JPH09217701A - Vibration control method for structures - Google Patents

Abstract

(57) [Abstract] [Problem] It is difficult to realize damping control of a structure by a method of approximating state feedback using an observer or a design theory of a dynamic compensator such as H∞ control theory. ,
The solution was desired. SOLUTION: A small cycle obtained by dividing one operation cycle of an actuator 6 into a plurality of times is set as a state quantity detection cycle of the structure 1,
Each state quantity detection value is multiplied by a feedback coefficient determined for each detection time in these detection cycles, and the linear sum thereof is set as the operation amount command value for the actuator 6. Alternatively, a small cycle obtained by dividing one detection cycle of the state quantity into a plurality is set as an operation cycle of the actuator 6, and a feedback coefficient determined for each operation time by these operation cycles is set as a state quantity detection value within one detection cycle. It is multiplied to obtain the operation amount command value for the actuator 6 at each operation time.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a vibration control method for suppressing vibration of a structure by applying a vibration control force to the structure by an actuator installed in the structure such as a high-rise building.

[0002]

2. Description of the Related Art Conventionally, in a structure vibration control system,
An observer is configured and a state feedback control system based on a feedback coefficient obtained based on the optimum regulator theory or the like is used to approximately realize the control, or the dynamics obtained by using the H∞ control theory or the like are used. Vibration suppression control is realized by constructing an output feedback system using a dynamic compensator.

[0003]

In the method of approximating the state feedback control system using the observer, the robustness (the robustness of the control system against changes in the characteristics of the controlled object) becomes insufficient, and the observer It is not easy to realize because it requires design and adjustment. Further, in the design theory of the dynamic compensator represented by the H ∞ control theory, the compensator to be obtained becomes complicated (high-order dynamic system) and has extremely high gain, and it is possible to realize an extremely high frequency mode. There is a problem that it is not easy to realize because there is a strong tendency to need it.

In view of the above problems, the present invention forms a feedback control system by using state quantity detection values for a limited number of variables and an arithmetic unit that performs a simple arithmetic process, and vibrates a structure. To effectively suppress the

[0005]

In order to solve the above-mentioned problems, the invention according to claim 1 detects a state quantity of a structure as a vibration control target, and calculates an operation amount of an actuator installed in the structure. In a structure damping control method that suppresses vibration of a structure by applying a damping force from the actuator to the structure by calculating by a feedback control system, a small cycle obtained by dividing one operation cycle of the actuator into a plurality of cycles. Is the state quantity detection cycle of the structure, and a linear coefficient (sum) is obtained by multiplying the state quantity detection values such as displacement, velocity, and acceleration of the structure by the feedback coefficient determined for each detection time by these detection cycles. This is the operation amount command value for the actuator.

In contrast to the invention described in claim 1, the invention described in claim 2 sets a small cycle obtained by dividing one detection cycle of the state quantity into a plurality of times as an operation cycle of the actuator, and The feedback coefficient determined for each operation time is multiplied by the state quantity detection value within one detection cycle to obtain the operation quantity command value for the actuator at each operation time. That is, in the present invention, the operation amount command value is switched at each operation time within one detection cycle.

First, the operation of the invention according to claim 1 will be described. The dynamic characteristics of the structure to be damped are represented by the state equation of Equation 1, and are controllable and observable. In Expression 1, X (t) is a state quantity vector at time t, U (t) is a manipulation quantity vector at time t, and Y is
(T) is a control amount vector at time t, and A, B, and C are constant matrices.

[0008]

[Equation 1]

On the other hand, it is assumed that the operation according to the control law expressed by the equation 2 is performed. In Expression 2, k is a number (integer) representing the sampling step of the state quantity, n
Is the number of state quantity detections within one operation cycle T of the actuator,
U _{k + 1} is an operation amount vector held for one operation cycle ((k + 1) T ≦ t <(k + 2) T) from the sampling time at the k + 1th step.

[0010]

[Formula 2] U _{k + 1} = [G ₁ G ₂ ... G _n ] · [Y (kT) ^T
Y (kT + T / n) ^T ... Y {kT + (n-1) T / n} ^T ] ^T

Here, by introducing the following Equation 3, Equation 4 can be obtained, and Equation 2 can be expressed as Equation 5. However, the condition is Equation 6.

[0012]

(Equation 3)

[0013]

(Equation 4)

[0014]

(Equation 5)

[0015]

(Equation 6)

On the other hand, the control law of the state feedback of the discrete time system by the sampling period T is expressed by the formula 7, and further the formula 8 is obtained from the formula 7.

[0017]

(7) U _k = F · X (kT)

[0018]

U _{k + 1} = F · X {(k + 1) T} = F {A _* ⁿ X (kT)} + F (CB _* + CA _* B _* + CA _* ² B _* + ... CA _* ^{n- 1} ) U _k

Therefore, if [G ₁ G ₂ ... G _n ] is calculated so that the following Expression 9 is established, Expression 2 and Expression 5 are obtained.
And Equation 8 are equivalent. If n is properly selected, Equation 6 becomes the column full rank, and by Equation 10, [G ₁ G ₂ ... G
_n ] can be obtained. However, the last term on the right side of Expression 10 represents the general inverse matrix of Expression 6.

[0020]

[Equation 9]

[0021]

(Equation 10)

From the above, first, the state feedback coefficient for vibration suppression is obtained by the usual way of thinking by the optimal regulator theory or the pole placement theory, and then [G ₁ G ₂ ... G _n ] is obtained by the equation 10. By executing the feedback control according to the control law of Expression 2, it is possible to realize a system equivalent to the vibration suppression control system by the state feedback control in which the sampling period is T.

Next, the operation of the invention described in claim 2 will be described. In the present invention, the control law of Expression 11 is applied to the controlled object expressed by Expression 1. However, under the condition of Expression 12, in Expressions 11 and 12, t is time, T is one detection cycle of the state quantity, m is the number of operations within one detection cycle T (operation quantity switching times), and U (t) is The operation amount vector at time t, Y (kt) is the control amount vector at time kt (that is, the state amount detection time), E
(T) is a feedback coefficient that determines the operation amount at time t.

[0024]

[Equation 11] U (t) = E (t) · Y (kT)

[0025]

(Equation 12)

Since Y (kt) = C · X (kt),
The state transition of each state quantity detection cycle of the feedback control system is represented by Expression 13. This Expression 13 can be converted into Expression 15 by Expression 14.

[0027]

(Equation 13)

[0028]

[Equation 14]

[0029]

[Equation 15] X (kT + T) = [exp (AT) + K * C] * X (kT)

The stability of the discrete-time behavior for each period T according to Equation 15 is determined by the eigenvalue of [exp (A · T) + K · C], but if {exp (A · T), C} is observable, For example, these values can be set to arbitrary values by appropriately selecting K.

Since E (t) is a constant during the operation time (operation amount switching time) (one operation cycle), the integration section on the left side of Expression 14 is divided by the operation time to make E (t) a constant E _1. , E
₂ , ..., E _m is taken out of the integrand, and the integration results of the remaining ones are rearranged and expressed as B _* , as shown in Formula 16.

[0032]

[Equation 16] B _* · [E ₁ ^T E ₂ ^T ... E _m ^T ] ^T = K

By appropriately selecting m in Expression 16, B _{* has a} row full rank in most T, so that for a given K, Expression 16 or Expression 14 is satisfied [E ₁ ^T E ₂ You can ask for ^T …… E _m ^T ]. Therefore, first, in order for the state transition according to Expression 15 to be one in which vibration is sufficiently suppressed, [exp (A ·
T) + K · C], the eigenvalue is specified to obtain K, and then [E ₁ ^T E ₂ ^T ... E _m ^T ] is calculated so that Expression 16 holds, and based on this, Expression 11 and Expression By executing the feedback control of 12, it is possible to suppress the vibration of the structure.

[0034]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the present invention will be described below with reference to the drawings. FIG. 1 shows an embodiment of the invention described in claim 1. In the figure, 1 is a structure to be damped, and this structure 1 is approximately the points 2, 3,
It is possible to model by a state equation configured by using positions X1, X2, X3, X4 and velocities V1, V2, V3, V4, which are state quantities of 4, 5 as state variables. Also,
The operation for damping is to generate and apply a damping force in the horizontal direction by the actuator 6 attached to the point 4, and the amount Y detectable by the sampler 7 is the position X2.
And

With the above structure 1 as the control target,
Feedback control by various methods. Actuator 6
For example, one operation cycle T is divided into eight, and the operation time is
8 times including
Y out in order₁, Y_Two, ……, Y ₈And

The arithmetic unit 8 carries out the operation represented by the formula 17 for each operation cycle T, and holds the result by the holder 9 from the next operation time to the next operation time (that is, during the next operation cycle). Then, the operation amount command value for the actuator 6 is set. This process is repeated for each operation cycle T.

[0037]

[Equation 17] U = [G ₁ G ₂ ... G ₈ ] · [Y ₁ Y ₂ ... Y ₈ ] ^T = G · [Y ₁ Y ₂ ... Y ₈ ] ^T

Feedback coefficient G in Equation 17
(= [G ₁ G ₂ ...... G ₈ ]) first obtains the feedback coefficient F of the control law by the state feedback (see Formula 18) from the optimal regulator theory based on the state equation model of the controlled object. The coefficient matrix of the equation is substituted into Equation 10 to obtain it in advance.

[0039]

[Equation 18] U = F · [X1 X2 X3 X4 V1
V2 V3 V4] ^T

In this way, the total state quantity (X1, X2, X3, X4, V1, V2, is determined by the detected value of only Y (= X2).
A feedback system equivalent to the feedback control based on the detected values of V3, V4) is configured, and vibration suppression equivalent to that by the state feedback control is realized.

Next, an embodiment of the invention described in claim 2 will be described. In this embodiment, the structure 1 to be damped is the same as in FIG. 1, and the operation amount and the detected state amount are also the same as in FIG. The quantity Y (= X2) is sampled at every detection cycle T by the sampler 10, and the arithmetic unit 11 divides one detection cycle T into eight equal parts based on this detection quantity Y, for example, at each time interval (operation cycle) (operation time). manipulated variable U ₁ corresponding to the operation time), U _2, ........., equation a U ₈ 19
Ask by

[0042]

[Equation 19] [U ₁ U ₂ ... U ₈ ] ^T = [E ₁ E ₂ ... E ₈ ] ^T · Y

These values U ₁ , U ₂ , ..., U ₈ are respectively transferred to T by the holders 12 to 19 corresponding to each time interval.
It is held for only / 8 time and used as the operation amount command value for the actuator 6. The holding start time of the holder is set by sequentially shifting it by T / 8 from the holder 12, and the sum of these is set to U, so that the values are U ₁ , U ₂ , ..., U.
Switch to ₈ . This is repeated every detection cycle T.

[E ₁ E ₂ ... E ₈ ] ^T in Equation 19
Is preliminarily obtained from the relationship between the coefficient K obtained by the pole placement theory and the mathematical expression 16 by designating the eigenvalue of [exp (A · T) + K · C]. Thus, the vibration of the structure 1 is suppressed by arranging the eigenvalues when the feedback system of FIG.

In each of the above embodiments, the number of divisions of one operation cycle of the actuator 6 and the number of divisions of one detection cycle of the state quantity are not limited to "8".

[0046]

As described above, according to the first aspect of the invention, not only the total state quantity related to the vibration of the structure is detected, but only the state quantity relatively easily detectable such as the displacement is detected by the actuator. The operation cycle is detected in a finely divided short cycle, and the linear sum of these state quantity detection values multiplied by a predetermined feedback coefficient is used as the operation quantity command value to the actuator for each operation cycle. This allows
The control equivalent to the state feedback control can be easily realized by a simple arithmetic processing using a limited number of detection signals, and the structure vibration of the structure is effective while saving the structure of the state quantity detecting means and the equipment cost. Can be suppressed.

Further, according to the second aspect of the present invention, one detection cycle of the state quantity is subdivided to set a short operation cycle, and the state quantity detection value is multiplied by a feedback coefficient determined for each operation time based on this. The operation amount command value at the operation time is obtained. As a result, the eigenvalue of the system can be set to a desired value by simple arithmetic processing using a limited number of detection signals, and effective vibration suppression can be performed.

[Brief description of drawings]

FIG. 1 is a configuration diagram showing an embodiment of the invention according to claim 1.

FIG. 2 is a configuration diagram showing an embodiment of the invention according to claim 2;

[Explanation of symbols]

 1 Structure 2-5 points 6 Actuator 7,10 Sampler 8,11 Arithmetic device 9,12-19 Holder

─────────────────────────────────────────────────── ─── Continuation of the front page (51) Int.Cl. ⁶ Identification code Office reference number FI technical display location // G05B 21/02 G05B 21/02 A

Claims (2)

[Claims] 1. A state quantity of a structure as a vibration control target is detected, an operation amount of an actuator installed in the structure is calculated by a feedback control system, and a damping force is applied from the actuator to the structure. In a structure damping control method for suppressing structure vibration, a small cycle obtained by dividing one operation cycle of the actuator into a plurality of times is defined as a state quantity detection cycle of the structure, and at each detection time by these detection cycles. 2. A method for controlling vibration control of a structure, characterized in that each of the detected state quantities is multiplied by the feedback coefficient defined in 1. and the linear sum of these is used as an operation quantity command value for the actuator. 2. A state quantity of a structure to be damped is detected, an operation amount of an actuator installed on the structure is calculated by a feedback control system, and a damping force is applied to the structure from the actuator. In a structure vibration damping control method for suppressing structure vibration, a small cycle obtained by dividing one detection cycle of the state quantity into a plurality is defined as an actuator operation cycle, and the operation cycle is determined for each operation time. A vibration damping control method for a structure, wherein a feedback coefficient is multiplied by a state quantity detection value within one detection cycle to obtain an operation amount command value for an actuator at each operation time.