A control system of a large-aperture piezoelectric fast steering mirror

Abstract

The present application belongs to the field of control system, and particularly relates to a control system of a large-aperture piezoelectric fast steering mirror, aiming at solving the technical problem that the existing large-aperture PFSM is easily affected by high-order resonance, nonlinear disturbance and hysteresis nonlinearity of the piezoelectric actuator caused by dynamic coupling stiffness of large-inertia load and flexible accessories, thereby affecting the control accuracy and closed-loop bandwidth of the PFSM and causing instability. The system comprises a sliding mode controller SMC, a neural network adapter, an extended state observer ESO, a high-order extended state observer HESO and a differential speed detector. The present application comprises a cascade high-order extended state observer composed of the extended state observer ESO and the high-order extended state observer HESO, and a PFSM control system based on the cascade high-order extended state observer, the sliding mode controller SMC and the neural network adapter. Compared with the prior art, the control system has stronger disturbance suppression capability and control accuracy.

Description

TECHNICAL FIELD

[0001] The application relates to a control system, in particular to a control system of a large-aperture piezoelectric fast steering mirror. BACKGROUND

[0002] Fast steering mirror (FSM) is widely used in astronomical observation, laser communication and remote sensing. Since 1980s, many scholars at home and abroad have proposed different design indexes of deflection range, response speed and positioning accuracy according to different application requirements, and developed different types of FSM systems. Among them, the piezoelectric FSM (PFSM) system has been widely used because of its advantages of large output force, small size, no electromagnetic interference, high resolution and fast response speed. In recent years, with the development of precision optical instruments and the continuous improvement of application requirements, on the one hand, the demand for the clear aperture of PFSM is getting larger and larger, especially in the fields of astronomical observation and high-energy laser, the clear aperture of PFSM usually needs to be greater than 100 mm or even larger; on the other hand, the requirements for the stability accuracy and aiming accuracy of PFSM in the order of micro-arc or even sub-micro-arc are increasingly urgent. Therefore, it has important application value to study the high-precision and wide-frequency-domain large-aperture PFSM. However, the larger the clear aperture of PFSM is, the lower the mechanical resonance frequency is and the more the resonance peaks are, which seriously limits the improvement of the closed-loop bandwidth and the beam pointing accuracy of the large-aperture PFSM.

[0003] There are mainly three reasons restricting the closed-loop bandwidth and the beam pointing accuracy of the large-aperture PFSM. Firstly, the low open-loop cutoff frequency and low resonance frequency caused by large inertia load limit the improvement of the open-loop gain, and the size of the load inertia of the PFSM is directly determined by the clear aperture. Secondly, the high-order resonance and nonlinear disturbance caused by the dynamic coupling stiffness and nonlinear effect of the flexible accessories in the large-aperture PFSM. The flexible accessories in the large-aperture PFSM mainly include a compliant amplification mechanism and a flexible support mechanism, the former is used to amplify the output displacement of the piezoelectric ceramic actuator so that the PFSM obtains a larger stroke, and the latter acts as a hinge of the PFSM driving mechanism to support and rotate. Thirdly, the hysteresis nonlinearity of the piezoelectric actuator causes the nonlinear relationship between the output displacement and the voltage, which limits the improvement of the beam pointing accuracy.

[0004] With the increase of the aperture of the PFSM, the above factors and other various disturbances have a more significant impact on the control accuracy and the closed-loop bandwidth of the PFSM, and even cause instability. Therefore, it has very important practical significance to study the modeling and closed-loop control technology of the large-aperture PFSM. SUMMARY

[0005] The application aims to solve the technical problems that the existing large-aperture PFSM is easily affected by high-order resonances, nonlinear disturbances and hysteresis nonlinearities of piezoelectric actuators caused by dynamic coupling stiffness and nonlinear effects of large-inertia loads and flexible accessories, thereby affecting the control accuracy and closed-loop bandwidth of the PFSM and causing instability, and to provide a control system of a large-aperture piezoelectric fast steering mirror.

[0006] To achieve the above-mentioned purpose, the technical solution adopted by the application is:

[0007] A control system of a large-aperture piezoelectric fast steering mirror, which is characterized in that:

[0008] The control system comprises a sliding mode controller SMC, a neural network adapter, an extended state observer ESO, a high-order extended state observer HESO and a differential speed detector.

[0009] The first input end of the neural network adapter receives a compliant mechanism output displacement estimation error e z1 output by the high-order extended state observer HESO, a piezoelectric actuator displacement estimation error e ζ1 output by the extended state observer ESO and a sliding mode surface σ output by the sliding mode controller SMC, and the output end outputs a sliding mode control estimation value to the first input end of the sliding mode controller SMC.

[0010] The second input end of the sliding mode controller SMC receives an external reference input r, and the third input end receives a piezoelectric actuator displacement estimation value output by the output end of the extended state observer ESO. The two fourth input ends respectively receive compliant mechanism output displacement estimation values output by the two output ends of the high-order extended state observer HESO. The two fifth input ends respectively receive compliant mechanism output displacements z1 output by capacitive sensors in the large-aperture piezoelectric fast steering mirror to be controlled and piezoelectric actuator displacements ζ1 output by strain sensors, and the two sixth input ends respectively receive compliant mechanism output displacement measurement values z2 output by the differential speed detector and piezoelectric actuator displacement measurement values ζ2, and the output end outputs an actual control u to the second input end of the neural network adapter, the first input end of the extended state observer ESO and the control end of the large-aperture piezoelectric fast steering mirror to be controlled.

[0011] The second input end of the extended state observer ESO receives a piezoelectric actuator output displacement ζ1 output by a strain sensor.

[0012] The two input ends of the high-order extended state observer HESO respectively receive compliant mechanism output displacements z1 output by capacitive sensors and piezoelectric actuator displacements ζ1 output by strain sensors.

[0013] The two inputs of the differential speedometer respectively receive the compliant mechanism output displacement z1 and the piezoelectric actuator displacement ζ1 output by the capacitance sensor of the large-aperture piezoelectric fast steering mirror to be controlled.

[0014] Further, the state equation of the high-order extended state observer HESO is:

[0015]

[0016] In the formula, z i is the compliant mechanism output displacement, i=1, 2, 3, 4; is the estimated value of z i , i=1, 2, 3, 4; β zi is the high-order extended state observer gain, β zi >0, i=1, 2, 3, 4; e z1 is the compliant mechanism output displacement estimation error, ζ1 is the piezoelectric actuator displacement; g1 is the model parameter of the high-order extended state observer.

[0017] Further, the state equation of the extended state observer ESO is:

[0018]

[0019] In the formula, ζ i is the piezoelectric actuator displacement, i=1, 2, 3, 4; is the estimated value of the piezoelectric actuator displacement, i=1, 2, 3; β ζi is the extended state observer gain, β ζi >0, i=1, 2, 3; e ζ1 is the piezoelectric actuator displacement estimation error, g2 is the model parameter of the extended state observer; u is the actual control; is the derivative of the total disturbance.

[0020] Further, the state equation of the sliding mode controller SMC is:

[0021]

[0022] In the formula, ξ is the sliding mode control, is an unknown constant, W T is the neural network weight, and ε is the neural network approximation error, x=[e z1 , e ζ1 , u] T is the neural network input, and h(x) is a Gaussian function; is the estimated value of ξ; u eq is the equivalent control; uSM is a sliding mode control law; and i is a constant, and i > 0, i = 1, 2, 3; r is a reference input, and is a derivative of r; s is a sliding surface; k is a control gain; sgn() is a sign function; and k is a switching gain.

[0023] Further, the sliding surface is:

[0024] s = e4 + l3e3 + l2e2 + l1e1;

[0025] wherein: e i is a tracking error, i = 1, 2, 3, 4.

[0026] Further, the adaptive law of the neural network adapter is:

[0027]

[0028] wherein: g i is a constant, and g i > 0, i = 1, 2. is an estimated value of . is an estimated value of W T .

[0029] The beneficial effects of the present application are:

[0030] The present application comprises a cascade high-order extended state observer by expanding a state observer ESO and a high-order extended state observer HESO, and a PFSM control system based on the cascade high-order extended state observer, a sliding mode controller SMC and a neural network adapter, compared with the prior art, the control system has stronger disturbance suppression ability and control accuracy. BRIEF DESCRIPTION OF DRAWINGS

[0031] Figure 1 is a structural schematic diagram of a prior large-diameter PFSM system;

[0032] Figure 2 is a schematic diagram of the arrangement structure of a piezoelectric actuator in the prior large-diameter PFSM system;

[0033] Figure 3 is a rotational dynamics equivalent model diagram of a flexible support mechanism in the prior large-diameter PFSM system;

[0034] Figure 4 is a double-port dynamic stiffness model of a diamond-shaped compliant amplification mechanism in the prior large-diameter PFSM system;

[0035] Figure 5This is an equivalent model diagram of the piezoelectric actuator in an existing large-diameter PFSM system;

[0036] Figure 6 This is a control principle diagram of a large-aperture piezoelectric fast tilting mirror and its control system according to the present invention.

[0037] Figure 7 The diagram shows simulation results of existing sliding mode control systems and the control system of a large-aperture piezoelectric fast tilting mirror of the present invention under step input and sinusoidal disturbance.

[0038] In the diagram: 1-FSM mirror, 2-flexible amplification mechanism, 3-flexible support mechanism, 4-strain sensor, 5-capacitive sensor, 6-base, 7-piezoelectric ceramic drive amplification circuit, 8-strain sensor signal conditioning circuit, 9-capacitive sensor signal acquisition module, 10-main control module, 11-computer. Detailed Implementation

[0039] To make the objectives, advantages, and features of the present invention clearer, the control system for a large-aperture piezoelectric fast tilting mirror proposed in this invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. The advantages and features of the present invention will become clearer from the following specific embodiments.

[0040] 1) Modeling of large-diameter PFSM

[0041] like Figure 1 As shown, the large-diameter PFSM mainly includes an FSM mirror 1, a flexible amplification mechanism 2, a flexible support mechanism 3, a strain sensor 4, a capacitance sensor 5, a base 6, a piezoelectric ceramic drive amplification circuit 7, a strain sensor signal conditioning circuit 8, a capacitance sensor signal acquisition module 9, a main control module 10, and a computer 11.

[0042] Specifically, the large-aperture PFSM model is decomposed into three parts: the first part is the rotation dynamics model of the tilted mirror, which includes the flexible support mechanism 3 and the FSM mirror 1; the second part is the dynamic stiffness model of the flexible amplification mechanism 2 (compliant mechanism); and the third part is the piezoelectric ceramic model, which includes the linear dynamics model and hysteresis model of the piezoelectric actuator.

[0043] Figure 1 PZT_A, PZT_B, PZT_C, and PZT_D are four piezoelectric actuators, arranged as follows: Figure 2 As shown, PZT_A and PZT_D drive PFSM to rotate around the X-axis through a flexible amplification mechanism, while PZT_B and PZT_C drive PFSM to rotate around the Y-axis through a flexible amplification mechanism.

[0044] Step 1.1. The tilting mirror body and the flexible support mechanism are regarded as a spring-mass-damper system, whose single-axis direction can be equivalent to a torsional system as shown in Fig. 1. Figure 3

[0045] The moment balance equation of the PFSM can be expressed as:

[0046]

[0047] where J is the moment of inertia of the tilting mirror body, R is the distance between the driving point and the rotation axis, k0 is the stiffness of the flexible support mechanism, μ is the equivalent damping coefficient of the system rotation, θ(t) is the deflection angle of the fast steering mirror, M(t) is the output moment of the driving mechanism, and t is the time.

[0048] Further, the tilting mirror body rotation dynamics model can be expressed as:

[0049]

[0050] where x o (t) is the output displacement of the flexible amplification mechanism, F o (t) is the output force of the flexible amplification mechanism.

[0051] The above model in the Laplace domain is expressed as:

[0052]

[0053] where s is the Laplace operator.

[0054] Step 1.2. Generally, under the conditions of small displacement and small load, the flexible amplification mechanism is regarded as a linear amplifier with static stiffness. However, under the conditions of high frequency and large load, the dynamic behavior of the flexible amplification mechanism becomes very complex. In order to maintain sufficient accuracy of the model under the condition of a simplified model, a two-port dynamic stiffness model as shown in Fig. 2 is adopted. Figure 4

[0055] Assuming that the damping and mass of the diamond-shaped flexible amplification mechanism are concentrated at the left and right and the top and bottom ends, and the middle connecting part is a flexible component with elasticity, the above two-port dynamic stiffness model is a special spring-mass-damper system.

[0056] Figure 4 where m o , F o , and x o are the equivalent output mass, output force, and output displacement of the flexible amplification mechanism, respectively; m i , F i , and x i ​​are the equivalent input mass, input force and input displacement of the flexible amplification mechanism, respectively, where the input displacement x i of the flexible amplification mechanism is the output displacement of the piezoelectric actuator. The modeling concept of the flexible amplification mechanism is to solve the elastic mechanics to establish the frequency-dependent relationship between the input and output force-displacement.

[0057] The two-port dynamic stiffness model can be expressed in the Laplace domain as:

[0058]

[0059] where λ > 0 is a constant; K1(s), K2(s), K3(s) and K4(s) are the dynamic stiffness of the flexible support mechanism.

[0060]

[0061] where a 21 , a 11 , a 01 , a 12 , a 02 , a 23 , a 13 and a 03 are the dynamic stiffness model parameters of the flexible support mechanism.

[0062] Substituting (4) into (3) gives

[0063]

[0064] where b o2 = J + 2R 2 a 23 , b o1 = 2R 2 (μ + a 13 ) / b o2 , b o0 = 2R 2 (k + a 03 ) / b o2 , c o1 = 2R 2 a 12 / b o2 , c o0 = 2R 2 a 02 / b o2 . b O2 , b o0 , c o1 and c o0 are mathematical expressions without actual physical meaning.

[0065] A sweep voltage signal is input to the piezoelectric actuator, and a piezoelectric actuator displacement signal x is measured by a strain sensor i A flexible amplification mechanism output displacement x is measured by a capacitance sensor o The relevant parameters of the model in (6) can be identified by a frequency domain identification algorithm.

[0066] Step 1.3, The dynamic model of the piezoelectric actuator is proposed by Goldfarb and Celanovic, which is based on the positive and negative effects of the piezoelectric actuator and consists of a dynamic equation and a charge equation. The driving voltage is decomposed into a linear voltage U P (t) and a hysteresis voltage U H (t). The linear voltage is assumed to be applied to the actuator, and the hysteresis voltage is regarded as voltage loss. The equivalent model of the piezoelectric actuator is shown in Figure 5

[0067] The piezoelectric actuator model is as follows:

[0068]

[0069] In the formula: m p is the equivalent mass of the piezoelectric actuator, μ p is the damping of the piezoelectric actuator, k p is the equivalent stiffness of the piezoelectric actuator, α is the electromechanical conversion coefficient, q is the charge quantity, U is the driving voltage, is the Maxwell resistance capacitance (MRC) hysteresis model.

[0070] Substituting (4) into (6), the transfer function of the linear voltage U P (t) to the piezoelectric actuator displacement x i is:

[0071]

[0072] In the formula: H(s) = m p s 2 + μ p s + k p , b i2 = λJ + 2R 2 (m p + λa 23 + a 21 ), b i1 = 2R 2 (λμ + μ p + λa 13 + a 11 ) / b i2 , b i0 = 2R 2 (λk + k p + λa 03 ​+a 01 ) / b i2 ,c i0 =2R 2 α / b i2 。H(s)、b i2 、b i1 、b i0 、c i0 are mathematical expressions without actual physical meaning.

[0073] The sweep voltage signal is input to the piezoelectric actuator, and the piezoelectric actuator displacement signal x i is measured by the strain sensor. The relevant parameters of the model in (8) can be identified by a frequency domain identification algorithm. Thus, the linear model of the large-diameter PFSM can be obtained, which is a cascade of two second-order systems (6) and (8). Considering external disturbances, model uncertainties, high-order nonlinearities and piezoelectric actuator hysteresis, let z1=x O , ζ1=x i , The dynamic model of the large-diameter PFSM can be represented in the following cascade form:

[0074]

[0075] wherein: u=U, d1 and d2 are the generalized disturbances at the load end and the driving end, respectively, including external disturbances, model uncertainties and high-order nonlinearities.

[0076] 2) Large-diameter PFSM sliding mode control method based on cascade high-order extended state observer (HCESO) and neural network self-adaptation (HCESO based NNSMC)

[0077] Step 2.1: Design of cascade high-order extended state observer

[0078] Let z3=ψ1=-b o1 z2-b o0 z1+c o1 ζ2+d1, The first subsystem of (9) can be represented as:

[0079]

[0080] wherein: g1 is the model parameter of the high-order extended state observer, g1=c o0 .

[0081] Let ζ3=ψ2=-b i1 ζ2-b i0 ζ1-c i0 U H +d2, the second subsystem of (9) can be represented as

[0082]

[0083] where g2is the model parameter of the extended state observer, g2= c i0 ; is the derivative of the total disturbance.

[0084] (10) The corresponding high-order extended state observer (HESO) is designed as:

[0085]

[0086] where z i is the compliant mechanism output displacement, i = 1, 2, 3, 4; is the estimated value of z i , i = 1, 2, 3, 4; β zi is the high-order extended state observer gain, β zi > 0, i = 1, 2, 3, 4; e z1 is the compliant mechanism output displacement estimation error, g1is the model parameter of the high-order extended state observer.

[0087] (10) The corresponding extended state observer (ESO) is designed as:

[0088]

[0089] where ζ i is the piezoelectric actuator displacement, i = 1, 2, 3, 4; is the estimated value of the piezoelectric actuator displacement, i = 1, 2, 3; β ζi is the extended state observer gain, β ζi > 0, i = 1, 2, 3; e ζ1 is the piezoelectric actuator displacement estimation error, g2is the model parameter of the extended state observer; u is the actual control; is the derivative of the lumped disturbance.

[0090] (12) and (13) are collectively referred to as the high-order cascaded extended state observer (HCESO).

[0091] Step 2.2: Sliding mode surface design

[0092] Define the following generalized tracking error

[0093]

[0094] where e i is the tracking error, i = 1, 2, 3, 4; e z3 is the sliding mode tracking error, r、 For reference input and derivatives of each order.

[0095] Design such as a sliding mold surface

[0096] σ=e4+λ3e3+λ2e2+λ1e1 (15)

[0097] In the formula: λ i >0, i = 1, 2, 3 are constants, and it is required that

[0098]

[0099] It is Hurwitz stable.

[0100] Step 2.3: Controller Design

[0101] Differentiating (15) gives

[0102]

[0103] In the formula: ξ represents sliding mode control, ξ = g1e ζ3z +λ2e z3 Suppose that ξ can be expressed as follows:

[0104]

[0105] In the formula: W is an unknown constant. T Let x be the weights of the neural network, ε be the approximation error of the neural network, and x = [e^(-ε)]. z1 ,e ζ1 ,u] T The input to the neural network is h(x), which is a Gaussian function.

[0106]

[0107] In the formula: δ>0 and c j ∈R 3×1 It is a constant.

[0108] The sliding mode controller (SMC) is designed as follows:

[0109]

[0110] In the formula: It is an estimate of ξ; u eq For equivalent control quantity; u SM For sliding mode control law; λ i λ is a constant. i >0, i = 1, 2, 3; r is the reference input. and where r is the each order derivative of r; s is the sliding mode surface; k is the control gain; sgn() is the sign function; k is the switching gain

[0111] The above formula satisfies the following adaptive law:

[0112]

[0113] where: γ i is a constant, γ i > 0, i = 1, 2; is the estimated value of W is the estimated value of W T .

[0114] Referring to Figure 6 , the control system of the large-aperture piezoelectric fast steering mirror comprises a sliding mode controller SMC, a neural network adapter, an extended state observer ESO, a high-order extended state observer HESO and a differential speed detector.

[0115] The first input end of the neural network adapter receives the compliant mechanism output displacement estimation error e z1 output by the high-order extended state observer HESO, the piezoelectric actuator displacement estimation error e ζ1 output by the extended state observer ESO and the sliding mode surface s output by the sliding mode controller SMC, and the output end outputs the sliding mode control estimation value to the first input end of the sliding mode controller SMC; the second input end of the sliding mode controller SMC receives the external reference input r, and the third input end receives the piezoelectric actuator displacement estimation value output by the output end of the extended state observer ESO; the two fourth input ends respectively receive the compliant mechanism output displacement estimation values and ​The two fifth input terminals respectively receive the compliant mechanism output displacement z1 and the piezoelectric actuator displacement ζ1 output by the capacitive sensor in the large-aperture piezoelectric fast steering mirror to be controlled, the two sixth input terminals respectively receive the compliant mechanism output displacement measurement value z2 and the piezoelectric actuator displacement measurement value ζ2 output by the differential speedometer, the output terminal outputs the actual control u to the second input terminal of the neural network adaptive unit, the first input terminal of the extended state observer ESO, and the control terminal of the large-aperture piezoelectric fast steering mirror to be controlled; the second input terminal of the extended state observer ESO receives the piezoelectric actuator output displacement ζ1 output by the strain sensor; the two input terminals of the high-order extended state observer HESO respectively receive the compliant mechanism output displacement z1 output by the capacitive sensor and the piezoelectric actuator displacement ζ1 output by the strain sensor; the two input terminals of the differential speedometer respectively receive the compliant mechanism output displacement z1 output by the capacitive sensor in the large-aperture piezoelectric fast steering mirror to be controlled and the piezoelectric actuator displacement ζ1 output by the strain sensor.

[0116] Since the x-axis and y-axis dynamics of the large-aperture PFSM are very similar, the embodiment takes the x-axis of the PFSM as an example, and first gives the x-axis frequency domain model as follows:

[0117]

[0118] Step 1, write (22) and (23) as the cascaded state space model (9);

[0119] Step 2, same as step 1 in 2);

[0120] Step 3, same as step 2 in 2);

[0121] According to the above steps, the controller is designed, and the controller parameters are selected as:

[0122] Control parameter Numerical value s 4 +β z1 s 3 +β z2 s 2 +β z3 s+β z4 =(s+ω o1 ) 4 ]]> o1 = 500 ​ s 3 +β z1 s 2 +β z2 s+β z3 =(s+ω o2 ) 3 ]]> o2 = 800 ​ s 3 +λ1s 2 +λ2s+λ3=(s+ω c ) 3 ]]> c = 2000 ​ [["g1"]] ​ 10000 [gamma]2 10000 κ 2000 k 2000

[0123] Under the step input and the sinusoidal disturbance, the simulation experiment results are as shown in Figure 7 It can be seen that compared with the traditional sliding mode control system, the control system of the embodiment has faster response speed and stronger disturbance suppression ability.

Claims

1. A control system of a large-aperture piezoelectric fast steering mirror, characterized in that: it comprises a sliding mode controller (SMC), a neural network adapter, an extended state observer (ESO), a high-order extended state observer (HESO) and a differential speedometer; A first input of the neural network adaptive is configured to receive a compliant mechanism output displacement estimation error e output by a high order extended state observer (HESO) z1 A second input of the neural network adaptive is configured to receive a piezoelectric actuator displacement estimation error e output by an extended state observer (ESO) ζ1 A third input of the neural network adaptive is configured to receive a sliding mode surface σ output by a sliding mode controller (SMC) A first input of the sliding mode controller is configured to receive the compliant mechanism output displacement estimation error e output by the high order extended state observer (HESO) The second input end of the sliding mode controller SMC receives an external reference input r, and the third input end receives a piezoelectric actuator displacement estimation value output by an extended state observer ESO output end Two fourth input ends respectively receive compliant mechanism output displacement estimation values output by two output ends of a high-order extended state observer HESO And Two fifth input ends respectively receive compliant mechanism output displacements z1 output by capacitive sensors in a large-aperture piezoelectric fast steering mirror to be controlled and piezoelectric actuator displacements ζ1 output by strain sensors, two sixth input ends respectively receive compliant mechanism output displacement measurement values z2 output by a differential speed detector and piezoelectric actuator displacement measurement values ζ2, and an output end outputs an actual control u to a second input end of a neural network adapter, a first input end of an extended state observer ESO, and a control end of the large-aperture piezoelectric fast steering mirror to be controlled; a second input end of the ESO receives a piezoelectric actuator output displacement ζ1 output by a strain sensor; two input ends of the HESO respectively receive a compliant mechanism output displacement z1 output by a capacitance sensor and a piezoelectric actuator displacement ζ1 output by a strain sensor; two input ends of the differential speedometer respectively receive a compliant mechanism output displacement z1 output by a capacitance sensor and a piezoelectric actuator displacement ζ1 output by a strain sensor in a large-aperture piezoelectric fast steering mirror to be controlled.

2. The control system of a large aperture piezoelectric fast steering mirror according to claim 1, wherein, a state equation of the HESO is: In the formula: z i For the output displacement of the compliant mechanism, i = 1, 2, 3, 4; For z i The estimated values, i = 1, 2, 3, 4; β zi For the gain of the higher-order extended state observer, β zi >0, i = 1, 2, 3, 4; e z1 The output displacement estimation error of the compliant mechanism. ζ1 represents the piezoelectric actuator displacement; g1 represents the model parameters of the higher-order extended state observer.

3. The control system of a large aperture piezoelectric fast steering mirror according to claim 2, wherein, a state equation of the ESO is: where ζ i is the piezoelectric actuator displacement, i = 1, 2, 3, 4; is the piezoelectric actuator displacement estimate, i = 1, 2, 3; β ζi is the extended state observer gain, β ζi > 0, i = 1, 2, 3; e ζ1 is the piezoelectric actuator displacement estimation error, g2is the model parameter of the extended state observer; u is the actual control; is the derivative of the total disturbance.

4. The control system of a large aperture piezoelectric fast steering mirror according to claim 3, wherein, a state equation of the SMC is: where ξ is the sliding mode control, is an unknown constant, W T is the neural network weight, ε is the neural network approximation error, x = [e z1 ,e ζ1 ,u] T is the neural network input, h(x) is the Gaussian function; is the estimation of ξ; u eq is the equivalent control; u SM is the sliding mode control law; λ i is a constant, λ i > 0, i = 1, 2, 3; r is the reference input, and for each order derivative of r; s is the sliding surface; k is the control gain; sgn() is the sign function; and k is the switching gain.

5. The control system of a large aperture piezoelectric fast steering mirror according to claim 4, wherein, a sliding surface σ is: σ = e4 + λ3e3 + λ2e2 + λ1e1; where: e i is the tracking error, i = 1, 2, 3, 4.

6. A control system for a large aperture piezoelectric fast steering mirror according to claim 4 or 5, wherein, an adaptive law of the neural network adapter is: where: γ i is a constant, γ i > 0, i = 1, 2; is an estimate of ; and is an estimate of W T .

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