Sliding mode-extended state observer vibration control method based on time delay compensation

Abstract

The invention discloses a sliding mode-extended state observer vibration control method based on time delay compensation in the field of vibration control. The sliding mode-extended state observer vibration control method comprises the following steps: step 1) carrying out novel modeling on a four-side fixed support plate system; 2) designing an extended state observer; 3) designing a sliding mode controller; 4) designing a time delay compensator; and step 5) calculating the control quantity by using the NI-PCIe acquisition card and the Simulink. According to the invention, based on NI-PCIe hardware-in-the-loop platform development, the problems of system time lag, model uncertainty, influence of an inertial actuator and external excitation existing in a four-side fixed support plate are solved, and the total disturbance of the system including internal and external disturbance is estimated through an extended state observer. A content system is simplified into an integral series connection type for control by eliminating total disturbance through feedforward, and a delay compensator based on an enhanced differentiator is introduced to carry out non-delay design on the system, so that the vibration suppression performance of the sliding mode controller is improved.

Description

Technical Field

[0001] The invention belongs to the technical field of vibration control, and in particular relates to a sliding mode-expanded state observer vibration control method based on time delay compensation. Background Art

[0002] Thin plate materials have been widely used in aerospace engineering, shipbuilding engineering, vehicle engineering, mechanical engineering and other engineering fields due to their advantages such as light weight and high flexibility. However, due to model uncertainty, high-order harmonics and unknown external excitations, they are very likely to cause resonance and noise, structural damage, reduced safety and system collapse. Therefore, vibration control has important research significance in the engineering field.

[0003] In order to effectively suppress the vibration of the four-sided fixed plate, various advanced methods have been studied. Such as direct velocity feedback control, proportional control, integral control, derivative control, phase compensation method, optimal velocity feedback control, etc. Although these vibration control methods have the advantages of simple structure and convenient application, the realization of their performance depends largely on the accurate mathematical model of the system. In actual vibration experiments, due to the uncertainty of model parameters, the complexity of boundary conditions, measurement noise, unknown external forces and high-order harmonics, modeling errors are inevitable. Therefore, ESO and anti-disturbance algorithm are considered to reduce the impact of model uncertainty.

[0004] The Extended State Observer (ESO) is a disturbance estimation method for total disturbance. The Extended State Observer (ESO) is the core link in the self-disturbance rejection control technology. It is a practical disturbance observation technology that regards the total disturbance as a new state of the system and compensates it in the feedforward channel to improve the system performance. The control based on the Extended State Observer has been proven to be effective in reducing internal and external disturbances and model uncertainties through feedforward channel compensation. The Extended State Observer is introduced into the Sliding Mode Control (SMC) to form a composite sliding mode control. In order to reduce the anti-disturbance burden of the sliding mode control, the switching gain of the sliding mode controller is also reduced, which improves the anti-disturbance ability and further reduces the jitter.

[0005] In actual control, multiple links such as controller calculation time and actuator actuation hysteresis will produce time delay. If the existence of time delay is ignored, the signal acquisition of the control system and the output of the control quantity will be misaligned, thereby reducing the vibration suppression effect. In the prior art, Smith Predictor is often used as a time delay compensator to eliminate the adverse effects of time delay, but the traditional Smith Predictor will amplify noise and is difficult to apply in complex environments. Summary of the invention

[0006] In view of the problems of system time lag, model uncertainty, influence of inertial actuator and external unknown disturbance of four-sided fixed-support plate, the present invention proposes a sliding mode-extended state observer vibration control method based on time delay compensation, and constructs a model of the four-sided fixed-support plate-inertial actuator system by using a new modeling method. The difficulty of adjusting the observer's parameters and the high-bandwidth noise gain are reduced by using a linear extended state observer. The control effect of the controller is improved by using the feedforward compensation of the total disturbance of the observer. An improved Smith predictor is introduced to compensate for the time delay occurring in the control process, thereby improving the control performance of the system.

[0007] To achieve the above object, the present invention adopts the following technical solution: a sliding mode-extended state observer vibration control method based on time delay compensation, comprising the following steps:

[0008] Step 1) New modeling of the four-sided clamped plate system

[0009] The four-sided clamped plate system is modeled using partial differential equations, and the system's kinematic modeling is performed based on the vibration characteristics of the plate structure and internal and external excitations. The force applied by the actuator, i.e., the inertial actuator, is defined as a disturbance, which is regarded as a secondary excitation to the four-sided clamped plate, and secondary modeling is performed based on this.

[0010] Step 2) Design of the extended state observer

[0011] The bandwidth method is used to design the linear ESO as follows:

[0012]

[0013] Where e1 is the error between the observer's estimated value and the actual value; x i (i=1,2,3) is the system state variable; z i (i=1,2,3) is x i The estimated value of (i=1,2,3); For z i The first derivative of (i=1,2,3); β i is the adjustable gain of the observer; b0 is the model parameter of the controlled object; u is the system control quantity; based on the bandwidth method, the parameters are set to β1=3ω, β2=3ω respectively 2 ,β3=ω 3 , ω is the bandwidth of the extended state observer;

[0014] Step 3) Design of sliding mode controller

[0015] Design the following system sliding surface function:

[0016] s=cx1+x2 (3.1)

[0017] In the formula, c>0 is the design constant of the sliding surface, which satisfies the Hurwitz condition, so the derivative of the sliding surface can be obtained:

[0018]

[0019] Where b0 is the model parameter of the controlled object; v is the sliding mode control input; ε is the total disturbance of the error;

[0020] Select an exponential approach rate:

[0021]

[0022] Where η>0 is the sign function sgns switch gain; k>0 is the rate at which the system reaches the sliding mode surface, and ks is the exponential approach term; According to equations (3.2) and (3.3), the sliding mode control input v is:

[0023]

[0024] In the formula, the switching term gain satisfies η′≥η+ε, and the magnitude of the sliding mode chattering depends on this value; through the accurate estimation of ESO, the total interference is approximately zero to achieve the reduction of sliding mode chattering; the system control input can be obtained by the information z2 and z3 obtained from ESO:

[0025] u=-(1 / b0)(cz2+ks+η′sgns+z3); (3.5)

[0026] Step 4) Design of delay compensator

[0027] The vibration reduction method based on SMC-ESO is combined with the proposed enhanced Smith Predictor algorithm, namely the delay compensation method of SMC-ESO, to improve the vibration reduction performance of active disturbance rejection control according to the vibration acquisition characteristics of the plate structure;

[0028] Step 5) Use NI-PCIe acquisition card and Simulink to complete the calculation of control quantity

[0029] The control modules in step 2) to step 4) are constructed in the Simulink environment. After the construction is completed, the hardware-in-the-loop control is realized with the help of the NI-PCIe acquisition card. The vibration signal of the accelerometer enters the Simulink control algorithm after passing through the constant current source adapter. The control quantity obtained by the algorithm is transmitted to the actuator, i.e., the electromagnetic inertial actuator, by the power amplifier to complete the control.

[0030] As a further improvement of the present invention, the second-order ordinary differential equation of the novel model of the four-sided fixed support plate system in step 1) is as follows:

[0031]

[0032] Where η m , m and ω m are the displacement, damping ratio and natural frequency associated with the m-th order mode; b m 、f cm and f dm are the control gain, the output force of the inertial actuator and the external unknown disturbance of the clamped plate, respectively.

[0033] As a further improvement of the present invention, step 3) is specifically:

[0034] The system model is converted into a delay-free form by introducing the Smith Predictor, the specific form of which is as follows:

[0035] X0(s)=X s (s)+X s1 (s) = G p (s)e -τs U(s)+G p (s)(1-e -τs )U(s)=G p (s)U(s)

[0036] Where, X0(s) is the output without delay after compensation; X s (s) is the system output; X s1 (s) is the output of the delay estimator; G p (s) is the transfer function of the controlled system; U(s) is the output control quantity of the controller;

[0037] According to Taylor series expansion When the delay constant τ is small, we have So we can get:

[0038] X0(s)=G p (s)U(s)=G p (s)e -τs U(s)e τs ≈X s (s)(1+τs)=X s (s)+τX s (s)s

[0039] That is, the system output X0(s) with delay compensation can be obtained by the system output X s (s) and the output differential τX s (s)s are obtained together; in order to make the differential signal more ideal, the following new differentiator that is insensitive to noise is used:

[0040]

[0041] By combining the enhanced time delay compensator composed of the new differentiator with the extended state observer and the sliding mode controller, the sliding mode-extended state observer vibration control method based on time delay compensation can be fully described:

[0042]

[0043] In the formula, e2 is the error between the observed value and the actual value, that is, the observation error; x0 is the delay-free output after compensation; r is the expected value of the control system; is the model parameter of the controlled object; x s is the system output; c>0 is the design constant of the sliding surface; τ is the system delay constant; τ1 and τ2 are time constants; η′ is the switching term gain value; sgns is the sign function; k>0 is the rate at which the system reaches the sliding surface, and ks is the exponential approach term.

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] (1) A new modeling method is used to more accurately model the four-sided fixed-support plate system. The characteristic of sliding mode control that is insensitive to matching disturbances makes the closed-loop system have good robustness. The extended state observer is used to eliminate the mismatching disturbance as a total disturbance, so that the controlled object of the sliding mode controller is simplified to an integral series system, which greatly reduces the difficulty of controller design and improves the control effect. The linear extended state observer used has a lower bandwidth gain and is more insensitive to disturbances, reducing the interference caused by high-frequency noise to the system. It is proposed to use a new Smith predictor to compensate for the delay. The new delay compensator fully considers the influence of noise when designing it, and uses a noise-insensitive differentiator, which expands the application scenarios of the compensator while ensuring the effect.

[0046] (2) The design of the observer is simpler. The linear extended state observer has only one bandwidth parameter that needs to be adjusted. In addition, the observer gain adjusted by the bandwidth method is significantly reduced, which improves the ability to resist high-frequency noise interference.

[0047] (3) The design of the controller is relatively simple. Due to the existence of the extended state observer, the controlled system can be reconstructed and simplified into an integral series system. Therefore, the sliding mode controller used in the present invention is as simple as other traditional control methods (such as PD) and does not increase the difficulty of the control algorithm.

[0048] (4) Compared with the traditional differentiator used in the traditional delay compensator which amplifies the noise, the application of the new delay compensator reduces the adverse effects of the delay link on the control system. The present invention innovatively adopts a new noise-insensitive differentiator to obtain a new delay compensator, which ensures the delay compensation effect while being less susceptible to external random noise. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 Schematic diagram of the novel differentiator in the present invention.

[0050] Figure 2 It is the Lissajous fitting diagram of the time delay constant in the present invention.

[0051] Figure 3 It is a flow chart of the control system in the present invention.

[0052] Figure 4 This is a physical picture of the experimental verification platform.

[0053] Figure 5 This is a time domain analysis diagram of the control effect.

[0054] Figure 6 This is the frequency domain analysis diagram of the overall control effect.

[0055] Figure 7 This is a frequency domain analysis diagram of the local control effect. DETAILED DESCRIPTION

[0056] The acquisition and execution devices required by the algorithm in the present invention include NI-PCIe acquisition card, accelerometer, constant current source adapter and power amplifier. The acceleration signal is collected by the accelerometer in conjunction with the constant current source adapter as the input of the control algorithm, and the output of the control algorithm is output to the electromagnetic inertial actuator as the actuator through the power amplifier to suppress the vibration of the plate structure.

[0057] A sliding mode-extended state observer vibration control method based on time delay compensation comprises the following steps:

[0058] Step 1) New modeling of the four-sided clamped plate system

[0059] The partial differential equations are used to more accurately model the four-sided clamped plate system, and the system kinematic modeling is performed based on the vibration characteristics of the plate structure and the internal and external excitations. In order to reduce the number of sensors required for the experiment, the force applied by the actuator, i.e., the inertial actuator, can be defined as a disturbance, which is regarded as a secondary excitation to the four-sided clamped plate, and then secondary modeling is performed.

[0060] The vibration model of the four-sided clamped plate can be approximated by solving the following motion equation:

[0061]

[0062] In the formula, F(x, y, t) is the external exciting force function acting on the clamped plate; ρh is the mass per unit area of ​​the clamped plate; w, δ and D are the deflection, viscous damping coefficient and bending stiffness of the clamped plate, respectively;

[0063] According to the vibration superposition principle, the motion equation of the dynamic system can be expressed by the linear combination of the main modes, namely:

[0064]

[0065] In the formula, w m is the deflection associated with the m-th mode; W m (x,y) and η m (t) are the mode function and the displacement associated with the mth mode, respectively. In addition, the external exciting force acting on the clamped plate can also be expanded into the mode function:

[0066]

[0067] The modal damping ratio satisfies the equation When the shaker is excited at the modal frequency, F m It can be regarded as the sum of the external exciting force and the execution force of the inertial actuator.

[0068] Combining equations (1.1), (1.2) and (1.3) we can obtain the following second-order ordinary differential equation:

[0069]

[0070] Where η m , m and ω m are the displacement, damping ratio and natural frequency associated with the m-th order mode; b m 、f cm and f dm are the control gain, the output force of the inertial actuator and the external unknown disturbance of the clamped plate, respectively.

[0071] Step 2) Design of the extended state observer

[0072] There are too many parameters that need to be adjusted in nonlinear ESO, which makes the control system design complicated. Therefore, the bandwidth method is used to design linear ESO. The details are as follows: while ensuring the control effect, the number of parameters is reduced, so that the gain term of ESO can be obtained through the bandwidth, which can be more widely used in actual engineering.

[0073]

[0074] Where e1 is the error between the observer's estimated value and the actual value; x i (i=1,2,3) is the system state variable; zi (i=1,2,3) is x i The estimated value of (i=1,2,3); For z i The first derivative of (i=1,2,3); β i is the adjustable gain of the observer; b0 is the model parameter of the controlled object; u is the system control quantity; based on the bandwidth method, the parameters are set to β1=3ω, β2=3ω respectively 2 ,β3=ω 3 , ω is the bandwidth of the extended state observer.

[0075] Step 3) Design of sliding mode controller

[0076] Design the following system sliding surface function:

[0077]

[0078] In the formula, c>0 is the design constant of the sliding surface, which satisfies the Hurwitz condition, so the derivative of the sliding surface can be obtained:

[0079]

[0080] Where b0 is the model parameter of the controlled object; v is the sliding mode control input; ε is the total disturbance of the error;

[0081] Select an exponential approach rate:

[0082]

[0083] Wherein, η>0 is the sign function sgns switch gain; k>0 is the rate at which the system reaches the sliding surface, ks is the exponential approach term. When s is large, that is, the moving point is far away from the switching surface, the system can quickly approach the switching surface. When s is small, the exponential approach term is slow when the moving point is about to reach the switching surface. At this time, the sign function is used to achieve the system reaching the sliding surface in a finite time. According to equations (3.2) and (3.3), the sliding mode control input v is:

[0084]

[0085] In the formula, the switching term gain value should satisfy η′≥η+ε, and the magnitude of the sliding mode chattering depends on this value; through the accurate estimation of ESO, the total interference is approximately zero to achieve the reduction of sliding mode chattering; the system control input can be obtained by the information z2 and z3 obtained from ESO:

[0086] u=-(1 / b0)(cz2+ks+η′sgn s+z3) (3.5)

[0087] Step 4) Design of delay compensator

[0088] Commonly used control laws usually do not consider the impact of system delays, but in actual structural vibration control systems, system delays caused by sensor / actuator mismatch, calculation delays, and acquisition card sampling time are inevitable. Delay links under non-ideal conditions will reduce the control performance of the system and even destroy the stability of the system. Therefore, the system delay is taken into account in the modeling stage, and the delay link is reasonably equivalent and introduced into the system model function. The second-order vibration system with delay is derived as follows:

[0089]

[0090] In the formula, a i (i=0,1,2) is the system model parameter, τ is the system delay constant;

[0091] The system model is converted into a delay-free form by introducing the Smith Predictor; the Smith Predictor is essentially a pure lag compensation control based on the model, which eliminates or weakens the lag time by introducing a compensator connected in parallel with the controlled object, such as Figure 1 As shown, the specific form of the Smith Predictor is as follows:

[0092] X0(s)=X s (s)+X s1 (s) = G p (s)e -τs U(s)+G p (s)(1-e -τs )U(s)=G p (s)U(s) (4.2)

[0093] Where, X0(s) is the output without delay after compensation; X s (s) is the system output; X s1 (s) is the output of the delay estimator; G p (s) is the transfer function of the controlled system; U(s) is the output control quantity of the controller.

[0094] In actual experiments, it is difficult to directly obtain the output value X of the Smith predictor. s1 (s), according to Taylor series expansion When the delay constant τ is small, we have So we can get:

[0095] X0(s)=G p (s)U(s)=G p (s)e -τs U(s)e τs ≈X s (s)(1+τs)=X s(s)+τX s (s)s (4.3)

[0096] From formula (4.3), we can see that X0(s) can be obtained by s (s) and τX s (s)s is derived (that is, the system output and its differential form); according to the commonly used traditional differentiator Derived after differentiation X s (s) The signal is as follows:

[0097]

[0098] Write equation (4.4) in time domain form:

[0099]

[0100] Considering that in the actual vibration system, the accelerometer is easily affected by external random noise, the system output differential signal with noise in the system is obtained as follows:

[0101]

[0102] In the formula, n(t) is the external noise; it can be seen from formula (4.6) that the noise is amplified by 1 / τ, so the traditional differentiator will cause noise amplification; in order to reduce the influence of noise, the following new differential form is proposed:

[0103]

[0104] The delayed signal x s (t-τ1) and x s (t-τ2) respectively uses the inertia link and Indicates that the improved differential equation is as follows:

[0105]

[0106] In the formula, ω * is an improved differential link; when the time constants τ1 and τ2 are close to the system delay constant τ, the new differentiator can be approximated as:

[0107]

[0108] According to the extreme value theorem, we can get Therefore, the noise signal can be ignored after passing through the new differentiator; the improved time delay compensator of the present invention adopts the new differentiator, which can accurately compensate for the time delay and is insensitive to noise.

[0109] Test the system delay constant and perform delay compensation. Perform continuous excitation at the first-order resonant frequency of 48.5Hz and draw the collected input and output signals. This set of input and output data can be used as x and y coordinates to draw the Lissajous curve, such as Figure 2 As shown. Because the hysteresis loop is elliptical, there is a time delay in this system. In order to estimate the time delay coefficient of the entire control system, the Lissajous curve of the vibration mode is fitted as follows:

[0110]

[0111] In the formula, the natural frequency is f = 48.5Hz, and the phase difference is Using x and y in the above formula as the horizontal and vertical coordinates, respectively, the solid line in the Lissajous figure is fitted. It is easy to see that the experimental signal and the fitted signal of the Lissajous curve are roughly the same. Based on the above phase lag identification results, the delay time constant of the entire system can be obtained as: This delay constant is introduced into the new Smith Predictor to eliminate the delay effect.

[0112] Bringing the new Smith predictor obtained in this way into the extended state observer and the sliding mode controller, the overall expression of the control system is as follows:

[0113]

[0114] In the formula, e2 is the error between the observed value and the actual value, that is, the observation error; x0 is the delay-free output after compensation; r is the expected value of the control system; is the model parameter of the controlled object; x s is the system output; c>0 is the design constant of the sliding surface; τ is the system delay constant; τ1 and τ2 are time constants; η′ is the switching term gain value; sgns is the sign function; k>0 is the rate at which the system reaches the sliding surface, and ks is the exponential approach term.

[0115] Step 5) Use NI-PCIe acquisition card and Matlab / simulink to complete hardware-in-the-loop vibration control

[0116] The controller, observer and other links mentioned in step 2) to step 4) are built in Simulink, the vibration signal is collected and input into the Analog Input module in the Real-time environment of MATLAB / Simulink, and the control quantity is generated through the control algorithm mentioned above and transmitted to the Analog Output module. The control quantity is output to the actuator through the power amplifier by the acquisition card. The overall experimental control structure diagram is shown in the figure. Figure 3 As shown in Figure 4 shown.

[0117] Step 6) Check the amplitude signal in the Analog Input module to determine the vibration suppression effect of the present invention

[0118] Time domain control effect Figure 5 When there is no control intervention, the vibration amplitude is about 5V; when the sliding mode-expanded state observer method intervenes, the vibration amplitude drops to 1.7V, a decrease of 66%; when the sliding mode-expanded state observer-traditional delay compensator method intervenes, the vibration amplitude drops to 1.4V, a decrease of 72%; when the sliding mode-expanded state observer-new delay compensator intervenes, the vibration amplitude drops to 1.08V, a decrease of 78%.

[0119] The frequency domain control results are as follows: Figure 6 and Figure 7 As shown. When the sliding mode-extended state observer-new time delay compensator intervenes, the amplitude of the first mode vibration is reduced by 12.925dB, which is better than the sliding mode-extended state observer-traditional time delay compensation controller (10.1dB) and the sliding mode-extended state observer controller (9.25dB). At the same time, the amplitude of the new controller is reduced by 7.33dB (97Hz), 12.6dB (146Hz), 9.4dB (194.05Hz), 6.373dB (242Hz) and 5.89dB (291Hz) at 2 to 6 times the main mode frequency, respectively, which is better than the other two controllers.

[0120] Experiments have shown that the advantage of the present invention is that the present invention can have a better vibration suppression effect than the traditional sliding mode-delay compensation controller no matter from the perspective of time domain or frequency domain.

[0121] The traditional control system development model requires a lot of time and effort in code development, while the present invention is completed in a hardware-in-the-loop system with MATLAB / Simulink as the core, using the Desktop real-time toolbox in Simulink to communicate software and hardware, and conveniently and quickly complete the communication and acquisition functions. It only needs to build a simulation model in Simulink to complete the calculation of the control quantity. The entire process does not require complex code development, and the development cycle, development difficulty, and algorithm replacement difficulty are greatly reduced.

[0122] The present invention is not limited to the above-mentioned embodiments. On the basis of the technical solution disclosed in the present invention, technicians in this field can make some substitutions and deformations to some technical features therein according to the disclosed technical content without creative labor, and these substitutions and deformations are all within the protection scope of the present invention.

Claims

1. A sliding mode-extended state observer vibration control method based on time delay compensation, characterized in that: The following steps are involved: Step 1) New modeling of the four-sided clamped plate system The four-sided clamped plate system is modeled using partial differential equations, and the system's kinematic modeling is performed based on the vibration characteristics of the plate structure and internal and external excitations. The force applied by the actuator, i.e., the inertial actuator, is defined as a disturbance, which is regarded as a secondary excitation to the four-sided clamped plate, and secondary modeling is performed based on this. Step 2) Design of the extended state observer The bandwidth method is used to design the linear ESO as follows: Where e1 is the error between the observer's estimated value and the actual value; x i (i=1,2,3) is the system state variable; z i (i=1,2,3) is x i The estimated value of (i=1,2,3); z i (i=1,2,3) is z i The first derivative of (i=1,2,3); β i is the adjustable gain of the observer; b0 is the model parameter of the controlled object; u is the system control quantity; based on the bandwidth method, the parameters are set to β1=3ω, β2=3ω respectively 2 ,β3=ω 3 , ω is the bandwidth of the extended state observer; Step 3) Design of sliding mode controller Design the following system sliding surface function: s=cx1+x2(3.1) In the formula, c>0 is the design constant of the sliding surface, which satisfies the Hurwitz condition, so the derivative of the sliding surface can be obtained: Where b0 is the model parameter of the controlled object; v is the sliding mode control input; ε is the total disturbance of the error; Select an exponential approach rate: Where η>0 is the sign function sgns switch gain; k>0 is the rate at which the system reaches the sliding mode surface, and ks is the exponential approach term; According to equations (3.2) and (3.3), the sliding mode control input v is: In the formula, the switching term gain satisfies η′≥η+ε, and the magnitude of the sliding mode chattering depends on this value; through the accurate estimation of ESO, the total interference is approximately zero to achieve the reduction of sliding mode chattering; the system control input can be obtained by the information z2 and z3 obtained from ESO: u=-(1 / b0)(cz2+ks+η′sgns+z3); (3.5) Step 4) Design of delay compensator The vibration reduction method based on SMC-ESO is combined with the proposed enhanced Smith Predictor algorithm, namely the delay compensation method of SMC-ESO, to improve the vibration reduction performance of active disturbance rejection control according to the vibration acquisition characteristics of the plate structure; Step 5) Use NI-PCIe acquisition card and Simulink to complete the calculation of control quantity The control modules in step 2) to step 4) are constructed in the Simulink environment. After the construction is completed, the hardware-in-the-loop control is realized with the help of the NI-PCIe acquisition card. The vibration signal of the accelerometer enters the Simulink control algorithm after passing through the constant current source adapter. The control quantity obtained by the algorithm is transmitted to the actuator, i.e., the electromagnetic inertial actuator, by the power amplifier to complete the control.

2. The sliding mode-extended state observer vibration control method based on time delay compensation according to claim 1 is characterized in that: The second-order ordinary differential equation of the new model of the four-sided fixed plate system described in step 1) is as follows: Where η m , m and ω m are the displacement, damping ratio and natural frequency associated with the m-th order mode; b m 、f cm and f dm are the control gain, the output force of the inertial actuator and the external unknown disturbance of the clamped plate, respectively.

3. The sliding mode-extended state observer vibration control method based on delay compensation according to claim 1 is characterized in that: Step 3) is specifically: The system model is converted into a delay-free form by introducing the Smith Predictor, the specific form of which is as follows: X0(s)=X s (s)+X s1 (s)=G p (s)e -τs U(s)+G p (s)(1-e -τs )U(s)=G p (s)U(s) Where, X0(s) is the output without delay after compensation; X s (s) is the system output; X s1 (s) is the output of the delay estimator; G p (s) is the transfer function of the controlled system; U(s) is the output control quantity of the controller; According to Taylor series expansion When the delay constant τ is small, we have So we can get: X0(s)=G p (s)U(s)=G p (s)e -τs U(s)e τs ≈X s (s)(1+τs)=X s (s)+τX s (s)s That is, the system output X0(s) with delay compensation can be obtained by the system output X s (s) and the output differential τX s (s)s are obtained together; in order to make the differential signal more ideal, the following new differentiator that is insensitive to noise is used: By combining the enhanced time delay compensator composed of the new differentiator with the extended state observer and the sliding mode controller, the sliding mode-extended state observer vibration control method based on time delay compensation can be fully described: In the formula, e2 is the error between the observed value and the actual value, that is, the observation error; x0 is the delay-free output after compensation; r is the expected value of the control system; is the model parameter of the controlled object; x s Output for the system; c>0 is the design constant of the sliding surface; τ is the system delay constant; τ1 and τ2 are time constants; η′ is the gain value of the switching term; sgns is the sign function; k>0 is the rate at which the system reaches the sliding surface, and ks is the exponential approach term.

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