A Finite-Time Adaptive Fuzzy Dynamic Surface Control Method for a Piezoelectric Micropositioning Platform Considering Asymmetric Law-Related Hysteresis Input

Abstract

This invention discloses a finite-time adaptive fuzzy dynamic surface control method for a piezoelectric micro-positioning platform considering asymmetric law-dependent hysteresis input. The purpose of this invention is to solve the problems of current control methods, such as difficulty in obtaining state variables, poor transient performance of the controller, and difficulty in handling asymmetric law-dependent hysteresis characteristics. The steps are as follows: Step 1: Establish a mathematical model of the piezoelectric micro-positioning platform; Step 2: Eliminate asymmetric law-dependent hysteresis using a hysteresis compensator and construct a fuzzy state observer to estimate the difficult-to-measure system state; Step 3: Design an adaptive update law, a tracking differential compensation mechanism, and a virtual control law based on a first-order tracking differentiator and dynamic surface technology; update the fuzzy logic system; Step 4: Utilize a finite-time adaptive fuzzy dynamic surface controller, combined with Lyapunov stability theory and finite-time convergence criteria, to select appropriate design parameters to ensure the stability of the closed-loop system within a finite time.

Description

Technical Field

[0001] This invention belongs to the field of tracking and control technology of piezoelectric micro-positioning platforms. Specifically, it relates to a finite-time adaptive fuzzy dynamic surface control method for piezoelectric micro-positioning platforms that considers asymmetric law-related hysteresis input. Technical Background

[0002] The development of modern industrial technology has placed higher demands on high-precision positioning technology. Therefore, micro-nano positioning control based on novel materials has become a widely studied technical field. Among them, piezoelectric micro-positioning platforms, with piezoelectric materials as their core components, have attracted researchers' attention due to their advantages such as fast response speed, high stiffness, and high resolution. However, the inherent complex hysteresis characteristics of piezoelectric materials pose a challenge to the control of piezoelectric micro-positioning platforms. Researchers have done a great deal of work to eliminate the impact of hysteresis on positioning accuracy. Mainstream hysteresis handling methods can be divided into two categories: adaptive estimation methods and inverse hysteresis compensation methods. Adaptive estimation methods utilize adaptive techniques to estimate and update hysteresis nonlinearities online, and then compensate for them in the controller design based on the obtained estimates. This method has strong theoretical compatibility; however, the introduction of the adaptive update law inevitably increases the complexity of the controller and exacerbates the conflict between control performance and controller energy. The core idea of ​​the inverse hysteresis compensation method is to establish a compensator based on the inverse hysteresis model, eliminate the hysteresis nonlinearity in the main control loop, and then design the controller. This control method is intuitive and easy to understand, but the difficulty lies in constructing a hysteresis model that can accurately describe the asymmetric and rate-dependent characteristics, and designing the corresponding inverse model.

[0003] Furthermore, most current control schemes for piezoelectric micro-positioning platforms focus on steady-state performance, i.e., positioning accuracy. However, settling time is also a crucial performance indicator for piezoelectric micro-positioning control systems. Therefore, existing asymptotically stable control schemes struggle to meet the requirements for rapid convergence. Finite-time control exhibits superior transient performance; however, traditional finite-time control requires measurable system states, while the internal states of piezoelectric micro-positioning platforms are difficult to measure and possess unknown hysteresis nonlinearities, thus failing to meet this requirement. Summary of the Invention

[0004] This paper addresses the challenges of current control methods for piezoelectric micro-positioning platforms with asymmetric and rate-dependent hysteresis issues, including difficulties in obtaining state variables, poor transient performance of controllers, and the inability to handle asymmetric rate-dependent hysteresis characteristics.

[0005] This invention designs an output feedback control method with fast convergence, high precision, and low complexity, and proposes a control scheme for a piezoelectric micro-positioning platform that takes into account both transient and steady-state performance.

[0006] This invention proposes a finite-time adaptive fuzzy dynamic surface control method for a piezoelectric micro-positioning platform considering asymmetric law-dependent hysteresis input. Note: In this invention... Indicates an estimate. Indicates the actual quantity.

[0007] The steps of the technical solution adopted in this invention are as follows:

[0008] Step 1: Considering the asymmetric law-dependent hysteresis of the piezoelectric micro-positioning platform, the following mathematical model of the piezoelectric micro-positioning platform is established: The mathematical model is as follows:

[0009]

[0010] in , for , The true value , For the system's state variables, This is the system output; and For an unknown nonlinear function as defined, and The system is an unknown nonlinear function; For actuator output; Input to the actuator;

[0011] The actuator is an asymmetric rate-dependent hysteresis nonlinearity, and its expression is as follows:

[0012]

[0013] in, and For the parameters to be identified, For asymmetric law-dependent Play operators; This is the upper bound of the integral; It is the density function;

[0014] Step 2: Use an asymmetric law-correlated inverse hysteresis compensator to solve the hysteresis problem of the piezoelectric micro-positioning platform; use the ability of fuzzy logic systems to approximate unknown nonlinear functions to construct a fuzzy state observer to estimate the system state that is difficult to measure.

[0015] The asymmetric law-related inverse hysteresis compensator for:

[0016]

[0017] For the desired controller input, and For the parameters to be identified, Let be the density function of the inverse hysteresis compensator. This is the upper bound of the integral of the inverse hysteresis compensator;

[0018] Density function Based on experimental data, the inverse hysteresis compensator is estimated by the density function. Build; for The estimated value, then

[0019]

[0020] in, To compensate for the bounded error, and satisfy the following conditions: normal numbers To compensate for the error boundary; the formula is... Substitution The compensated system is as follows:

[0021]

[0022] in For the new unknown nonlinear function after compensation, To compensate for the difference in unknown nonlinear functions before and after;

[0023] Approximating the new unknown nonlinear function after compensation using a fuzzy logic system:

[0024]

[0025] in, and They are respectively to and The filtered signal obtained after passing through the Butterworth low-pass filter; and For the approximation error of the fuzzy logic system; and The ideal weight vector for the fuzzy logic system; and For fuzzy basis functions of fuzzy logic systems;

[0026] based on Construct a fuzzy state observer to estimate the state of a system that is difficult to measure:

[0027]

[0028] in, and They are respectively and The estimated value; and yes and The estimated value; and Define the gain of the fuzzy state observer; define the matrix. ;

[0029] Step 3: Design an adaptive law, a tracking differential compensation mechanism, and a virtual control law based on a first-order tracking differentiator and dynamic surface technology; estimate the weight vector of the fuzzy logic system using the adaptive update law. and Adaptive update:

[0030]

[0031] in Positive design parameters;

[0032] and The first and second order tracking differential compensation errors are defined as follows:

[0033]

[0034] Mode middle and For the first and second order tracking differential compensation mechanism variables:

[0035]

[0036] in, , To design the positive parameters for control gain; and To design finite-time positive parameters;

[0037] Mode middle and Defined first and second order dynamic error surfaces:

[0038]

[0039] in For the desired trajectory; This is the output of a first-order differential tracker, which is:

[0040]

[0041] in This is a virtual control law, used as the input variable for a first-order differential tracker; and For the output variable of the first-order differential tracker, As an intermediate variable, and For the positive design parameters of the first-order differential tracker;

[0042] The virtual control law is as follows:

[0043]

[0044] in and To design positive parameters;

[0045] Step 4: Based on the finite-time convergence criterion and Lyapunov stability theory, the following finite-time adaptive fuzzy dynamic surface controller is designed:

[0046]

[0047] in To design positive parameters;

[0048] Based on the asymmetric law-related inverse hysteresis compensator designed in step 2 and fuzzy state observer The tracking differential compensation mechanism in step 3 Virtual control law and adaptive update law And the finite-time adaptive fuzzy dynamic surface controller in step 4 By substituting the derivative of the Lyapunov function and selecting appropriate design parameters, the stability of the closed-loop system in a finite time can be guaranteed.

[0049] The Lyapunov function defined for the closed-loop system is as follows:

[0050]

[0051] in This is the observation error vector; , This is the observation error;

[0052] Derivative of Lyapunov function in closed-loop system

[0053]

[0054] in, , , ; , ; It is a second-order positive definite matrix; It is a second-order symmetric positive definite matrix, and satisfies ;

[0055] The Lyapunov function designed to track the differential compensation mechanism is as follows:

[0056]

[0057] The derivative of the Lyapunov function in the tracking differential compensation mechanism

[0058] .

[0059] The relevant parameters are selected according to the following principles:

[0060] Design parameters for a first-order tracking differentiator and Its value should be selected within the range of 0.0001 to 0.1 according to the actual system conditions. The design parameters of the first-order tracking differentiator of this invention are as follows: ;

[0061] The parameters of the inverse hysteresis compensator were identified using a genetic algorithm and experimental data. The inverse hysteresis compensator was discretized, and eight Play operators were selected. Therefore, the parameter vector to be identified is... ,in For parameters of asymmetric terms, , The discretized density parameters of the Play operator; the identification result is For a fuzzy state observer, its gain and The matrix should be Given the Herwitz matrix, the gain of the fuzzy state observer is designed as follows: ;

[0062] For differential tracking compensation mechanisms, adaptive laws, virtual control laws, and final controllers: design parameters The value of affects the stability of the closed-loop system, and the range of values ​​can be determined by Lyapunov stability theory. and Affects the finite-time convergence speed; and The value of affects the adjustment effect of the adaptive law; the specific parameter values ​​in this design are: , , , , , , .

[0063] The beneficial effects of this invention are as follows:

[0064] This invention addresses the asymmetric rate-dependent hysteresis nonlinearity problem of piezoelectric micro-positioning platforms and proposes a finite-time adaptive fuzzy dynamic surface control method. This method offers three advantages: First, it proposes an asymmetric rate-dependent inverse hysteresis compensator, designed directly based on the asymmetric rate-dependent hysteresis model, avoiding the construction of a complex analytical inverse model. Furthermore, it eliminates the need for adaptive techniques in designing the hysteresis update law, reducing the computational burden on the controller. Second, based on a fuzzy state observer, it combines finite-time convergence quasi-measurement with dynamic surface techniques, overcoming the limitation of traditional finite-time control being applicable only to state-measurable systems and resolving the issue of unreliable convergence time in existing piezoelectric micro-positioning platform control strategies. Third, it introduces a first-order differential tracker into the dynamic surface technique, solving the inherent complexity explosion problem of backstepping control, and designs a differential tracking compensation mechanism to avoid the impact of tracking differential errors on control accuracy.

[0065] The control method of the present invention takes into account the inherent asymmetric rate-related hysteresis problem of the piezoelectric micro-positioning platform, and provides a feasible and effective control scheme for the application of the piezoelectric micro-positioning platform in practical engineering.

[0066] Attached Figure Description

[0067] Figure 1 The control block diagram of the finite-time adaptive fuzzy dynamic surface control method for a piezoelectric micro-positioning platform considering asymmetric law-dependent hysteresis input;

[0068] Figure 2 A schematic diagram of the piezoelectric micro-positioning platform experimental system;

[0069] Figure 3 A schematic diagram illustrating the construction principle of the piezoelectric micro-positioning platform experimental system;

[0070] Figure 4A schematic diagram illustrating the tracking performance of the finite-time adaptive fuzzy dynamic surface control method;

[0071] Figure 5 A schematic diagram illustrating the tracking error of a finite-time adaptive fuzzy dynamic surface control method;

[0072] Figure 6 A schematic diagram of the control input signal for a finite-time adaptive fuzzy dynamic surface control method;

[0073] Figure 7 Adaptive parameters for a finite-time adaptive fuzzy dynamic surface control method A schematic diagram of vector adjustment;

[0074] Figure 8 Adaptive parameters for a finite-time adaptive fuzzy dynamic surface control method A schematic diagram of vector adjustment; Detailed Implementation

[0075] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0076] The control block diagram of the finite-time adaptive fuzzy dynamic surface control method for a piezoelectric micro-positioning platform considering asymmetric law-related hysteresis input described in this embodiment is as follows: Figure 1 As shown. The specific steps are as follows:

[0077] Step 1: Considering the asymmetric law-dependent hysteresis of the piezoelectric micro-positioning platform, the following mathematical model of the piezoelectric micro-positioning platform is established:

[0078]

[0079] in , for , The true value , For the system's state variables,

[0080] This is the system output; and The system is an unknown nonlinear function; For actuator output; Input to the actuator; The actuator is an asymmetric rate-dependent hysteresis nonlinearity, and its expression is as follows:

[0081]

[0082] in, and For the parameters to be identified, For asymmetric law-dependent Play operators; This is the upper bound of the integral; It is the density function;

[0083] For subsequent controller design, the following unknown nonlinear function is defined: and And transform the system into:

[0084]

[0085] Step 2:

[0086] Using the direct construction method, an asymmetric law-correlated inverse hysteresis compensator is designed to solve the hysteresis problem of the piezoelectric micro-positioning platform; leveraging the ability of fuzzy logic systems to approximate unknown nonlinear functions, a fuzzy state observer is constructed to estimate the difficult-to-measure system state; the specific steps are as follows:

[0087] Step 2.1, Design an asymmetric law-dependent inverse hysteresis compensator for:

[0088]

[0089] in, For the desired controller input, and For the parameters to be identified, Let be the density function of the inverse hysteresis compensator. This is the upper bound of the integral of the inverse hysteresis compensator;

[0090] Density function The inverse hysteresis compensator can be estimated from experimental data, and thus from the estimated density function. Build, define The estimate is Then there is

[0091]

[0092] in, To compensate for the bounded error, and satisfy the following conditions: normal numbers To define the boundary for compensation error; substituting equation (5) into (3), we obtain the compensated system:

[0093]

[0094] in For the new unknown nonlinear function after compensation, To compensate for the difference in unknown nonlinear functions before and after;

[0095] Step 2.2 involves processing the unknown nonlinear function of the system and approximating it using a fuzzy logic system. The steps are as follows:

[0096] The unknown nonlinear function is transformed as follows:

[0097]

[0098] in, and They are respectively to and The filtered signal obtained after passing through the Butterworth low-pass filter; approximated using a fuzzy logic system. and Therefore:

[0099]

[0100] in and For the approximation error of the fuzzy logic system; and The ideal weight vector for the fuzzy logic system; and For fuzzy basis functions of fuzzy logic systems;

[0101] Based on (8), the fuzzy state observer designed in step 2 is:

[0102]

[0103] in, and They are respectively and The estimated value; and yes and The estimated value; and Define the gain of the fuzzy state observer; define the matrix. ;

[0104] Step 3: Design adaptive laws, tracking differential compensation mechanisms, and virtual control laws based on first-order tracking differentiators and dynamic surface techniques;

[0105] Step 3.1:

[0106] Before designing the adaptive law, the tracking differential compensation mechanism, and the virtual control law, the following error variables are defined:

[0107] definition and For the first and second order dynamic error surfaces:

[0108]

[0109] in For the desired trajectory; This is the output of a first-order differential tracker; the first-order differential tracker is:

[0110]

[0111] in This is a virtual control law, used as the input variable for a first-order differential tracker; and For the output variable of the first-order differential tracker, As an intermediate variable, and For the positive design parameters of the first-order differential tracker;

[0112] definition and For the first and second order tracking differential compensation errors:

[0113]

[0114] in and The variables for the first and second order tracking differential compensation mechanisms are designed;

[0115] Step 3.2:

[0116] Based on the error variable defined in step 3.1, the specific steps for designing the tracking differential compensation mechanism, adaptive law, and virtual control law are as follows:

[0117] The second-order differential tracking compensation mechanism is designed as follows:

[0118]

[0119] in, , The positive parameter is the control gain to be designed. and The positive parameters to be designed are within a finite time period;

[0120] For estimating the weight vector of a fuzzy logic system and Design Adaptive Update Law:

[0121]

[0122] in The parameter to be designed is positive;

[0123] The virtual control law is designed using dynamic surface technology as follows:

[0124]

[0125] in and These are the positive parameters to be designed;

[0126] Step 4:

[0127] Based on Lyapunov stability theory and finite-time convergence criterion, a finite-time adaptive fuzzy dynamic surface controller for a piezoelectric micro-positioning platform is designed.

[0128] The Lyapunov function is defined as follows for a closed-loop system:

[0129]

[0130] in This is the observation error vector; , This is the observation error;

[0131] To track the differential compensation mechanism, the following Lyapunov function is designed:

[0132]

[0133] For Lyapunov functions Differentiating gives

[0134]

[0135] in, , , ; , ; It is a second-order positive definite matrix; It is a second-order symmetric positive definite matrix, and satisfies ;

[0136] For Lyapunov functions Differentiating gives

[0137]

[0138] Based on the finite-time convergence criterion and Lyapunov stability theory, the following finite-time adaptive fuzzy dynamic surface controller is designed:

[0139]

[0140] in These are the positive parameters to be designed;

[0141] Asymmetric law-related inverse hysteresis compensator and fuzzy state observer The tracking differential compensation mechanism in step 3 Virtual control law and adaptive update law And the finite-time adaptive fuzzy dynamic surface controller in step 4 Substituting the derivative of the Lyapunov function and In the middle, by transforming it using Young's inequality and the finite-time convergence criterion, we can obtain:

[0142]

[0143] in, , , , , , , ;in For the positive constants introduced by Young's inequality, , Let Lipschitz be the constant. This represents the maximum value of the approximation error of the fuzzy logic system. This represents the maximum value of the Butterworth filter error;

[0144]

[0145] in, , , .

[0146] The main results of this invention can be summarized as the following theorems:

[0147] Theorem 1: For piezoelectric micro-positioning platforms By designing an asymmetric law-dependent inverse hysteresis compensator Fuzzy state observer Tracking differential compensation mechanism Virtual control law Adaptive update law and finite-time adaptive fuzzy dynamic surface controller By selecting appropriate design parameters, the stability of the closed-loop system can be guaranteed within a finite time.

[0148] The proof of Theorem 1 is as follows:

[0149] make , , Equation (21) can be transformed into

[0150]

[0151] According to the finite-time convergence criterion and equation (23), it can be seen that Includes all variables and finite time It then converges to a bounded neighborhood near the origin; by choosing a suitable To satisfy Then, according to equation (22) and the finite-time convergence criterion, after a finite time... back, and Converging to 0; due to

[0152]

[0153] and and , Both converge in finite time, therefore the tracking error and In time It then enters a steady state; at this point, all signals in the closed-loop system are bounded in finite time, and the closed-loop system is finite-time stable.

[0154] The beneficial effects of the present invention are verified using the following specific implementation examples.

[0155] Implementation Case:

[0156] The finite-time adaptive fuzzy dynamic surface control method designed in this invention is applied to, for example... Figure 2 The piezoelectric micro-positioning platform shown.

[0157] The experimental platform setup structure diagram for the case implementation is as follows: Figure 3As shown. Its main components include: a piezoelectric micro-positioning platform, a data acquisition card, an integrated positioning controller (including a drive module and a sensor module), and a host computer. The workflow is as follows: the designed control method is run in the RTW real-time working environment (Matlab / Simulink) of the host computer. The generated digital control signal is converted into an analog control signal by the data acquisition card, and then amplified by the drive module of the integrated positioning controller, which acts on the piezoelectric micro-positioning platform. The piezoelectric micro-positioning platform generates displacement, which is acquired by the sensor module, converted from analog to digital by the data acquisition card, and transmitted back to the host computer, forming a closed loop.

[0158] To verify the control method, the following desired displacement trajectory was selected:

[0159] ;

[0160] The controller parameters involved are selected as follows:

[0161] The first-order tracking differentiator has the following values: The parameters of the inverse hysteresis compensator are selected as follows: The gain of the fuzzy state observer is designed as follows: For the differential tracking compensation mechanism, adaptive law, virtual control law, and the specific parameter values ​​of the final controller: , , , , , , All parameters are initially set to 0.

[0162] Experimental results are as follows Figures 4-8 As shown.

[0163] The tracking performance of the piezoelectric micro-positioning platform controlled by the finite-time adaptive fuzzy dynamic surface control method of the present invention is as follows: Figure 4 As shown in the figure. It can be seen that, under the control method of this invention, the output displacement of the piezoelectric micro-positioning platform can track the desired trajectory of the variable amplitude frequency quite well. The tracking error of the piezoelectric micro-positioning platform in tracking the desired trajectory is as follows: Figure 5 As shown, thanks to the application of finite-time techniques, the tracking error can converge to a satisfactory error band within a short time, demonstrating the excellent transient performance of the finite-time control method. Furthermore, the error value in the steady-state phase is within 0.2. Within m, the tracking differential compensation mechanism is demonstrated, proving that the control method of the present invention takes into account excellent steady-state performance. Figure 6 The control input signal of the present invention is shown. It can be seen that no large-energy control signal peak phenomenon occurred in the initial stage of the tracking experiment, demonstrating the feasibility of the control method in practical applications. Figure 7 and Figure 8 This is the adjustment curve for the adaptive parameter vector. From Figures 4-8 The experimental results verify that the finite-time adaptive fuzzy dynamic surface control method described in this invention has ideal control effect and practicality.

Claims

1. A finite-time adaptive fuzzy dynamic surface control method for a piezoelectric micro-positioning platform considering asymmetric law-dependent hysteresis input, characterized in that, The steps of this method are as follows: Step 1: Considering the asymmetric law-dependent hysteresis of the piezoelectric micro-positioning platform, the following mathematical model of the piezoelectric micro-positioning platform is established: The mathematical model is as follows: in , for , The true value , For the system's state variables, This is the system output; and For an unknown nonlinear function as defined, and The system is an unknown nonlinear function; For actuator output; Input to the actuator; The actuator is an asymmetric rate-dependent hysteresis nonlinearity, and its expression is as follows: in, and For the parameters to be identified, For asymmetric law-dependent Play operators; This is the upper bound of the integral; It is the density function; Step 2: Use the asymmetric rate-correlation inverse hysteresis compensator designed by the direct construction method to solve the hysteresis problem of the piezoelectric micro-positioning platform; use the ability of fuzzy logic system to approximate unknown nonlinear functions to construct a fuzzy state observer to estimate the system state that is difficult to measure. The asymmetric law-related inverse hysteresis compensator for: For the desired controller input, and For the parameters to be identified, Let be the density function of the inverse hysteresis compensator. The integral upper bound of the inverse hysteresis compensator; density function Based on experimental data, the inverse hysteresis compensator is estimated by the density function. Build; for The estimated value, then in, To compensate for the bounded error, and satisfy the following conditions: normal numbers To compensate for the error boundary; the formula is... Substitution The compensated system is as follows: in For the new unknown nonlinear function after compensation, To compensate for the difference between the unknown nonlinear functions before and after; Approximating the new unknown nonlinear function after compensation using a fuzzy logic system: in, and They are respectively to and The filtered signal obtained after passing through the Butterworth low-pass filter; and For the approximation error of the fuzzy logic system; and The ideal weight vector for the fuzzy logic system; and For fuzzy basis functions of fuzzy logic systems; based on Construct a fuzzy state observer to estimate the state of a system that is difficult to measure: in, and They are respectively and The estimated value; and yes and The estimated value; and Define the gain of the fuzzy state observer; define the matrix. ; Step 3: Design an adaptive law, a tracking differential compensation mechanism, and a virtual control law based on a first-order tracking differentiator and dynamic surface technology; estimate the weight vector of the fuzzy logic system using the adaptive update law. and Adaptive update: in Positive design parameters; and The first and second order tracking differential compensation errors are defined as follows: Mode middle and For the first and second order tracking differential compensation mechanism variables: in, , To design the positive parameters for control gain; and To design finite-time positive parameters; Mode middle and Defined first and second order dynamic error surfaces: in For the desired trajectory; This is the output of a first-order differential tracker, which is: in This is a virtual control law, used as the input variable for a first-order differential tracker; and For the output variable of the first-order differential tracker, As an intermediate variable, and For the positive design parameters of the first-order differential tracker; The virtual control law is as follows: in and To design positive parameters; Step 4: Based on the finite-time convergence criterion and Lyapunov stability theory, the following finite-time adaptive fuzzy dynamic surface controller is designed: in To design positive parameters; Based on the asymmetric law-related inverse hysteresis compensator designed in step 2 and fuzzy state observer The tracking differential compensation mechanism in step 3 Virtual control law and adaptive update law And the finite-time adaptive fuzzy dynamic surface controller in step 4 By substituting the derivative of the Lyapunov function and selecting appropriate design parameters, the stability of the closed-loop system in a finite time can be guaranteed. The Lyapunov function defined for the closed-loop system is as follows: in This is the observation error vector; , This is the observation error; The derivative of the Lyapunov function of a closed-loop system in, , , ; , ; It is a second-order positive definite matrix; It is a second-order symmetric positive definite matrix, and satisfies ; The Lyapunov function designed to track the differential compensation mechanism is as follows: The derivative of the Lyapunov function in the tracking differential compensation mechanism 。 2. The finite-time adaptive fuzzy dynamic surface control method for a piezoelectric micro-positioning platform considering asymmetric law-dependent hysteresis input as described in claim 1, characterized in that, The relevant design parameters are selected according to the following principles: Design parameters for a first-order tracking differentiator and The value can be: ; The parameters of the inverse hysteresis compensator were identified using a genetic algorithm and experimental data. The inverse hysteresis compensator was discretized, and eight Play operators were selected. Therefore, the parameter vector to be identified is... ,in For parameters of asymmetric terms, , The discretized density parameters of the Play operator; the identification result is ; For a fuzzy state observer, its gain and The matrix should be Given the Herwitz matrix, the gain of the fuzzy state observer is designed as follows: ; For differential tracking compensation mechanisms, adaptive laws, virtual control laws, and final controllers: design parameters The value of affects the stability of the closed-loop system, and the range of values ​​can be determined by Lyapunov stability theory. and This affects the finite-time convergence speed; and The value of affects the adjustment effect of the adaptive law; the specific parameter values ​​are: , , , , , , .

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