Control method of piezoelectric micro-motion system and related device

Abstract

The invention discloses a control method of a piezoelectric micro-motion system and a related device, and relates to the technical field of control engineering, and the method comprises the steps: obtaining hysteresis loop data of a piezoelectric material in the piezoelectric micro-motion system to construct a Hammerstein modular structure of the piezoelectric micro-motion system; a Bouc-Wen model and a proportion-integral model are constructed; performing inverse compensation control processing on the piezoelectric micro-motion system based on a Bouc-Wen model and a proportional-integral model to obtain the piezoelectric micro-motion system after the inverse compensation control processing; frequency response analysis is carried out on the piezoelectric micro-motion system after inverse compensation control processing so as to generate an uncertainty upper bound weighting function; and constructing a robust controller based on the uncertainty upper bound weighting function, and performing stable control on the piezoelectric micro-motion system after the inverse compensation control processing based on the robust controller in combination with a stability regulator. According to the invention, the steady-state precision optimization of the piezoelectric micro-motion system is realized, and the control precision of the piezoelectric micro-motion system is improved.

Description

Technical Field

[0001] This invention relates to the field of control engineering technology, and in particular to a control method and related device for a piezoelectric micro-motion system. Background Technology

[0002] As the manufacturing industry demands increasingly higher precision from actuators, traditional devices can no longer meet the micro- and nano-level requirements of precision positioning technology. Therefore, piezoelectric micro-motion systems have emerged. These systems are compact micro-positioning mechanisms with sub-millimeter strokes and nanometer-level displacement resolution, significantly improving the accuracy of positioning operations. However, the hysteresis inherent in the piezoelectric materials within these systems can cause significant positioning errors, reducing control precision. Furthermore, the modeling errors and uncertainties of piezoelectric micro-motion systems necessitate robust controllers to improve control performance. However, current robust controllers based on the robust H-infinity method struggle to guarantee steady-state accuracy and robust stability. Therefore, compensating for the hysteresis of piezoelectric materials and constructing high-precision robust controllers are crucial research areas. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings of the prior art. This invention provides a control method and related device for a piezoelectric micro-motion system, which optimizes the steady-state accuracy of the piezoelectric micro-motion system and improves the control accuracy of the piezoelectric micro-motion system.

[0004] To address the aforementioned technical problems, this invention provides a control method for a piezoelectric micro-motion system, the method comprising: Acquire hysteresis loop data of the piezoelectric material in the piezoelectric micro-motion system, and construct the Hammerstein modular structure of the piezoelectric micro-motion system based on the hysteresis loop data; Construct a Bouc-Wen model and a proportional-integral model with a Hammerstein modular structure; The piezoelectric micro-motion system is subjected to inverse compensation control based on the Bouc-Wen model and the proportional-integral model to obtain the piezoelectric micro-motion system after inverse compensation control. Frequency response analysis is performed on the piezoelectric micro-motion system after inverse compensation control processing to obtain frequency response data, and an uncertainty upper bound weighting function is generated based on the frequency response data. A robust controller is constructed based on the weighted function of the uncertainty upper bound, and the piezoelectric micro-motion system after inverse compensation control is stabilized based on the robust controller and combined with a stabilizing regulator.

[0005] Optionally, the step of acquiring hysteresis loop data of the piezoelectric material in the piezoelectric micro-motion system and constructing a Hammerstein modular structure of the piezoelectric micro-motion system based on the hysteresis loop data includes: The input voltage signal and output displacement signal of the piezoelectric micro-motion system are acquired, and the input voltage signal and output displacement signal are discretely sampled and normalized to obtain the input voltage vector and output displacement vector. Based on the input voltage vector and output displacement vector, determine the hysteresis loop data of the piezoelectric material in the piezoelectric micro-motion system; Based on the hysteresis loop data, static nonlinear modules and dynamic linear modules are determined, and the Hammerstein modular structure of the piezoelectric micro-motion system is constructed based on the static nonlinear modules and dynamic linear modules.

[0006] Optionally, the Bouc-Wen model and proportional-integral model for constructing the Hammerstein modular structure include: In the Hammerstein modular structure, a Bouc-Wen model is constructed based on hysteresis components, and a proportional-integral model is constructed based on the dead-zone operator. The expression of the Bouc-Wen model is as follows: , Where y is the output displacement, k and d are model parameters, u is the driving voltage, and z is the hysteresis component.

[0007] Optionally, the expression for the proportional-integral model is: , in, It is a proportional-integral model. Let T be the first weight vector, and T be the transpose operation. For dead zone operators, This is the second weight vector. Let u be the play operator vector, and u be the driving voltage. t represents the output displacement at the current moment, where t is time.

[0008] Optionally, the step of performing inverse compensation control processing on the piezoelectric micro-motion system based on the Bouc-Wen model and the proportional-integral model to obtain the piezoelectric micro-motion system after inverse compensation control processing includes: Determine the first inverse model of the Bouc-Wen model and the second inverse model of the proportional-integral model; A feedforward controller is generated based on the first inverse model and the second inverse model; The piezoelectric micro-motion system is subjected to inverse compensation control processing based on the feedforward controller to obtain the piezoelectric micro-motion system after inverse compensation control processing.

[0009] Optionally, the step of performing frequency response analysis on the piezoelectric micro-motion system after inverse compensation control processing to obtain frequency response data, and generating an uncertainty upper bound weighting function based on the frequency response data, includes: Frequency response analysis of the piezoelectric micro-motion system after inverse compensation control is performed based on the spectral density function to obtain frequency response data. The frequency response data is compared with the nominal model frequency response to obtain the comparison result, and the upper bound of the difference is determined based on the comparison result. Curve fitting is performed based on the upper bound of the difference to obtain the uncertainty upper bound weighted function.

[0010] Optionally, the expression for the frequency response data is:

[0011] in, Here is the frequency response data, and N is the length of the time window. Let j be the autocorrelation function of the signal, and j be the imaginary unit. For frequency components, Let ω be the angular frequency and T be the time variable.

[0012] Optionally, the step of constructing a robust controller based on the weighted function of the uncertainty upper bound, and performing stable control of the piezoelectric micro-motion system after inverse compensation control based on the robust controller and a stabilizing regulator, includes: Obtain the error performance weighting function of the piezoelectric micro-motion system after inverse compensation control processing; A robust controller is constructed based on the uncertainty upper bound weighting function and the error performance weighting function, combined with the Bouc-Wen model and the proportional-integral model. The conditional constraints of the robust controller are determined, and the target controller is generated by coprime decomposition based on the conditional constraints and the robust controller combined with a stable regulator. The piezoelectric micro-motion system after inverse compensation control is stably controlled based on the target controller.

[0013] In addition, the present invention also provides a control device for a piezoelectric micro-motion system, the device comprising: Modular structure module: used to acquire hysteresis loop data of piezoelectric material in piezoelectric micro-motion system, and to construct Hammerstein modular structure of piezoelectric micro-motion system based on the hysteresis loop data; Model building module: used to build Bouc-Wen models and proportional-integral models with a Hammerstein modular structure; Inverse compensation control module: used to perform inverse compensation control processing on the piezoelectric micro-motion system based on the Bouc-Wen model and the proportional-integral model, to obtain the piezoelectric micro-motion system after inverse compensation control processing; Function generation module: used to perform frequency response analysis on the piezoelectric micro-motion system after inverse compensation control processing, obtain frequency response data, and generate an uncertainty upper bound weighted function based on the frequency response data; Stability control module: used to construct a robust controller based on the uncertainty upper bound weighting function, and to perform stable control of the piezoelectric micro-motion system after inverse compensation control processing based on the robust controller and the stability regulator.

[0014] In addition, the present invention also provides a computer-readable storage medium that stores computer instructions that, when executed on an electronic device, cause the electronic device to perform the control method of the piezoelectric micro-motion system described above.

[0015] In this embodiment of the invention, a Hammerstein modular structure for the piezoelectric micro-motion system is constructed based on the hysteresis loop data of the piezoelectric material. A Bouc-Wen model and a proportional-integral model of the Hammerstein modular structure are constructed, providing a more reliable foundation for the inverse compensation control of the system and significantly reducing the impact of the hysteresis factor of the piezoelectric material on the system. Inverse compensation control is performed on the piezoelectric micro-motion system based on the Bouc-Wen model and the proportional-integral model, resulting in a piezoelectric micro-motion system with improved control accuracy. Frequency response analysis is performed on the piezoelectric micro-motion system with inverse compensation control to obtain frequency response data, and an uncertainty upper bound weighting function is generated based on the frequency response data. A robust controller is constructed based on the uncertainty upper bound weighting function, generating a more accurate robust controller. Stable control of the piezoelectric micro-motion system with inverse compensation control is performed using the robust controller combined with a stabilizer, achieving steady-state accuracy optimization and improving the control accuracy of the piezoelectric micro-motion system. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is a flowchart illustrating the control method of the piezoelectric micro-motion system in an embodiment of the present invention; Figure 2This is a flowchart illustrating the control method of a piezoelectric micro-motion system according to another embodiment of the present invention; Figure 3 This is a schematic diagram of the structure of the control device of the piezoelectric micro-motion system in an embodiment of the present invention. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] Example 1 Please see Figure 1 , Figure 1 This is a flowchart illustrating the control method of the piezoelectric micro-motion system in an embodiment of the present invention, the method comprising: S11: Obtain the hysteresis loop data of the piezoelectric material in the piezoelectric micro-motion system, and construct the Hammerstein modular structure of the piezoelectric micro-motion system based on the hysteresis loop data; In the specific implementation of this invention, the input voltage signal and output displacement signal of the piezoelectric micro-motion system are acquired, and the input voltage signal and output displacement signal are discretely sampled and normalized to obtain the input voltage vector and output displacement vector. Based on the input voltage vector and output displacement vector, the hysteresis loop data of the piezoelectric material in the piezoelectric micro-motion system is determined. Based on the hysteresis loop data, a static nonlinear module and a dynamic linear module are determined, and a Hammerstein modular structure of the piezoelectric micro-motion system is constructed based on the static nonlinear module and the dynamic linear module, thereby improving the understanding of the hysteresis characteristics of the piezoelectric material and providing stronger support for model construction.

[0020] S12: Construct the Bouc-Wen model and proportional-integral model of the Hammerstein modular structure; In the specific implementation of this invention, in the Hammerstein modular structure, a Bouc-Wen model is constructed based on the hysteresis component, and a proportional-integral model is constructed based on the dead zone operator. The Bouc-Wen model and the proportional-integral model can accurately describe the hysteresis nonlinearity and improve the accuracy of inverse compensation control.

[0021] S13: Perform inverse compensation control processing on the piezoelectric micro-motion system based on the Bouc-Wen model and the proportional-integral model to obtain the piezoelectric micro-motion system after inverse compensation control processing; In the specific implementation of this invention, the first inverse model of the Bouc-Wen model and the second inverse model of the proportional-integral model are determined; a feedforward controller is generated based on the first and second inverse models; the piezoelectric micro-motion system is subjected to inverse compensation control processing based on the feedforward controller to obtain the piezoelectric micro-motion system after inverse compensation control processing, which can eliminate the hysteresis effect of the piezoelectric micro-motion system and effectively suppress the nonlinear disturbance of the system.

[0022] S14: Perform frequency response analysis on the piezoelectric micro-motion system after inverse compensation control processing, obtain frequency response data, and generate an uncertainty upper bound weighting function based on the frequency response data; In the specific implementation of this invention, frequency response analysis is performed on the piezoelectric micro-motion system after inverse compensation control based on the spectral density function to obtain frequency response data; the frequency response data is compared with the nominal model frequency response to obtain comparison results, and the upper bound of the difference is determined based on the comparison results; curve fitting is performed based on the upper bound of the difference to obtain the uncertainty upper bound weighting function, which can better address the uncertainty of the system and ensure the stability of the robust controller.

[0023] S15: Construct a robust controller based on the weighted function of the upper bound of uncertainty, and perform stable control on the piezoelectric micro-motion system after inverse compensation control based on the robust controller and the stable regulator.

[0024] In the specific implementation of this invention, the error performance weighting function of the piezoelectric micro-motion system after inverse compensation control processing is obtained; a robust controller is constructed based on the uncertainty upper bound weighting function and the error performance weighting function, combined with the Bouc-Wen model and the proportional-integral model; the condition constraints of the robust controller are determined; based on the condition constraints and the robust controller, a target controller is generated by coprime decomposition using a stable regulator; and the piezoelectric micro-motion system after inverse compensation control processing is stably controlled based on the target controller, thereby achieving high-precision control and high robust stability of the piezoelectric micro-motion system, while improving the anti-interference capability of the piezoelectric micro-motion system.

[0025] In this embodiment of the invention, a Hammerstein modular structure for the piezoelectric micro-motion system is constructed based on the hysteresis loop data of the piezoelectric material. A Bouc-Wen model and a proportional-integral model of the Hammerstein modular structure are constructed, providing a more reliable foundation for the inverse compensation control of the system and significantly reducing the impact of the hysteresis factor of the piezoelectric material on the system. Inverse compensation control is performed on the piezoelectric micro-motion system based on the Bouc-Wen model and the proportional-integral model, resulting in a piezoelectric micro-motion system with improved control accuracy. Frequency response analysis is performed on the piezoelectric micro-motion system with inverse compensation control to obtain frequency response data, and an uncertainty upper bound weighting function is generated based on the frequency response data. A robust controller is constructed based on the uncertainty upper bound weighting function, generating a more accurate robust controller. Stable control of the piezoelectric micro-motion system with inverse compensation control is performed using the robust controller combined with a stabilizer, achieving steady-state accuracy optimization and improving the control accuracy of the piezoelectric micro-motion system.

[0026] Example 2 Please see Figure 2 , Figure 2 This is a flowchart illustrating a control method for a piezoelectric micro-motion system according to another embodiment of the present invention, the method comprising: S201: Obtain the hysteresis loop data of the piezoelectric material in the piezoelectric micro-motion system, and construct the Hammerstein modular structure of the piezoelectric micro-motion system based on the hysteresis loop data; In a specific implementation of this invention, the step of acquiring hysteresis loop data of the piezoelectric material in the piezoelectric micro-motion system and constructing a Hammerstein modular structure of the piezoelectric micro-motion system based on the hysteresis loop data includes: acquiring the input voltage signal and output displacement signal of the piezoelectric micro-motion system, and performing discrete sampling and normalization processing on the input voltage signal and output displacement signal to obtain the input voltage vector and output displacement vector; determining the hysteresis loop data of the piezoelectric material in the piezoelectric micro-motion system based on the input voltage vector and output displacement vector; determining the static nonlinear module and the dynamic linear module based on the hysteresis loop data, and constructing the Hammerstein modular structure of the piezoelectric micro-motion system based on the static nonlinear module and the dynamic linear module.

[0027] Specifically, the input voltage signal and output displacement signal of the piezoelectric micro-motion system are acquired, and the input voltage signal and output displacement signal are discretely sampled and normalized. Discrete sampling is the process of converting a continuously changing analog signal into a time-discrete digital signal. Normalization is the process of converting the input voltage and output displacement to a preset range or scale to eliminate differences caused by factors such as amplitude offset. The input voltage signal and output displacement signal can be sampled, held, quantized and encoded. Then the encoded input voltage signal and output displacement signal are normalized to obtain the input voltage vector and output displacement vector.

[0028] Based on the input voltage vector and output displacement vector, the hysteresis loop data of the piezoelectric material in the piezoelectric micro-motion system is determined. The input voltage vector and output displacement vector and their corresponding time points are obtained. Curves are plotted based on the input voltage vector and output displacement vector and their corresponding time points, and the hysteresis loop data is presented in the form of a voltage-displacement curve.

[0029] Based on the hysteresis loop data, static nonlinear modules and dynamic linear modules are determined. A system model structure that allows for the separation of hysteresis nonlinearity and dynamic characteristics is established according to the hysteresis loop data. The static nonlinear module describes the hysteresis characteristics, while the dynamic linear module describes its dynamic response characteristics. Based on these static and dynamic nonlinear modules, a Hammerstein modular structure for the piezoelectric micro-motion system is constructed. That is, the Hammerstein modular structure is composed of static and dynamic nonlinear modules. The Hammerstein modular structure is a typical nonlinear system model, consisting of a static nonlinear element and a linear dynamic element connected in series. This structure is suitable for describing systems with nonlinear input characteristics but linear dynamic responses. The modular nonlinear model is composed of static nonlinear elements and linear dynamic elements connected together. Each module does not necessarily correspond to the actual physical system, and the intermediate variables between modules may be unmeasurable. This high degree of flexibility allows modular models to describe many complex nonlinear systems.

[0030] S202: Constructing the Bouc-Wen model and proportional-integral model of the Hammerstein modular structure; In the specific implementation of this invention, the construction of the Bouc-Wen model and proportional-integral model with a Hammerstein modular structure includes: constructing a Bouc-Wen model based on hysteresis components and a proportional-integral model based on dead-zone operators within the Hammerstein modular structure. The expression of the Bouc-Wen model is as follows: , Where y is the output displacement, k and d are model parameters, u is the driving voltage, and z is the hysteresis component.

[0031] Furthermore, the expression for the proportional-integral model is: , in, It is a proportional-integral model. Let T be the first weight vector, and T be the transpose operation. For dead zone operators, This is the second weight vector. Let u be the play operator vector, and u be the driving voltage. t represents the output displacement at the current moment, where t is time.

[0032] Specifically, based on the static nonlinear modules in the Hammerstein modular structure, a Bouc-Wen model is constructed using hysteresis components. These hysteresis components are obtained from the hysteresis loop data in the Hammerstein modular structure. The Bouc-Wen model is a classical mechanical model describing nonlinear hysteretic behavior, used to simulate the hysteretic response of structures, materials, or dampers. The expression for the Bouc-Wen model is as follows: , Where y is the output displacement, k and d are model parameters, u is the driving voltage, and z is the hysteresis component. The model parameters can control the shape and size of the hysteresis loop.

[0033] A proportional-integral model is constructed based on the dead-zone operator. The expression of the proportional-integral model is as follows: , in, It is a proportional-integral model. Let T be the first weight vector, and T be the transpose operation. For dead zone operators, This is the second weight vector. Let u be the play operator vector, and u be the driving voltage. Let t be the output displacement at the current moment and t be the time. The classical proportional-integral model has nonlocal memory, and the hysteresis loop it represents is always counterclockwise and odd symmetric. Therefore, by cascading a model consisting of a weighted superposition of memoryless, non-convex, and non-odd symmetric dead zone operators on the proportional-integral model, the improved proportional-integral model can have properties such as nonlocal memory, non-convexity, and non-odd symmetry. Its advantages are small numerical calculation error and adaptability to more complex hysteresis shapes.

[0034] S203: Perform inverse compensation control processing on the piezoelectric micro-motion system based on the Bouc-Wen model and the proportional-integral model to obtain the piezoelectric micro-motion system after inverse compensation control processing; In a specific implementation of this invention, the step of performing inverse compensation control processing on the piezoelectric micro-motion system based on the Bouc-Wen model and the proportional-integral model to obtain the piezoelectric micro-motion system after inverse compensation control processing includes: determining the first inverse model of the Bouc-Wen model and the second inverse model of the proportional-integral model; generating a feedforward controller based on the first inverse model and the second inverse model; and performing inverse compensation control processing on the piezoelectric micro-motion system based on the feedforward controller to obtain the piezoelectric micro-motion system after inverse compensation control processing.

[0035] Specifically, the first inverse model of the Bouc-Wen model and the second inverse model of the proportional-integral model are determined. Both the first and second inverse models use the driving voltage as the output and the output displacement as the input. An inverse model is a model with the opposite input-output propagation relationship to the given system. Its core function is to compensate for or cancel the nonlinear characteristics of the original system by connecting it in series with the original system, thereby transforming the composite system into a linear or pseudo-linear system. A feedforward controller is generated based on the first and second inverse models, i.e., the first and second inverse models are used as the feedforward controller.

[0036] The piezoelectric micro-motion system is subjected to inverse compensation control based on the feedforward controller to obtain the piezoelectric micro-motion system after inverse compensation control. That is, the feedforward controller is connected in series before the piezoelectric micro-motion system to achieve compensation for hysteresis nonlinearity and achieve the purpose of approximating the linearization of the piezoelectric micro-motion system.

[0037] S204: Frequency response analysis of the piezoelectric micro-motion system after inverse compensation control processing is performed based on the spectral density function to obtain frequency response data; In a specific implementation of this invention, the expression for the frequency response data is:

[0038] in, Here is the frequency response data, and N is the length of the time window. Let j be the autocorrelation function of the signal, and j be the imaginary unit. For frequency components, Let ω be the angular frequency and T be the time variable.

[0039] Specifically, frequency response analysis is performed on the piezoelectric micro-motion system after inverse compensation control based on the spectral density function to obtain frequency response data. That is, the frequency response value of the piezoelectric micro-motion system after inverse compensation control is calculated according to the formula of the spectral density function. The expression of the frequency response data is as follows:

[0040] in, Here is the frequency response data, and N is the length of the time window. Let j be the autocorrelation function of the signal, and j be the imaginary unit. For frequency components, Let ω be the angular frequency and T be the time variable.

[0041] S205: Compare the frequency response data with the nominal model frequency response to obtain the comparison result, and determine the upper limit of the difference based on the comparison result; In the specific implementation of this invention, the frequency response data is compared with the nominal model frequency response, that is, the ratio of the frequency response data to the nominal model frequency response is calculated. The nominal model frequency response is extracted from the database. The upper bound of the difference is estimated based on the calculated ratio. A deep neural network can be used to assist in estimating the upper bound of the difference.

[0042] S206: Perform curve fitting based on the upper bound of the difference to obtain the uncertainty upper bound weighting function; In the specific implementation of this invention, curve fitting is performed on the upper bound of the difference to obtain the uncertainty upper bound weighting function. This optimizes the model parameters by quantifying the fitting error. The core idea is that during the fitting process, not only is the residual between the data points and the fitted curve minimized, but also the uncertainty upper bound is introduced as a weight, so that the fitting result assigns lower weights to data points with larger errors, thereby improving the robustness and prediction accuracy of the model. A weighting function is constructed using the difference upper bound, and then optimized within the least squares framework to obtain the final uncertainty upper bound weighting function. This uncertainty upper bound weighting function serves as an estimate of the system uncertainty.

[0043] S207: Construct a robust controller based on the weighted function of the upper bound of uncertainty, and perform stable control on the piezoelectric micro-motion system after inverse compensation control based on the robust controller and the stable regulator.

[0044] In a specific implementation of this invention, the step of constructing a robust controller based on the uncertainty upper bound weighting function, and then using the robust controller in conjunction with a stabilizing regulator to perform stable control on the piezoelectric micro-motion system after inverse compensation control, includes: obtaining the error performance weighting function of the piezoelectric micro-motion system after inverse compensation control; constructing a robust controller based on the uncertainty upper bound weighting function and the error performance weighting function, combined with a Bouc-Wen model and a proportional-integral model; determining the conditional constraints of the robust controller; generating a target controller based on the conditional constraints and the robust controller in conjunction with a stabilizing regulator using coprime decomposition; and performing stable control on the piezoelectric micro-motion system after inverse compensation control based on the target controller.

[0045] Specifically, to obtain the error performance weighting function of the piezoelectric micro-motion system after inverse compensation control processing, a first weighting function and a second weighting function can be set to determine the system's sensitivity to errors, and a third weighting function can be set to limit the energy of the control signal. The error performance weighting function is then obtained based on the first weighting function, the second weighting function, and the third weighting function.

[0046] A robust controller is constructed based on the uncertainty upper bound weighting function and the error performance weighting function, combined with the Bouc-Wen model and the proportional-integral model. The structure of the robust control system is generated by combining the uncertainty upper bound weighting function, the error performance weighting function, the Bouc-Wen model, the proportional-integral model and their inverse models, and a pre-filter. This robust controller is designed to address the uncertainty of the system and ensure the robust stability of the piezoelectric micro-motion system, enabling stable operation of the piezoelectric micro-motion system under environmental disturbances and uncertainties.

[0047] The conditional constraints of the robust controller are determined, including: when the system is stable and there are no modeling errors and no external disturbances, the steady-state response must satisfy: , The steady-state response is , For linear dynamic components, For pre-filter, For reference only.

[0048] Simultaneously, the voltage-controlled system precisely tracks the reference input, ensuring that the pre-filter meets the following requirements: , For linear dynamic components, This is a pre-filter.

[0049] Robust control constraints are set to frequency-weight the system error signal to suppress external disturbances in the controlled frequency band. Constraints on the robust controller are also set to ensure system robust stability and that the transfer function from external disturbances to the error signal satisfies... T is the transfer function. The H∞ norm is the performance index for H∞ control, representing the H∞ norm of the closed-loop system, and is used to measure the robustness of the system under disturbances.

[0050] Based on the aforementioned constraints and robust controller combined with a stable regulator, a target controller is generated using coprime decomposition. The robust controller is then adjusted according to the constraints to satisfy left coprime decomposition, expressed as: , Where K represents the robust controller after adjustment settings. and These are the different operator matrices for coprime decomposition. Left coprime decomposition is a decomposition form of rational fractional matrices or functions, expressed as the ratio of the matrices or functions, where the numerator and denominator satisfy the coprime condition. This decomposition is used in control theory and system analysis to simplify system models or design controllers.

[0051] A stable regulator is added to the robust controller to achieve robust stability of the closed loop, generating a target controller. Based on the target controller, the piezoelectric micro-motion system after inverse compensation control is stabilized. The combination of the robust controller and the stable regulator can simultaneously improve the steady-state accuracy, anti-interference ability, and robust stability of the piezoelectric micro-motion system under environmental disturbances and uncertainties. This ensures that even when environmental disturbances and uncertainties exist, the piezoelectric micro-motion system can still accurately track the reference signal and achieve the requirements of micro-nano-level high-precision positioning.

[0052] In this embodiment of the invention, a Hammerstein modular structure for the piezoelectric micro-motion system is constructed based on the hysteresis loop data of the piezoelectric material. A Bouc-Wen model and a proportional-integral model of the Hammerstein modular structure are constructed, providing a more reliable foundation for the inverse compensation control of the system and significantly reducing the impact of the hysteresis factor of the piezoelectric material on the system. Inverse compensation control is performed on the piezoelectric micro-motion system based on the Bouc-Wen model and the proportional-integral model, resulting in a piezoelectric micro-motion system with improved control accuracy. Frequency response analysis is performed on the piezoelectric micro-motion system with inverse compensation control to obtain frequency response data, and an uncertainty upper bound weighting function is generated based on the frequency response data. A robust controller is constructed based on the uncertainty upper bound weighting function, generating a more accurate robust controller. Stable control of the piezoelectric micro-motion system with inverse compensation control is performed using the robust controller combined with a stabilizer, achieving steady-state accuracy optimization and improving the control accuracy of the piezoelectric micro-motion system.

[0053] Example 3 Please see Figure 3 , Figure 3 This is a schematic diagram of the structural composition of the control device of the piezoelectric micro-motion system in an embodiment of the present invention. The device includes: Modular structure module 31: used to acquire hysteresis loop data of piezoelectric material in piezoelectric micro-motion system, and to construct Hammerstein modular structure of piezoelectric micro-motion system based on the hysteresis loop data; Model building module 32: Used to build Bouc-Wen models and proportional-integral models with a Hammerstein modular structure; Inverse compensation control module 33: used to perform inverse compensation control processing on the piezoelectric micro-motion system based on the Bouc-Wen model and the proportional-integral model, to obtain the piezoelectric micro-motion system after inverse compensation control processing; Function generation module 34: used to perform frequency response analysis on the piezoelectric micro-motion system after inverse compensation control processing, obtain frequency response data, and generate an uncertainty upper bound weighted function based on the frequency response data; Stability control module 35: used to construct a robust controller based on the uncertainty upper bound weighting function, and to perform stable control on the piezoelectric micro-motion system after inverse compensation control processing based on the robust controller and the stability regulator.

[0054] In the specific implementation of this invention, the specific implementation of the device item can be referred to the implementation of the method item above, and will not be repeated here.

[0055] In this embodiment of the invention, a Hammerstein modular structure for the piezoelectric micro-motion system is constructed based on the hysteresis loop data of the piezoelectric material. A Bouc-Wen model and a proportional-integral model of the Hammerstein modular structure are constructed, providing a more reliable foundation for the inverse compensation control of the system and significantly reducing the impact of the hysteresis factor of the piezoelectric material on the system. Inverse compensation control is performed on the piezoelectric micro-motion system based on the Bouc-Wen model and the proportional-integral model, resulting in a piezoelectric micro-motion system with improved control accuracy. Frequency response analysis is performed on the piezoelectric micro-motion system with inverse compensation control to obtain frequency response data, and an uncertainty upper bound weighting function is generated based on the frequency response data. A robust controller is constructed based on the uncertainty upper bound weighting function, generating a more accurate robust controller. Stable control of the piezoelectric micro-motion system with inverse compensation control is performed using the robust controller combined with a stabilizer, achieving steady-state accuracy optimization and improving the control accuracy of the piezoelectric micro-motion system.

[0056] This invention provides a computer-readable storage medium storing a computer program. When executed by a processor, this program implements the control method of the piezoelectric micro-motion system in any of the above embodiments. The computer-readable storage medium includes, but is not limited to, any type of disk (including floppy disk, hard disk, optical disk, CD-ROM, and magneto-optical disk), ROM (Read-Only Memory), RAM (Random Access Memory), EPROM (Erasable Programmable Read-Only Memory), EEPROM (Electrically Erasable Programmable Read-Only Memory), flash memory, magnetic cards, or optical cards. In other words, the storage device includes any medium that stores or transmits information in a readable form by a device (e.g., a computer, a mobile phone), and can be a read-only memory, a disk, or an optical disk, etc.

[0057] Furthermore, the control method and related device of the piezoelectric micro-motion system provided by the embodiments of the present invention have been described in detail above. Specific examples have been used to illustrate the principle and implementation of the present invention. The description of the above embodiments is only for the purpose of helping to understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation and application scope based on the idea of ​​the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A control method for a piezoelectric micro-motion system, characterized in that, The method includes: Acquire hysteresis loop data of the piezoelectric material in the piezoelectric micro-motion system, and construct the Hammerstein modular structure of the piezoelectric micro-motion system based on the hysteresis loop data; Construct a Bouc-Wen model and a proportional-integral model with a Hammerstein modular structure; The piezoelectric micro-motion system is subjected to inverse compensation control based on the Bouc-Wen model and the proportional-integral model to obtain the piezoelectric micro-motion system after inverse compensation control. Frequency response analysis is performed on the piezoelectric micro-motion system after inverse compensation control processing to obtain frequency response data, and an uncertainty upper bound weighting function is generated based on the frequency response data. A robust controller is constructed based on the weighted function of the uncertainty upper bound, and the piezoelectric micro-motion system after inverse compensation control is stabilized based on the robust controller and combined with a stabilizing regulator.

2. The control method for the piezoelectric micro-motion system according to claim 1, characterized in that, The step of acquiring hysteresis loop data of the piezoelectric material in the piezoelectric micro-motion system and constructing a Hammerstein modular structure of the piezoelectric micro-motion system based on the hysteresis loop data includes: The input voltage signal and output displacement signal of the piezoelectric micro-motion system are acquired, and the input voltage signal and output displacement signal are discretely sampled and normalized to obtain the input voltage vector and output displacement vector. Based on the input voltage vector and output displacement vector, determine the hysteresis loop data of the piezoelectric material in the piezoelectric micro-motion system; Based on the hysteresis loop data, static nonlinear modules and dynamic linear modules are determined, and the Hammerstein modular structure of the piezoelectric micro-motion system is constructed based on the static nonlinear modules and dynamic linear modules.

3. The control method for the piezoelectric micro-motion system according to claim 1, characterized in that, The Bouc-Wen model and proportional-integral model for constructing the Hammerstein modular structure include: In the Hammerstein modular structure, a Bouc-Wen model is constructed based on hysteresis components, and a proportional-integral model is constructed based on the dead-zone operator. The expression of the Bouc-Wen model is as follows: ， Where y is the output displacement, k and d are model parameters, u is the driving voltage, and z is the hysteresis component.

4. The control method for the piezoelectric micro-motion system according to claim 3, characterized in that, The expression for the proportional-integral model is: ， in, It is a proportional-integral model. Let T be the first weight vector, and T be the transpose operation. For dead zone operators, This is the second weight vector. Let u be the play operator vector, and u be the driving voltage. t represents the output displacement at the current moment, where t is time.

5. The control method for the piezoelectric micro-motion system according to claim 1, characterized in that, The process of performing inverse compensation control on the piezoelectric micro-motion system based on the Bouc-Wen model and the proportional-integral model to obtain the piezoelectric micro-motion system after inverse compensation control includes: Determine the first inverse model of the Bouc-Wen model and the second inverse model of the proportional-integral model; A feedforward controller is generated based on the first inverse model and the second inverse model; The piezoelectric micro-motion system is subjected to inverse compensation control processing based on the feedforward controller to obtain the piezoelectric micro-motion system after inverse compensation control processing.

6. The control method for the piezoelectric micro-motion system according to claim 1, characterized in that, The piezoelectric micro-motion system after inverse compensation control processing undergoes frequency response analysis to obtain frequency response data, and an uncertainty upper bound weighting function is generated based on the frequency response data, including: Frequency response analysis of the piezoelectric micro-motion system after inverse compensation control is performed based on the spectral density function to obtain frequency response data. The frequency response data is compared with the nominal model frequency response to obtain the comparison result, and the upper bound of the difference is determined based on the comparison result. Curve fitting is performed based on the upper bound of the difference to obtain the uncertainty upper bound weighted function.

7. The control method for the piezoelectric micro-motion system according to claim 6, characterized in that, The expression for the frequency response data is: in, Here is the frequency response data, and N is the length of the time window. Let j be the autocorrelation function of the signal, and j be the imaginary unit. For frequency components, Let ω be the angular frequency and T be the time variable.

8. The control method for the piezoelectric micro-motion system according to claim 1, characterized in that, The process of constructing a robust controller based on the weighted function of the uncertainty upper bound, and then using the robust controller in conjunction with a stabilizing regulator to perform stable control on the piezoelectric micro-motion system after inverse compensation control processing, includes: Obtain the error performance weighting function of the piezoelectric micro-motion system after inverse compensation control processing; A robust controller is constructed based on the uncertainty upper bound weighting function and the error performance weighting function, combined with the Bouc-Wen model and the proportional-integral model. The conditional constraints of the robust controller are determined, and the target controller is generated by coprime decomposition based on the conditional constraints and the robust controller combined with a stable regulator. The piezoelectric micro-motion system after inverse compensation control is stably controlled based on the target controller.

9. A control device for a piezoelectric micro-motion system, characterized in that, The device includes: Modular structure module: used to acquire hysteresis loop data of piezoelectric material in piezoelectric micro-motion system, and to construct Hammerstein modular structure of piezoelectric micro-motion system based on the hysteresis loop data; Model building module: used to build Bouc-Wen models and proportional-integral models with a Hammerstein modular structure; Inverse compensation control module: used to perform inverse compensation control processing on the piezoelectric micro-motion system based on the Bouc-Wen model and the proportional-integral model, to obtain the piezoelectric micro-motion system after inverse compensation control processing; Function generation module: used to perform frequency response analysis on the piezoelectric micro-motion system after inverse compensation control processing, obtain frequency response data, and generate an uncertainty upper bound weighted function based on the frequency response data; Stability control module: used to construct a robust controller based on the uncertainty upper bound weighting function, and to perform stable control of the piezoelectric micro-motion system after inverse compensation control processing based on the robust controller and the stability regulator.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions that, when executed on an electronic device, cause the electronic device to perform the control method of the piezoelectric micro-motion system as described in any one of claims 1 to 8.

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