Modeling and Compensation Method for Dynamic Composite Hysteresis of Piezoelectric Actuators under Time-Varying Large Loads

Abstract

The present invention belongs to the field of piezoelectric actuator characteristic measurement, and relates to a method for modeling and compensating dynamic composite hysteresis of a piezoelectric actuator under a time-varying large load. A dynamic hysteresis characteristic test system of the piezoelectric actuator is built to collect load and displacement signals. Based on the improved asymmetric slope Prandtl-Ishlinskii algorithm, the asymmetry and zero drift characteristics of the hysteresis loop are modeled, the static hysteresis loops of force-displacement and voltage-displacement are fitted, and superimposed into a static composite hysteresis model; aiming at the wide-frequency excitation requirement of the actuator, a dynamic composite hysteresis model is established, and an ASPI parameter controller is designed based on the LSTM algorithm to dynamically regulate the slope and threshold of the model; a fault tolerance mechanism of the parameter controller is designed to constrain the model instability caused by mutation disturbance and control overshoot, and ensure high-precision real-time hysteresis prediction; by solving the inverse model of the dynamic composite hysteresis model and inputting the desired displacement, the calculation of the real-time control voltage and the compensation of dynamic hysteresis are realized.

Description

Technical Field

[0001] The present invention belongs to the field of piezoelectric actuator characteristic measurement, and relates to a dynamic modeling and compensation method for the dynamic composite hysteresis characteristics of piezoelectric actuators under time-varying large loads. Background Art

[0002] As a micro-nano precision actuator that can realize the mutual conversion of electrical energy and mechanical energy, the piezoelectric actuator has the characteristics of small volume, high displacement resolution, fast response speed, etc., and is widely used in fields such as optical scanning positioning and biomedical micro-control for high-precision micro-positioning. In recent years, due to the advantages of high compact layout, high power density, and large driving force of the stacked piezoelectric actuator, it has gradually been used as a force / displacement driving element in fields such as mechanical precision machining and aerospace testing. Such tasks are often accompanied by large time-varying loads and dynamic disturbances, which have a great impact on the output performance of the actuator. For example, in the dynamic stability evaluation test of an aircraft, the piezoelectric actuator is used as the driving element of the aircraft motion simulation device. By outputting a micro-displacement, it is amplified by a transmission mechanism to drive the aircraft model to realize multi-degree-of-freedom motion simulation in the high-speed flow field environment of the wind tunnel, and complete the test of the aircraft's dynamic stability. First, the inverse piezoelectric hysteresis error of the piezoelectric ceramic actuator itself reduces the actuation accuracy of the ceramic. Second, the aerodynamic load under a complex flow field has the characteristics of large time-variation and strong disturbance, which makes the hysteresis characteristics of the ceramic change significantly under the influence of the time-varying load, thus bringing greater challenges to the accurate modeling and compensation control of the ceramic hysteresis.

[0003] In recent years, modeling and compensating the hysteresis effect of piezoelectric actuators has always been a research hotspot, and many scholars have reduced external disturbances through composite control methods. However, most models only consider the hysteresis influence of voltage input on piezoelectric actuators, and rarely consider the hysteresis characteristics of piezoelectric actuators under time-varying loads.

[0004] The patent "Method for Modeling Dynamic Hysteresis Characteristics of Piezoelectric Ceramics" by Cao Kairui et al., with the patent number CN202310434548.6, introduces a method for modeling the dynamic hysteresis characteristics of piezoelectric ceramics, which can more accurately describe the dynamic hysteresis characteristics of piezoelectric ceramics and thus achieve high-precision position prediction. However, this method only fits the output displacement for the mixed-frequency voltage and cannot be applied to piezoelectric ceramic actuator systems with time-varying large loads that need to consider the force-displacement hysteresis elasticity characteristics.

[0005] In the paper "Kalman Filter Output Feedback Predictive Control of Piezoelectric Ceramic Actuators" published by Yu Shuyou et al. in the 11th issue of Optics and Precision Engineering in 2024, the static hysteresis nonlinearity is represented by an asymmetric Bouc-Wen model, the signal rate dependence is characterized by a dynamic linear model, and the predictive control of the actuator is realized based on the Kalman filter, reducing the hysteresis error. However, this method still only models and compensates the mapping relationship between voltage and displacement, lacking the error estimation and compensation for external time-varying load disturbances.

[0006] The above modeling research provides sufficient accuracy guarantee for the dynamic response prediction of piezoelectric actuators. However, when facing the driving task with large load disturbances, there is still a lack of research on issues such as the output characteristic prediction and hysteresis error compensation of piezoelectric ceramic actuators under dynamic loads. Based on the problems existing in the above technologies, it is necessary to propose a modeling and compensation method for the composite hysteresis characteristics of piezoelectric ceramic actuators under time-varying large loads. Summary of the Invention

[0007] In order to overcome the deficiencies of the existing technology, the present invention proposes a modeling and compensation method for the dynamic composite hysteresis characteristics of piezoelectric actuators under time-varying large loads, realizing a more accurate model description of the force-electricity-potential composite hysteresis of piezoelectric actuators and then realizing high-precision output compensation control. This method first builds a test system for the force-electricity-potential dynamic hysteresis characteristics of piezoelectric actuators to collect load and displacement signals during the actuation process; improves the traditional PI hysteresis model, proposes an asymmetric slope Prandtl-Ishlinskii (ASPI) algorithm, which has better adaptability to the asymmetry and zero-point drift characteristics of the hysteresis loop, and respectively fits and models the static hysteresis loops of force-displacement and electricity-displacement, and superimposes them to form a static composite hysteresis model; aiming at the wide-frequency excitation requirement of the actuator, a dynamic composite hysteresis model is proposed, a parameter controller of ASPI is established based on the LSTM algorithm, and the slope and threshold of the existing model are adjusted according to the dynamic load and dynamic voltage input; designs a fault tolerance mechanism for the parameter controller to constrain the model instability caused by sudden disturbances and overshoot of the model parameter controller, ensuring real-time high-precision hysteresis prediction; solves the inverse model of the dynamic composite hysteresis model, inputs the expected displacement, and calculates the control voltage in real time to compensate for the dynamic composite hysteresis. Compared with other modeling and compensation methods, the present invention can stably and accurately output the hysteresis magnitude under the conditions of variable loads and multi-frequency mixed drive signals, and ensure a high compensation accuracy. The compensation control effect has the advantages of small hysteresis and high calculation efficiency compared with composite control.

[0008] The technical solution of the present invention is as follows:

[0009] Based on the established force-electricity-potential dynamic hysteresis characteristic test system of the piezoelectric actuator, observe the dynamic composite hysteresis output of the piezoelectric ceramic actuator and collect the corresponding data; then construct the ASPI algorithm based on the asymmetric play operator, and propose a force-electricity static composite hysteresis modeling method; then establish a model parameter controller based on the LSTM neural network algorithm, identify and optimize the neural network parameters, and form a force-electricity dynamic composite hysteresis model; through the fault tolerance mechanism of the parameter controller, improve the anti-interference ability of the compensation algorithm to sudden disturbances and ill-conditioned data; then solve the dynamic composite hysteresis inverse model, calculate the compensation voltage based on the expected displacement, realize the linearization of the input and output of the actuator, and form the modeling and compensation control of the force-electricity dynamic composite hysteresis characteristic of the actuator.

[0010] The specific steps are as follows:

[0011] The first step: Construction of the force-electricity-potential dynamic hysteresis characteristic test system and data acquisition;

[0012] Construct a piezoelectric ceramic force-electricity-potential dynamic hysteresis characteristic test system: The flexible sleeve 11 is embedded in the round hole of the pressure application slider 6, and the guide rail 2 passes through the flexible sleeve 11; the pressure application slider 6 is fixed to the device main body 3 and tightened by bolts; the force sensor 10 and the pre-tightening pressing plate 1 are respectively fixed in the installation grooves at both ends of the device main body 3, and the force measuring head 9 is screwed onto the force sensor 10; the force application driver 4 and the front gasket 5 are attached, the actuator to be measured 7 and the rear gasket 8 are attached, the front gaskets 5 at both ends of the force application driver 4 are in close contact with the spherical arc surfaces of the pre-tightening pressing plate 1 and the pressure application slider 6, and the rear gaskets 8 at both ends of the actuator to be measured 7 are in close contact with the spherical arc surfaces of the force measuring head 9 and the pressure application slider 6. The pre-tightening pressing plate 1 is tightened by bolts to apply a pre-tightening force to the force application driver 4 and the actuator to be measured 7, eliminating the device gap. Thus, the construction of the motion structure of the piezoelectric ceramic force-electricity-potential dynamic hysteresis characteristic test system is completed;

[0013] The power supply lines of the force application driver 4 and the actuator under test 7 are connected to the power amplifier 15, and the strain lines and force signal lines are connected to the data acquisition module 12. The data acquisition module 12 is connected to the real-time controller 14, and the real-time controller 14 is respectively connected to the power amplifier 15 and the PC host computer 13. Thus, the construction of the piezoelectric ceramic force-electricity-potential dynamic hysteresis characteristic test system is completed; the PC host computer 13 is responsible for displaying data and transmitting instructions. The real-time controller 14 receives instructions, generates drive signals, outputs drive voltages through the power amplifier 15, and loads them onto the force application driver 4 and the actuator under test 7. The force application driver 4 outputs displacement to drive the pressure application slider 6 to generate a time-varying load on the actuator under test 7. The actuator under test 7 resists the load and outputs displacement to do work. The strain gauge buried in the actuator under test 7 monitors its telescopic displacement. The load received by the actuator under test 7 is conducted to the force sensor 10 through the rear spacer 8 and the force measuring head 9. The force sensor 10 captures the load signal, transmits it to the data acquisition module 12 together with the strain signal, and is stored, calculated by the real-time controller 14, and transmitted to the PC host computer 13 for display. As Figure 2 is a schematic diagram of the force-electricity-potential dynamic hysteresis characteristic test system.

[0014] After the test system is built, a constant amplitude and constant frequency signal and a constant frequency attenuation wave signal are designed as drive signals to respectively control the force application driver 4 and the actuator under test 7 to generate a constant frequency attenuation / constant amplitude and constant frequency force and displacement. The function of the drive signal is defined by the following formula (1):

[0015]

[0016] where U is the drive voltage quantity, A is the drive amplitude, f is the drive frequency, and k is the linear attenuation slope.

[0017] Collect the input voltage, output displacement and output force data of the actuator under test 7 to form various hysteresis loops of the actuator under test 7. Among them, the voltage-displacement hysteresis loop is composed of Figure 3 、 Figure 4 shown, which are the constant frequency attenuation signal and the constant amplitude and constant frequency signal respectively; the load-displacement signal is composed of Figure 5 , Figure 6 shown, and the drive type is the same as above.

[0018] Step 2: Establish a composite static hysteresis modeling method based on the asymmetric play operator;

[0019] An asymmetric play operator is proposed, and the function structure is as follows:

[0020]

[0021] where: u(t) is the input of the operator at time t, H r,a,b[u](t) is the output of the asymmetric play operator, r is the threshold of the operator, a and b are the asymmetric correction coefficients of the upper and lower edges respectively, and T is the sampling interval;

[0022] The asymmetric correction coefficients a and b of the upper and lower edges can control the slopes of the operator during the lifting and return strokes, thereby enhancing the fitting adaptability in different segments of the domain; the operator threshold vector r = (r 1 , …, r n ) T is an arithmetic progression determined by the number of operators:

[0023]

[0024] where r i represents the i-th operator, n is the number of asymmetric play operators, and u max (t) is the maximum input voltage;

[0025] The weighted superposition of multiple asymmetric play operators with different thresholds yields the ASPI algorithm, which realizes the characterization of the hysteresis characteristics of the piezoelectric actuator; Equation (4) is the functional form of the ASPI algorithm:

[0026]

[0027] where the weight coefficient is w;

[0028] Based on the ASPI algorithm, the voltage-displacement hysteresis loop and the load-displacement hysteresis loop are respectively fitted to form a static piezoelectric hysteresis model and a static mechanical hysteresis-elasticity model; the outputs of the static piezoelectric hysteresis model and the static mechanical hysteresis-elasticity model are superimposed and corrected, that is, a static composite hysteresis model y static (t) with double inputs of load and voltage quantity is formed, and its form is as shown in Equation (5):

[0029] y static = y p [u](t) + y m [F](t) + p 1 u + p 2 F + p 3 (5)

[0030] where y p [u](t) and y m [F](t) are the outputs of the static piezoelectric hysteresis model and the static mechanical hysteresis-elasticity model respectively, u and F are the input voltage and load, and p 1 , p 2 , p 3 are constants;

[0031] Step 3: Establish a hysteresis model parameter controller to form a dynamic composite hysteresis model of the piezoelectric actuator based on the LSTM-ASPI algorithm;

[0032] Propose an LSTM-regulated asymmetric slope Prandtl-Ishlinskii algorithm; design a hysteresis model parameter controller based on the static composite hysteresis model, construct the mapping relationship between the hysteresis model parameter vector and the force and position time-domain signals through the LSTM time series neural network, adjust the parameter vector of the hysteresis model according to the dynamic time-domain signal of the actuator, and substitute it into the ASPI algorithm to calculate the dynamic composite hysteresis displacement of the actuator, and its form is shown in Equation (6):

[0033]

[0034] where, is the output of the LSTM neural network, and its dimension is the same as the parameter dimension of the static composite hysteresis model; [S t-1 ,...,S t-m T , [F t-1 ,...,F t-m T are the time-varying signals of displacement and load respectively, m is the time series length; G(·) represents the network function framework of the LSTM neural network;

[0035] Establish a fault tolerance mechanism for the parameter controller. First, set a monitoring window. Through the load and displacement signals within the monitoring window, identify strong disturbances by calculating the mutation degree q. The formula is as follows:

[0036]

[0037] where, m is the time series length, S m×1 is the displacement signal within the monitoring window, and diff(S m×1 ) is its difference vector; when the calculated mutation degree q = 1 within the window, it is judged that the disturbance is too large, and the parameter target control amount of the current parameter controller remains unchanged from the previous step; that is, as shown in Equation (8):

[0038]

[0039] where, is the model parameter target control amount;

[0040] Introduce a parameter asymptotic link, set a parameter correction gain ρ, and the parameters of the ASPI algorithm are iteratively updated in each prediction time step as shown in Equation (9) and asymptotically approach the model parameter target control amount:

[0041] ​​

[0042] Among them, [a t , b t , w t T are the ASPI algorithm parameters at time t, and [Δa, Δb, Δw] T is the increment of the ASPI algorithm parameters at each prediction time step and is less than the upper limit ξ to ensure the stability of the parameter regulation process;

[0043] Substitute the parameter control quantity output by the LSTM neural network into the static composite hysteresis model, and name it the LSTM - ASPI algorithm, that is, realize the adaptive adjustment of the ASPI algorithm parameters under the dynamic changes of load and displacement, and form the dynamic composite hysteresis model of the piezoelectric actuator, as shown in Equation (10) specifically:

[0044]

[0045] Among them, y dynamic is the output of the dynamic composite hysteresis model, and H r,a,b [u](t), H r,a,b [F](t) are the outputs of the asymmetric slope play operator with the voltage time - domain signal and the displacement time - domain signal as inputs respectively;

[0046] Step 4: Parameter identification and optimization of the LSTM neural network;

[0047] To realize the parameter optimization of the LSTM neural network, use the existing voltage - load - displacement composite hysteresis loop as the training data set, and adopt the Adam optimization algorithm for optimization to determine the parameters of the LSTM as k q×r , and e×f is its dimension; construct the neural network parameter loss function as shown in Equation (11):

[0048]

[0049] Among them, l is the time step size of the training data set, and y exp is the real - time displacement of the actuator collected;

[0050] Select the numerical gradient method to calculate the gradient of the neural network parameter loss function value with respect to the LSTM neural network parameter k e×f , and optimize in the e×f - dimensional real - number space according to the gradient to complete the parameter identification of the LSTM neural network;

[0051] Step 5: Establishment and control of the compensation controller;

[0052] ​First, swap the voltage and displacement of the aforementioned training dataset to form a displacement-voltage compensation loop. Take the displacement information as the input and the driving voltage as the output to identify the parameters of the ASPI algorithm and obtain the static inverse model. Design a parameter controller for the static inverse model based on the LSTM neural network. Use the force-position data as the input of the parameter controller and the parameter vector [cdv] of the static inverse model T as the output to dynamically adjust the parameter vector of the static inverse model, thereby forming a dynamic hysteresis inverse model;

[0053] Design a compensation controller based on the dynamic hysteresis inverse model. Through the load feedback F Exp Solve the dynamic force-position hysteresis component y in the static composite hysteresis model F , subtract it from the desired displacement y Target to obtain the desired driving quantity y p ; Through the dynamic hysteresis inverse model, calculate the compensation voltage u d (t), which acts on the actuator 7 to be measured to achieve a linear displacement output y d (t); The functional form of the compensation controller is shown in Equation (12):

[0054]

[0055] where, H 2 [F Exp is the dynamic force-position hysteresis component in the static composite hysteresis model, H -1 r,c,d (·) is the dynamic hysteresis inverse model, v j represents the jth dynamic hysteresis inverse model operator [v t , c t , d t T is the parameter vector of the dynamic hysteresis inverse model at time t, [Δv, Δc, Δd] T is the increment of the parameter vector of the dynamic hysteresis inverse model at each prediction time step.

[0056] ​Advantages of the present invention: The method for modeling and compensating the dynamic composite hysteresis of a piezoelectric ceramic actuator under time-varying large loads established in the present invention includes, but is not limited to, a force-electric-potential dynamic hysteresis characteristic test system, a superimposed composite model of a voltage-displacement hysteresis model and a force-displacement hysteresis model, a parameter controller based on an LSTM neural network and a model fault tolerance mechanism, and a hysteresis compensation control method for a piezoelectric actuator based on the inverse model of the former. The proposed method respectively tests the mechanical anelasticity, piezoelectric hysteresis and their combined effects of stacked piezoelectric ceramics, and details the actuation mechanism of piezoelectric ceramics under time-varying large loads, quantitatively analyzes the force-electric-potential composite hysteresis characteristics of piezoelectric ceramics; proposes an ASPI algorithm to realize the construction of a static composite hysteresis model; establishes a hysteresis model parameter controller to realize the accurate modeling of the hysteresis displacement output of a piezoelectric actuator under dynamic loads and dynamic voltage inputs; constructs a hysteresis compensator to achieve accurate compensation of displacement hysteresis considering time-varying loads. Compared with existing composite modeling methods, it has stronger adaptability to the rate-related characteristics of its load and input voltage. At the same time, it ensures the advantages of simple hysteresis control solution and small compensation calculation amount, and can achieve hysteresis compensation with low hysteresis and high efficiency. Description of the Drawings

[0057] Figure 1 Flowchart of the method for modeling and compensating the force-electric dynamic composite hysteresis of the piezoelectric ceramic actuator of the present invention;

[0058] Figure 2 Schematic connection diagram of the force-electric-potential dynamic hysteresis characteristic test system of the piezoelectric ceramic of the present invention; In the figure: 1 - preloading pressing plate, 2 - guide rail, 3 - device main body, 4 - force application driver, 5 - front spacer, 6 - pressure application slider, 7 - actuator to be measured, 8 - rear spacer, 9 - force measuring head, 10 - force sensor, 11 - flexible sleeve, 12 - data acquisition module, 13 - PC host computer, 14 - real-time controller, 15 - power amplifier;

[0059] Figure 3 Piezoelectric hysteresis loop under decaying voltage wave;

[0060] Figure 4 Piezoelectric hysteresis loops at different frequencies;

[0061] Figure 5 Anelastic hysteresis loop under decaying load wave;

[0062] Figure 6 Mechanical anelastic loops at different frequencies;

[0063] Figure 7 Asymmetric slope play operator in the present invention;

[0064] Figure 8 Piezoelectric hysteresis model based on the ASPI algorithm in the present invention;

[0065] Figure 9 This is the mechanical anelastic model based on the ASPI algorithm in the present invention;

[0066] Figure 10 This is the schematic diagram of the compensation controller in the present invention;

[0067] Figure 11 This is the displacement output result of the dynamic hysteresis model in the present invention under a time-varying load;

[0068] Figure 12 This is the fitting result diagram of the dynamic hysteresis model of the present invention for the hysteresis loop.

[0069] Figure 13 This is the displacement control result diagram of the compensation controller of the present invention. Detailed implementation manners

[0070] The implementation process of the present invention is introduced in detail below.

[0071] The first step: Assemble the force-electricity-potential dynamic hysteresis characteristic test system

[0072] Assemble the force-electricity-potential dynamic hysteresis characteristic test system in sequence. Connect the power supply lines of the force application driver 4 and the actuator 7 to be tested to the power amplifier 15 to provide the necessary driving voltage; connect the strain signal line and the force signal line to the data acquisition module 12 for collecting relevant measurement data; connect the data acquisition module 12 to the real-time controller 14, and the real-time controller 14 is respectively connected to the power amplifier 15 and the PC host computer 13. The PC host computer 13 is responsible for displaying real-time data and transmitting control instructions. The real-time controller 14 receives the instructions and generates driving signals, and outputs the driving voltage through the power amplifier 15; the force application driver 4 pushes the pressure application slider 6 through the output displacement, thereby applying a time-varying load to the actuator 7 to be tested; the actuator 7 to be tested outputs displacement under the action of the load, and its telescopic displacement is monitored through the embedded strain gauge. The load received by the actuator 7 to be tested is conducted to the force sensor 10 by the rear spacer 8 and the force measuring head 9 to capture the load signal; the load signal and the strain signal are transmitted to the data acquisition module 12 together, stored and calculated by the real-time controller 14, and finally the result is transmitted to the PC host computer 13 for display. As Figure 2 This is the schematic diagram of the force-electricity-potential dynamic hysteresis characteristic test system.

[0073] After the test system is built, design the characteristic test experiment. The peak value of the voltage attenuation wave driving signal is 790V and the frequency is 1Hz, and the peak value of the fixed-frequency signal is 900V and the frequency is 1 / 2 / 6 / 10Hz. The peak value of the load attenuation wave driving signal is 790N and the frequency is 1Hz, and the peak value of the fixed-frequency signal is 1585N; the frequency is 1 / 2 / 6 / 10Hz. The function form is as shown in the following formula:

[0074]

[0075] Among them, U is the driving voltage quantity and F is the load; a data set of the piezoelectric ceramic is measured and plotted as a voltage-displacement curve as Figure 3 、 Figure 4 shown, and a force-displacement curve as Figure 5 、 Figure 6 shown.

[0076] Step 2: Establish a composite static hysteresis modeling method based on the asymmetric play operator

[0077] Filter and preprocess the measured data set to eliminate noise and outliers. Data normalization can be performed to facilitate subsequent modeling. The data set is divided into a load-displacement hysteresis group, a voltage-displacement hysteresis group, and a load-voltage-displacement composite hysteresis group. The ASPI algorithm based on the weighted superposition of the asymmetric play operator is proposed. Through LM optimization, fitting is performed for the voltage-displacement hysteresis group and the load-displacement hysteresis group respectively, so as to obtain a static piezoelectric hysteresis model and a static mechanical anelastic model. Combine the two models to form a static composite hysteresis model, whose form is shown in Equation (5). Furthermore, fitting is performed for the load-voltage-displacement composite hysteresis group for P 1 、P 2 、P 3 , so as to realize the parameter optimization of the static composite hysteresis model. Evaluate the accuracy of the model through methods such as cross-validation to ensure that the model can effectively capture the hysteresis characteristics and maintain robustness under different working conditions. Among them, the form of the asymmetric play operator is as Figure 7 shown, and the static piezoelectric hysteresis model and the static mechanical anelastic model are respectively as Figure 8 、 Figure 9 shown.

[0078] Step 3: Establish a hysteresis model parameter controller to form a dynamic composite hysteresis model of the piezoelectric actuator based on the LSTM-ASPI algorithm

[0079] Select a damped wave signal of 1-10 hz to drive the force actuator and the actuator to be measured of the measurement system. The measured load-voltage-displacement composite hysteresis data set contains the dynamic hysteresis characteristics of the piezoelectric actuator. Use its force-displacement dynamic data as the input and the parameters of the hysteresis model as the output. Establish a mapping relationship through the LSTM neural network, and substitute the output parameters into the hysteresis model to obtain the model displacement output. Thus, the real-time calculation of the model parameters can be realized.

[0080] Build a fault-tolerant mechanism for the parameter controller. Select a window length of 5, calculate the mutation degree of the displacement data within the window, judge the distortion degree of the input of the parameter controller, and then select whether to maintain the previous calculation result. Build a parameter asymptotic link, calculate the deviation between the target control quantity of the model parameter and the current parameter value in real time, and multiply it by the gain of 0.7 to achieve the asymptote of the model parameter to the target control quantity. Avoid instability caused by large fluctuations in model parameters. The output result of the piezoelectric actuator dynamic composite hysteresis model is as Figure 11 , 12 shown.

[0081] Step 4: Parameter optimization of the LSTM model

[0082] Based on the model displacement output and the measured displacement data, construct a loss function, select the Adam algorithm for loss minimization optimization, and complete the parameter optimization of the LSTM neural network. First, use the numerical gradient method to calculate the gradient of the loss function value with respect to the LSTM network parameters. By quantifying the difference between the network output and the actual target, the loss function value can be solved, and the numerical gradient method is used to make small perturbations to each parameter, so as to approximately calculate the gradient information. These gradients represent the change trend of the loss function in the parameter space, and then optimize in the e×f-dimensional real number space. With the help of these gradient information, we can apply the Adam algorithm to adjust the parameters of the LSTM network to gradually reduce the value of the loss function and finally achieve the accurate identification of the network parameters.

[0083] Step 5: Establishment and control of the compensation controller

[0084] First, by swapping the voltage and displacement relationship in the training data, construct a displacement-voltage compensation loop, use the displacement information as the input variable, and the driving voltage as the output variable, so as to realize the identification of the ASPI algorithm parameters and obtain the static inverse model. Design a parameter controller for the static inverse model based on the LSTM neural network, use the force-displacement data as the input of the parameter controller, and the parameter control quantity vector of the ASPI model as the output to dynamically adjust the parameter vector of the static compensation model, thus forming a dynamic hysteresis inverse model.

[0085] Based on the inverse model design method, it is used to construct a compensation controller, and the dynamic force-displacement hysteresis component in the composite hysteresis model is solved through load feedback. Subtract the expected displacement from this hysteresis component to obtain the expected driving quantity. Subsequently, the required compensation voltage is calculated through the above inverse model and applied to the actuator to achieve linear displacement output. This method effectively integrates the hysteresis compensation mechanism and improves the precise control ability of the system under dynamic load conditions. The flow schematic diagram of its compensation controller is as Figure 10 shown, and the final compensation result is as Figure 13 shown.

[0086] The dynamic composite hysteresis modeling and compensation method of a piezoelectric actuator under time-varying large loads according to the present invention takes into account factors such as the composite hysteresis and dynamic hysteresis of the force-displacement and electro-displacement of the piezoelectric ceramic actuator. Its forward model can achieve the prediction of the output displacement of the piezoelectric ceramic under a driving voltage signal with variable amplitude and variable frequency, and its inverse model can ensure the accurate compensation of displacement hysteresis under time-varying loads, which is more accurate and effective compared with the traditional voltage-displacement modeling method. Saving the neural network model parameters, and then only substituting the trained parameters is required when using the model, without the need to repeat training. It can provide high-precision output data for the application of piezoelectric ceramics, filling the gap in the existing technical field. Moreover, this method has strong adaptability and can be applied to the system modeling and hysteresis compensation control of systems containing piezoelectric actuators.

Claims

1. A modeling and compensation method for dynamic composite hysteresis of a piezoelectric actuator under time-varying large load, characterized in that: Here are the steps: Step 1: Construction of force-electricity-position dynamic hysteresis characteristics test system and data collection; A piezoelectric ceramic force-electric-potential dynamic hysteresis characteristic test system is constructed: a flexible sleeve (11) is embedded in the circular hole of a pressure slider (6), and a guide rail (2) passes through the flexible sleeve (11); the pressure slider (6) is fixed to the device body (3) and fastened by bolts; a force sensor (10) and a preload plate (1) are respectively fixed to the mounting grooves at both ends of the device body (3), and a force measuring head (9) is tightened on the force sensor (10); a force driver (4) and a front gasket (5) are fitted, and the actuator to be tested (7 ) and the rear gasket (8) are fitted, the front gaskets (5) at both ends of the force driver (4) are tightly attached to the spherical arc surfaces of the pre-tightening plate (1) and the pressure slider (6), and the rear gaskets (8) at both ends of the actuator to be tested (7) are tightly attached to the spherical arc surfaces of the force measuring head (9) and the pressure slider (6), and the pressure plate (1) is pre-tightened by bolts, thereby applying a pre-tightening force to the force driver (4) and the actuator to be tested (7), eliminating the gap in the device, and thus completing the construction of the motion structure of the piezoelectric ceramic force-electricity-potential dynamic hysteresis characteristic test system; The power lines of the force driver (4) and the actuator to be tested (7) are connected to the power amplifier (15), the strain lines and the force signal lines are connected to the data acquisition module (12), the data acquisition module (12) is connected to the real-time controller (14), and the real-time controller (14) is respectively connected to the power amplifier (15) and the PC host computer (13), thereby completing the construction of the piezoelectric ceramic force-electric-potential dynamic hysteresis characteristic test system; the PC host computer (13) is responsible for displaying data and transmitting instructions, and the real-time controller (14) receives instructions, generates a driving signal, outputs a driving voltage through the power amplifier (15), and loads it to the force driver On the actuator (4) and the actuator to be tested (7), the force driver (4) outputs displacement to drive the pressure slider (6) to generate a time-varying load on the actuator to be tested (7), the actuator to be tested (7) resists the load output displacement to perform work, and the strain gauge embedded in the actuator to be tested (7) monitors its expansion and contraction displacement, and the load on the actuator to be tested (7) is transmitted to the force sensor (10) through the rear gasket (8) and the force measuring head (9), and the force sensor (10) captures the load signal and transmits it to the data acquisition module (12) together with the strain signal, and is stored and calculated by the real-time controller (14), and transmitted to the PC host computer (13) for display; A characteristic test experiment is designed, and a fixed-amplitude fixed-frequency signal and a fixed-frequency attenuated wave signal are designed as driving signals to control the force driver (4) and the actuator to be tested (7) to generate a fixed-frequency attenuation / fixed-amplitude fixed-frequency force and displacement, respectively. The function of the driving signal is defined by the following formula (1): Among them, U is the driving amount, A is the driving amplitude, f is the driving frequency, and k is the linear attenuation slope; Collecting input voltage, output displacement and output force data of the actuator to be tested (7) to form various hysteresis loops of the actuator to be tested (7), which are respectively a fixed-frequency attenuation signal and a fixed-amplitude fixed-frequency signal; Step 2: Establish a composite static hysteresis modeling method based on asymmetric play operator; An asymmetric play operator is proposed, and the function structure is as follows: Where: u(t) is the operator input at time t, H r,a,b [u](t) is the output of the asymmetric play operator, r is the threshold of the operator, a and b are the asymmetric correction coefficients of the upper and lower edges respectively, and T is the sampling interval; The asymmetric correction coefficients a and b of the upper and lower edges can control the slope of the operator during the lift and return stroke, thereby enhancing the fitting adaptability of different segments in the definition domain; the operator threshold vector r = (r1,…,r n ) T is a set of arithmetic progressions determined by the number of operators: Where ri represents the i-th operator, n is the number of asymmetric play operators, and u max (t) is the maximum input voltage; The ASPI algorithm is obtained by weighted superposition of multiple asymmetric play operators with different thresholds to characterize the hysteresis characteristics of the piezoelectric actuator. Formula (4) is the functional form of the ASPI algorithm: Among them, the weight coefficient is w; Based on the ASPI algorithm, the voltage-displacement hysteresis loop and the load-displacement hysteresis loop are fitted respectively to form a static piezoelectric hysteresis model and a static mechanical hysteresis elastic model; the outputs of the static piezoelectric hysteresis model and the static mechanical hysteresis elastic model are superimposed and corrected, that is, a static composite hysteresis model y with dual inputs of load and voltage is formed. static (t), whose form is shown in formula (5): y static =y p [u](t)+y m [F](t)+p1u+p2F+p3 (5) Among them, y p [u](t),y m [F](t) are the outputs of the static piezoelectric hysteresis model and the static mechanical hysteresis elastic model, u and F are the input voltage and load, and p1, p2, and p3 are constants; Step 3: Establish a hysteresis model parameter controller to form a dynamic composite hysteresis model of the piezoelectric actuator based on the LSTM-ASPI algorithm; An asymmetric slope Prandtl-Ishlinskii algorithm regulated by LSTM is proposed. A hysteresis model parameter controller is designed based on the static composite hysteresis model. The mapping relationship between the hysteresis model parameter vector and the force and position time domain signals is constructed through the LSTM time series neural network. The parameter vector of the hysteresis model is adjusted according to the dynamic time domain signal of the actuator. It is substituted into the ASPI algorithm to calculate the dynamic composite hysteresis displacement of the actuator, which is shown in formula (6): in, is the output of the LSTM neural network, and its dimension is the same as the parameter dimension of the static compound hysteresis model; [S t-1 ,...,S t-m ] T 、[F t-1 ,...,F t-m ] T are the time-varying signals of displacement and load, respectively, m is the length of the time series; G(·) represents the network function framework of the LSTM neural network; To establish a fault-tolerant mechanism for parameter controller, first set the monitoring window, monitor the load and displacement signals within the window, and identify strong disturbances by calculating the mutation degree q. The formula is as follows: Among them, m is the length of the time series, S m×1 To monitor the displacement signal in the window, diff(S m×1 ) is its differential vector; when the mutation degree q calculated in the window is 1, it is judged that the disturbance is too large, and the parameter target control amount of the current parameter controller remains unchanged in the previous step; that is, as shown in formula (8): in, is the target control quantity of the model parameter; The parameter asymptotic link is introduced, and the parameter correction gain ρ is set. The parameters of the ASPI algorithm are iteratively updated in each prediction time step as shown in formula (9), asymptotically approaching the model parameter target control amount: Among them, [a t ,b t ,w t ] T are the ASPI algorithm parameters at time t, [Δa, Δb, Δw] T is the increment of the ASPI algorithm parameters at each prediction time step, and is less than the upper limit ξ to ensure the stability of the parameter control process; The parameter control quantity output by the LSTM neural network is substituted into the static composite hysteresis model, which is named LSTM-ASPI algorithm, that is, the adaptive adjustment of the ASPI algorithm parameters under the dynamic changes of load and displacement is realized, and the dynamic composite hysteresis model of the piezoelectric actuator is formed, as shown in formula (10): Among them, y dynamic is the output of the dynamic composite hysteresis model, H r,a,b [u](t),H r,a,b [F](t) is the output of the asymmetric slope play operator with voltage time domain signal and displacement time domain signal as input respectively; Step 4: Parameter identification and optimization of LSTM neural network; In order to optimize the parameters of the LSTM neural network, the existing voltage-load-displacement composite hysteresis loop is used as the training data set, and the Adam optimization algorithm is used to optimize it. The LSTM parameter k is determined. q×r , e×f is its dimension; the neural network parameter loss function is constructed as shown in formula (11): Among them, l is the time step size of the training data set, y exp The real-time displacement of the force-applying driver (4) is collected; Select the numerical gradient method to calculate the neural network parameter loss function value for the LSTM neural network parameter k e×f The gradient of is used to find the optimal value in the e×f dimensional real number space to complete the parameter identification of the LSTM neural network. Step 5: Establishment and control of compensation controller; First, the voltage and displacement of the training data set are swapped to form a displacement-voltage compensation loop. The displacement information is used as input and the driving voltage is used as output to identify the ASPI algorithm parameters and obtain the static inverse model. The parameter controller of the static inverse model is designed based on the LSTM neural network. The force and position data are used as the input of the parameter controller. The parameter vector [cdv] of the static inverse model T As output, the parameter vector of the static inverse model is dynamically adjusted to form a dynamic hysteresis inverse model; The compensation controller is designed based on the dynamic hysteresis inverse model, and the load feedback F Exp Solving the dynamic force-position hysteresis component y in the static composite hysteresis model F , the expected displacement y Target Subtract it from the expected driving amount y p ; Through the dynamic hysteresis inverse model, the compensation voltage u is calculated d (t), acting on the actuator to be tested (7) to achieve linear displacement output y d (t); the function form of the compensation controller is shown in formula (12): Among them, H2[F Exp ] is the dynamic force-position hysteresis component in the static composite hysteresis model, H -1 r,c,d (·) is the dynamic hysteresis inverse model, v j represents the jth dynamic hysteresis inverse model operator [v t ,c t ,d t ] T is the parameter vector of the dynamic hysteresis inverse model at time t, [Δv, Δc, Δd] T The increment of the dynamic hysteresis inverse model parameter vector at each prediction time step.

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