JPH0652016B2 - Vibration control device for structures - Google Patents

Description

The present invention relates to a structure vibration damping device, and more particularly to LQ control theory (optimal control theory that minimizes a linear quadratic evaluation function).
The present invention relates to a vibration control device for a structure, in which the active mass damper is driven and controlled by a software servo based on the control system to control the vibration of the structure.

[Prior Art] Vibration damping devices are roughly classified into passive type and active type. The active vibration damping device includes a vibration damper, an actuator that drives the vibration damper, and a control circuit that controls the actuator based on a detection signal from the sensor. Since the active type vibration damping device is supplied with energy for damping from the outside and has a feedback control system, a large damping force can be obtained compared to the passive type, and the vibration of the damping target It is possible to cope with a change in characteristics to some extent.

[Problems to be Solved by the Invention] However, in the active vibration damping device, if the control of the actuator is abandoned, the vibration damper may serve as a vibration source. Also,
For example, for two-dimensional vibration control, a dedicated vibration control device is provided in each direction, so a total of two vibration control masses are required for each vibration control device. It becomes a large one.

By the way, the recent progress in vibration analysis of mechanical structures, vibration response measurement based on FFT technology, and data processing technology is remarkable, and it is expected that these technologies will be used more and more in the design of vibration control devices. Has been done. However, since the structure is a distributed constant system, it has infinite degrees of freedom.However, due to restrictions such as computer calculation speed and memory capacity, this is required for designing a control system for damping. Must be truncated to a finite degree of freedom. At that time, the interaction between the truncated higher-order mode and the controlled mode may cause the control system to become unstable. This phenomenon is called spillover instability, and flexible lightweight structures represented by space structures (solar cell paddles, antennas, and other space structures are flexible structures with almost no damping, but high-level vibration control is required). ) Has become a major problem in active vibration control, and its countermeasures are strongly desired.

An object of the present invention is to solve the above-mentioned problems of the prior art, and to provide a general-purpose vibration damping device that is compact and lightweight and that can perform good vibration damping. Another object of the present invention is to provide a vibration damping device capable of eliminating spillover instability.

[Means for Solving the Problems] In order to achieve the above-mentioned object, the first invention is attached to the most vibrating portion of a structure to be damped that vibrates in two horizontal directions or in the vicinity thereof, and A two-dimensional active mass damper having a two-dimensional active mass provided so as to be able to vibrate in two directions, an actuator that applies a displacement force in the two-dimensional direction to the two-dimensional active mass, and a sensor that detects vibration of a structure to be damped , Having an observer of a vibration model that approximates the structure to be damped, and by operating the observer with the detection signal of the sensor as an input, a state quantity close to a phenomenon actually occurring in the structure to be damped is obtained. Observe and calculate the state feedback gain that minimizes the linear quadratic evaluation function for this state quantity and the control quantity of the actuator. And a control device for determining the control amount of the actuator by multiplying the state quantity by the state feedback gain.

A second aspect of the present invention is a two-dimensional structure having a two-dimensional active mass, which is attached to or near the largest vibrating portion of a structure to be damped, which vibrates in two horizontal directions, and has a two-dimensional active mass provided so as to vibrate in the two directions. An active mass damper,
An actuator that applies a displacement force in a two-dimensional direction to the two-dimensional active mass, a sensor that detects the vibration of the structure to be damped, and an observer of a vibration model that approximates the structure to be damped are detected by the sensor. A state quantity close to a phenomenon actually occurring in the structure to be damped is observed by operating the observer with a signal as an input, and a linear quadratic evaluation function for this state quantity and the control quantity of the actuator is observed. A state feedback gain that minimizes, and a control device that determines the control amount of the actuator by multiplying the obtained state feedback gain by the state amount, and a vibration mode that is intended to be damped by this control device. And a dynamic vibration absorber attached to the structure to be damped in order to absorb high-order mode vibrations.

[Operation] An observer (pseudo-circuit) of a vibration model that approximates the structure to be damped is created in the vibration damping device, and this observer observes the state quantity close to the phenomenon actually occurring in the structure to be damped. , This state quantity is multiplied by the feedback gain to make a control quantity. Then, the actuator is operated by this control amount to control the vibration damping force of the active mass damper.

In the first aspect of the invention, the two-dimensional active mass is displaced in the two-dimensional direction by the actuator, so that the two-dimensional vibration can be suppressed by one two-dimensional active mass. Further, in the second aspect of the present invention, since the vibration mode higher than the vibration mode to be damped by the control circuit is absorbed by the passive dynamic vibration absorber, the spillover instability can be alleviated and suppressed.

Embodiments Embodiments of the present invention will be described below with reference to the drawings. In this embodiment, vibration suppression of tower-like structures such as towers, buildings and columns will be described as an example.

FIG. 1 shows an outline of the vibration damping device of this embodiment.

A two-dimensional active mass damper 2 is provided at the upper end of the tower structure 1.
Is attached, and a double dynamic vibration absorber 4 is attached to the mass 3 added in the middle in the x direction and the y direction for damping of the two-dimensional mode. The vibration of the tower-shaped structure 1 is detected by a non-contact type displacement sensor 5 attached in the x-axis and y-axis directions and sent to a two-dimensional software servo control device 6 and a four-channel FFT analyzer 7. The software servo control device 6 is composed of one personal computer having a 16-bit CPU with a built-in A / D converter and a numerical operation processor, and two drive units. The FFT analyzer 7 is for vibration analysis.

The tower-like structure 1 shown in Figs. 1 and 3 is for vibration damping research, and has an actuator mount on the upper end of a mild steel hollow prism with a side of 50 mm, a wall thickness of 2.3 mm and a length of 1500 mm. The additional mass 3 of 5.3 kg is attached at a position 900 mm from the fixed end of the lower end.

FIG. 3 shows the primary and secondary vibration modes of the tower-shaped structure 1. It can be seen that the antinode of the secondary mode is at the position of mass 3. The antinode has the greatest influence on the vibration characteristics of the mode, and when the mass is attached thereto, the natural frequency is most reduced. In this way, the position of the mass 3 is set to the antinode of the secondary mode by decreasing the natural frequency of the secondary mode and strengthening the influence on the primary mode.
This structure is intentionally used to facilitate instability of spillover. It should be noted from FIG. 3 that the node of the secondary mode is 210 mm below the upper end.

FIG. 2 shows the calculation result of the compliance with the displacement generated at the position when the upper end of the tower-shaped structure 1 is vibrated. 1st natural frequency is 11.9Hz, 2nd is 70Hz, 3rd is 33
Allowed at 5Hz. The secondary natural frequency was 100 Hz when there was no mass 3 on the antinode, but 70 Hz due to the addition of mass 3.
Fell to.

The equivalent mass Mi (i = 1,2) and the equivalent rigidity Ki (i = 1,2) of each mode at the actuator mounting position at the upper end are the equivalent mass identification method of the multi-degree-of-freedom system proposed by the present inventors (Shodo et al. , The Japan Society of Mechanical Engineers Theory Collection (C), Volume 53, No. 485, P.52-52
(1987)). The equivalent masses of the first and second modes were M ₁ = 6.6 kg, M ₂ = 10.0 kg, and the equivalent stiffness was K ₁ = 2.86 × 10 ⁴ N / m, K ₂ = 1.56 × 10 ⁶ N / m. . Although these vibration characteristics are related to the x-axis direction, almost the same values are obtained in the y-axis direction.

The structure of the two-dimensional active mass damper 2 is shown in FIG.
Square plate-shaped mass 9 arranged in the center of the casing 8
Is supported on its four sides by four ring-shaped springs 10. By adopting such a structure, the movement of the mass 9 in the vertical direction is restricted without mechanical contact, and the mass 9 can move only in the horizontal two-dimensional direction. Therefore, this is called a two-dimensional active mass. Permanent magnets 11 are adhered to the upper and lower surfaces of the mass 9, respectively. The permanent magnet 11 has an S-pole on the adhesive surface on the active mass 9 side and an N-pole on the opposite outer surface (the polarities may be reversed). Electromagnets 12 and 12 are provided above and below the permanent magnets 11 and 11 with the active mass 9 interposed therebetween.
The electromagnets 12, 12 are arranged so as to be offset from each other by 90 degrees, and the direction between the magnetic poles of one electromagnet 12 is the x direction, and the direction between the magnetic poles of the other electromagnet 12 is the y direction. By supplying a + current and a −current to the electromagnet 12, an attractive force and a repulsive force are generated between the electromagnet 12 and the permanent magnet 11, and the control force of the active mass 9 is obtained. A displacement force in the x direction is applied to the active mass 9 by the one electromagnet 12 and the permanent magnet 11, and a displacement force in the y direction is applied by the other electromagnet 12 and the permanent magnet 11. Therefore, the electromagnets 12, 12
The permanent magnets 11 and 11 are linear actuators of the two-dimensional active mass 9 in the two-dimensional direction.

FIG. 5 shows the static characteristic of the displacement of the active mass 9 with respect to the input current to this actuator. Although the sensitivities are somewhat different depending on the x-axis and the y-axis, it can be seen that good linearity is obtained for both.

The specifications of the two-dimensional active mass damper 2 are as follows.

Akuchiibu mass m = 0.25 kg x-axis spring constant k _x = 2850N / m y-axis spring constant k _y = 2850N / m Therefore, the natural frequency of the axial, x-axis, y-axis co-17
It becomes Hz.

FIG. 6 shows the calculated value of compliance when the active mass damper 2 is attached to the upper end of the tower-shaped structure 1 and is vibrated in the x-axis direction without operating the control system.
Compared to Fig. 2, active mass damper 2 near 17Hz
It can be seen that there is no change except for the influence of the natural frequency of.

Next, a method for realizing a control system for controlling the vibration associated with the primary natural vibration of the tower-shaped structure 1 around 12 Hz by the active mass damper 2 by the software servo system will be described.

FIG. 7 shows a dynamic model when the active mass damper is attached to a controlled object that approximates vibration in one direction of the tower-shaped structure 1 to a system of one degree of freedom. In LQ control theory,
It is necessary to express the equation of state based on this figure.
This equation of state is expressed as follows.

Where x (t) is the state vector, Is a coefficient matrix, and y (t) is an output amount (in this case, the displacement of the tip of the tower-like structure), which are expressed as follows.

Where x ₁ is the displacement of the tip of the tower-like structure, ₁ is the velocity of the tip of the tower-like structure, x ₀ is the displacement of the active mass damper,
₀ is the velocity of the active mass damper, M ₁ is the mass of the tower structure approximated to the one-degree-of-freedom system, k ₁ is the spring constant of the tower structure approximated to the degrees of freedom, and m is the mass of the active mass damper. , K is the spring constant of the active mass damper, and k _f is the force conversion coefficient.

Next, when equation (1) is converted into a discrete time system for application to a discrete time control system, the following is obtained.

here, However, Δt is a sampling interval.

In the LQ control theory, an optimum control result is obtained when the following control amount u (i) is determined by the vector product of the state feedback vector K (i) which determines the state amount x (i) by the equation (9). .

u (i) = - K ( i) x (i) = - [K 1 (i) 1 (i) + K 2 (i) 0 (i) + K 3 (i) x 1 (i) + K 4 (i) x ₀ (i)] ...
(5) where K ₁ (i) to K ₄ (i) are the respective state quantities ₁ , ₀ ,
It is a state feedback gain of x ₁ and x ₀ .

This state feedback gain vector K (i) is a linear quadratic evaluation function J (sum of state quantity and control quantity) for the state quantity x (i) and the control quantity u (i), that is, The following Riccati equation that minimizes Is given by the convergent solution of.

here, However, Is a weighting coefficient given in advance.

However, the state vector x (i) included in equation (5) is
State quantities x ₁ , ₁ , x ₀ , ₀ are values that cannot be determined unless they can be measured, which is not easy in practice.

Therefore, in the structure vibration damping device of the present invention, the required state quantity is obtained by an observer created by software in the control device. The vibration damping device (software controller) shown in FIG. 7 integrates the function of an observer for estimating the state quantity based on the detection signal x _{1 of the} sensor and the function of calculating the control quantity.

FIG. 8 shows a block diagram of the LQ control system according to the present invention. This control system is an actual target of damping (transfer function G
(Z)) does not directly feed back the state quantity, but uses the state quantity x ₁ which is easy to measure State quantity estimated by To feed back. This state quantity x ₁ which can be easily measured corresponds to the detection signal x ₁ of the sensor shown in FIG.
Estimated state quantity by constantly inputting the detection signal x _{1 of the} sensor and operating the observer Is constantly updated. In this case, by using the measured value x ₁ as a part of the state quantity, the actual state quantity of the vibration suppression target and the estimated state quantity The error between and can be suppressed as small as possible.

FIG. 9 shows a computational flowchart in the control device of this LQ control system. A new measurement value (sensor detection signal x ₁ ) is always taken in the loop that is repeatedly calculated, and the state quantity And state feedback gain And are multiplied to obtain the controlled variable u. This control amount u is output to the actual controlled object and the observer, and the next state amount Has been obtained.

Although the tower-shaped structure 1 is a multi-degree-of-freedom system, the LQ control system was designed and the damping effect was investigated by simulation for a damping target considering only the first-order mode.

FIG. 10 shows a simulation result by numerical calculation of the relationship between the control amount u and the damping effect (vibration displacement x ₁ ) by changing the weight ω of the control amount of the evaluation function. As described above, as ω is reduced, a large damping effect is obtained, but it is understood that a large control current is required accordingly. By selecting the weight ω, it is possible to achieve a harmony between the damping effect and the energy consumption amount required for damping.

When the LQ control system is realized by software, there is an advantage that it is possible to flexibly deal with the change of parameters of the vibration suppression object by only changing a part of the program. On the other hand, since it is restricted by the computing speed of the computer, it is not possible to handle a mathematical model large enough to accurately represent the dynamic characteristics of the object to be damped. Inevitably, it is a low-dimensional observer.

Therefore, the control considering only the first-order mode in the observer for the vibration suppression target in which the first-order and second-order dynamic characteristics (transfer functions G ₁ (Z) and G ₂ (Z)) as shown in FIG. Shall constitute the system. In this case, since only the displacement of the secondary mode is observed, the control force to the secondary mode is not the state feedback but the local feedback and may become unstable due to the selection of the weighting factor ω. Such instability is called observation spillover. Although a modal filter or the like has been conventionally proposed as a countermeasure against such spillover, a method of reducing the influence of the secondary mode by a dynamic vibration absorber is adopted in the present invention. In the double dynamic vibration absorber 4 used in this embodiment, leaf springs are respectively extended from the central support body to both sides, and the free ends of the leaf springs are provided with copper mass bodies having an I-shaped cross section. A pair of permanent magnets are provided on both sides of each mass body at regular intervals. The dynamic vibration reducer 4 utilizes magnetic damping generated when the mass body moves in the magnetic field formed by the pair of permanent magnets without mechanical contact, and the mass body also serves as a magnetic damper. The effect is shown by the following experiments.

For the vibration measurement, a method of vibrating the upper part of the tower-shaped structure 1 with an impulse hammer and analyzing the time response and the frequency response with the FFT analyzer 7 in the configuration of FIG. 1 was adopted.

FIG. 12 (a) shows the compliance of the tower-shaped structure 1 alone. It is in good agreement with the calculation result of FIG. Fig. 12
In (b), the double dynamic vibration absorber 4 is not optimally adjusted to suppress the secondary mode, but the secondary resonance peak is suppressed for the time being.

FIG. 13 shows a state in which the dynamic vibration absorber 4 is not provided.
0.00001, Figure (b) shows the case of ω = 0.000001. In this way, when the weight ω is reduced to increase the vibration damping effect, conversely, the spillover becomes unstable. Figure 14 shows
This situation was investigated by the frequency response. As the weight ω is reduced, the peak of the secondary mode grows,
I can understand well that it is the cause of instability.

FIG. 15 shows an experimental result corresponding to FIG. 14 when the dynamic vibration absorber 4 is attached. As can be seen, the peaks of the secondary mode are excellently suppressed by the dynamic vibration reducer 4. FIG. 16 shows the experimental result corresponding to FIG. 13 when the dynamic vibration absorber 4 is attached. Spillover instability is completely suppressed. Further, FIG. 17 shows displacement response waveforms in the x and y axis directions when impulse excitation is performed in the direction of 45 °. Thus, it can be seen that the same damping effect is obtained in both directions.

In this way, the two-dimensional active mass damper 2 has a good vibration damping effect on the tower-shaped structure 1 etc. in which horizontal two-way vibration is a problem, and is also useful for designing a control system that cuts off higher-order modes. It was confirmed that the dynamic vibration absorber is effective as a countermeasure against the spillover instability. In addition, it was confirmed that the software servo control device has general versatility in vibration control of this kind of structure by the active mass damper method.

Although the two-dimensional active mass damper 2 of the above-described embodiment uses electromagnetic force, the vibration damping device may be configured using the hydraulic two-dimensional active mass damper 13 shown in FIG. That is, a hydraulic cylinder 16 having a servo valve 15 is attached to each of the four sides of the two-dimensional active mass 14, and a control current is supplied to each servo valve 15 from a control circuit 18 including a servo amplifier according to a detection signal of a displacement sensor 17. It is supposed to be output. (Note that the position feedback from the displacement sensor 17 can serve as a spring.) [Advantages of the Invention] The present invention has the following advantages.

(1) Since one mass (two-dimensional active mass) is moved in two directions instead of one direction to suppress two-dimensional vibration, the vibration control device can be made lightweight and compact.

(2) Since the control system is composed of software servos using the LQ control theory, it is possible to suppress vibration with versatility.
Moreover, even if the structure changes, it can be easily handled by changing the software.

(3) Since the vibration mode higher than the vibration mode to be damped by the control circuit is absorbed by the passive dynamic vibration absorber, the interaction between the vibration suppression mode and the cut off higher-order mode is weakened, resulting in spillover. Instability is suppressed.

[Brief description of drawings]

FIG. 1 is a configuration diagram showing an embodiment of a vibration damping device according to the present invention, FIG. 2 is a graph showing compliance of the tower-like structure of FIG. 1, and FIG. 3 is a vibration mode of the tower-like structure. FIG. 4 shows a shape, FIG. 4 is a partially cutaway perspective view of the two-dimensional active mass damper of FIG. 1, FIG. 5 is a graph showing static characteristics of active mass displacement with respect to input current from an actuator, and FIG. Fig. 7 is a graph showing the compliance of tower-shaped structures with the addition of a two-dimensional active mass damper.
FIG. 8 is a diagram showing a dynamic model of the Q control system, FIG. 8 is a block diagram of the LQ control system, and FIG. 9 is a flowchart of the LQ control system.
FIG. 10 is a graph showing the relationship between the control amount and the damping effect, FIG. 11 is a block diagram of the LQ control system to which a secondary mode is added, and FIGS. 12 to 17 show experimental results. FIG. 12 is a graph showing the compliance of a tower structure without active control, and FIGS. 13 and 14 are graphs showing the time response and frequency response of the tower structure without a dynamic vibration absorber, respectively. FIG. 15 is a graph showing the frequency response of a tower-shaped structure when a dynamic vibration absorber is added, FIG.
FIG. 17 is a graph showing the time response of the tower-shaped structure when a dynamic vibration absorber is added, and FIG. 18 is a diagram showing another embodiment of the two-dimensional active mass damper. In the figure, 1 is a tower-like structure (structure to be damped), 2 is a two-dimensional active mass damper, 4 is a double dynamic vibration absorber, 5 is a displacement sensor, 6 is a software servo controller, 7 is an FFT analyzer, 8 is a casing, 9 is a two-dimensional active mass, 10 is a ring-shaped spring, 11 is a permanent magnet, 12 is an electromagnet, 13 is a two-dimensional active mass damper, 14 is an active mass, 15 is a servo valve, 16 is a hydraulic cylinder, 17
Is a displacement sensor, and 18 is a control circuit.

Claims (2)

[Claims] 1. A two-dimensional active mass damper having a two-dimensional active mass, which is attached to or near the largest vibrating portion of a structure to be damped and which vibrates in two horizontal directions, and has a two-dimensional active mass provided so as to be vibrable in the two directions. An actuator that applies a displacement force in a two-dimensional direction to the two-dimensional active mass, a sensor that detects the vibration of the structure to be damped,
It has an observer of a vibration model that approximates the structure to be damped, and observes the state quantity close to the phenomenon actually occurring in the structure to be damped by operating the observer with the detection signal of the sensor as input. Then, the state feedback gain that minimizes the linear quadratic evaluation function for this state amount and the control amount of the actuator is calculated, and the obtained state feedback gain is multiplied by the state amount to control the actuator. A vibration damping device for a structure, comprising: a control device for determining an amount. 2. A two-dimensional active mass damper having a two-dimensional active mass, which is attached to or near the most vibrating portion of a structure to be damped which vibrates in two horizontal directions and has a two-dimensional active mass provided so as to be vibrable in the two directions. An actuator that applies a displacement force in a two-dimensional direction to the two-dimensional active mass, a sensor that detects the vibration of the structure to be damped,
It has an observer of a vibration model that approximates the structure to be damped, and observes the state quantity close to the phenomenon actually occurring in the structure to be damped by operating the observer with the detection signal of the sensor as input. Then, the state feedback gain that minimizes the linear quadratic evaluation function for this state amount and the control amount of the actuator is calculated, and the obtained state feedback gain is multiplied by the state amount to control the actuator. A control device that determines the amount, and a dynamic vibration absorber that is attached to the structure to be damped in order to absorb the vibration of a higher order mode than the vibration mode to be damped by the control device. Vibration control device for characteristic structures.