High-precision msma driver platform system identification method based on ld-gpi model

Abstract

The application discloses a high-precision MSMA driver platform system identification method based on an LD-GPI model, which is used for characterizing MSMA driver platform characteristics under variable load application scene conditions, and steps are as follows: firstly, the application scene under the variable load is characterized by using the LD-GPI model, two characteristics of strong saturation and asymmetry are characterized, and the dynamic characteristics are characterized by using a second-order linear system, so that the input and output characteristics of the MSMA driver platform are completely characterized; secondly, the problem of solving unknown parameters is converted into a system identification problem, and system identification is performed on the established high-precision model through an iterative calculation mode; finally, the system identification of the high-precision model is effectively performed through the calculation iteration of the improved LM method. The system identification effect of the high-precision model is greatly improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of control, in particular to a high-precision MSMA driver platform system identification method based on an LD-GPI model. BACKGROUND

[0002] The magnetic shape memory alloy (hereinafter referred to as MSMA) driver is currently a new type of intelligent material driver for realizing the flexible driving output of mechatronic systems, and is one of the new drivers for realizing the flexible driving performance of "artificial muscles" in mechatronic systems represented by robots. The performance of the flexible driving component based on intelligent materials has a great influence on the precision and controllability of the flexible driving system. The MSMA driver shows superiority in high-precision flexible driving due to its large output displacement range, fast response speed and other characteristics, and can meet the special precision requirements of certain flexible driving systems. Although the MSMA driver has good performance, the external interference and internal uncertainty of the MSMA driver are the main limiting factors for improving the driving precision. The hysteresis effect, load dependence and frequency dependence are the main nonlinear factors affecting the improvement of driving performance. In order to overcome the adverse effects of the nonlinearities of the MSMA driver on the precision, reliability and stability of the flexible driving system, it is necessary to consider the internal nonlinearities of the MSMA driver and accurately model the input and output characteristics thereof.

[0003] At present, the main internal nonlinearity of the MSMA driver is hysteresis nonlinearity, and a large number of scholars have conducted a lot of research on this characteristic. At present, a commonly used modeling method for hysteresis nonlinearity is to describe the hysteresis characteristics by using a hysteresis model, and to model the hysteresis nonlinearity in combination with a linear dynamic system. In order to establish a model closer to the actual input and output characteristics of the MSMA driver, a series of model identification algorithms have been proposed by many scholars, such as the traditional LM algorithm, genetic algorithm, ant colony algorithm, etc. However, the traditional LM algorithm is prone to numerical oscillation in the process of high-precision model system identification, so it is of research significance to improve the traditional LM algorithm to avoid numerical oscillation in the process of system identification for the high-precision modeling of the MSMA driver platform and the subsequent high-precision positioning. SUMMARY

[0004] The purpose of the present application is to solve the above-mentioned defects in the prior art, and to provide a high-precision MSMA driver platform system identification method based on an LD-GPI model.

[0005] The purpose of the present application can be achieved by adopting the following technical solutions:

[0006] A high-precision MSMA driver platform system identification method based on an LD-GPI model, the system identification method comprising the following steps:

[0007] S1, build the MSMA driver platform, measure the displacement of the MSMA driver in the horizontal direction under the excitation of the variable frequency current signal through the laser displacement measuring device;

[0008] S2, establish the internal dynamic model of the MSMA driver platform, the expression is as follows:

[0009]

[0010] Wherein, L is the abbreviation of L(t), L(t) represents the pre-pressure of the MSMA driver platform, I is the abbreviation of I(t), I(t) represents the driving current of the MSMA driver platform, Γ[L,I](t) is the internal hysteresis characteristic of the MSMA driver, x(t) is the displacement of the MSMA driver in the horizontal direction, And The first-order derivative and the second-order derivative of x(t) respectively, Is the first parameter and the second parameter of the internal electromechanical characteristic of the MSMA driver, the LD-GPI model is used to describe the internal hysteresis characteristic of the MSMA driver, wherein, the LD-GPI model is the abbreviation of Load-Dependent Generalized Prandtl-Ishlinskii hysteresis model,

[0011]

[0012] At the same time,

[0013] Wherein, H[I](t) is the driving current correction function, Λ i [L,I](t) is the generalized play operator, p i Is the weight function of the i-th generalized play operator, and satisfies p i ≥0, q is the number of generalized play operators, k0, k1, k2, k3 are respectively the first parameter, the second parameter, the third parameter and the fourth parameter of the driving current correction function when the driving current change is non-negative, w0, w1, w2, w3 are respectively the first parameter, the second parameter, the third parameter and the fourth parameter of the driving current correction function when the driving current change is negative, the definition of the weight function of the i-th generalized play operator is ρ,τ,r i Are respectively the first parameter, the second parameter and the third parameter of the weight function of the i-th generalized play operator, ΔI represents the unit change of the driving current of the MSMA driver platform;

[0014] S3, the improved LM algorithm is used to identify the internal dynamic model of the MSMA driver platform, the process is as follows:

[0015] S31. Define the mathematical expressions involved in the system identification process:

[0016]

[0017] at the same time,

[0018]

[0019] Where X = {x1, x2, ..., x} n} is the parameter vector to be identified, n is the number of parameters to be identified, m is the number of actual displacement values ​​of the MSMA actuator, and f(X) is the error vector. and Let X represent the nth and mth order real number fields respectively, and F(X) be the objective function. j (X) is the error between the j-th LD-GPI model value and the actual displacement value of the j-th MSMA actuator, J f (X) is the Jacobian matrix of f(X). Represents an m×n matrix in the real number field;

[0020] S32, Initialize constants ε1≥0, ε2≥0, k max ≥0, and parameters

[0021] k = 0, X = X0, β = 2, and define:

[0022]

[0023] Where ε1 is the minimum global update step size, ε2 is the minimum descent trial step size, and k max η is the maximum number of iterations, k is the number of iterations, X0 is the initial value of the parameter vector to be identified, μ is the damping parameter, and η is the initial correction value of the damping parameter. It is a matrix The element in row l and column l is β, which is the first parameter for updating the damping parameter; A is the first matrix for calculating the descent trial step; and G is the second matrix for calculating the descent trial step.

[0024] S33, Iterative calculation of descent trial step h lm :

[0025] h lm =-(A+μI) -1 G (7)

[0026] Where I is the identity matrix. ||h lm || represents h lm The square root of the sum of the squares of all elements of a vector, if ||h lm If ||≤ε2, then the iteration terminates;

[0027] S34, calculating an actual reduction amount Acth lm and a predicted reduction amount Preh lm , and the calculation formula is as follows:

[0028]

[0029] wherein L(·) is a domain approximation function of the objective function F(·), that is,

[0030]

[0031] calculating a ratio θ of the actual reduction amount and the predicted reduction amount:

[0032]

[0033] S35, if θ>0, updating the to-be-identified parameter vector X, calculating a first matrix A of the descent trial step, calculating a second matrix G of the descent trial step, and a damping parameter μ:

[0034]

[0035] μ=μ·max(0.4,3.4·θ 3 -5.1·θ 2 +0.1·θ+2) (11)

[0036] if θ≤0, updating the damping parameter and a first parameter for realizing the damping parameter update:

[0037]

[0038] S36, increasing the iteration number k by 1, and ||G|| ∞ representing the maximum value in the absolute values of all elements in the G matrix, if ||G|| ∞ ≤ε1 or k>k max , ending the system identification, otherwise returning to step S33.

[0039] Further, the MSMA driver platform comprises a data acquisition and signal transmission device, an MSMA driver, a current amplifier and a laser displacement measuring device. The data acquisition and signal transmission device adopts a dSPACE real-time simulation system of an A / D, D / A converter with a configuration precision of 16 bits, is connected with an upper computer and receives a control signal generated by the upper computer after D / A conversion to form an analog voltage signal. The signal is amplified by a current amplifier connected with the data acquisition and signal transmission device, drives the MSMA driver to produce displacement in the horizontal direction, and the measured displacement is converted into a digital signal by an A / D conversion module of the dSPACE real-time simulation system of the data acquisition and signal transmission device and then transmitted back to the upper computer. Using the MSMA driver platform, the input and output characteristic data of the MSMA driver can be collected in real time and efficiently, and high-precision experimental data is provided for the system identification method.

[0040] Further, assuming that L(t) and I(t) are continuous functions in the time domain, the time domain can be divided into N subintervals, and is a monotonic function in any subinterval, the generalized play operator is defined as follows:

[0041]

[0042] wherein λ r (I) and λ l (I) are the first correction function and the second correction function of the generalized play operator respectively, g0, g1, g2, g3 are the first weight parameter, the second weight parameter, the third weight parameter and the fourth weight parameter of λ r (I) respectively, h0, h1, h2, h3 are the first weight parameter, the second weight parameter, the third weight parameter and the fourth weight parameter of λ l (I) respectively. Using the generalized play operator, the strong saturation and the asymmetric hysteresis characteristics can be represented, and the internal hysteresis characteristics of the MSMA driver can be represented completely.

[0043] Further, in order to determine how to update the damping coefficient μ, the ratio θ of the actual descent and the predicted descent is defined, and different from the traditional LM algorithm, the update of the damping parameter μ in the improved LM algorithm adopts a cubic polynomial related to θ for smoothing, which is beneficial to the system identification method to avoid numerical oscillation in the iterative calculation process and exhibits higher modeling accuracy.

[0044] The present application has the following advantages and effects relative to the prior art:

[0045] The high-precision MSMA driver platform system identification method provided by the application adopts an LD-GPI model to describe the hysteresis characteristics inside the MSMA driver, and then combines a second-order linear system to accurately model the input and output characteristics of the MSMA driver platform. The system identification method improves the update rule of the damping parameter μ in the LM algorithm, adopts a cubic polynomial for smoothing, effectively avoids the oscillation of the numerical value in the system identification process, and makes the established model have more accurate ability to describe the hysteresis asymmetry, load dependence and frequency dependence, so as to facilitate the high-precision modeling and high-precision positioning of the MSMA driver platform. BRIEF DESCRIPTION OF DRAWINGS

[0046] The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this application, illustrate embodiments of the application and serve to explain the principles of the application, and do not limit the application. In the drawings:

[0047] Figure 1 It is a high-precision MSMA driver platform system identification method based on the LD-GPI model of the application;

[0048] Figure 2 It is an experimental result graph of the MSMA driver platform under the condition of variable load and constant frequency of the application;

[0049] Figure 3 It is an experimental result graph of the MSMA driver platform under the condition of variable frequency and constant load of the application;

[0050] Figure 4 It is a comparison graph of experimental data and model output when the input load is 0.1 MPa of the application;

[0051] Figure 5 It is a comparison graph of experimental data and model output when the input load is 0.2 MPa of the application;

[0052] Figure 6 It is a comparison graph of experimental data and model output when the input load is 0.5 MPa of the application;

[0053] Figure 7 It is a comparison graph of experimental data and model output when the input frequency is 0.5 Hz of the application;

[0054] Figure 8 It is a comparison graph of experimental data and model output when the input frequency is 1.0 Hz of the application;

[0055] Figure 9 It is a comparison graph of experimental data and model output when the input frequency is 2.0 Hz of the application. DETAILED DESCRIPTION

[0056] In order to make the purposes, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort belong to the scope of protection of the present application.

[0057] Embodiment 1

[0058] The high-precision MSMA driver platform system identification method based on the LD-GPI model proposed in this embodiment includes the following steps:

[0059] S1, building an MSMA driver platform

[0060] The MSMA driver platform includes a data acquisition and signal transmission device, an MSMA driver, a current amplifier and a laser displacement measurement device. The specific working principle is as follows: the data acquisition and signal transmission device is connected with the host computer, receives the control signal generated by the host computer and forms an analog voltage signal after D / A conversion, the signal is amplified by the current amplifier connected with the data acquisition and signal transmission device, then drives the MSMA driver to produce displacement in the horizontal direction, and the measured displacement is converted into a digital signal by the A / D conversion module in the data acquisition and signal transmission device, and then transmitted back to the host computer.

[0061] In order to realize accurate modeling of the MSMA driver platform under variable frequency conditions, an MSMA driver platform is built based on the MSMA driver with an outer contour size of about 3mm*5mm*19mm from Goodfellow Company, and the displacement of the MSMA driver in the horizontal direction under the excitation of different frequency current signals is measured by a laser displacement measurement system. The specific components of the experimental device are:

[0062] Data acquisition and signal transmission device: a dSPACE real-time simulation system with A / D and D / A converters with a precision of up to 16 bits is configured, connected with the host computer, realizes data acquisition and signal transmission, and realizes real-time analysis and processing of the collected data.

[0063] MSMA driver: the MSMA driver from Goodfellow Company has an outer contour size of about 3mm*5mm*19mm, and its metal composition ratio is Ni 50%, Mn 28% and Ga 22%.

[0064] Current amplifier: AE 7224 type current amplifier is adopted, which can output current range of-12A~+12A, and the voltage signal output by the D / A converter of dSPACE is amplified to drive the MSMA driver.

[0065] Laser displacement measuring device: laser displacement measuring device is composed of LK-G85 type laser displacement sensor of Keyence company and LK-GD500 type displacement signal amplifier of Keyence company.

[0066] S2, the internal dynamic model of the MSMA driver platform is established, and the expression formula is as follows:

[0067]

[0068] Wherein, L is the abbreviation of L(t), L(t) represents the pre-pressure of the MSMA driver platform, I is the abbreviation of I(t), I(t) represents the driving current of the MSMA driver platform, Γ[L,I](t) is the internal hysteresis characteristic of the MSMA driver, x(t) is the displacement of the MSMA driver in the horizontal direction, And The first-order derivative and the second-order derivative of x(t) are respectively, And the first parameter and the second parameter of the internal electromechanical characteristic of the MSMA driver, the LD-GPI model is used to describe the internal hysteresis characteristic of the MSMA driver, wherein the LD-GPI model is the abbreviation of Load-Dependent Generalized Prandtl-Ishlinskii hysteresis model,

[0069]

[0070] At the same time,

[0071]

[0072] Wherein, H[I](t) is the driving current correction function, Λ i [L,I](t) is a generalized play operator, p i Is the weight function of the i-th generalized play operator, and satisfies p i ≥0, q is the number of generalized play operators, k0, k1, k2, k3 are respectively the first parameter, the second parameter, the third parameter and the fourth parameter of the driving current correction function when the driving current change is non-negative, w0, w1, w2, w3 are respectively the first parameter, the second parameter, the third parameter and the fourth parameter of the driving current correction function when the driving current change is negative, and the weight function of the i-th generalized play operator is defined as ρ,τ,r iare the first, second and third parameters of the weight function of the ith generalized play operator, and ΔI represents the unit change of the driving current of the MSMA driver platform;

[0073] S3, the improved LM algorithm is used to identify the internal dynamic model of the MSMA driver platform, and the process is as follows:

[0074] S31, the mathematical expressions involved in the system identification process are defined:

[0075]

[0076] At the same time,

[0077]

[0078] Where X = {x1, x2, …, x n} is the parameter vector to be identified, n is the number of parameters to be identified, and f(X) is the error vector, and Rn and Rm represent the n-order and m-order real number fields respectively, F(X) is the objective function, and f j (X) is the error between the jth LD-GPI model value and the jth MSMA driver actual displacement value, m is the number of data of the MSMA driver actual displacement value, and J f (X) is the Jacobian matrix of f(X), represents an m×n matrix in the real number field;

[0079] S32, constants ε1≥0, ε2≥0, k max ≥0, and parameters are initialized, and the following definitions are made:

[0080]

[0081] Where ε1 is the minimum global update step, ε2 is the minimum descent step, k max is the maximum number of iterations, k is the iteration number, X0 is the initial value of the parameter vector to be identified, μ is the damping parameter, η is the initial correction value of the damping parameter, is the element in the lth row and the lth column of the matrix β is the first parameter for realizing damping parameter update, A is the first matrix for calculating the descent step, and G is the second matrix for calculating the descent step;

[0082] S33, the descent step h lm is calculated iteratively:

[0083] h lm =-(A+μI) -1 G (7)

[0084] where I is the identity matrix.||h lm || represents the square sum of all elements of vector h lm , and if||h lm ||≤ε2, the iteration is terminated.

[0085] S34, calculate the actual descent amount Acth lm and the predicted descent amount Preh lm , and the calculation formula is as follows:

[0086]

[0087] where L(·) is the domain approximation function of the objective function F(·), that is,

[0088]

[0089] Calculate the ratio θ of the actual descent amount and the predicted descent amount:

[0090]

[0091] S35, if θ>0, update the to-be-identified parameter vector X, calculate the first matrix of the descent trial step, calculate the second matrix of the descent trial step, and the damping parameter μ:

[0092]

[0093] μ=μ·max(0.4,3.4·θ 3 -5.1·θ 2 +0.1·θ+2) (11)

[0094] If θ≤0, update the damping parameter and the first parameter for realizing the damping parameter update:

[0095]

[0096] S36, let the iteration number k increase by 1.||G|| ∞ represents the maximum value of all element absolute values in the G matrix, and if||G|| ∞ ≤ε1 or k>k max , the system identification is ended, otherwise return to step S33.

[0097] Assuming that L(t) and I(t) are continuous functions in the time domain, the time domain can be divided into N subintervals, and they are monotonic functions in any subinterval, and the generalized play operator is defined as follows:

[0098]

[0099] where λ r(I) and λ l (I) are the first and second correction functions of the generalized play operator respectively, g0, g1, g2, g3 are the first, second, third and fourth weight parameters of λ r (I) are the first, second, third and fourth weight parameters of λ l (I) are the first, second, third and fourth weight parameters of λ

[0100] Different from the traditional LM algorithm, the update of the damping parameter μ in the improved LM algorithm uses a cubic polynomial to smooth, effectively avoiding the oscillation of the numerical value in the system identification process.

[0101] Example 2

[0102] In order to obtain the working characteristics of the MSMA driver platform, the performance test of the MSMA driver platform was carried out according to the steps in Example 1, and the input and output data of variable load and variable frequency were obtained. The MSMA driver platform considered two groups of working conditions: the first group was the variable load constant frequency condition, the input load was set to 0.1 MPa, 0.2 MPa and 0.5 MPa to realize the load change; the second group was the variable frequency constant load condition, the input current frequency was set to 0.5 Hz, 1.0 Hz and 2.0 Hz to realize the input current frequency change. The experimental results under the variable load constant frequency condition are shown in Figure 2 , and the experimental results under the variable frequency constant load condition are shown in Figure 3 . The results show that the working characteristics of the MSMA driver platform have strong saturation and asymmetry characteristics, and this characteristic is related to the input load change and the input current frequency change, that is, the working characteristics of the MSMA driver platform have hysteresis asymmetry, load dependence and frequency dependence.

[0103] Example 3

[0104] According to the system identification method in Example 1, the number of generalized play operators is set to q = 1, then the number of system model identification parameters n = 21; the minimum global update step size is set to ε1 = 1E-9, the minimum descent step size is set to ε2 = 1E-10, the maximum iteration number is set to k max = 500, all elements in the initial value X0 of the parameter are set to 0.1, and the initial correction value of the damping parameter is set to η = 1E-6; and the system identification is carried out according to the variable load constant frequency input and output data in Example 2. The identification results of the identification parameters are shown in Table 1.

[0105] Table 1. System identification results under variable load constant frequency condition

[0106]

[0107]

[0108] Figure 4 、 Figure 5 、 Figure 6 The comparison between the system model output and the measured MSMA driver platform actual output under the input load of 0.1 MPa, 0.2 MPa and 0.5 MPa respectively is shown in the local enlarged view, and it can be seen that the system model output curve identified by the improved LM algorithm is closer to the actual output curve than the curve identified by the traditional LM algorithm. In order to quantify and compare the system identification accuracy of the traditional LM algorithm and the improved LM algorithm, according to the calculation formula (14) of the mean square error average (MEAN) and the calculation formula (15) of the standard deviation (STD), table 2 can be obtained.

[0109]

[0110]

[0111] In the formula, is the optimal solution obtained by the system identification algorithm in the i th experiment, f (·) is the loss function (i.e. the mean square error of the LD-GPI model output and the actual output), n run is the number of independent identifications.

[0112] Table 2. Error table of modeling and identification method under variable load and constant frequency conditions

[0113]

[0114] As can be seen from table 2, under the variable load and constant frequency conditions, the mean square error average and the standard deviation of the hysteresis characteristic identified by the improved LM algorithm are smaller than those of the traditional LM algorithm, which proves the effectiveness of the method proposed in the application.

[0115] Example 4

[0116] According to the system identification method in example 1, the number of generalized play operators is set to q = 1, then the number of system model parameters to be identified is n = 21; the minimum global update step size of the algorithm is set to ε 1 = 1E-9, the minimum descent exploration step size is set to ε 2 = 1E-10, the maximum iteration number is set to k max = 300, all elements in the initial value X 0 of the parameter are set to 0.1, and the initial correction value of the damping parameter is set to η = 1E-5; and the system identification is performed according to the variable frequency and constant load input and output data in example 2. The identification result of the to-be-identified parameter is shown in table 3.

[0117] Table 3. System identification result table under variable frequency and constant load conditions

[0118]

[0119]

[0120] Figure 7 、 Figure 8 、 Figure 9 The comparison between the system model output and the measured MSMA driver platform actual output at 0.5 Hz, 1.0 Hz and 2.0 Hz input current frequency, respectively, in a view of its local amplification, it can be seen that the system model output curve identified by the improved LM algorithm is closer to the actual output curve than the curve identified by the traditional LM algorithm. In order to quantify and compare the system identification accuracy of the traditional LM algorithm and the improved LM algorithm, according to formula (14) and formula (15) in embodiment 3, table 4 can be obtained.

[0121] Table 4. Error table of modeling identification method under variable frequency and constant load conditions

[0122]

[0123] It can be seen from table 4 that under the variable frequency and constant load conditions, the mean value and standard deviation of the mean square error of the hysteresis characteristic identified by the improved LM algorithm are smaller than those of the traditional LM algorithm, which proves the effectiveness of the method proposed in the application.

[0124] The above embodiments are the preferred embodiments of the present application, but the embodiments of the present application are not limited by the above embodiments, and any changes, modifications, substitutions, combinations and simplifications made without departing from the spirit and principles of the present application shall be equivalent replacement modes and shall be included in the protection scope of the present application.

Claims

1. A high-precision MSMA driver platform system identification method based on the LD-GPI model, characterized in that, The system identification method includes the following steps: S1. Build an MSMA driver platform and measure the horizontal displacement of the MSMA driver under the excitation of the frequency conversion current signal using a laser displacement measuring device. S2. Establish the internal dynamic model of the MSMA driver platform, expressed as follows: Where L is short for L(t), representing the preload of the MSMA actuator platform; I is short for I(t), representing the drive current of the MSMA actuator platform; Γ[L,I](t) represents the internal hysteresis characteristic of the MSMA actuator; and x(t) is the horizontal displacement of the MSMA actuator. and Take the first and second derivatives of x(t), respectively. These are the first and second parameters of the internal electromechanical characteristics of the MSMA driver. The LD-GPI model is used to describe the internal hysteresis characteristics of the MSMA driver. LD-GPI stands for Load-Dependent Generalized Prandtl-Ishlinskii hysteresis model. at the same time, Where H[I](t) is the drive current correction function, Λ i [L,I](t) is the generalized play operator, p i It is the weight function of the i-th generalized play operator, and satisfies p i ≥0, q is the number of generalized play operators, k0, k1, k2, k3 are the first, second, third, and fourth parameters of the drive current correction function when the change in drive current is non-negative, w0, w1, w2, w3 are the first, second, third, and fourth parameters of the drive current correction function when the change in drive current is negative, and the weight function of the i-th generalized play operator is defined as follows: ρ,τ,r i These are the first, second, and third parameters of the weight function of the i-th generalized play operator, respectively, and ΔI represents the unit change in the drive current of the MSMA driver platform. S3. The improved LM algorithm is used to perform system identification of the internal dynamic model of the MSMA driver platform. The process is as follows: S31. Define the mathematical expressions involved in the system identification process: at the same time, Where X = {x1, x2, ..., x} n } is the parameter vector to be identified, n is the number of parameters to be identified, m is the number of actual displacement values ​​of the MSMA actuator, and f(X) is the error vector. and Let X represent the nth and mth order real number fields respectively, and F(X) be the objective function. j (X) is the error between the j-th LD-GPI model value and the actual displacement value of the j-th MSMA actuator, J f (X) is the Jacobian matrix of f(X). Represents an m×n matrix in the real number field; S32, Initialize constants ε1≥0, ε2≥0, k max ≥0, and parameters k=0, X=X0, β = 2, and define: Where ε1 is the minimum global update step size, ε2 is the minimum descent trial step size, and k max η is the maximum number of iterations, k is the number of iterations, X0 is the initial value of the parameter vector to be identified, μ is the damping parameter, and η is the initial correction value of the damping parameter. It is a matrix The element in row l and column l is β, which is the first parameter for updating the damping parameter; A is the first matrix for calculating the descent trial step; and G is the second matrix for calculating the descent trial step. S33, Iterative calculation of descent trial step h lm : h lm =-(A+μI) -1 G (7) Where I is the identity matrix; ||h lm || represents h lm The square root of the sum of the squares of all elements of a vector, if ||h lm If ||≤ε2, then the iteration terminates; S34. Calculate the actual descent amount Acth lm and the predicted decrease Preh lm The calculation formula is as follows: Where L(·) is the neighborhood approximation function of the objective function F(·), i.e. Calculate the ratio θ between the actual decrease and the predicted decrease: S35. If θ > 0, then update the parameter vector to be identified X, calculate the first matrix A of the descent trial step, calculate the second matrix G of the descent trial step, and the damping parameter μ: μ=μ·max(0.4,3.4·θ 3 -5.1·θ 2 +0.1·θ+2) (11) If θ≤0, then update the damping parameters and the first parameter to achieve the damping parameter update: S36. Increment the iteration count k by 1, ||G|| ∞ Let G be the maximum absolute value of all elements in matrix G. If ||G|| ∞ ≤ε1 or k>k max If the system identification fails, the process ends; otherwise, return to step S33.

2. The high-precision MSMA driver platform system identification method based on the LD-GPI model according to claim 1, characterized in that, The MSMA driver platform includes: a data acquisition and signal transmission device, an MSMA driver, a current amplifier, and a laser displacement measurement device. The data acquisition and signal transmission device employs a dSPACE real-time simulation system with a 16-bit A / D and D / A converter. It connects to a host computer and receives control signals generated by the host computer. After D / A conversion, the signals are converted into analog voltage signals. These signals are amplified by a current amplifier connected to the data acquisition and signal transmission device and drive an MSMA driver to generate displacement in the horizontal direction. The laser displacement measuring device converts the measured displacement into a digital signal through the A / D conversion module of the dSPACE real-time simulation system in the data acquisition and signal transmission device before transmitting it back to the host computer.

3. The high-precision MSMA driver platform system identification method based on the LD-GPI model according to claim 1, characterized in that, Assuming L(t) and I(t) are continuous functions in the time domain, and the time domain can be divided into N sub-intervals, and are monotonic functions in any sub-interval, the generalized play operator is defined as follows: Where, λ r (I) and λ l (I) are the first and second correction functions of the generalized play operator, respectively, and g0, g1, g2, g3 are λ r (I) The first, second, third, and fourth weight parameters, h0, h1, h2, and h3 are respectively λ l (I) The first weight parameter, the second weight parameter, the third weight parameter and the fourth weight parameter.

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