Hysteresis compensation control method and system of micro-vibration suppression platform and storage medium

Abstract

The invention provides a hysteresis compensation control method and system for a micro-vibration suppression platform and a storage medium, and relates to the technical field of nonlinear system control, and the method comprises the steps: obtaining micro-vibration data, and generating a micro-vibration evaluation factor according to the micro-vibration data; designing a fuzzy PI D algorithm according to the micro-vibration evaluation factor, and obtaining a micro-vibration compensation signal; related data of the piezoelectric array are obtained, and a piezoelectric intelligent structure dynamic model is established according to the data; describing the hysteresis behavior of the piezoelectric material by using a Bouc-Wen model; carrying out nonlinear regression fitting on the parameters of the Bouc-Wen model by using MATLAB (Matrix Laboratory); acquiring a hysteresis strength coefficient of a piezoelectric array material, and combining the piezoelectric intelligent structure dynamic model and the Bouc-Wen model to obtain a dynamic nonlinear hysteresis model; acquiring a hysteresis compensation signal by using a dynamic nonlinear hysteresis model; and acquiring a micro-vibration hysteresis compensation signal according to the micro-vibration compensation signal and the hysteresis compensation signal.

Description

Technical Field

[0001] This invention relates to the field of nonlinear system control technology, specifically to a hysteresis compensation control method, system, and storage medium for a micro-vibration suppression platform. Background Technology

[0002] The rapid development of high-tech fields such as optical communication, aerospace, biomedical technology, and ultra-precision machining has created an urgent need for high-precision and high-stability precision mechanical systems. The control of micro-vibrations has become one of the key bottleneck technologies restricting the accuracy and stability of these systems. The causes of micro-vibrations are highly complex, potentially arising from internal coupling within the system or from external excitations. In mechanical systems, especially precision mechanical systems, the presence of micro-vibrations significantly impacts the actuation accuracy and stability of the system's end-effectors.

[0003] With the development of smart materials technology, the design of smart material structures for micro-vibration control has become a research hotspot both domestically and internationally. The design of piezoelectric smart structures using the sensing and actuation characteristics of piezoelectric ceramic materials and their application in vibration control is increasingly favored by researchers worldwide. However, existing control models generally do not consider the hysteresis effect of the piezoelectric smart structure itself, or they establish static hysteresis models for the piezoelectric smart structure but rely solely on optimizing control parameters to achieve improved vibration control, without addressing the dynamic nonlinear hysteresis mechanism and characteristics of the piezoelectric smart structure. This makes it difficult to achieve precise control of micro-vibrations. Therefore, it is necessary to establish dynamic nonlinear hysteresis effect models for piezoelectric smart structures and design targeted intelligent active compensation control methods to achieve precise and effective control of micro-vibrations.

[0004] In the prior art, CN115857311A discloses a hysteresis compensation control method for a micro-vibration suppression platform. This method involves introducing a rate factor based on the Bouc-Wen model to obtain an improved Bouc-Wen model; calculating the parameters using the least squares method based on the improved Bouc-Wen model to determine the model's parameter values; and employing incremental PID control, which uses a linear combination of the proportional, integral, and derivative values ​​of the deviation to control the micro-vibration suppression platform. This method offers advantages such as simple hysteresis modeling, improved dynamic performance and steady-state accuracy of the micro-vibration suppression platform, and full-cycle control, giving it strong adaptability and robustness, and achieving full-cycle control of the hysteresis nonlinearity and vibration of the micro-vibration suppression platform. However, the prior art still has shortcomings. It treats micro-vibration control as a separate problem, failing to fully integrate the system's dynamic characteristics and neglecting the influence of micro-vibration itself on hysteresis compensation. This separation may lead to an incomplete understanding of micro-vibration behavior, thus affecting the control effect.

[0005] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0006] The purpose of this invention is to provide a hysteresis compensation control method, system, and storage medium for a micro-vibration suppression platform to solve the problems mentioned in the background art.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] The specific steps of a hysteresis compensation control method for a micro-vibration suppression platform include:

[0009] Step 1: Acquire micro-vibration data and generate micro-vibration evaluation factors based on the micro-vibration data; design a fuzzy PID algorithm based on the micro-vibration evaluation factors to obtain micro-vibration compensation signals; the micro-vibration data includes the vibration amplitude, frequency, and deformation of the piezoelectric material of each piezoelectric array block; and obtain the maximum value of the vibration amplitude, the maximum value of the vibration frequency, the variance of the vibration amplitude, and the variance of the vibration frequency.

[0010] Step 2: Obtain the property parameters, modal coordinates, external disturbance force, and control input signal of the piezoelectric array; establish a dynamic model of the piezoelectric smart structure based on the property parameters, external disturbance force, and control input signal; the property parameters include the mass matrix and stiffness matrix;

[0011] Step 3: Describe the hysteresis behavior of piezoelectric materials using the Bouc-Wen model; and use MATLAB to perform nonlinear regression fitting on the parameters of the Bouc-Wen model;

[0012] Step 4: Obtain the hysteresis strength coefficient of the piezoelectric array material, merge the dynamic model of the piezoelectric smart structure and the Bouc-Wen model to obtain a dynamic nonlinear hysteresis model; use the dynamic nonlinear hysteresis model to obtain the hysteresis compensation signal;

[0013] Step 5: Obtain the micro-vibration hysteresis compensation signal based on the micro-vibration compensation signal and the hysteresis compensation signal, and use the micro-vibration hysteresis compensation signal to perform hysteresis compensation on the micro-vibration suppression platform.

[0014] Furthermore, the specific logic for generating the micro-vibration assessment factor is as follows: acquire micro-vibration data, generate the micro-vibration assessment factor based on the micro-vibration data, and the specific formula for generating the micro-vibration assessment factor is as follows:

[0015]

[0016] in, P is a micro-vibration assessment factor. if is the vibration amplitude of the i-th region of the piezoelectric array. i P is the vibration frequency of the i-th piezoelectric array; max For the maximum vibration amplitude, f max X is the maximum vibration frequency; i σ represents the deformation of the piezoelectric material in the i-th piezoelectric array; P The variance of the vibration amplitude, σ f The variance of the vibration frequency, where N is the number of regions in the piezoelectric array.

[0017] Furthermore, the design logic of the fuzzy PID algorithm is as follows: select a micro-vibration evaluation factor as the error, define fuzzy rules, use the fuzzy rules to perform fuzzy inference, and make specific adjustments to the fuzzy inference results; the error is represented as:

[0018]

[0019] Where e(t) is the error at time t. is the micro-vibration assessment factor at time t, where t is the time variable;

[0020] The specific logic underlying the definition of fuzzy rules is as follows: Preset error threshold, error rate of change threshold, differential gain adjustment value, integral adjustment value, and proportional gain adjustment threshold; define an error less than the error threshold as small positive error, an error greater than the error threshold but less than twice the error threshold as medium positive error, and an error greater than twice the error threshold as large positive error; define an error rate of change less than the error rate of change threshold as small positive error rate, an error rate of change greater than the error rate of change threshold but less than twice the error rate of change threshold as medium positive error rate, and an error rate of change greater than twice the error rate of change threshold as large positive error rate. The rate of change threshold is defined as the error rate of change being positive; -1 times the differential gain adjustment value is defined as the differential gain being positively small, the differential gain adjustment value is defined as the differential gain being positively medium, and 2 times the differential gain adjustment value is defined as the differential gain being positively large; -1 times the integral gain adjustment value is defined as the integral gain being positively small, the integral gain adjustment value is defined as the integral gain being positively medium, and 2 times the integral gain adjustment value is defined as the integral gain being positively large; -1 times the proportional gain adjustment value is defined as the proportional gain being positively small, the proportional gain adjustment value is defined as the proportional gain being positively medium, and 2 times the proportional gain adjustment value is defined as the proportional gain being positively large.

[0021] If both the error and the rate of change of error are positive and small, the adjustment amount is the derivative gain with a positive and small value. If the error is positive and the rate of change of error is moderate, the adjustment amount is the derivative gain with a moderate value. If the error is moderate and the rate of change of error is positive and small, the adjustment amount is the derivative gain with a positive and large value. If the error gain is positive and the rate of change of error is positive and small, the adjustment amount is the integral gain with a positive and small value. If the error is moderate and the rate of change of error is moderate, the adjustment amount is the integral gain with a moderate value. If the error is positive and the rate of change of error is positive and large, the adjustment amount is the integral gain with a positive and large value. If the error is positive and the rate of change of error is moderate, the adjustment amount is the proportional gain with a positive and small value. If the error is moderate and the rate of change of error is positive and large, the adjustment amount is the proportional gain with a moderate value. If the error is positive and the rate of change of error is positive and large, the adjustment amount is the proportional gain with a positive and large value. The specific formulas used are as follows:

[0022]

[0023] Where Kp is the current proportional gain, Kp0 is the original proportional gain, ΔKp is the proportional gain adjustment, Kd is the current differential gain, Ki0 is the original differential gain, ΔKi is the differential gain adjustment, Ki is the current integral gain, Ki0 is the original integral gain, and ΔKi is the integral gain adjustment.

[0024] The specific logic underlying the acquisition of micro-vibration compensation signals is as follows:

[0025]

[0026] Among them, u Z (t) represents the micro-vibration compensation signal.

[0027] Furthermore, the specific logic underlying the establishment of the piezoelectric smart structure dynamic model is as follows: The modal matrix is ​​calculated using the mass matrix and stiffness matrix; the modal coordinates are transformed into generalized coordinates using the modal matrix; and the piezoelectric smart structure dynamic model is constructed based on the generalized coordinates and Lagrange dynamics theory. The specific formula used to calculate the modal matrix is:

[0028] KΦ=MΦΛ

[0029] Where Φ is the modal matrix, M is the mass matrix, K is the stiffness matrix, and Λ is the eigenvalue matrix;

[0030] The specific formula used to transform modal coordinates into generalized coordinates is as follows:

[0031] q=Φη

[0032] Where q is the generalized coordinate matrix and η is the modal coordinate matrix;

[0033] The dynamic model of the piezoelectric smart structure is expressed as follows:

[0034]

[0035] Where L is the Lagrange quantity, q i Let F be the generalized coordinates of the i-th region of the piezoelectric array. i Let be the external perturbation force experienced by the i-th region of the piezoelectric array, and u(t) be the control input signal. Further, the hysteresis behavior of the piezoelectric material is described using the Bouc-Wen model, which is expressed as:

[0036]

[0037] Where z is the hysteresis variable of the Bouc-Wen model, q is the generalized coordinate matrix of the piezoelectric array, and α, β, γ, and n are the parameters of the Bouc-Wen model;

[0038] Furthermore, the specific logic underlying the dynamic nonlinear hysteresis model is as follows: Obtain the hysteresis strength coefficient of the piezoelectric array material, and merge the piezoelectric smart structure dynamic model and the Bouc-Wen model to obtain the dynamic nonlinear hysteresis model; the dynamic nonlinear hysteresis model can be expressed as:

[0039]

[0040] Where L is the Lagrange quantity, q i Let F be the generalized coordinates of the i-th region of the piezoelectric array. i Let u be the external disturbance force experienced by the i-th region of the piezoelectric array. c (t) is the hysteresis compensation signal, λ is the hysteresis strength coefficient of the piezoelectric array material, z is the hysteresis variable of the Bouc-Wen model, and u(t) is the control input signal.

[0041] Furthermore, the distance logic used to obtain the micro-vibration hysteresis compensation signal is as follows: the micro-vibration hysteresis compensation signal is obtained based on the micro-vibration compensation signal and the hysteresis compensation signal; the specific formula used to obtain the micro-vibration hysteresis compensation signal is as follows:

[0042] u Zb (t)=u z (t)+u c (t)

[0043] Among them, u Zb (t) represents the micro-vibration hysteresis compensation signal, u z (t) represents the micro-vibration compensation signal, u c (t) represents the hysteresis compensation signal.

[0044] This invention further provides a hysteresis compensation control system for a micro-vibration suppression platform. The system is used to implement the hysteresis compensation control method for the micro-vibration suppression platform, specifically including:

[0045] The vibration assessment module is used to generate micro-vibration assessment factors from micro-vibration data; a fuzzy PID algorithm is designed based on the micro-vibration assessment factors to obtain micro-vibration compensation signals; the micro-vibration data includes the vibration amplitude, frequency, and deformation of the piezoelectric material of each piezoelectric array block; the maximum value of the vibration amplitude, the maximum value of the vibration frequency, the variance of the vibration amplitude, and the variance of the vibration frequency;

[0046] The dynamic analysis module is used to acquire the property parameters, modal coordinates, external disturbance forces, and control input signals of the piezoelectric array, and to establish a dynamic model of the piezoelectric smart structure based on the property parameters, external disturbance forces, and control input signals; the property parameters include the mass matrix and stiffness matrix; the hysteresis modeling module is used to describe the hysteresis behavior of the piezoelectric material using the Bouc-Wen model; and to perform nonlinear regression fitting on the Bouc-Wen model parameters using MATLAB;

[0047] The hysteresis analysis module is used to obtain the hysteresis strength coefficient of the piezoelectric array material, and to merge the dynamic model of the piezoelectric smart structure and the Bouc-Wen model to obtain a dynamic nonlinear hysteresis model; the dynamic nonlinear hysteresis model is used to obtain the hysteresis compensation signal.

[0048] The hysteresis compensation module is used to obtain the micro-vibration hysteresis compensation signal based on the micro-vibration compensation signal and the hysteresis compensation signal, and to perform hysteresis compensation on the micro-vibration suppression platform using the micro-vibration hysteresis compensation signal.

[0049] The present invention further provides a computer-readable storage medium, wherein the storage medium stores a computer program that can be executed by a processor, and the computer program, when executed by the processor, can implement the hysteresis compensation control method of the micro-vibration suppression platform.

[0050] Compared with the prior art, the beneficial effects of the present invention are:

[0051] The compensation signal of this invention can be dynamically adjusted according to real-time feedback, thereby effectively responding to micro-vibrations under different working modes, ensuring stable operation of the system under various conditions and improving overall performance.

[0052] This invention takes into account the influence of the inherent characteristics of micro-vibrations on the hysteresis properties of materials, and establishes a link between this influence and hysteresis compensation. By comprehensively considering the interaction between micro-vibrations and material behavior, we have achieved a more precise hysteresis compensation mechanism, which significantly improves the suppression effect of micro-vibrations. Attached Figure Description

[0053] Figure 1 This is a schematic diagram of the overall method flow of the present invention.

[0054] Figure 2 This is a schematic diagram of the overall system structure of the present invention. Detailed Implementation

[0055] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0056] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0057] Example:

[0058] Please see Figure 1 The present invention provides a technical solution:

[0059] A hysteresis compensation control method for a micro-vibration suppression platform, comprising the following steps:

[0060] Step 1: Acquire micro-vibration data and generate micro-vibration evaluation factors based on the micro-vibration data; design a fuzzy PID algorithm based on the micro-vibration evaluation factors to obtain micro-vibration compensation signals; the micro-vibration data includes the vibration amplitude, frequency, and deformation of the piezoelectric material of each piezoelectric array block; and obtain the maximum value of the vibration amplitude, the maximum value of the vibration frequency, the variance of the vibration amplitude, and the variance of the vibration frequency.

[0061] The specific logic for generating micro-vibration assessment factors is as follows: acquire micro-vibration data, generate micro-vibration assessment factors based on the micro-vibration data, and the specific formula for generating micro-vibration assessment factors is as follows:

[0062]

[0063] in, P is a micro-vibration assessment factor. i f is the vibration amplitude of the i-th block of the piezoelectric array. i P is the vibration frequency of the i-th piezoelectric array; max For the maximum vibration amplitude, f max X is the maximum vibration frequency; iσ represents the deformation of the piezoelectric material in the i-th piezoelectric array; P The variance of the vibration amplitude, σ f The variance of the vibration frequency, where N is the number of regions in the piezoelectric array. Micro-vibration evaluation factor. It reflects the overall vibration state of the vibration system. The larger the value, the higher the degree of micro-vibration in the system, and the more significant the response of the piezoelectric array to vibration.

[0064] The design logic of the fuzzy PID algorithm is as follows: select a vibration evaluation factor as the error, define fuzzy rules, use the fuzzy rules to perform fuzzy inference, and make specific adjustments to the fuzzy inference results; the error is represented as:

[0065]

[0066] Where e(t) is the error at time t. is the micro-vibration assessment factor at time t, where t is the time variable;

[0067] The specific logic underlying the definition of fuzzy rules is as follows: Preset error threshold, error rate of change threshold, differential gain adjustment value, integral adjustment value, and proportional gain adjustment threshold; define an error less than the error threshold as small positive error, an error greater than the error threshold but less than twice the error threshold as medium positive error, and an error greater than twice the error threshold as large positive error; define an error rate of change less than the error rate of change threshold as small positive error rate, an error rate of change greater than the error rate of change threshold but less than twice the error rate of change threshold as medium positive error rate, and an error rate of change greater than twice the error rate of change threshold as large positive error rate. The rate of change threshold is defined as the error rate of change being positive; -1 times the differential gain adjustment value is defined as the differential gain being positively small, the differential gain adjustment value is defined as the differential gain being positively medium, and 2 times the differential gain adjustment value is defined as the differential gain being positively large; -1 times the integral gain adjustment value is defined as the integral gain being positively small, the integral gain adjustment value is defined as the integral gain being positively medium, and 2 times the integral gain adjustment value is defined as the integral gain being positively large; -1 times the proportional gain adjustment value is defined as the proportional gain being positively small, the proportional gain adjustment value is defined as the proportional gain being positively medium, and 2 times the proportional gain adjustment value is defined as the proportional gain being positively large.

[0068] If both the error and the rate of change of error are positive and small, the adjustment amount is the derivative gain with a positive and small value. If the error is positive and the rate of change of error is moderate, the adjustment amount is the derivative gain with a moderate value. If the error is moderate and the rate of change of error is positive and small, the adjustment amount is the derivative gain with a positive and large value. If the error gain is positive and the rate of change of error is positive and small, the adjustment amount is the integral gain with a positive and small value. If the error is moderate and the rate of change of error is moderate, the adjustment amount is the integral gain with a moderate value. If the error is positive and the rate of change of error is positive and large, the adjustment amount is the integral gain with a positive and large value. If the error is positive and the rate of change of error is moderate, the adjustment amount is the proportional gain with a positive and small value. If the error is moderate and the rate of change of error is positive and large, the adjustment amount is the proportional gain with a moderate value. If the error is positive and the rate of change of error is positive and large, the adjustment amount is the proportional gain with a positive and large value. The specific formulas used are as follows:

[0069]

[0070] Where Kp is the current proportional gain, Kp0 is the original proportional gain, ΔKp is the proportional gain adjustment, Kd is the current differential gain, Ki0 is the original differential gain, ΔKi is the differential gain adjustment, Ki is the current integral gain, Ki0 is the original integral gain, and ΔKi is the integral gain adjustment.

[0071] The specific logic underlying the acquisition of micro-vibration compensation signals is as follows:

[0072]

[0073] Among them, u z (t) represents the micro-vibration compensation signal.

[0074] Step 2: Obtain the property parameters, modal coordinates, external disturbance force, and control input signal of the piezoelectric array; establish a dynamic model of the piezoelectric smart structure based on the property parameters, external disturbance force, and control input signal; the property parameters include the mass matrix and stiffness matrix;

[0075] Lagrange dynamics theory is convenient for dealing with complex systems with multiple degrees of freedom. It allows you to choose the most suitable generalized coordinates for the problem, simplifying equation derivation and calculation. It does not require direct analysis of forces and accelerations; you only need to consider the energy form of the system.

[0076] The specific logic underlying the establishment of the piezoelectric smart structure dynamic model is as follows: The modal matrix is ​​calculated using the mass matrix and stiffness matrix; the modal coordinates are transformed into generalized coordinates using the modal matrix; and the piezoelectric smart structure dynamic model is constructed based on the generalized coordinates and Lagrange dynamics theory. The specific formula for calculating the modal matrix is ​​as follows:

[0077] KΦ=MΦΛ

[0078] Where Φ is the modal matrix, M is the mass matrix, K is the stiffness matrix, and Λ is the eigenvalue matrix;

[0079] The specific formula used to transform modal coordinates into generalized coordinates is as follows:

[0080] q=Φη

[0081] Where q is the generalized coordinate matrix and η is the modal coordinate matrix;

[0082] The dynamic model of the piezoelectric smart structure is expressed as follows:

[0083]

[0084] Where L is the Lagrange quantity, q i Let F be the generalized coordinates of the i-th region of the piezoelectric array. i Let u(t) be the external perturbation force acting on the i-th region of the piezoelectric array, and u(t) be the control input signal. Step 3: Describe the hysteresis behavior of the piezoelectric material using the Bouc-Wen model; and use MATLAB to perform nonlinear regression fitting on the parameters of the Bouc-Wen model;

[0085] The Bouc-Wen model, an existing technique, is a mathematical model used to describe nonlinear hysteresis phenomena and can be used to simulate the hysteretic behavior of structures. It represents the dynamic characteristics of a system through a set of differential equations and can capture complex hysteresis effects.

[0086] The Bouc-Wen model is used to describe the hysteresis behavior of piezoelectric materials. The Bouc-Wen model is expressed as follows:

[0087]

[0088] Where z is the hysteresis variable of the Bouc-Wen model, q is the generalized coordinate matrix of the piezoelectric array, and α, β, γ, and n are the Bouc-Wen model parameters.

[0089] Multiple sets of historical experimental data were acquired, and the historical lagged variables z and generalized coordinates q were imported. MATLAB's nonlinear regression tools were then used to optimize the model parameters α, β, γ, and n. The parameters were adjusted by minimizing the error between the experimental data and the model's predicted values ​​to achieve the best fit. Finally, the accuracy and stability of the fitting results were examined, and the model's applicability was evaluated through residual analysis and goodness-of-fit analysis.

[0090] Step 4: Obtain the hysteresis strength coefficient of the piezoelectric array material, merge the dynamic model of the piezoelectric smart structure and the Bouc-Wen model to obtain a dynamic nonlinear hysteresis model; use the dynamic nonlinear hysteresis model to obtain the hysteresis compensation signal;

[0091] The specific logic underlying the dynamic nonlinear hysteresis model is as follows: Obtain the hysteresis strength coefficient of the piezoelectric array material, and merge the piezoelectric smart structure dynamic model and the Bouc-Wen model to obtain the dynamic nonlinear hysteresis model; the dynamic nonlinear hysteresis model can be expressed as:

[0092]

[0093] Where L is the Lagrange quantity, q i Let F be the generalized coordinates of the i-th region of the piezoelectric array. i Let u be the external disturbance force experienced by the i-th region of the piezoelectric array. c (t) is the hysteresis compensation signal, λ is the hysteresis strength coefficient of the piezoelectric array material, z is the hysteresis variable of the Bouc-Wen model, and u(t) is the control input signal.

[0094] Hysteresis signal u c (t) reflects the inherent complex behavior of piezoelectric materials due to the hysteresis effect in their dynamic response. Specifically, the hysteresis compensation signal describes the nonlinear relationship between the material and the structural dynamic response to the external input signal.

[0095] Step 5: Obtain the micro-vibration hysteresis compensation signal based on the micro-vibration compensation signal and the hysteresis compensation signal, and use the micro-vibration hysteresis compensation signal to perform hysteresis compensation on the micro-vibration suppression platform.

[0096] The distance logic used to obtain the micro-vibration hysteresis compensation signal is as follows: the micro-vibration hysteresis compensation signal is obtained based on the micro-vibration compensation signal and the hysteresis compensation signal; the specific formula used to obtain the micro-vibration hysteresis compensation signal is as follows:

[0097] u Zb (t)=u z (t)+u c (t)

[0098] Among them, u Zb (t) represents the micro-vibration hysteresis compensation signal, u z (t) represents the micro-vibration compensation signal, u c (t) represents the hysteresis compensation signal. The micro-vibration hysteresis compensation signal u Zb (t) reflects the overall effect of precise system control to reduce or eliminate the influence of micro-vibrations. It incorporates the micro-vibration compensation signal u z (t) and hysteresis compensation signal u c (t) is used to address instability caused by vibration and hysteresis in the system. This signal enables comprehensive compensation for micro-vibrations and hysteresis effects, improving the system's response accuracy and stability.

[0099] Please see Figure 2The present invention further provides a hysteresis compensation control system for a micro-vibration suppression platform. The system is used to implement the hysteresis compensation control method for the micro-vibration suppression platform, specifically including:

[0100] The vibration assessment module is used to acquire micro-vibration data to generate vibration assessment factors; design a fuzzy PID algorithm based on the vibration assessment factors to acquire vibration compensation signals; the micro-vibration data includes the vibration amplitude, frequency and deformation of each piezoelectric array block; and acquire the maximum value of vibration amplitude, the maximum value of vibration frequency, the variance of vibration amplitude and the variance of vibration frequency.

[0101] The dynamic analysis module is used to acquire the property parameters, modal coordinates, external disturbance forces, and control input signals of the piezoelectric array, and to establish a dynamic model of the piezoelectric smart structure based on these parameters. The property parameters include the mass matrix and stiffness matrix. The hysteresis modeling module uses the Bouc-Wen model to describe the hysteresis behavior of the piezoelectric material and performs nonlinear regression fitting on the Bouc-Wen model parameters using MATLAB. The hysteresis analysis module is used to acquire the hysteresis strength coefficient of the piezoelectric array material, merge the piezoelectric smart structure dynamic model and the Bouc-Wen model to obtain a dynamic nonlinear hysteresis model, and use this dynamic nonlinear hysteresis model to acquire the hysteresis compensation signal.

[0102] The hysteresis compensation module is used to obtain the micro-vibration hysteresis compensation signal based on the micro-vibration compensation signal and the hysteresis compensation signal, and to perform hysteresis compensation on the micro-vibration suppression platform using the micro-vibration hysteresis compensation signal.

[0103] The present invention further provides a computer-readable storage medium, wherein the storage medium stores a computer program that can be executed by a processor, and the computer program, when executed by the processor, can implement the hysteresis compensation control method of the micro-vibration suppression platform.

[0104] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0105] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0106] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0107] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A hysteresis compensation control method for a micro-vibration suppression platform, characterized in that, The specific steps include: Step 1: Acquire micro-vibration data and generate micro-vibration evaluation factors based on the micro-vibration data; design a fuzzy PID algorithm based on the micro-vibration evaluation factors to obtain micro-vibration compensation signals; the micro-vibration data includes the vibration amplitude, frequency, and deformation of the piezoelectric material of each piezoelectric array block; and obtain the maximum value of the vibration amplitude, the maximum value of the vibration frequency, the variance of the vibration amplitude, and the variance of the vibration frequency. Step 2: Obtain the property parameters, modal coordinates, external disturbance force, and control input signal of the piezoelectric array; establish a dynamic model of the piezoelectric smart structure based on the property parameters, external disturbance force, and control input signal; the property parameters include the mass matrix and stiffness matrix; Step 3: Describe the hysteresis behavior of piezoelectric materials using the Bouc-Wen model; and use MATLAB to perform nonlinear regression fitting on the parameters of the Bouc-Wen model; Step 4: Obtain the hysteresis strength coefficient of the piezoelectric array material, merge the dynamic model of the piezoelectric smart structure and the Bouc-Wen model to obtain a dynamic nonlinear hysteresis model; use the dynamic nonlinear hysteresis model to obtain the hysteresis compensation signal; Step 5: Obtain the micro-vibration hysteresis compensation signal based on the micro-vibration compensation signal and the hysteresis compensation signal, and use the micro-vibration hysteresis compensation signal to perform hysteresis compensation on the micro-vibration suppression platform.

2. The hysteresis compensation control method for a micro-vibration suppression platform according to claim 1, characterized in that: The specific logic for generating micro-vibration assessment factors is as follows: acquire micro-vibration data, generate micro-vibration assessment factors based on the micro-vibration data, and the specific formula for generating micro-vibration assessment factors is as follows: in, P is a micro-vibration assessment factor. i f is the vibration amplitude of the i-th region of the piezoelectric array. i P is the vibration frequency of the i-th piezoelectric array; max For the maximum vibration amplitude, f max X is the maximum vibration frequency; i σ represents the deformation of the piezoelectric material in the i-th piezoelectric array; P The variance of the vibration amplitude, σ f The variance of the vibration frequency, where N is the number of regions in the piezoelectric array.

3. The hysteresis compensation control method for a micro-vibration suppression platform according to claim 1, characterized in that: The design logic of the fuzzy PID algorithm is as follows: a micro-vibration evaluation factor is selected as the error; fuzzy rules are defined; fuzzy inference is performed using these rules; and the fuzzy inference results are then adjusted accordingly. The error is represented as follows: Where e(t) is the error at time t. is the micro-vibration assessment factor at time t, where t is the time variable; The specific logic underlying the definition of fuzzy rules is as follows: Preset error threshold, error rate of change threshold, differential gain adjustment value, integral adjustment value, and proportional gain adjustment threshold; define an error less than the error threshold as small positive error, an error greater than the error threshold but less than twice the error threshold as medium positive error, and an error greater than twice the error threshold as large positive error; define an error rate of change less than the error rate of change threshold as small positive error rate, an error rate of change greater than the error rate of change threshold but less than twice the error rate of change threshold as medium positive error rate, and an error rate of change greater than twice the error rate of change threshold as large positive error rate. The rate of change threshold is defined as the error rate of change being positive; -1 times the differential gain adjustment value is defined as the differential gain being positively small, the differential gain adjustment value is defined as the differential gain being positively medium, and 2 times the differential gain adjustment value is defined as the differential gain being positively large; -1 times the integral gain adjustment value is defined as the integral gain being positively small, the integral gain adjustment value is defined as the integral gain being positively medium, and 2 times the integral gain adjustment value is defined as the integral gain being positively large; -1 times the proportional gain adjustment value is defined as the proportional gain being positively small, the proportional gain adjustment value is defined as the proportional gain being positively medium, and 2 times the proportional gain adjustment value is defined as the proportional gain being positively large. If both the error and the rate of change of error are positive and small, the adjustment amount is the derivative gain with a positive and small value. If the error is positive and the rate of change of error is moderate, the adjustment amount is the derivative gain with a moderate value. If the error is moderate and the rate of change of error is positive and small, the adjustment amount is the derivative gain with a positive and large value. If the error gain is positive and the rate of change of error is positive and small, the adjustment amount is the integral gain with a positive and small value. If the error is moderate and the rate of change of error is moderate, the adjustment amount is the integral gain with a moderate value. If the error is positive and the rate of change of error is positive and large, the adjustment amount is the integral gain with a positive and large value. If the error is positive and the rate of change of error is moderate, the adjustment amount is the proportional gain with a positive and small value. If the error is moderate and the rate of change of error is positive and large, the adjustment amount is the proportional gain with a moderate value. If the error is positive and the rate of change of error is positive and large, the adjustment amount is the proportional gain with a positive and large value. The specific formulas used are as follows: Where Kp is the current proportional gain, Kp0 is the original proportional gain, ΔKp is the proportional gain adjustment, Kd is the current differential gain, Ki0 is the original differential gain, ΔKi is the differential gain adjustment, Ki is the current integral gain, Ki0 is the original integral gain, and ΔKi is the integral gain adjustment. The specific logic underlying the acquisition of micro-vibration compensation signals is as follows: Among them, u z (t) represents the micro-vibration compensation signal.

4. The hysteresis compensation control method for a micro-vibration suppression platform according to claim 2, characterized in that: The specific logic underlying the establishment of the piezoelectric smart structure dynamic model is as follows: The modal matrix is ​​calculated using the mass matrix and stiffness matrix; the modal coordinates are transformed into generalized coordinates using the modal matrix; and the piezoelectric smart structure dynamic model is constructed based on the generalized coordinates and Lagrange dynamics theory. The specific formula for calculating the modal matrix is ​​as follows: KΦ=MΦΛ Where φ is the modal matrix, M is the mass matrix, K is the stiffness matrix, and Λ is the eigenvalue matrix; The specific formula used to transform modal coordinates into generalized coordinates is as follows: q=φη Where q is the generalized coordinate matrix and η is the modal coordinate matrix; The dynamic model of the piezoelectric smart structure is expressed as follows: Where L is the Lagrange quantity, q i Let F be the generalized coordinates of the i-th region of the piezoelectric array. i Let t be the external disturbance force on the i-th region of the piezoelectric array, and u(t) be the control input signal.

5. The hysteresis compensation control method for a micro-vibration suppression platform according to claim 1, characterized in that: The Bouc-Wen model is used to describe the hysteresis behavior of piezoelectric materials. The Bouc-Wen model is expressed as follows: Where z is the hysteresis variable of the Bouc-Wen model, q is the generalized coordinate matrix of the piezoelectric array, and α, β, γ, and n are the Bouc-Wen model parameters.

6. The hysteresis compensation control method for a micro-vibration suppression platform according to claim 1, characterized in that: The specific logic underlying the dynamic nonlinear hysteresis model is as follows: Obtain the hysteresis strength coefficient of the piezoelectric array material, and merge the piezoelectric smart structure dynamic model and the Bouc-Wen model to obtain the dynamic nonlinear hysteresis model; the dynamic nonlinear hysteresis model can be expressed as: Where L is the Lagrange quantity, q i Let F be the generalized coordinates of the i-th region of the piezoelectric array. i Let u be the external disturbance force experienced by the i-th region of the piezoelectric array. c (t) is the hysteresis compensation signal, λ is the hysteresis strength coefficient of the piezoelectric array material, z is the hysteresis variable of the Bouc-Wen model, and u(t) is the control input signal.

7. The hysteresis compensation control method for a micro-vibration suppression platform according to claim 1, characterized in that: The distance logic used to obtain the micro-vibration hysteresis compensation signal is as follows: the micro-vibration hysteresis compensation signal is obtained based on the micro-vibration compensation signal and the hysteresis compensation signal; the specific formula used to obtain the micro-vibration hysteresis compensation signal is as follows: u Zb (t)=u z (t)+u c (t) Among them, u Zb (t) represents the micro-vibration hysteresis compensation signal, u z (t) represents the micro-vibration compensation signal, u c (t) is the hysteresis compensation signal.

8. The hysteresis compensation control system for a micro-vibration suppression platform according to claim 1, characterized in that: The system is used to implement the hysteresis compensation control method of the micro-vibration suppression platform according to claims 1-7, specifically including: The vibration assessment module is used to acquire micro-vibration data and generate micro-vibration assessment factors; based on the micro-vibration assessment factors, a fuzzy PLD algorithm is designed to acquire micro-vibration compensation signals; the micro-vibration data includes the vibration amplitude, frequency, and deformation of the piezoelectric material of each piezoelectric array block; and the maximum value of the vibration amplitude, the maximum value of the vibration frequency, the variance of the vibration amplitude, and the variance of the vibration frequency are acquired. The dynamic analysis module is used to acquire the property parameters, modal coordinates, external disturbance forces, and control input signals of the piezoelectric array, and to establish a dynamic model of the piezoelectric smart structure based on the property parameters, external disturbance forces, and control input signals; the property parameters include the mass matrix and stiffness matrix; The hysteresis modeling module uses the Bouc-Wen model to describe the hysteresis behavior of piezoelectric materials; and uses MATLAB to perform nonlinear regression fitting on the parameters of the Bouc-Wen model. The hysteresis analysis module is used to obtain the hysteresis strength coefficient of the piezoelectric array material, and to merge the dynamic model of the piezoelectric smart structure and the Bouc-Wen model to obtain a dynamic nonlinear hysteresis model; the dynamic nonlinear hysteresis model is used to obtain the hysteresis compensation signal. The hysteresis compensation module is used to obtain the micro-vibration hysteresis compensation signal based on the micro-vibration compensation signal and the hysteresis compensation signal, and to perform hysteresis compensation on the micro-vibration suppression platform using the micro-vibration hysteresis compensation signal.

9. A computer-readable storage medium, characterized in that: The storage medium contains a computer program that can be executed by a processor. When the computer program is executed by the processor, it can implement the hysteresis compensation control method of the micro-vibration suppression platform according to any one of claims 1-7.

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