JPH0765407B2 - Control method for damping 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, habitability due to vibration due to wind and earthquakes becomes a problem.

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.

This method attaches passive damping elements to the structure,
A passive vibration control device that reduces the vibration by absorbing the vibration energy of the structure and a control device for vibration control are attached to the structure, and the vibration control energy is supplied from the outside to positively increase the vibration of the structure. There is an active vibration control device for reducing vibration suppression.

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.

A linearly movable additional mass 2 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. A support spring 4 is present between the additional mass 2 and the actuator 3 to maintain the neutral position of the additional mass 2.

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 structure velocity is calculated from the structure acceleration by the integrator 1 / s, the deviation between this and the additional mass velocity is calculated, this signal is amplified by the power amplifier a and output as an actuator current, and the additional mass is output. 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.

(Problems to be solved by the invention) The operation stroke of the additional mass is almost determined by the size of the vibration damping device, but when the additional mass reaches the stroke end, a shock occurs, causing vibration to the structure contrary to the vibration damping. Will give. The damping device is designed to have a certain damping effect depending on the characteristics of the structure, etc., but in order to cope with large vibration to a certain extent, the stroke of the additional mass should be increased Therefore, there is a problem that the vibration damping device becomes large as a result.

The present invention has been made in view of the problems of the above-described conventional example, and a vibration damping device for reducing the size of the vibration damping device by changing the vibration damping effect of the vibration damping device from the size of the vibration of the structure and the position of the additional mass. The purpose is to provide a control method.

(Means for Solving the Problems) In order to achieve the above object, the present invention provides a vibration control device including an additional mass movable in a vibration direction of a structure and a means for moving the additional mass. The controller stores a plurality of optimum feedback vectors having different damping effects, which are obtained from the characteristics of the additional mass, and the displacement of the additional mass is determined based on the signals obtained from the displacement detection means and the operation direction detection means of the additional mass. In response to the,
The optimum feedback vector having different damping effect is selected, and the optimum feedback vector is selected by the controller, the displacement of the structure obtained from the state variable detection means, the displacement of the additional mass, and the state quantity of the state variable related to other vibrations. And a control input for moving the additional mass is obtained from the product of

In the controller, various variables related to vibration with the static state set to 0 are expressed as a state variable vector from the state variable detecting means, and the optimum feedback vector is Required by. Optimal feedback vector Is designed to minimize the quadratic evaluation function, Given in.

Satisfies the Riccati matrix equation of.

Is a weighting matrix of the control input u and prevents reaching an unrealizable solution in which 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) Since the present invention is configured as described above, when the structure vibrates, the optimum feedback vector optimum for damping at that time is based on the signals obtained from the displacement detecting means and the moving direction detecting means of the additional mass. And a signal based on the stationary state is detected from the state variable detecting means installed in the structure and the additional mass, and various variables related to vibration are used as state variables from this signal, and the optimum feedback vector is multiplied. The control input signal for moving the additional mass is obtained and output, and the output signal reciprocates the additional mass to absorb the vibration energy of the structure and reduce the vibration of the structure.

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

FIG. 6 shows a side view of the vibration damping device installed above the structure, and FIG. 7 shows a plan view thereof.

A rectangular parallelepiped additional mass 2 is installed on 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. Wheels 10 are attached to the bottom of the additional mass 2 and 4
The additional mass 2 can freely move on the horizontal plane surrounded by the wall 8 depending on the way of supplying oil from the cylinder of the book. In addition, the horizontal plane surrounded by the wall 8 reduces the frictional force and makes the wheel 10 easy to move.

FIG. 1 shows a model diagram of an embodiment 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. 1, the additional mass 2 is 1 for simplification.
It was made to move with the cylinder of the book. In addition, 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 11a and 11b and speed detecting means 12a and 12b as state variable detecting means, respectively, and the displacement x ₁ of the structure 1 as the state quantity and the additional mass 2 are provided.
Detecting the displacement x ₂ structure 1 speed ₁ speed ₂ additional masses 2. The displacements x ₁ and x ₂ have positive and negative values with 0 when the structure 1 and the additional mass 2 are stationary. Also
₁ and ₂ also take positive and negative values depending on the operating direction of the additional mass.

The signals from the displacement detecting means 11a, 11b and the speed detecting means 12a, 12b are input to the controller z, where the relative displacement ▲ x ^′ ₂ ▼ (x ₂ −x ₁ ) of the structure 1 and the additional mass 2 and , Relative velocity ▲ ^′ ₂ ▼.

Further, the operation direction of the additional mass 2 is detected by the sign of the command input to the servo valve. Then, enter the X _'2 of the signal vector selector y of vibration damper Z, from these signals, from among the eight best feedback vectors having different vibration damping effect which is stored in the controller z, additional Select the one according to the situation of the cell 2.

The selected optimal feedback vector is assigned to x ₁ , ▲ x ^′ ₂ ▼, ₁ , ▲ ^′ ₂ ▼. F ₁ , f ₂ , f ₃ and f ₄ are multiplied respectively and the respective values are added by an arithmetic unit, and the control input u = f ₁ x ₁ + f ₂ ▲ x ^' ₂ ▼ + f ₃
We get ₁ + f ₄ ▲ ^' ₂ ▼.

The control input u output from the controller z energizes the solenoid 15 that slides the 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 is a pump P (not shown).
The left and right ports 17 and 18 communicate with the tank T (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. 1, 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.

Assuming that the structure 1 starts to sway in the upward direction of FIG. 1 (the upward direction is the rightward direction in an actual device) under the influence of wind or an earthquake, the swaying condition is detected by the displacement detecting means 11a, 11b, the speed detecting means 12a, 1
2b, this signal is input to the controller z, and the control input u
Is calculated.

The control input u is supplied to the solenoid 15 to slide the spool 14 of the servo valve 13 to the right in FIG. When the spool 14 slides to the right, the port 17 is closed and the oil from the pump P flows to the ports 16, 20 and the lower cylinder chamber.
The piston in the cylinder 6 is pushed up, and the oil in the upper cylinder chamber is guided to the tank T via the ports 19 and 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 later than the movement of the structure 1 (the rod 7 slides in the vertical direction because FIG. 1 is a model diagram). It has become).

When the structure 1 swings to the left, the sign of the control input u is reversed, the spool 14 of the servo valve 13 slides in the opposite direction, and the additional mass 2
The moving direction of is also reversed. Therefore, the reaction force generated by moving the additional mass 2 applies a control force in the direction opposite to the external force to the structure to reduce the vibration of the structure 1.

Next, a method of selecting the optimum feedback vector f will be described.

Eight types of optimum feedback vectors A1 to A8 having different damping effects are stored in the controller z. Of these, A1 has the highest damping effect and decreases in the order of A2 ... A8, and A8 is the feedback vector with the smallest damping effect.

2 (A) (B) (C), when the optimum feedback vectors A1, A5, A7 used in the present embodiment are independently used in the vibration damping device, the structure displacement x ₁ , the additional mass displacement x ₂ , Structure speed
The relationship of ₁ is shown. As is clear from the graph, A1 has the largest displacement of the additional mass, and the largest damping effect.

FIG. 3 illustrates the optimum feedback vector selection table, in which the stationary position of the additional mass 2 is set to 0 and the additional mass is displaced, and both ends thereof correspond to the motion stroke ends.

The operating range of the operating stroke of the additional mass 2 is divided into 12 left and right as shown in FIG.
The optimum feedback vectors A1 to A8 are selected by detecting the position of the additional mass 2 and the moving direction of the additional mass 2. The operation direction of the additional mass 2 differs depending on whether the current of the control input u is positive or negative and the sliding direction of the rod 7 is reversed, but in FIG. 3, the additional mass 2 is left when the current i is positive. From the right to the right, and when the current i is negative, it operates from the right to the left.

That is, when the additional mass 2 moves, when the rod 7 moves from one stroke end to the center position (0), the optimum feedback vector A1 with a high vibration damping effect (the additional mass is easy to move) is selected and the center position is selected. When going from one stroke end to another stroke end, the optimum feedback vectors A2 to A7 with a small damping effect are selected gradually, and immediately before reaching the stroke end, the feedback vector A8 with a minimum damping effect is selected. ing. Further, as shown in FIG. 3 (B), it goes without saying that a feedback vector that makes all the feedback coefficients zero may be included in order to realize the braking function.

Then each 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,
Assuming that the mass of the structure 1 is M ₁ , the damping constant of the structure ₁ is C ₁ , and the spring constant of the 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)

If the mass of the additional mass is M ₂ , the equation of motion of the additional mass becomes 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 , Cylinder damping constant C ₂ , Cylinder spring constant K
_2, and the output and the 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: 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 to become ₅ (5).

In the model considering the flow from the cylinder chamber, R ₁ R ₂
When the coefficient of the diaphragm expressions of diaphragm _{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, rated differential pressure Δ
If Pr and supply pressure are Ps, then i ≧ 0 When i <0 Becomes

2. Linearization of differential equations (7) to (10) below the balance point _{(P 1 = P 10 P 2} = P 20 i = i 0)
Linearize near And treat ΔF as a disturbance, Express with. At this time, the matrices A and b have 4 rows and 4 columns, respectively.
The matrix has 4 columns and 1 row, 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)} output vector y, where To The output equation is defined 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 Q for state variables 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 ⁰ is the optimal feedback vector Is represented by (u ⁰ = Δi ⁰ ), 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 , the relative displacement x ₂ of the additional mass 2 with respect to the structure 1, the velocity x _{1 of} the structure ₁ , the relative velocity of the structure 1 and the additional mass 2. Although expressed by x ₂ , other variables related to vibration and variables related to control of the hydraulic cylinder may be considered as the state quantity.

That is, the displacement of the structure 1 at the damping device mounting position
x _1, displacement x ₂ additional mass 2, the structure 1 of the bottom or the ground displacement xo, structure relative displacement x ₂ additional mass 2 with respect to 1, the pressure p ₁ of the cylinder chambers, p _2, servo valve 13 It is also possible to take the element important for control out of this as the displacement x ₃ of the spool 14 and express 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 .

Fig. 5 (A) shows the case where the additional mass operation is controlled by using only the optimum feedback vector A1, and Fig. 5 (B) shows 8
A simulation based on an actual earthquake was performed for the case where the vibration control device was controlled using various types of optimal feedback vectors A1 to A8.

When a single optimal feedback vector is used for the same seismic input, the maximum stroke of additional mass displacement is
It becomes 11.9 cm, which is 9.7 cm when using eight types of optimal feedback vectors, and it is clear that the latter has a shorter maximum stroke for additional mass displacement. Also, it can be seen from the structural displacement that the damping effect of both is the same.

(Effect of the Invention) As described above, according to the present invention, when the additional mass moves from one operation stroke end to the other stroke end based on the signals obtained from the additional mass displacement detection means and the operation direction detection means. Then, the optimum feedback vector with a small vibration effect is sequentially selected from the optimum feedback vector with a large vibration effect, and the reciprocating motion of the additional mass is controlled by the optimum regulator theory using the value related to the vibration as the state variable. Therefore, when the additional mass reaches immediately before the stroke end, the additional mass having a small vibration effect is controlled, so that the impact due to the additional mass reaching the stroke end is not given. When there is no danger of the additional mass reaching the stroke end, the additional mass having a large vibration damping effect is controlled. Therefore, since the additional mass is efficiently moved, the maximum stroke of the additional mass can be shortened to obtain the vibration damping effect required for the structure, and the vibration damping device can be downsized.

[Brief description of drawings]

FIG. 1 is a model diagram of a vibration damping device showing an embodiment of the present invention,
2 (A), (B) and (C) are explanatory views showing the damping effect of the optimum feedback vectors A1, A5, A7 used in the present embodiment, and FIG. 3 is an explanatory view of the selection method of the optimum feedback vector, FIG. 4 is a block diagram of the control system, and FIG. 5 (A).
(B) is an explanatory view showing a damping effect when the method of the present invention is used for the damping device, FIG. 6 is a side view of the damping device using the present invention, FIG. 7 is a plan view of the damping device, FIG. 8 is a model diagram of a conventional vibration damping device. 1 ... Structure, 2 ... Additional mass 6 ... Cylinders 11a, 11b ... Displacement detecting means 12a, 12b ... Velocity detecting means (moving direction detecting means) z ... Controller

Claims (1)

[Claims] 1. A vibration control device comprising an additional mass movable in a vibration direction of a structure and a means for moving the additional mass, comprising several types of different damping effects obtained from the characteristics of the structure and the additional mass. The optimum feedback vector is stored in the controller, and the displacement of the additional mass is based on the signals obtained from the displacement detection means and the movement direction detection means of the additional mass according to the movement direction,
The optimum feedback vector having different damping effect is selected, and the optimum feedback vector is selected by the controller, the displacement of the structure obtained from the state variable detection means, the displacement of the additional mass, and the state quantity of the state variable related to other vibrations. A control method of the control device, wherein a control input for moving the additional mass is obtained from a product of