阅读说明：本技术 一种用于航天器柔性结构的加速度反馈振动控制方法 (Acceleration feedback vibration control method for spacecraft flexible structure ) 是由 王晓宇 王祥 曾福明 王磊 刘绍奎 王慧 李冰岩 柴洪友 于 2021-09-10 设计创作，主要内容包括：本发明公开了一种用于航天器柔性结构的加速度反馈振动控制方法,首先根据仿真建模分析或结构试验测试,获得结构的动力学方程及传递函数；然后设计基于加速度反馈的控制器,引入一个二阶系统补偿器和一个一阶系统补偿器,并配置补偿器阻尼参数ζ-(f)和频率参数ω-(f)；最后配置控制器的反馈增益α和β,控制输出为两个补偿器的变量相加并作负反馈。本发明以加速度作为反馈物理量,避免了误差累积；引入二阶系统补偿器,直接以补偿器变量作负反馈,通过其低通滤波特性克服了高频控制溢出问题；增加了一阶系统补偿器,通过配置两个补偿器增益参数,解决闭环控制系统因存在时滞而产生的控制效果下降问题,提升系统的振动控制能力。(The invention discloses an acceleration feedback vibration control method for a spacecraft flexible structure, which comprises the following steps of firstly, obtaining a dynamic equation and a transfer function of a structure according to simulation modeling analysis or structural test; then designing a controller based on acceleration feedback, introducing a second-order system compensator and a first-order system compensator, and configuring a damping parameter zeta of the compensator f And a frequency parameter omega f (ii) a Finally, feedback gains alpha and beta of the controller are configured, and the control output is the addition of the variables of the two compensators and negative feedback is carried out. The invention takes the acceleration as the feedback physical quantity, thus avoiding error accumulation; a second-order system compensator is introduced, the variable of the compensator is directly used as negative feedback, and the problem of high-frequency control overflow is solved through the low-pass filtering characteristic of the compensator; the first-order system compensator is added, and the problem of control effect reduction caused by time lag of a closed-loop control system is solved by configuring two compensator gain parameters, so that the vibration control capability of the system is improved.)

1. An acceleration feedback vibration control method for a spacecraft flexible structure is characterized by comprising the following steps:

s1, carrying out simulation modeling analysis or experimental test on the structure to be controlled to obtain a kinetic equation and a transfer function of the structure to be controlled; the structure to be controlled is a flexible structure in a spacecraft;

s2, constructing a vibration control system for the structure to be controlled, designing a controller based on acceleration feedback, introducing a second-order system compensator and a first-order system compensator into the controller, and configuring a compensator damping parameter zeta_fFrequency parameter omega_f；

And S3, configuring feedback gains alpha and beta of the controller, and adding the control output into the variables of the second-order system compensator and the first-order system compensator and performing negative feedback.

2. The acceleration feedback vibration control method for a spacecraft flexible structure of claim 1, wherein the vibration system of the structure to be controlled is a single degree of freedom vibration system, and S2 comprises the following steps:

s21: the second order system compensator equation is constructed as follows:

where y is the second order system compensator variable,is the second derivative of y and is,is the first derivative of y, ζ_fIs the compensator damping parameter, ω_fIs the compensator frequency parameter, x is the modal coordinate,is the second derivative of x;

the first order system compensator equation is constructed as follows:

wherein z is a first order system compensator variable,is the first derivative of z;

s22: writing the compensator in a transfer function form, the transfer function form of the acceleration response input a(s) and the control output y(s) of the second order system compensator is as follows:

the transfer function form of the acceleration response input A(s) and the control output Z(s) of the first order system compensator is as follows:

3. an acceleration feedback vibration control method for a spacecraft flexible structure as claimed in claim 2, characterized in that the compensator frequency parameter ω_fClose to the natural frequency of the vibrating system, ω, i.e. ω_fω. Damping parameter ζ_fCan be set according to the specific conditions of the test.

4. The acceleration feedback vibration control method for the spacecraft flexible structure of claim 1, wherein the vibration system is a k-order degree of freedom system, and when k is greater than or equal to 2:

constructed second-order system compensatorThe equation is

The first order system compensator equation is constructed as

Wherein, gamma is_f∈R^k×kAs a compensator damping parameter matrix, R^k×kA real number array of scale k × k; omega_f∈R^k×kIs a compensator frequency parameter matrix; y is the second order system compensator variable for the k-order degree of freedom,is a second derivative of Y and is,is a first derivative of Y, q is a modal coordinate vector,is the second derivative of q, D is the actuator configuration matrix in the vibration system, Z is the first order system compensator variable for k degrees of freedom,is the first derivative of Z.

5. The method of claim 4, wherein the frequency parameter matrix Ω is guaranteed_fThe medium design frequency is close to the k-order natural frequency, i.e. omega, of the vibrating system to be controlled_fi≈ω_i(i ═ 1,2, …, k), where ω is_fiAs a frequency parameter matrix omega_fOf (d) the ith design frequency, ω_iThe ith order natural frequency of the vibration system; damping parameter matrix gamma_fDesign damping ζ in_fiAnd setting according to the specific conditions of the test.

6. The acceleration feedback vibration control method for the spacecraft flexible structure as claimed in any one of claims 1,2 or 3, wherein the vibration system is a single degree of freedom system, and the specific step S3 includes:

the expression of the control output of the controller based on the acceleration feedback is

u＝-(αy+βz) (9)

Wherein u is the control output of a controller designed based on acceleration feedback for controlling the vibration system; alpha is the feedback gain of the second-order system compensator, and beta is the feedback gain of the first-order system compensator;

the system time lag of the closed loop of the vibration system, which is generated by the sensing measurement, the calculation of the controller and the execution of the driving process of the actuator, is t_kThe delayed phase of the vibration system is theta_k＝t_kω, ω is the natural frequency of the vibrating system, let ω_fω, then the configuration of the feedback gains α and β of the controller should satisfy the following equation:

7. the acceleration feedback vibration control method for the spacecraft flexible structure according to any one of claims 1, 4 or 5, wherein the vibration system is a multiple degree of freedom system, and S3 specifically includes the following steps:

the control expression of the controller based on the acceleration feedback is

U＝-(A_αY+B_βZ) (10)

Wherein U is a control output matrix of the controller designed based on acceleration feedback, A_α∈R^k×kIs a second-order system compensator gain matrix,α₁～α_krespectively 1 st to kth gain parameters, B_β∈R^k×kIn the form of a first order system compensator gain matrix,β₁～β_k1 st to kth gain parameters respectively;

by configuring the gain parameter A_αAnd B_βCompensating the time lag of the system control loop to make the active vibration control of each order of the decoupled system equivalent to direct speed feedback, A_αAnd B_βShould satisfy

In the formula, theta_i,kDelayed phase theta for each order mode of vibration system_i,k＝t_k·ω_i，ω_iIs the ith order modal frequency.

Technical Field

The invention relates to the technical field of vibration control, in particular to an acceleration feedback vibration control method suitable for a flexible structure of a spacecraft.

Background

With the continuous development of the aerospace technology, the ultra-large-scale and multifunctional spacecraft is an important direction for the development of the spacecraft structure technology in the future. Along with the gradual increase of the size, the spacecraft structure has the characteristics of large flexibility, low frequency, small damping and the like, is influenced by the space environment, is easy to generate low-frequency vibration, is slowly attenuated once being generated, influences the high-precision and high-stability performance of the spacecraft, and even possibly endangers the normal operation of the spacecraft, so that the vibration control of the spacecraft flexible structure has important significance.

At present, a commonly used spacecraft structure vibration feedback control method is based on a modern control theory, feedback quantities are displacement and speed, and if the physical quantities are directly measured and need equipment such as laser or photogrammetry, the spacecraft structure vibration feedback control method occupies more resources and has high cost; if the acceleration sensor is adopted for indirect measurement, one-time integration and two-time integration are required, the influence of sensor measurement noise and zero drift is easily caused, and a large accumulated error is generated, so that the control output is rapidly saturated and goes wrong, and a control system is invalid.

The existing positive acceleration feedback method is improved based on Positive Position Feedback (PPF), has a good control effect on vibration control caused by steady-state disturbance, is a high-pass filter in essence, is easy to generate the problem of high-frequency control overflow, and is not suitable for active control of low-frequency vibration of a spacecraft caused by transient disturbance. In addition, the closed loop of the active control of the acceleration feedback vibration has inevitable time lag in the processes of sensing measurement, controller calculation and actuator driving execution, so that the control effect is reduced, and the amplitude decay time after control is increased.

Therefore, there is a need to develop a new acceleration feedback vibration control method, which is suitable for controlling the low-frequency vibration of a spacecraft flexible structure caused by transient disturbance, and can overcome the high-frequency overflow of a control system and eliminate the time lag influence of the control system.

Disclosure of Invention

In view of the above, the invention provides an acceleration feedback vibration control method for a spacecraft flexible structure, which overcomes the high-frequency overflow of a control system, solves the problem of control effect reduction caused by time lag of a closed-loop control system, and improves the vibration control capability of the system.

In order to achieve the purpose, the technical scheme of the invention comprises the following steps:

s1, carrying out simulation modeling analysis or experimental test on the structure to be controlled to obtain a kinetic equation and a transfer function of the structure to be controlled; the structure to be controlled is a flexible structure in the spacecraft.

S2, constructing a vibration control system for a structure to be controlled, designing a controller based on acceleration feedback, introducing a second-order system compensator and a first-order system compensator into the controller, and configuring a compensator damping parameter zeta_fFrequency parameter omega_f。

And S3, configuring feedback gains alpha and beta of the controller, and adding the control output into the variables of the second-order system compensator and the first-order system compensator and performing negative feedback.

Further, if the vibration system of the structure to be controlled is a single-degree-of-freedom vibration system, S2 includes the following steps:

s21: the second order system compensator equation is constructed as follows:

where y is the second order system compensator variable,is the second derivative of y and is,is the first derivative of y, ζ_fIs the compensator damping parameter, ω_fIs the compensator frequency parameter, x is the modal coordinate,is the second derivative of x;

the first order system compensator equation is constructed as follows:

wherein z is a first order system compensator variable,is the first derivative of z;

s22: writing the compensator into a transfer function form, the transfer function form of the acceleration response input A(s) and the control output Y(s) of the second-order system compensator is as follows:

the transfer function form of the acceleration response input A(s) and the control output Z(s) of the first order system compensator is as follows:

further, the compensator frequency parameter ω_fClose to the natural frequency ω, i.e. ω, of the vibrating system_fω. Damping parameter ζ_fCan be set according to the specific conditions of the test.

Further, the vibration system is a k-order degree of freedom system, and when k is larger than or equal to 2:

the second-order system compensator equation is constructed as

The first order system compensator equation is constructed as

Wherein, gamma is_f∈R^k×kAs a compensator damping parameter matrix, R^k×kA real number array of scale k × k; omega_f∈R^k×kIs a compensator frequency parameter matrix; y is the second order system compensator variable for the k-order degree of freedom,is a second derivative of Y and is,is a first derivative of Y, q is a modal coordinate vector,is the second derivative of q, D is the actuator configuration matrix in the vibration system, Z is the first order system compensator variable for k degrees of freedom,is the first derivative of Z.

Further, the frequency parameter matrix Ω is ensured_fThe medium design frequency is close to the k-order natural frequency, i.e. omega, of the vibrating system to be controlled_fi≈ω_i(i ═ 1,2, …, k), where ω is_fiAs a frequency parameter matrix omega_fOf (d) the ith design frequency, ω_iThe ith order natural frequency of the vibration system; damping parameter matrix gamma_fDesign damping ζ in_fiAnd setting according to the specific conditions of the test.

Further, the vibration system is a single degree of freedom system, and the specific step S3 includes:

the expression of the control output of the controller based on the acceleration feedback is

u＝-(αy+βz) (9)

Wherein u is the control output of a controller designed based on acceleration feedback for controlling the vibration system; alpha is the feedback gain of the second-order system compensator, and beta is the feedback gain of the first-order system compensator;

the system time lag of the closed loop of the vibration system, which is generated by the sensing measurement, the calculation of the controller and the execution of the driving process of the actuator, is t_kThe delayed phase of the vibration system is theta_k＝t_kω, ω is the natural frequency of the vibrating system, let ω_fω, then the configuration of the feedback gains α and β of the controller should satisfy the following equation:

further, the vibration system is a multiple degree of freedom system, and S3 specifically includes the following steps:

the control expression of the controller based on the acceleration feedback is

U＝-(A_αY+B_βZ) (10)

Wherein U is a control output matrix of the controller designed based on acceleration feedback, A_α∈R^k×kIs a second-order system compensator gain matrix,α₁～α_krespectively 1 st to kth gain parameters, B_β∈R^k×kIn the form of a first order system compensator gain matrix,β₁～β_k1 st to kth gain parameters respectively;

by configuring the gain parameter A_αAnd B_βCompensating the time lag of the system control loop to make the active vibration control of each order of the decoupled system equivalent to direct speed feedback, A_αAnd B_βShould satisfy

In the formula, theta_i,kDelayed phase theta for each order mode of vibration system_i,k＝t_k·ω_i，ω_iIs the ith order modal frequency.

Has the advantages that:

(1) the invention provides an acceleration feedback vibration control method, which takes acceleration as a direct feedback physical quantity to avoid error accumulation caused when the acceleration physical quantity is converted into a speed quantity and a displacement quantity through primary integration and secondary integration; secondly, a second-order system compensator is introduced, negative feedback is directly carried out on a compensator variable, and the problem of high-frequency control overflow is solved through the low-pass filtering characteristic of the compensator; moreover, a first-order system compensator is added, and the problem of control effect reduction caused by time lag of a closed-loop control system can be solved by configuring two compensator gain parameters, so that the vibration control capability of the system is improved.

(2) The existing displacement feedback control and speed feedback control technologies need to perform primary integration or secondary integration on signals acquired by an acceleration sensor, and are influenced by measurement noise of the acceleration sensor, so that a large accumulated error can be generated.

(3) In the conventional positive acceleration feedback technology, the introduced second-order system compensator takes the second derivative of a compensator variable as positive feedback, and is essentially a high-pass filter, so that high-frequency components in acceleration response can be amplified, the problem of high-frequency control overflow is easily caused, and the spacecraft is not suitable for active control of low-frequency vibration caused by transient disturbance and the like. The second-order system compensator introduced by the invention uses the compensator variable as negative feedback, is essentially a low-pass filter, filters high-frequency components in acceleration response, and solves the problem of high-frequency control overflow caused by the active control of low-frequency vibration of a flexible structure.

(4) In the existing positive acceleration feedback technology, the control effect is reduced because of system time lag generated in the closed loop of a control system in the processes of sensing measurement, controller operation and actuator driving execution is not considered. The invention adds a first-order system compensator, compensates the influence of system time lag by configuring two compensator gain parameters, further improves the control effect and further shortens the time required by amplitude attenuation.

Drawings

FIG. 1 is a flow chart of the present invention;

FIG. 2 is a schematic diagram of a control method of the present invention;

FIG. 3 is a diagram of the simulation result of the acceleration response of the positive acceleration feedback control method and the method of the present invention in embodiment 2;

FIG. 4 is a graph of simulation results of the control force output of the positive acceleration feedback control method of the embodiment 2 and the method of the present invention;

FIG. 5 shows vibration control verification system for truss scale test piece in example 3

Fig. 6 is a graph showing the results of the test before and after the control of example 3 in which the gain parameter α is 1 and β is 0

Fig. 7 is a graph showing the results of the test before and after the control of example 3 in which the gain parameter α is 0.5 and β is 0.5.

Detailed Description

The invention is described in detail below by way of example with reference to the accompanying drawings.

The invention provides an acceleration feedback vibration control method which mainly comprises three steps, as shown in figure 1, and the specific process is described as follows:

s1: obtaining a low-frequency kinetic equation and a transfer function of the structure according to simulation modeling analysis or structural test;

if the vibration system is a single degree of freedom system, the structural dynamics equation is as follows

Where x is the modal coordinate and 2 ξ ω and ω correspond respectively to the damping and natural frequency of the structure itself.

As shown in FIG. 2, the transfer function of the control input U(s) and the acceleration response output A(s) if written as follows

If the vibration system is a multi-degree-of-freedom system, a k-order vibration control equation which is truncated by a modal and contains m actuators/sensors can be written, the structural dynamics equation is as follows

In the formula, D is belonged to R^m×kArranging the matrix for the actuators, DD^T＝E_m；q∈R^k×1Is a modal coordinate vector; omega belongs to R^k×kTo construct the natural frequency matrix, Ω ═ diag (ω)₁,ω₂,...,ω_k)；Γ∈R^k×kIs a structural modal damping matrix, Γ ═ diag (ζ)₁,ζ₂,...,ζ_k)。

S2: designing a controller based on acceleration feedback, introducing a second-order system compensator and a first-order system compensator, and configuring a damping parameter zeta of the compensator_fFrequency parameter omega_f；

If the vibration system is a single degree of freedom system, the second-order system compensator equation is as follows

The first order system compensator equation is as follows

Where y is the second order system compensator variable,is the second derivative of y and is,is the first derivative of y, ζ_fIs the compensator damping parameter, ω_fIs the compensator frequency parameter, x is the modal coordinate,is the second derivative of x; z is a first order system compensator variable,is the first derivative of z.

Frequency parameter omega in compensator for ensuring acceleration feedback_fClose to the natural frequency of the system, ω, i.e. ω_fω. Damping parameter ζ_fCan be set according to the specific conditions of the test. Zeta_fAn inadequately taken excessive zeta_fToo large may result in a too rapid decrease in control output as the acceleration response amplitude decays.

As shown in FIG. 2, if the compensator is written as a transfer function, the second order system compensator has a transfer function of the acceleration response input A(s) and the control output Y(s), as follows

The first order system compensator acceleration response input is also in the form of a transfer function of A(s) and control output Z(s), as follows

Where s is the complex variable of the transfer function.

If the vibration system is a k-degree-of-freedom system, and k is more than or equal to 2, the equations of the corresponding second-order system compensator and first-order system compensator are as follows

In the formula, gamma_f∈R^k×kIn order to be a matrix of the damping parameters of the compensator,Ω_f∈R^k×kin order to be a matrix of frequency parameters of the compensator,y is the second order system compensator variable for the k-order degree of freedom,is a second derivative of Y and is,is a first derivative of Y, q is a modal coordinate vector,is the second derivative of q, Z is the first order system compensator variable for the k-order degrees of freedom,is the first derivative of Z.

Compensators, frequency parameter matrices omega, for which acceleration feedback should be guaranteed_fThe mid-design frequency is close to the natural frequency of the k-th order of the system to be controlled, i.e. omega_fi≈ω_i(i ═ 1,2, …, k); damping parameter matrix gamma_fDesign damping ζ in_fiCan be set according to the specific conditions of the test

S3: feedback gains alpha and beta of the controller are configured, and the control output is the addition of the variables of the two compensators and negative feedback is carried out.

If the vibration system is a single-degree-of-freedom system, the expression of the control output is

u＝-(αy+βz) (9)

Wherein u is the control output of a controller designed based on acceleration feedback for controlling the vibration system; alpha is the feedback gain of the second-order system compensator, and beta is the feedback gain of the first-order system compensator.

The free vibration response of a single degree of freedom undamped system is

x(t)＝A₀sin(ωt+θ₀) (10)

Considering the actual vibration control test system, the vibration active control closed loop has inevitable time lag due to sensing measurement, controller operation and actuator driving process execution. Setting the system time lag as t_kThe delay phase of the system is theta_k＝t_kω. Let omega_fAnd omega, then the second order system compensator and the first order system compensator essentially act as a second order and a first order low pass filter, and can obtain

If it isThe control system is actually simplified into direct speed feedback, the control output is equivalent to active damping, and the most direct and effective vibration control effect is achieved. Feedback gains alpha and beta of the two compensators are configured, wherein alpha is the feedback gain of the second-order system compensator, and beta is the feedback gain of the first-order system compensator; so that the control output u ═ - (α y + β z) can be equivalent to direct speed feedback, the following equation needs to be satisfied

As shown in fig. 2, which is a block diagram of the closed-loop control system of the present invention, gains α and β are proportional gains, and form a closed loop of the feedback control system by addition and negative feedback.

If the vibration system is a multi-degree-of-freedom system, the corresponding control expression is

U＝-(A_αY+B_βZ) (14)

Wherein U is a control output matrix of the controller designed based on acceleration feedback, A_α∈R^k×kIs a second-order system compensator gain matrix,α₁～α_krespectively 1 st to kth gain parameters, B_β∈R^k×kIn the form of a first order system compensator gain matrix,β₁～β_krespectively 1 st to kth gain parameters.

Similarly, by configuring the gain parameter A_αAnd B_βThe time lag of a system control loop is compensated, so that each order of modal active vibration control of the decoupled system can be equivalent to direct speed feedback. A. the_αAnd B_βShould satisfy

In the formula, the delay phase theta of each order mode_i,k＝t_k·ω_i，ω_i(i ═ 1,2, …, k) represents the modal frequencies of the respective orders. Example 2:

the steps of embodiment 1 are applied to verify the effectiveness and beneficial effects of the method provided by the invention, and the vibration control of a single-degree-of-freedom system is taken as a specific embodiment for explanation.

S1: the natural frequency ω of a single degree of freedom system is 1.0 and the damping ratio ζ is 0.005.

S2: the controller based on the acceleration feedback is designed to comprise a second-order system compensator and a first-order system compensator. Configuring compensator damping parameter ζ_fFrequency parameter omega_f。

Assuming that the exact value of ω cannot be specified, in terms of ω_fω, configure frequency parameterω_f1.1 damping parameter ζ_f＝0.707。

S3: feedback gains alpha and beta of the controller are configured, and the control output is the superposition and negative feedback of the calculation results of the two compensators in the controller.

It is known that the time lag t of the system from the receipt of a sensor command from the controller to the completion of the loading of the drive voltage_k0.6s, the delay phase theta of the system_k0.6 · 1.0 ═ 0.6 rad. The feedback gains alpha and beta of two compensators are configured to satisfy

Assuming that the vibration system contains unmodeled parts of the high-frequency residual mode ω_rDamping ratio ζ of 4.0_rAnd (3) verifying the vibration control effect of the method by comparing the conventional positive acceleration feedback control method with the acceleration feedback control method provided by the invention through simulation, wherein the vibration control effect is 0.005. The gains of the two methods are set to be consistent, and the sum of the gains is 1.

(1) Positive acceleration feedback control:

(2) the invention has the following acceleration feedback control: u ═ α y + β z), α ═ 0.25, and β ═ 0.75.

Observing the acceleration response curve shown in fig. 3, the existing positive acceleration feedback control method has obvious high-frequency overflow, and after vibration control, high-frequency acceleration response with higher amplitude always exists. The acceleration feedback control method solves the problem of high-frequency control overflow. As can be seen from the partially amplified acceleration curve graph, compared with a positive acceleration feedback control method, the vibration is more quickly inhibited by the invention, because a first-order system compensator is introduced and gain parameters of the two compensators are configured, the time lag t generated by closed-loop feedback of the system is further compensated_kAs shown in fig. 4.

Example 3:

the steps of example 1 are applied to verify the effectiveness and beneficial effects of the method provided by the invention, and the specific example is described by using the vibration control of a certain truss scale test piece, wherein the root of the truss scale test piece is fixedly supported, the end of the truss scale test piece is free, and zero gravity unloading is carried out in an air floatation or suspension mode, as shown in fig. 5. The structural parameters of the truss scale test piece are shown in the table below, wherein the piezoelectric stack actuator arranged at the root is used as control output, the acceleration sensor arranged at the end is used as control input, and the structural parameters of the truss scale test piece are shown in the table below

TABLE 1 truss shrinkage ratio test piece structural parameters

Parameter(s)	Numerical value
		Total length l	9m
Total mass m	About 15kg
		Fundamental frequency	0.69Hz
Modal damping ratio	About 0.03

S1: according to the structural test, the dynamic parameters of the truss scale test piece are obtained, wherein the modal damping ratio is about 0.03, and the fundamental frequency is about 0.69 Hz.

S2: the controller based on the acceleration feedback is designed to comprise a second-order system compensator and a first-order system compensator. Configuring compensator damping parameter ζ_fFrequency parameter omega_f。

Configuring frequency parameter omega in experiment_f2 pi · 0.7, damping parameter ζ_f0.707. And (4) carrying out numerical solution on the two compensator equations by adopting a forward difference method.

S3: feedback gains alpha and beta of the controller are configured, and the control output is the superposition and negative feedback of the calculation results of the two compensators in the controller.

The time step set by the control system is 100ms, the sensor instruction is received from the controller and sent to the controller, the loading of the driving voltage is finished, and the time lag t is about generated_kCalculating the delayed phase theta of the control of the fundamental frequency of the truss_kAnd 90ms/(1/0.69 × 1000) ≈ 1/8 pi, the ratio of alpha to beta is 1: 1.

And designing a contrast test to verify the control effect of the added first-order compensator. The gain parameter α is 1, β is 0, that is, a first-order system compensator is not added, and the test results before and after the initial disturbance control are shown in fig. 6, where 22.8 seconds are required for the acceleration amplitude to freely attenuate to below 3mg before control, 6.1 seconds are required for the acceleration amplitude to attenuate to below 3mg after control, and the attenuation time is shortened by 73.25%; the gain parameter α is 0.5, and β is 0.5, that is, a first-order system compensator is added, and the ratio of the parameter α to the parameter β is 1:1, the test result of the initial disturbance is shown in fig. 5, 4.4 seconds are required for the acceleration amplitude to decay to below 3mg after control, and the decay time is shortened by 80.70%. Test results prove that the method provided by the invention has a good control effect on the active control of the low-frequency vibration of the flexible truss; a comparison test shows that the method provided by the invention considers the system time lag and adds a first-order system compensator to shorten the attenuation time of the acceleration amplitude from 6.1s to 4.4s, thereby improving the vibration active control capability of the system and obtaining a better control effect. Fig. 7 is a graph showing the results of the test before and after the control of example 3 in which the gain parameter α is 0.5 and β is 0.5.

In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.