when the additional mass 2 is controlled by the method of the present invention, the control input u is given according to the displacement x ₂ from the neutral position. Then, the additional mass 2 is moved toward the neutral position. When a reaction force is applied to the structure 1 by the operation of the additional mass 2, the state quantity related to the vibration of the structure 1 is obtained from the displacement detecting means 11 and 12, and the control input u considering this value is obtained.
Then, the additional mass 2 is operated.

That is, if the additional mass 2 is moved upward in FIG. 2 in order to return to the neutral position, the structure 1 also starts swaying upward. The swaying condition is detected by the displacement detecting means 11 and 12, and this signal is input to the controller z to calculate the control input u.

The control input u is energized to the solenoid 15 to slide the spool 14 of the servo valve 13 to the right in FIG. Spool 14
Is slid to the right, port 17 is closed, oil from pump P flows to port 16, port 20 and the lower cylinder chamber, pushing up the piston in cylinder 6, and oil in the upper cylinder chamber to port 19, It is led to the tank T via the port 18.

As a result, the rod 7 of the cylinder 6 slides and the additional mass 2
Is moved to the upper side, which is the same side so as to follow the movement of the structure 1 with a phase difference of approximately 90 degrees (Fig. 2 is a model diagram, so the rod 7 slides in the vertical direction). Exist).

When the structure 1 swings to the left, the sign of the control input u reverses, the spool 14 of the servo valve 13 slides reversely, and the moving direction of the additional mass 2 also reverses.

Therefore, a reaction force is generated by the operation of the additional mass 2 and the structure 1
When sway, the additional mass 2 is moved to the neutral position while damping the structure 1.

Then the optimal feedback vector The setting of will be described.

1. Differential equation of system External force is F, force acting between structure 1 and additional mass 2 is U, mass of structure 1 is M ₁ , damping constant of structure ₁ is C ₁ , spring constant of structure 1 Is K ₁ , the equation of motion of the structure is FU = M _{1 1} + C _{1 1} + K ₁ x ₁ (1).

Assuming that the mass of the additional mass is M ₂ , the equation of motion of the additional mass is U = M _{2 2} (2).

The pressure receiving area of the cylinder is A, and the pressure of each chamber of the cylinder is P ₁
P _2, the damping constant of the cylinder C _2, the spring constant of the cylinder K ₂
And then, outputs and frictional force of the cylinder and the control force considered _{zero, U = A (P 1 -P} 2) -C 2 (2 - 1) -K 2 (x 2 -x 1)
(3)

The continuous equation for a cylinder is that the flow rate from the servo valve to the cylinder is Q ₁ , the flow rate from the cylinder to the servo valve is Q ₂ , the flow rate from each cylinder chamber to the outside is Q ₃ ,
Q _4, when the flow rate from the cylinder chamber at the bottom of Figure 1 leaks to the upper cylinder chamber and _{Q 5, 1 V 1 / K} = Q 1 -A (2 - 1) -Q 3 -Q 5 (4) 2 _{V 2 / K = -Q 2 +} a (2 - 1) -Q 4 + Q becomes ₅ (5).

In the model considering the flow from the cylinder chamber, R ₁
Coefficient to the stop of the formula squeeze R ₂ is _{Q 3 = R 1 P 1 Q} 4 = R 1 P 2 Q 5 = R 2 (P 1 -P 2) and made (6).

 Next, consider the characteristics of the servo valve.

Servo valve rated current Ir, rated flow Qr, supply pressure
If Ps, then if i ≧ 0 If i <0 Becomes

2. Linearization of differential equations Here, equations (7) to (10) are linearized by the differential variation method, and a linear approximation model of the entire system is created.

If p1 = p2 = ps / 2, i = i0 (when i ≧ 0) and i = −i0 (when i <0) are set as the equilibrium points, equation (7),
(9) and the expressions (8) and (10) can be unified into Q1 = αi−βp1 Q2 = αi + βp2 (α and β are constants), and can be linearly approximated with respect to the servo valve.

Then, as the state deformation vector x and the control input u, And treat ΔF as a disturbance, Express with. Then the matrix Is a matrix of 4 rows and 4 columns and 4 rows and 1 example, and each element of the matrix is as follows.

A ₁₁ = 0 A ₁₂ = 0 A ₁₃ = 1 A ₁₄ = 0 A ₂₁ = 0 A ₂₂ = 0 A ₂₃ = 0 A ₂₄ = 1 A ₃₁ = -K ₁ / M ₁ A ₃₂ = K ₂ / M ₁ A ₃₃ = -C ₁ / M ₁ A ₃₄ = (1 / M ₁ ) {2A ² / (β + R ₁ + 2R ₂ ) + C ₂ } A ₄₁ = K ₁ / M ₁ A ₄₂ = -K ₂ (M ₁ + M ₂ ) / M ₁ M ₂ A ₄₃ = C ₁ / M ₁ A ₄₄ =-{(M ₁ + M ₂ ) / M ₁ M ₂ } {2A ² / (β + R ₁ + 2R ₂ ) + C ₂ } b _{11 = 0 b 21 = 0 b 31} = - (1 / M 1) {2Aα / (β + R 1 + 2R 2)} b 41 = {M 1 + M 2 / M 1 M 2} {2Aα / (β + R 1 + 2R 2)} Where the output vector y is Then, the output equation is as follows.

3. Optimal regulator design In the control system expressed by Eqs. (12) and (14), the evaluation function The control input u that minimizes is obtained. That is, an optimal regulator that minimizes equation (15) is designed. Control input u
Is a scalar quantity, the input weighting coefficient r is also a scalar quantity.

Weight matrix for state variables To Then, the evaluation function J is become. Here, by setting the weighting factor q corresponding to the state variable that is desired to be controlled with high accuracy, the control system can be freely designed from a large damping effect to a small damping effect.

The optimal input u ゜ is the optimal feedback vector Is represented by (u = Δi), A block diagram of the control system is shown in FIG.

Optimal feedback vector that minimizes J expressed in equation (15) Is the general formula Given in. However, Is a positive definite unique solution that satisfies the Riccati matrix equation

In the above embodiment, the state variable vector is the displacement x _{1 of} the structure ₁ and the relative displacement ▲ x ^′ of the additional mass 2 with respect to the structure 1.
₂ ▼, the speed _{1 of} the structure 1 and the relative speed ▲ ^′ ₂ ▼ of the structure 1 and the additional mass 2 are described, but other variables related to vibration and variables related to the control of the hydraulic cylinder are considered as state quantities. You may.

That is, the displacement of the structure 1 at the damping device mounting position
x _1, displacement x ₂ additional mass 2, the displacement x ₀ of the bottom or the ground structure 1, the relative displacement of the additional mass 2 with respect to the structure 1 ▲ x ^'
₂ ▼, the pressures p ₁ and p _{2 in} each chamber of the cylinder, and the displacement x ₃ of the spool 14 of the servo valve 13 may be used, and an element important for control may be taken out of these to represent the state variable vector. In this case, it is appropriate that the evaluation function J be as follows.

Considering the compressibility of oil, it is effective to add p ₁ p ₂ .

(Effect of the invention) As described above, the present invention is in a control stop state in which the vibration damping device does not need to operate the additional mass, and when the additional mass deviates from the neutral position, when returning the neutral position to the neutral position. ,
The situation in which the structure shakes is detected from the reaction force generated by the operation of the additional mass, and the additional mass is moved to the neutral position while damping the structure. At that time, by performing linear approximation control using a hydraulic actuator having a non-linear characteristic, it is possible to perform accurate control and to return the additional mass to the neutral position without vibrating the structure. is there.

[Brief description of drawings]

FIG. 1 is an explanatory view showing a flow chart of the method of the present invention,
FIG. 2 is a model diagram of a vibration damping device used in the present invention, FIG. 3 is an explanatory view of an example showing a fixing means of an additional mass of the vibration damping device used in the present invention, FIG. 4 is a block diagram of a vibration damping system, 5 is a side view of the vibration damping device of the present invention, FIG. 6 is a plan view of the vibration damping device,
FIG. 7 is a model diagram of a conventional vibration damping device. 1 ... Structure, 2 ... Additional mass 6 ... Cylinder 11, 12 ... Displacement detection means z ... Controller

Claims (1)

[Claims] Claim: What is claimed is: 1. A vibration damping system, comprising: an additional mass movable in a vibration direction of a structure, and means for moving the additional mass, and suppressing the vibration of the structure by controlling the motion of the additional mass. In the control method of the device, there is a control stop state in which the vibration damping device does not need to move to the additional mass, and when the additional mass deviates from the neutral position of the operating range, the speed of the additional mass, the displacement from the neutral position, etc. The state variable vector indicating the state of the system in multivariable control by setting various state variables by determining the variables related to the vibration of the structure, and from the inner product of the preset optimal feedback vector and the state variable vector A control input signal for controlling the supply flow rate to the hydraulic cylinder is calculated by the following equation, and the optimum feedback vector is a state equation describing the dynamic characteristics of the system. And the output equation, the output variable of interest is selected from the state variables of the system, and the integral type evaluation function defined based on this output variable is set to be the minimum by the optimal control theory. A method for controlling a vibration damping device, characterized in that an optimum input signal is used to control the hydraulic cylinder with this optimum input to return the additional mass to the neutral position.