Sectional PI-PCHIP model parameter identification and compound control method

Abstract

The invention discloses a sectional PI-PCHIP model parameter identification and compound control method. The method comprises the following steps: step 1, constructing a PI hysteresis model; step 2, carrying out sectional type PI-PCHIP parameter identification; step 3, constructing a PI-PCHIP hysteresis model; and 4, substituting the PI-PCHIP hysteresis model parameters after optimization identification in the step 3 into an inverse model calculation formula to complete inverse model parameter calculation, realizing feed-forward compensation by using the finally obtained PI-PCHIP inverse model, and implementing a composite control strategy in combination with PID feedback adjustment. According to the invention, the precision driving control performance of the piezoelectric ceramic is obviously improved, and the method can be used for realizing the precision automatic adjustment of the position of the workbench in the precision measurement process of the Wolter-I type mandrel.

Description

Technical Field

[0001] The present invention relates to an inverse model feedforward compensation and PID composite control method based on a sequential quadratic programming (SQP) algorithm parameter identification piecewise Prandtl-Ishlinskii-PCHIP (PI-PCHIP) model. Background Art

[0002] During the ultra-precision machining and measurement of the Wolter-I optical mandrel, the inclination of the measuring platform will produce errors in the measurement results and machining accuracy, which will lead to the measurement accuracy and machining quality failing to meet the expected results. Therefore, it is essential to perform precise automatic leveling of the workbench before measurement.

[0003] The Wolter-I optical mandrel is a key component for manufacturing the Wolter-I optical collector mirror. Its surface processing quality is as high as that of the collector mirror surface, and it is difficult to manufacture and inspect. The manufacturing process of the mandrel mainly includes rough turning, inspection, chemical plating, fine turning, inspection and other steps. Among them, precision measurement is the key to ensure the processing quality of the mandrel. In the process of precision measurement, the adjustment error has a significant impact on the measurement accuracy. Therefore, the position of the mandrel needs to be adjusted repeatedly to ensure the accuracy of its inspection. Piezoelectric ceramics can obtain higher displacement resolution under voltage control. They have high frequency response, fast dynamic response, large load, good mechanical static pressure characteristics, simple structure and little interference from external forces. They can provide force to drive the micro-nano positioning mechanism and ensure sufficient dynamic stiffness. Compared with traditional motor drive and hydraulic drive, piezoelectric ceramics are small in size and can be used in compact or space-constrained environments. In addition, piezoelectric ceramics have a simple mechanical structure, low later maintenance costs, and better energy efficiency than motor drive and hydraulic drive. Therefore, using piezoelectric ceramics as a fine-tuning platform drive mechanism to design a leveling device during the mandrel measurement process can improve the adjustment accuracy. However, the nonlinearity caused by the hysteresis characteristics of piezoelectric ceramics will become a key factor affecting the leveling control accuracy of the fine-tuning platform. Therefore, it is of great significance for the precise measurement of the Wolter-I type mandrel to reduce the influence of the hysteresis characteristics to improve the displacement accuracy of the piezoelectric ceramics in the fine-tuning platform.

[0004] In order to improve the displacement accuracy of piezoelectric ceramics in micro-displacement platforms, feedforward compensation, feedback regulation and composite control combining the two are usually used. However, the control effect of single feedforward compensation or feedback regulation is often not as ideal as composite control.

[0005] Studies have shown that the hysteresis characteristics of piezoelectric ceramics have a significant effect on the output displacement, so it is crucial to establish a nonlinear hysteresis mathematical model to describe this phenomenon. At present, commonly used hysteresis models include Krasnoselskii-Pokrovskii (KP) hysteresis model, Prandtl-Ishlinskii (PI) hysteresis model, Preisach hysteresis model, Bouc-Wen hysteresis model and Duhem hysteresis model. Among them, the PI hysteresis model is widely used because of its simple structure, inverse model and fewer parameters to be identified. However, the PI hysteresis model is a centrally symmetric model composed of Play operators, while the actual piezoelectric ceramic hysteresis characteristics are asymmetric, that is, the corresponding displacements of the boost section and the buck section are different, and the displacement of the buck section is slightly higher than that of the boost section, presenting an asymmetric graph as a whole. Therefore, the hysteresis model established by the traditional PI hysteresis model parameter identification method has poor control effect. In addition, the control effect of the feedforward compensation depends greatly on the modeling accuracy of the model. Summary of the invention

[0006] Aiming at the influence of the hysteresis characteristics of piezoelectric ceramics on the control accuracy of a fine-tuning platform, the present invention provides a segmented PI-PCHIP model parameter identification and composite control method.

[0007] The objective of the present invention is achieved through the following technical solutions:

[0008] A segmented PI-PCHIP model parameter identification and composite control method comprises the following steps:

[0009] Step 1: Construct PI hysteresis model:

[0010]

[0011] Where y(t) is the displacement output at time t; u(t) is the input voltage at time t; w i =(w1,w2,w3...w n ) is the weight vector; r i =(r1,r2,r3...r n ) is the threshold vector; x(t) is the output at time t; r is the threshold; T s is the sampling time interval; i is the number of operators;

[0012] Step 2: Segmented PI-PCHIP parameter identification

[0013] Step 21: Construct the objective function:

[0014]

[0015] Where L(P) is the objective function substituted into the regularization term; P is the parameter to be optimized, namely the threshold r and the weight w vector; n is the number of parameters; λ is the preset coefficient used to control the regularization strength; y(i,P) is the simulated output; Y(i) is the actual output;

[0016] Step 2: Use the SQP algorithm to optimize the parameters of the boost section and the buck section respectively, and finally calculate the parameter value matching the objective function to achieve parameter identification. The specific steps are as follows:

[0017] (1) By giving the current point P in k iterations k , construct the QP subproblem:

[0018]

[0019] Where p is the search direction vector; H k The Hessian matrix calculated for the kth iteration; To calculate the gradient of the objective function in the kth iteration;

[0020] (2) The objective function is known to be L(P), and is continuously differentiable in the interval. Its first-order derivative is as follows:

[0021]

[0022] The second-order derivative has the following Hessian matrix definition:

[0023]

[0024] (3) Use the update method provided by BFGS to gradually approximate the Hessian matrix to simplify the calculation. The following is the update calculation formula of the BFGS algorithm:

[0025]

[0026] Where P k is the change in the parameter vector in the kth iteration; Δg k is the change of the gradient vector in the kth iteration; g k is the gradient vector of the objective function in the kth iteration, that is

[0027] (4) Using the solved p k Update the parameter vector. The following is the parameter vector update expression:

[0028] P k+1 =P k +a k p k

[0029] Where Pk is the current parameter vector, P k+1 is the updated parameter vector, a k is the step length;

[0030] (5) After the vector update is completed, a convergence check is performed, and δ is set as the convergence threshold value. The following is the convergence judgment expression:

[0031] ||P k+1 -P k ||≤δ

[0032] Step 3: Construct PI-PCHIP hysteresis model

[0033] Substitute the parameters identified in step 2 into the PI hysteresis model constructed in step 1 to obtain the displacement value, and insert the displacement value into the corresponding voltage node through the piecewise cubic Hermite interpolation method (PCHIP), so as to obtain the optimized identified PI-PCHIP hysteresis model, where a set of sorted nodes u is set i and the corresponding value y i , i = 1, 2, 3, ... N, N is the number of sampling points, calculate the interval length h i With slope l i :

[0034]

[0035] The following is the i ,u i+1 ]Interpolation expression:

[0036] L i (u) = y i +(u i -u i+1 )m i +(u i -u i+1 ) 2 c i

[0037] +(u i -u i+1 ) 3 d i

[0038]

[0039] In the formula, m i is the derivative at the node; c i , d i is the coefficient;

[0040] Step 4: Compound Control

[0041] By substituting the PI-PCHIP hysteresis model parameters optimized and identified in step 3 into the inverse model calculation formula, the inverse model parameter calculation is completed, and the feedforward compensation is realized by using the final PI-PCHIP inverse model, and the composite control strategy is implemented in combination with PID feedback regulation. The specific steps are as follows:

[0042] Step 41: Feedforward compensation

[0043] A PI-PCHIP hysteresis inverse model consistent with the PI-PCHIP hysteresis model is constructed. The weights and thresholds of the PI-PCHIP hysteresis model are used to calculate the corresponding parameters of the inverse model. The parameters are brought into the PI hysteresis inverse model and the PCHIP interpolation method is introduced. Finally, the PI-PCHIP hysteresis inverse model is obtained. The PI-PCHIP hysteresis inverse model is used for feedforward compensation. The specific expression of the PI hysteresis inverse model is as follows:

[0044]

[0045]

[0046] In the formula, w i ′ is the inverse model weight, r i ′ is the inverse model threshold;

[0047] Step 42: Compound Control

[0048] The error between the expected output displacement X fed back by the detection system and the actual output Y is used as the input of the PID control. The error is adjusted through PID control to generate a correction signal. The correction signal is superimposed on the feedforward compensation signal to obtain a total composite control signal, which is input into the driving power supply to drive the piezoelectric ceramic to generate the actual output Y. Finally, the actual output Y is fed back to the PID control through the monitoring system to form a closed-loop control.

[0049] Compared with the prior art, the present invention has the following advantages:

[0050] The present invention significantly improves the modeling accuracy of the PI hysteresis model by introducing the PCHIP interpolation method and using the SQP algorithm for parameter identification and optimization, reducing the error to 0.012μm and improving the accuracy by 95.1%. The optimized PI-PCHIP hysteresis inverse model is used for feedforward compensation, combined with PID feedback regulation, to form an efficient composite control strategy. The experimental results verify the effectiveness of this method, significantly improving the performance of piezoelectric ceramic precision drive control, and can be used to achieve precise automatic adjustment of the worktable position during the precision measurement of the Wolter-I type mandrel. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 It is the schematic diagram of compound control;

[0052] Figure 2 Comparison and error diagram of traditional PI hysteresis model;

[0053] Figure 3 It is the flow chart of SQP algorithm parameter identification;

[0054] Figure 4 It is a comparison chart of the segmented PI model;

[0055] Figure 5 It is the error diagram of the piecewise PI model;

[0056] Figure 6 To directly control the error;

[0057] Figure 7 is the composite control error of the traditional PI inverse model;

[0058] Figure 8 It is the fitting diagram of piecewise PI inverse model composite control;

[0059] Fig. 9 is the fitting error diagram. DETAILED DESCRIPTION

[0060] The technical solution of the present invention is further described below in conjunction with the accompanying drawings, but is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention should be included in the protection scope of the present invention.

[0061] The present invention provides a segmented PI-PCHIP model parameter identification and composite control method. In order to improve the modeling accuracy of the hysteresis model, the segmented cubic Hermite interpolation method (PCHIP) is introduced to maintain the monotonicity and smoothness of the model in each interval; the mean square error (MSE) is minimized as the standard for measuring the modeling accuracy, and a regular term is added on this basis to prevent overfitting, thereby constructing an optimization objective function; the SQP algorithm is used to perform parameter search for the boost section and the buck section respectively, and finally the parameter value matching the objective function is calculated to complete the parameter identification; in order to further reduce the influence of the hysteresis effect on the displacement accuracy of piezoelectric ceramics, the optimized PI-PCHIP hysteresis model parameters are substituted into the inverse model parameter calculation formula to obtain the inverse model parameters, and the corresponding voltage value is calculated by the PI inverse hysteresis model formula. Then, the voltage value is inserted into the corresponding displacement node using the PCHIP interpolation method, and the PI-PCHIP inverse model is finally constructed to realize feedforward compensation, and the composite control strategy is implemented in combination with PID feedback regulation. The specific steps are as follows:

[0062] 1. Hysteresis Model

[0063] 1. PI hysteresis model

[0064] The PI hysteresis model is a model obtained by weighted superposition of the Play operator. The Play operator can be expressed as:

[0065] x i (t)=max{u(t)-r,min{u(t)+r,x(t,T S )}} (1)

[0066] Where u(t) is the input voltage at time t; x(t) is the output at time t; r is the threshold; T s Sampling time interval; i is the number of operators. The initial input can be expressed as:

[0067] x(0)=max{u(0)-r,min{u(0)+r,x(0)}} (2)

[0068] The PI hysteresis model expression is as follows:

[0069]

[0070] Where y(t) is the displacement output at time t; u(t) is the input voltage at time t; w i =(w1,w2,w3…w n ) is the weight vector; r i =(r1,r2,r3…r n ) is the threshold vector.

[0071] 2. PCHIP interpolation method

[0072] In order to ensure that the constructed PI hysteresis model shows monotonicity and smoothness consistent with reality in the same interval, the PCHIP interpolation method is introduced. The PCHIP interpolation method is a method of interpolation under the premise of maintaining data monotonicity and smoothness. This method constructs a cubic Hermite polynomial on each data interval and determines the shape of the curve segment by calculating the first-order derivative of each interval. In addition, the PCHIP interpolation method ensures that the first-order derivative of the interpolation curve is continuous, thereby effectively ensuring the smoothness of the curve. Set a set of sorted nodes u i and the corresponding value y i , i = 1, 2, 3, ... N, N is the number of sampling points, calculate the interval length h i With slope l i :

[0073]

[0074] The following is the i ,u i+1 ]Interpolation expression:

[0075]

[0076] Where u is the interpolation point and is a standardized parameter; y is the displacement at the node; m i is the derivative at the node; c i , d i is the coefficient.

[0077] 2. Parameter Identification

[0078] 1. Traditional PI parameter identification

[0079] Traditional PI parameter identification constructs the objective function by minimizing the sum of squared errors and identifying the weights and thresholds of the PI hysteresis model. The objective function is:

[0080]

[0081] Where, Y(i) is the actual output; N is the number of sampling points; y(i) is the simulated output;

[0082] The recursive formula of the identification parameters can be obtained by the least squares method recursive formula:

[0083]

[0084] Where R(N) is the value of the update matrix; D(N) is the inverse matrix of the autocorrelation matrix of x(i);

[0085] The threshold selection rule is: Where i = 0, 1, 2…n-1, n is the number of parameters, V max 、V min are the maximum voltage and the minimum voltage respectively.

[0086] 2. Segmented PI-PCHIP parameter identification

[0087] (1) Objective function

[0088] In the objective function, the degree of model fit is measured by calculating the mean square error between the simulation value and the experimental value, that is, the optimal parameters are matched by minimizing the sum of squared errors.

[0089]

[0090] Where y(i,P) is the simulated output; Y(i) is the actual output;

[0091] By adding a regular term, that is, adding the sum of the squares of the weights to the function, the model weights are kept small, making the model simpler and smoother.

[0092]

[0093] Where L(P) is the objective function substituted into the regularization term; P is the parameter to be optimized, namely the threshold r and the weight w vector; n is the number of parameters; λ is a preset coefficient used to control the regularization strength. Large weights may cause the model to be too dependent on specific inputs, thus losing generalization ability. By penalizing large weight values, the model is forced to search for the most appropriate parameters.

[0094] (2) Sequential Quadratic Programming Algorithm

[0095] The SQP algorithm is a method for solving constrained optimization problems. It is suitable for dealing with nonlinear optimization problems with constraints. It approximates the objective function as a quadratic function, solves the quadratic programming subproblem to obtain an improved solution, and finally updates the linear approximation of the constraints and objective function to find the optimal solution.

[0096] By giving the current point P in k iterations k , construct the QP subproblem:

[0097]

[0098] Where p is the search direction vector, which is a direction specified by the algorithm at the current iteration point P. Along the specified direction, the parameters are adjusted to achieve the purpose of reducing the objective function value. Formula (11) is used to solve the p value; H k The Hessian matrix calculated for the kth iteration; is to calculate the gradient of the objective function at the kth iteration.

[0099] It is known that the objective function is L(P) and is continuously differentiable in the interval. Its first-order derivative, that is, the gradient expression, is as follows:

[0100]

[0101] The objective function L(P) is second-order continuously differentiable, so its second-order derivative has the following matrix definition. The second-order derivative matrix of the objective function L(P) is also called the Hessian matrix:

[0102]

[0103] The Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm is a quasi-Newton method used to approximate the Hessian matrix (i.e., the second-order derivative matrix) of the objective function during the optimization process. Since the method of directly calculating the Hessian matrix is ​​relatively complicated, BFGS provides an update method to gradually approximate the Hessian matrix to simplify the calculation. The following is the update calculation formula of the BFGS algorithm:

[0104]

[0105] Where P k is the change in the parameter vector in the kth iteration; Δg k is the change of the gradient vector in the kth iteration; g k is the gradient vector of the objective function in the kth iteration (i.e. ).

[0106] Using the solved p k Update the parameter vector. The following is the parameter vector update expression:

[0107] P k+1 =P k +a k p k (15)

[0108] Where P k is the current parameter vector, P k+1 is the updated parameter vector, a k is the step length.

[0109] After the vector update is completed, a convergence check is performed, and δ is set as the convergence threshold value. The following is the convergence judgment expression:

[0110] ||P k+1 -P k ||≤δ (16)

[0111] 3. Control Methods

[0112] 1. Feedforward compensation

[0113] Feedforward compensation is a control strategy that reduces or eliminates the effects of predicted disturbances on the system output by inputting them into the control system in advance. This method is often used to improve the control accuracy and dynamic response of the system. In the displacement control of piezoelectric ceramics, feedforward compensation compensates for the hysteresis nonlinearity of piezoelectric ceramics by using an inverse hysteresis model. This process is essentially a compensation for the displacement error of piezoelectric ceramics, and establishing an accurate inverse model is the key to the success of feedforward control. The accuracy of the inverse model directly determines the performance of the feedforward control.

[0114] For the hysteresis effect of piezoelectric ceramics, the PI hysteresis model is reversible, so feedforward compensation can be performed by constructing a corresponding hysteresis inverse model. The main difference between the PI hysteresis inverse model and the PI hysteresis model lies in the difference in weight and threshold parameters, and the mathematical expressions of the two are basically the same. The specific expression of the PI hysteresis inverse model is as follows:

[0115]

[0116] By using this inverse model, the hysteresis effect in the displacement control of piezoelectric ceramics can be effectively compensated, thereby significantly improving the control accuracy and dynamic response capability of the system. i ′ is the inverse model weight, r i ' is the inverse model threshold, where q = 1, and their calculation expressions are as follows:

[0117]

[0118] 2. Composite control

[0119] Feedforward compensation is a form of open-loop control that can only compensate for known disturbances, and cannot effectively control unknown disturbances that cannot be predicted or modeled. Moreover, it is based on predictive regulation of inputs, unlike feedback control, which can be adjusted based on actual outputs. Therefore, it is easily affected by input noise and may reduce system performance in the case of high noise.

[0120] Therefore, in order to improve control accuracy, closed-loop feedback control is particularly important in system design. In order to effectively compensate for the instability that may occur in the initial stage of open-loop control, feedback regulation is integrated into the system design. Currently, the commonly used feedback regulation is PID regulation, which has a simple algorithm structure, is easy to implement, and has strong adaptability. It can be applied to almost all automatic control scenarios regardless of whether the system is linear or not. Figure 1 The error between the expected output displacement X fed back by the detection system and the actual output Y is used as the input of the PID control. The error is adjusted through the PID control to generate a correction signal. The correction signal is superimposed with the feedforward compensation signal to obtain the total composite control signal, which is input to the driving power supply to drive the piezoelectric ceramics to generate the actual output Y. Finally, the actual output Y is fed back to the PID control through the monitoring system to form a closed-loop control.

[0121] Example:

[0122] 1. Parameter identification

[0123] (1) Traditional PI parameter identification

[0124] The initial value D(0) is set to the unit matrix, w(0) is set to a random value, and each data point is iteratively updated through equations (7) and (8) to gradually adjust the weights. In the threshold calculation formula, n = 10, v max =150,v min = 0. The sampling points are set to 121, and the traditional PI parameter identification results shown in Table 1 are finally obtained.

[0125] Table 1 Traditional PI parameter identification results

[0126]

[0127] According to Table 1, we can get Figure 2 The comparison of the traditional PI hysteresis model and the error diagram are shown, and the absolute average error of the modeling is 0.245μm.

[0128] (2) Segmented PI-PCHIP parameter identification

[0129] Table 2 shows the thresholds and weights of the rising and falling segments in the piecewise PI-PCHIP hysteresis model obtained through parameter identification. The initial thresholds and weights are set to random numbers, the number of sampling points is 121, the step size is 0.5, and λ = 0.086. In the MATLAB environment, the fmincon function is used to handle all the calculation details in the SQP algorithm, including gradient calculation, QP subproblem solution, and Hessian matrix update, and this process is not restricted by any constraints.

[0130] Table 2 shows the thresholds and weights of the rising and falling segments in the segmented PI-PCHIP hysteresis model obtained through parameter identification. Figure 3 The following is the flow chart of parameter identification of SQP algorithm. The initial threshold and weight are set as random numbers, the number of sampling points is 121, the step length is 0.5, and λ=0.086. In the MATLAB environment, the fmincon function is used to process all the calculation details in the SQP algorithm. First, the constraint r≥0 is set, then the gradient calculation, QP subproblem solution and Hessian matrix update are performed, and finally the parameters are output.

[0131] Table 2 Parameter identification results of segmented PI

[0132]

[0133]

[0134] According to the parameters in Table 2, we can get Figure 4 The segmented PI model comparison diagram shown in the figure and Figure 5 The error diagram of the segmented PI model shown in the figure shows that the maximum error is 0.08μm and the average absolute error is 0.012μm. Compared with the traditional PI model error, the model accuracy reaches 95.1%.

[0135] 2. Composite control

[0136] The experimental platform consists of stacked piezoelectric ceramics, E00.D3 piezoelectric driver from Core Tomorrow and LK-G5000 series laser micrometer from Keyence. The host computer communicates with the piezoelectric driver and laser micrometer through the USB interface. Using the voltage drive method, direct control experiments, traditional PI inverse hysteresis model composite control experiments and segmented PI-PCHIP inverse hysteresis model composite control experiments were carried out, and the experimental results were analyzed and compared.

[0137] Figure 6 The error is directly controlled, and its average absolute error is 0.29μm. It can be obviously seen that due to the influence of hysteresis characteristics, the absolute average error of the descending section is 0.518μm greater than that of the ascending section, and the average absolute error of the ascending section is 0.061μm.

[0138] Figure 7 It is the composite control error of the traditional PI inverse model, and its average absolute error is 0.08μm, of which the average absolute error in the rising section is 0.04μm, and the average absolute error in the descending section is 0.12μm.

[0139] Figure 8 It is the fitting diagram of the piecewise PI inverse model composite control. Fig. 9 To fit the error graph, experiments show that under the composite control of the segmented PI-PCHIP model identified by the SQP algorithm, the average absolute error of the displacement is 0.0146μm, of which the average absolute errors of the rising and falling segments are also 0.0146μm, and the maximum error is only 0.15μm.

[0140] The present invention can effectively solve the problem of insufficient precision of the traditional PI hysteresis model when processing asymmetric hysteresis characteristics by introducing the PCHIP interpolation method and combining it with the SQP algorithm for parameter identification and optimization. Experimental results show that the error of the hysteresis model is reduced to 0.012μm by the improved method, and the precision is improved by 95.1% compared with the traditional identification method. This result proves the effectiveness of introducing the PCHIP interpolation method and the SQP optimization algorithm. The segmented PI-PCHIP inverse model feedforward compensation and PID composite control method improves the positioning accuracy by 94.96% compared with direct control, and improves the positioning accuracy by 81.75% compared with the composite control based on the traditional PI inverse model. And compared with the research results mainly using the central symmetric PI model, this method shows higher precision in processing the displacement difference between the boost section and the buck section of the piezoelectric ceramic. This improvement is attributed to the advantages of the PCHIP interpolation method in maintaining data monotonicity and smoothness, and the high efficiency of the SQP algorithm in nonlinear optimization problems.

Claims

1. A segmented PI-PCHIP model parameter identification and composite control method, characterized in that The method comprises the following steps: Step 1: Construct PI hysteresis model: Where y(t) is the displacement output at time t; u(t) is the input voltage at time t; w i =(w1,w2,w3...w n ) is the weight vector; r i =(r1,r2,r3...r n ) is the threshold vector; x(t) is the output at time t; r is the threshold; T s is the sampling time interval; i is the number of operators; Step 2: Segmented PI-PCHIP parameter identification Step 21: Construct the objective function: Where L(P) is the objective function substituted into the regularization term; P is the parameter to be optimized, namely the threshold r and the weight w vector; n is the number of parameters; λ is the preset coefficient used to control the regularization strength; y(i,P) is the simulated output; Y(i) is the actual output; Step 2: Use the SQP algorithm to optimize the parameters of the boost section and the buck section respectively, and finally calculate the parameter value matching the objective function to achieve parameter identification; Step 3: Construct PI-PCHIP hysteresis model Substitute the parameters identified in step 2 into the PI hysteresis model constructed in step 1 to obtain the displacement value, and insert the displacement value into the corresponding voltage node through PCHIP to obtain the optimized identified PI-PCHIP hysteresis model; Step 4: Compound Control The inverse model parameter calculation is completed by substituting the PI-PCHIP hysteresis model parameters optimized and identified in step 3 into the inverse model calculation formula. The feedforward compensation is realized by using the final PI-PCHIP inverse model, and the composite control strategy is implemented by combining with PID feedback regulation.

2. The segmented PI-PCHIP model parameter identification and composite control method according to claim 1 is characterized in that The specific steps of step 22 are as follows: (1) By giving the current point P in k iterations k , construct the QP subproblem: Where p is the search direction vector; H k The Hessian matrix calculated for the kth iteration; To calculate the gradient of the objective function in the kth iteration; (2) The objective function is known to be L(P), and is continuously differentiable in the interval. Its first-order derivative is as follows: The second-order derivative has the following Hessian matrix definition: (3) Use the update method provided by BFGS to gradually approximate the Hessian matrix to simplify the calculation. The following is the update calculation formula of the BFGS algorithm: Where P k is the change in the parameter vector in the kth iteration; Δg k is the change of the gradient vector in the kth iteration; g k is the gradient vector of the objective function in the kth iteration, that is (4) Using the solved p k Update the parameter vector. The following is the parameter vector update expression: P k+1 =P k +a k p k Where P k is the current parameter vector, P k+1 is the updated parameter vector, a k is the step length; (5) After the vector update is completed, a convergence check is performed, and δ is set as the convergence threshold value. The following is the convergence judgment expression: ||P k+1 -P k ||≤δ。 3. The segmented PI-PCHIP model parameter identification and composite control method according to claim 1 is characterized in that In step 3, a set of sorted nodes u is set i and the corresponding value y i , i = 1, 2, 3, ... N, N is the number of sampling points, calculate the interval length h i With slope l i : The following is the i ,u i+1 ]Interpolation expression: L i (u)=y i +(u i -u i+1 )m i +(u i -u i+1 ) 2 c i +(u i -u i+1 ) 3 d i In the formula, m i is the derivative at the node; c i , d i is the coefficient.

4. The segmented PI-PCHIP model parameter identification and composite control method according to claim 1 is characterized in that The specific steps of step 4 are as follows: Step 41: Feedforward compensation A PI-PCHIP hysteresis inverse model is constructed in the same form as the PI-PCHIP hysteresis model. The weights and thresholds of the PI-PCHIP hysteresis model are used to calculate the corresponding parameters of the inverse model. The parameters are brought into the PI hysteresis inverse model and the PCHIP interpolation method is introduced. Finally, the PI-PCHIP hysteresis inverse model is obtained. The PI-PCHIP hysteresis inverse model is used for feedforward compensation. Step 42: Compound Control The error between the expected output displacement X fed back by the detection system and the actual output Y is used as the input of the PID control. The error is adjusted through PID control to generate a correction signal. The correction signal is superimposed on the feedforward compensation signal to obtain a total composite control signal, which is input into the driving power supply to drive the piezoelectric ceramic to generate the actual output Y. Finally, the actual output Y is fed back to the PID control through the monitoring system to form a closed-loop control.

5. The segmented PI-PCHIP model parameter identification and composite control method according to claim 4 is characterized in that The specific expression of the PI hysteresis inverse model is as follows: In the formula, w i ′ is the inverse model weight, r i ′ is the inverse model threshold.

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