Modeling and compensating method for dynamic composite hysteresis of piezoelectric actuator under time-varying large load

Abstract

The invention belongs to the field of characteristic measurement of piezoelectric actuators, and relates to a modeling and compensating method for 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 an improved asymmetric slope Prantl-Ishlinskii algorithm, carrying out modeling on asymmetry and zero drift characteristics of hysteresis rings, fitting static hysteresis rings of force-bit and electricity-bit, and superposing the static hysteresis rings to form a static composite hysteresis model; a dynamic composite hysteresis model is established according to the wide-frequency-domain excitation requirement of the driver, and an ASI parameter controller is designed based on an LSTM algorithm to dynamically regulate and control the slope and the threshold value of the model; a parameter controller fault-tolerant mechanism is designed to restrain model instability caused by sudden disturbance and control over-regulation, and high-precision real-time hysteresis prediction is ensured; and calculating the real-time control voltage and compensating the dynamic hysteresis by solving the inverse model of the dynamic composite hysteresis model and inputting the expected displacement.

Description

Technical Field

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

[0002] As a micro-nano precision actuator that can realize the mutual conversion between electrical energy and mechanical energy, piezoelectric actuators have the characteristics of small size, high displacement resolution, and fast response speed. They are widely used in optical scanning positioning, biomedical micro-control and other fields for high-precision positioning. In recent years, due to the advantages of highly compact layout, high power density, and large driving force of stacked piezoelectric actuators, they have gradually been used as force / displacement driving elements in mechanical precision machining, aerospace testing and other fields. Such tasks are often accompanied by large time-varying loads and dynamic disturbances, which have a great impact on the output performance of the driver. For example, in the aircraft dynamic stability evaluation test, the piezoelectric actuator is used as the driving element of the aircraft motion simulation device. By outputting micro-displacement and amplifying it through the transmission mechanism, it drives the aircraft model to achieve multi-degree-of-freedom motion simulation in the high-speed flow field environment in the wind tunnel, and completes the test of the aircraft 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 the complex flow field is characterized by large time variation and strong disturbance, which makes the ceramic hysteresis characteristics change significantly under the influence of time-varying load, thus bringing greater challenges to the accurate modeling and compensation control of ceramic hysteresis.

[0003] In recent years, modeling and compensating for the hysteresis effect of piezoelectric actuators has been a hot topic of research. Many scholars have also used composite control methods to reduce external disturbances, but most models only consider the hysteresis effect of voltage input on piezoelectric actuators, and few consider the hysteresis characteristics of piezoelectric actuators under time-varying loads.

[0004] Cao Kairui et al.'s patent "Modeling Method for Dynamic Hysteresis Characteristics of Piezoelectric Ceramics", patent number CN202310434548.6, introduces a modeling method for 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 of the mixed voltage, and cannot be applied to piezoelectric ceramic drive systems with time-varying large loads and that need to consider force-position hysteresis characteristics.

[0005] In the article "Kalman filter output feedback predictive control of piezoelectric ceramic actuators" published by Yu Shuyou et al. in the 11th issue of "Optical Precision Engineering" in 2024, the static hysteresis nonlinearity is represented by an asymmetric Bouc-wen model, the signal rate correlation is characterized by a dynamic linear model, and the predictive control of the actuator is realized based on the Kalman filter, which reduces the hysteresis error. However, this method still only models and compensates for the mapping relationship between voltage and displacement, and lacks 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 driving tasks with large load disturbances, there is still a lack of research on the output characteristics 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 drives under time-varying large loads. Summary of the invention

[0007] In order to overcome the shortcomings of the prior art, the present invention proposes a modeling and compensation method for the dynamic composite hysteresis characteristics of a piezoelectric actuator under time-varying large loads, so as to achieve a more accurate model description of the force-electric-potential composite hysteresis of the piezoelectric actuator and thus realize high-precision output compensation control. This method first builds a piezoelectric actuator force-electricity-position dynamic hysteresis characteristic test system to collect load and displacement signals during the actuation process; improves the traditional PI hysteresis model, and proposes an asymmetric slope Prandtl-Ishlinskii (ASPI) algorithm, which has better adaptability to the asymmetry and zero drift characteristics of the hysteresis loop. The static hysteresis loops of force-position and electric-potential are fitted and modeled respectively, and superimposed to form a static composite hysteresis model; in response to the demand for wide-band excitation of the driver, a dynamic composite hysteresis model is proposed, and an ASPI parameter controller is established based on the LSTM algorithm. According to the dynamic load and dynamic voltage input, the slope and threshold of the existing model are adjusted; the parameter controller fault-tolerant mechanism is designed to constrain the model instability caused by sudden disturbances and over-adjustment of the model parameter controller, thereby ensuring real-time and high-precision hysteresis prediction; solves the inverse model of the dynamic composite hysteresis model, inputs the expected displacement, calculates the control voltage in real time, and compensates for the dynamic composite hysteresis. Compared with other modeling and compensation methods, the present invention can stably and accurately output the hysteresis size under conditions of variable loads and mixed multi-frequency driving signals, and ensure high compensation accuracy. The compensation control effect has the advantages of small lag and high calculation efficiency compared with compound control.

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

[0009] Based on the constructed piezoelectric actuator force-electricity-position dynamic hysteresis characteristics test system, the dynamic composite hysteresis output of the piezoelectric ceramic driver is observed and the corresponding data is collected; then the ASPI algorithm based on the asymmetric play operator is constructed, and a force-electricity static composite hysteresis modeling method is proposed; then a model parameter controller based on the LSTM neural network algorithm is established to optimize the neural network parameters and form a force-electricity dynamic composite hysteresis model; through the fault-tolerant mechanism of the parameter controller, the compensation algorithm's anti-interference ability to sudden disturbances and pathological data is improved; then the dynamic composite hysteresis inverse model is solved, and the compensation voltage is calculated based on the expected displacement to realize the input and output linearization of the actuator, forming the modeling and compensation control of the force-electricity dynamic composite hysteresis characteristics of the driver.

[0010] The specific steps are as follows:

[0011] Step 1: Construction of force-electricity-position dynamic hysteresis characteristics test system and data collection;

[0012] Build a piezoelectric ceramic force-electric-potential dynamic hysteresis characteristic test system: the flexible sleeve 11 is embedded in the circular hole of the pressure slider 6, and the guide rail 2 passes through the flexible sleeve 11; the pressure slider 6 is fixed to the device body 3 and fastened by bolts; the force sensor 10 and the pre-tightening plate 1 are respectively fixed to the mounting grooves at both ends of the device body 3, and the force head 9 is tightened on the force sensor 10; the force driver 4 and the front gasket 5 are fitted, and the actuator 7 to be tested 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 surface of the pre-tightening plate 1 and the pressure slider 6, and the rear gaskets 8 at both ends of the actuator 7 to be tested are tightly attached to the spherical arc surface of the force head 9 and the pressure slider 6. The pressure plate 1 is pre-tightened by bolts, thereby applying a pre-tightening force to the force driver 4 and the actuator 7 to be tested, eliminating the device gap, and thus completing the construction of the motion structure of the piezoelectric ceramic force-electric-potential dynamic hysteresis characteristic test system;

[0013] 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, thus completing the construction of the piezoelectric ceramic force-electric-position dynamic hysteresis characteristic test system; the PC host computer 13 is responsible for displaying data and transmitting instructions, the real-time controller 14 receives instructions, generates a driving signal, outputs a driving voltage through the power amplifier 15, and loads it to On the force driver 4 and the actuator 7 to be tested, the force driver 4 outputs displacement to drive the pressure slider 6 to generate a time-varying load on the actuator 7 to be tested. The actuator 7 to be tested resists the load output displacement and performs work. The strain gauge embedded in the actuator 7 to be tested monitors its expansion and contraction displacement. The load on the actuator 7 to be tested is transmitted to the force sensor 10 by the rear gasket 8 and the force measuring head 9. 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. Figure 2 Schematic diagram of the force-electric-potential dynamic hysteresis characteristics test system.

[0014] After the test system is built, 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):

[0015]

[0016] Among them, U is the driving voltage, A is the driving amplitude, f is the driving frequency, and k is the linear attenuation slope.

[0017] The input voltage, output displacement and output force data of the actuator 7 to be tested are collected to form various hysteresis loops of the actuator 7 to be tested, wherein the voltage-displacement hysteresis loop is composed of Figure 3 , Figure 4 As shown in the figure, they are fixed frequency attenuation signal and fixed amplitude fixed frequency signal respectively; the load-displacement signal is Figure 5 , Figure 6 As shown, the drive type is the same as above.

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

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

[0020]

[0021] 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;

[0022] 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:

[0023]

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

[0025] 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:

[0026]

[0027] Among them, the weight coefficient is w;

[0028] 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):

[0029] y static =y p [u](t)+y m [F](t)+p1u+p2F+p3 (5)

[0030] 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;

[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] 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):

[0033]

[0034] 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;

[0035] 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:

[0036]

[0037] 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):

[0038]

[0039] in, is the target control quantity of the model parameter;

[0040] 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:

[0041]

[0042] Among them, [a t ,b t ,w t ] Tare 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;

[0043] 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):

[0044]

[0045] 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;

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

[0047] 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):

[0048]

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

[0050] 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.

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

[0052] 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 TAs output, the parameter vector of the static inverse model is dynamically adjusted to form a dynamic hysteresis inverse model;

[0053] 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), acts on the actuator 7 to achieve linear displacement output y d (t); the function form of the compensation controller is shown in formula (12):

[0054]

[0055] 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.

[0056] Beneficial effects of the present invention: The modeling and compensation method of dynamic composite hysteresis of piezoelectric ceramic drivers under time-varying large loads established by the present invention includes but is not limited to a force-electricity-potential dynamic hysteresis characteristic test system, a superposition 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-tolerant mechanism, and a hysteresis compensation control method for a piezoelectric actuator based on the inverse model of the former. The proposed method tests the mechanical hysteresis elasticity, piezoelectric hysteresis and their composite effects of stacked piezoelectric ceramics, and studies the actuation mechanism of piezoelectric ceramics under time-varying large loads in detail, and quantitatively analyzes the force-electricity-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 precise modeling of the hysteresis displacement output of the piezoelectric actuator under dynamic loads and dynamic voltage inputs; and constructs a hysteresis compensator to realize precise compensation of displacement hysteresis by considering time-varying loads. Compared with the existing composite modeling method, it has stronger adaptability to the rate-dependent characteristics of its load and input voltage. At the same time, it ensures the advantages of simple hysteresis control solution and small compensation calculation, and can achieve low hysteresis and high efficiency hysteresis compensation. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 Flow chart of the modeling and compensation method of the piezoelectric ceramic actuator force-electrodynamic composite hysteresis of the present invention;

[0058] Figure 2 It is a connection diagram of the piezoelectric ceramic force-electricity-potential dynamic hysteresis characteristic test system of the present invention; in the figure: 1-preload plate, 2-guide rail, 3-device body, 4-force driver, 5-front gasket, 6-pressure slider, 7-actuator to be tested, 8-rear gasket, 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 is the piezoelectric hysteresis loop under the decaying voltage wave;

[0060] Figure 4 is the piezoelectric hysteresis loop at different frequencies;

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

[0062] Figure 6 is the mechanical hysteresis ring at different frequencies;

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

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

[0065] Fig. 9 It is the mechanical hysteresis model based on the ASPI algorithm in the present invention;

[0066] Fig.10 It is a schematic diagram of the structure of the compensation controller in the present invention;

[0067] Fig.11 The displacement output result of the dynamic hysteresis model under time-varying load in the present invention;

[0068] Fig.12 This is a diagram showing the fitting results of the hysteresis loop using the dynamic hysteresis model of the present invention.

[0069] Fig.13 This is a diagram of the displacement control results of the compensation controller of the present invention. DETAILED DESCRIPTION

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

[0071] Step 1: Assemble the force-electric-potential dynamic hysteresis characteristics test system

[0072] Assemble the force-electric-potential dynamic hysteresis characteristic test system in sequence, connect the power lines of the force 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 to collect 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, and the real-time controller 14 receives instructions and generates driving signals, and outputs driving voltage through the power amplifier 15; the force driver 4 pushes the pressure slider 6 by outputting 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 expansion and contraction displacement is monitored by the embedded strain gauge. The load on the actuator 7 to be tested is transmitted to the force sensor 10 by the rear gasket 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, and are stored and calculated by the real-time controller 14, and finally the results are transmitted to the PC host computer 13 for display. Figure 2 Schematic diagram of the force-electric-potential dynamic hysteresis characteristics test system.

[0073] After the test system is built, a characteristic test is designed, in which the peak value of the voltage attenuation wave drive signal is 790V, the frequency is 1Hz, 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 drive signal is 790N, 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 shown in the following formula:

[0074]

[0075] Where U is the driving voltage and F is the load. The data set of the piezoelectric ceramic is measured and plotted as a voltage-displacement curve. Figure 3 , Figure 4 As shown in the figure, and the force-displacement curve is shown in the figure Figure 5 , Figure 6 shown.

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

[0077] The measured data set is filtered and preprocessed 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. An ASPI algorithm based on weighted superposition of asymmetric play operators is proposed. The voltage-displacement hysteresis group and the load-displacement hysteresis group are fitted through LM optimization to obtain a static piezoelectric hysteresis model and a static mechanical hysteresis elastic model. The two models are combined to form a static composite hysteresis model, which is shown in formula (5). Then, P1, P2, and P3 are fitted for the load-voltage-displacement composite hysteresis group to achieve parameter optimization of the static composite hysteresis model. The accuracy of the model is evaluated by cross-validation and other methods to ensure that the model can effectively capture the hysteresis characteristics and maintain robustness under different working conditions. The asymmetric play operator is in the form of Figure 7 As shown, the static piezoelectric hysteresis model and the static mechanical hysteresis model are respectively Figure 8 , Fig. 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] The attenuation wave signal of 1 to 10 Hz is selected to drive the force driver of the measurement system and the actuator to be measured. The measured load-voltage-displacement composite hysteresis data set contains the dynamic hysteresis characteristics of the piezoelectric actuator. The force-position dynamic data is used as input, and the parameters of the hysteresis model are used as output. The mapping relationship is established through the LSTM neural network, and the output parameters are substituted into the hysteresis model to obtain the model displacement output, so that the real-time calculation of the model parameters can be realized.

[0080] Construct a fault-tolerant mechanism for the parameter controller, select a window length of 5, calculate the mutation degree of the displacement data in the window, determine the degree of input distortion of the parameter controller, and then choose whether to maintain the last calculation result. Construct a parameter asymptotic link, calculate the deviation between the target control amount of the model parameter and the current parameter value in real time, and achieve the asymptotic approach of the model parameter to the target control amount by multiplying the gain by 0.7. Avoid instability caused by large fluctuations in model parameters. The output results of the dynamic compound hysteresis model of the piezoelectric actuator are as follows: Fig.11 , 12 shown.

[0081] Step 4: Optimizing LSTM model parameters

[0082] Based on the model displacement output and measured displacement data, the loss function is constructed, and the Adam algorithm is selected for minimum loss optimization to complete the parameter optimization of the LSTM neural network. First, the numerical gradient method is used to calculate the gradient of the loss function value relative 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 to approximately calculate the gradient information. These gradients represent the changing trend of the loss function in the parameter space, and then optimize it in the e×f dimensional real space. With the help of this 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 accurate identification of the network parameters.

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

[0084] First, by exchanging the voltage and displacement relationship in the training data, a displacement-voltage compensation loop is constructed, and the displacement information is used as the input variable, and the driving voltage is used as the output variable, so as to identify the parameters of the ASPI algorithm and obtain the static inverse model. The parameter controller of the static inverse model is designed based on the LSTM neural network, and the force position data is used as the input of the parameter controller. The parameter control vector of the ASPI model is used as the output to dynamically adjust the parameter vector of the static compensation model, thereby forming a dynamic hysteresis inverse model.

[0085] The inverse model-based design method is used to construct a compensation controller, which solves the dynamic force-position hysteresis component in the composite hysteresis model through load feedback. The desired drive amount can be obtained by subtracting the desired displacement from the hysteresis component. Subsequently, the required compensation voltage is calculated through the above inverse model and applied to the driver to achieve linear displacement output. This method effectively integrates the hysteresis compensation mechanism and improves the system's precise control capability under dynamic load conditions. The flow chart of its compensation controller is shown in the figure below. Fig.10 The final compensation result is as shown in Fig.13 shown.

[0086] The dynamic composite hysteresis modeling and compensation method of piezoelectric actuators under time-varying large loads of the present invention takes into account the composite hysteresis and dynamic hysteresis of the piezoelectric ceramic driving force-displacement and electric-displacement. Its positive model can realize the prediction of the output displacement of piezoelectric ceramics under variable amplitude and variable frequency driving voltage signals, and its inverse model can ensure the accurate compensation of displacement hysteresis under time-varying loads, which is more accurate and effective than the traditional voltage displacement modeling method. The neural network model parameters are saved, and the model only needs to be substituted with the trained parameters when using it later, without repeated training. It can provide high-precision output data for piezoelectric ceramic applications, making up for the gap in the existing technical field. In addition, this method has strong adaptability and can be applied to system modeling and hysteresis compensation control 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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