Piezoelectric ceramic compound control method and device based on improved PI model

Abstract

The invention provides a piezoelectric ceramic compound control method and device based on an improved PI model. The method comprises the steps of obtaining a standard input signal; inputting the standard input signal into the ILC-MPC control model to obtain a piezoelectric ceramic compensation result; wherein the ILC-MPC control model is established by adopting an ILC-MPC compound control method under an improved PI (Proportional Integral) model; the improved PI model is established by adopting an improved play operator, and a cubic term and an initial offset term about a standard input signal are added to a non-memory part function; according to the method, the asymmetric characteristic is achieved by changing the slope of an operator descending section through the improved play operator, the effect that the shape of the improved play operator changes along with the frequency is achieved by introducing a derivative about a standard input signal, on the basis of the method, fast response can be guaranteed, meanwhile, steady-state errors can be effectively restrained, and the stability of the system is improved. And the stability and the control precision of the piezoelectric ceramic system are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of precision driving and control, and in particular to a piezoelectric ceramic composite control method and device based on an improved PI model. Background Art

[0002] In the fields of precision manufacturing, optical positioning, and micro-nano manipulation, piezoelectric ceramic-driven micro-motion platforms have become indispensable precision driving components due to their high precision, zero friction loss, and compact structure. However, the inherent hysteresis nonlinearity of piezoelectric ceramics seriously affects the accuracy of their displacement output. The error caused by this characteristic can be as high as 50% of the platform's motion stroke, greatly limiting its performance in high-precision applications. In order to improve system performance, it is usually necessary to combine a displacement amplification mechanism to increase the output displacement of piezoelectric ceramics, but this further aggravates the hysteresis nonlinear effect, which not only reduces the system accuracy, but may also cause instability in the control system, seriously affecting the positioning accuracy and dynamic response capabilities of the micro-motion platform. Therefore, how to effectively compensate for the hysteresis nonlinearity of piezoelectric ceramics has become a key technical problem in improving the performance of micro-motion platforms.

[0003] In order to solve the hysteresis nonlinear problem of piezoelectric ceramics, academia and industry generally adopt a strategy that combines modeling with compensation control. Among them, the phenomenon model has become the mainstream direction of research and application because it can accurately predict the hysteresis effect. Among the phenomenon models, the Prandtl-Ishlinskii (PI) model is favored for its simple structure and high modeling efficiency. The PI model can better describe the hysteresis behavior of piezoelectric ceramics by superimposing a series of weighted threshold functions, providing a basis for designing an effective hysteresis compensation controller. Through the inverse model feedforward control based on the PI model or in combination with other feedback control methods (such as PID control, fuzzy control, neural network control, etc.), the displacement error caused by hysteresis can be significantly reduced and the control accuracy of the system can be improved.

[0004] Although the PI model has achieved remarkable results in piezoelectric ceramic hysteresis modeling and control compensation, its inherent symmetry assumption limits its accuracy in describing asymmetric hysteresis characteristics. In practical applications, the hysteresis curve of piezoelectric ceramics often shows asymmetry, which makes the traditional PI model unable to accurately fit the actual hysteresis behavior, thus affecting the compensation effect. In addition, as the output frequency of piezoelectric ceramics increases, the hysteresis curve will change, while the traditional PI model lacks dynamic adaptability and cannot automatically adjust the model parameters according to the change of output frequency, resulting in an increase in displacement error at high-frequency output. In terms of control strategy, although model predictive control (MPC) is widely used in piezoelectric ceramic control as an optimal control method, its performance is highly dependent on the accuracy of the system transfer function. In the case of errors in the identification of the piezoelectric ceramic transfer function, the optimal control performance of MPC is difficult to guarantee, which limits its application effect in complex dynamic environments. Therefore, exploring more accurate and adaptive hysteresis modeling and control methods is of great significance to improving the performance of piezoelectric ceramic-driven micro-motion platforms. Summary of the invention

[0005] In order to solve the above problems existing in the prior art, the present invention provides a piezoelectric ceramic composite control method and device based on an improved PI model.

[0006] The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0007] In a first aspect, the present invention provides a piezoelectric ceramic composite control method based on an improved PI model, comprising:

[0008] Get the standard input signal;

[0009] The standard input signal is input into the ILC-MPC control model to obtain the piezoelectric ceramic compensation result; wherein, the ILC-MPC control model is established under the improved PI model using the ILC-MPC composite control method; the improved PI model is established using the improved play operator, and the cubic term and the initial offset term about the standard input signal are added to the non-memory part function; the improved play operator realizes the asymmetric characteristics by changing the slope of the descending segment of the operator, and realizes the effect of the shape of the improved play operator changing with frequency by introducing the derivative about the standard input signal.

[0010] Optionally, the improved play operator is expressed as:

[0011]

[0012] in, represents the output of the improved play operator with input u at time k, is the derivative of u, u is the standard input signal ys The vector corresponding to the voltage signal obtained by scaling transformation is the standard input signal y s Perform enlargement processing with a preset multiple; is the derivative of u at time k, u(k) represents the value of vector u at time k, r represents the threshold of the improved play operator, α represents the first frequency correlation coefficient, β represents the second frequency correlation coefficient, represents the output of the improved play operator with input u at time k-1, b represents the asymmetric factor, u(k-1) represents the value corresponding to the vector u at time k-1, the first frequency correlation coefficient is the frequency correlation coefficient of the improved play operator in the rising stage, and the second frequency correlation coefficient is the frequency correlation coefficient of the improved play operator in the falling stage.

[0013] Alternatively, the improved PI model is expressed as:

[0014]

[0015] P[u](k)=du 3 (k)+au(k)+e

[0016] Among them, H[u](k) represents the value of the improved PI model when the input is u at time k, represents the value of the memory function when the input is u at time k, P[u](k) represents the value of the non-memory function when the input is u at time k, and p(r i ) is the weight coefficient of the i-th improved play operator, r i is the threshold of the i-th improved play operator, F oi [u](k) is the value of the i-th improved play operator when the input is u at time k, d is the coefficient of the cubic term, and u 3 (k) represents the cubic term with respect to u(k), e represents the initial offset term, and N represents the total number of improved play operators.

[0017] Optionally, the construction process of the ILC-MPC control model includes:

[0018] Obtaining an improved PI model;

[0019] The improved PI model is inversely transformed using the direct inverse method to obtain the inverse model;

[0020] Perform parameter identification on the inverse model to obtain the inverse model identification result;

[0021] The linear part of the Hammerstein model is used to construct the state space equation of the piezoelectric ceramic system;

[0022] The ILC-MPC control model is constructed by using state-space equations, inverse model identification results and ILC-MPC control method.

[0023] Optionally, performing parameter identification on the inverse model to obtain an inverse model identification result includes:

[0024] The parameters of the inverse model are identified by simulated annealing particle swarm optimization algorithm, and the inverse model identification result is obtained.

[0025] Optionally, the linear part of the Hammerstein model is used to construct the state space equations of the piezoelectric ceramic system, including:

[0026] Generate the system nominal transfer function using the linear part of the Hammerstein model;

[0027] Discretize the system nominal transfer function to obtain the discrete state space equation;

[0028] The discrete state space equation is spatially transformed according to a preset transformation rule to obtain the state space equation. Optionally, the ILC-MPC control model is expressed as:

[0029] W k (t) = k1u 1,k (t)-k2u M,k (t)+H[y s|k ](t);

[0030] Among them, W k (t) represents the piezoelectric ceramic compensation result at time t in the kth batch, k1 represents the first weight coefficient, k2 represents the second weight coefficient, H[y s|k ](t) means when the standard input signal is y in the kth batch s The value of the inverse model at time t, u 1,k (t) represents the output of the ILC control process at time t of the kth batch, u M,k (t) represents the control output of the kth batch at time t based on the objective function, and the objective function is constructed based on the quadratic form and the state space equation.

[0031] Optionally, the objective function is expressed as:

[0032] J=(Yy s ) T λ y (Yy s )+(U F|k -U s ) T λ u (U F|k -U s );

[0033] Among them, J represents the output of the objective function, Y represents the predicted output sequence, and y s represents the standard input signal, λ y represents the first positive definite coefficient matrix, λ u represents the second positive definite coefficient matrix, U F|k represents the predicted voltage sequence at time k, U s represents the supplementary matrix, which is used to make the control output u M,k (t) is more gentle, where Y and U F|k It is constructed based on the state space equation;

[0034] Y=[y k T (k+1) y k T (k+2) …y k T (k+Np)] T ;

[0035] Among them, y k (k+1) represents the predicted output of the piezoelectric ceramic system corresponding to the first input interval after time k, y k (k+2) represents the predicted output of the piezoelectric ceramic system corresponding to the second input interval after time k, y k (k+Np) represents the predicted output of the piezoelectric ceramic system corresponding to the Npth input interval after time k, and Np represents the number of prediction steps.

[0036] In a second aspect, the present invention provides a piezoelectric ceramic composite control device based on an improved PI model, comprising: an acquisition unit and a compensation unit;

[0037] The acquisition unit is used to: acquire a standard input signal;

[0038] The compensation unit is used to: input the standard input signal into the ILC-MPC control model to obtain the piezoelectric ceramic compensation result; wherein, the ILC-MPC control model is established under the improved PI model by using the ILC-MPC composite control method; the improved PI model is established by using the improved play operator, and the cubic term and the initial offset term about the standard input signal are added to the non-memory part function; the improved play operator realizes the asymmetric characteristic by changing the slope of the descending section of the operator, and realizes the effect of the shape of the improved play operator changing with the frequency by introducing the derivative about the standard input signal.

[0039] In a third aspect, the present invention provides a piezoelectric ceramic composite control device based on an improved PI model, comprising: a processor, a storage medium and a bus, wherein the storage medium stores machine-readable instructions executable by the processor. When the piezoelectric ceramic composite control device based on the improved PI model is running, the processor and the storage medium communicate via the bus, and the processor executes the machine-readable instructions to perform the steps of the piezoelectric ceramic composite control method based on the improved PI model as described in the first aspect above.

[0040] The present invention provides a piezoelectric ceramic composite control method and device based on an improved PI model. The piezoelectric ceramic composite control method based on the improved PI model includes: obtaining a standard input signal; inputting the standard input signal into an ILC-MPC control model to obtain a piezoelectric ceramic compensation result; wherein the ILC-MPC control model is established under the improved PI model by using an ILC-MPC composite control method; the improved PI model is established by using an improved play operator, and a cubic term and an initial offset term with respect to the standard input signal are added to the non-memory part function; the improved play operator realizes asymmetric characteristics by changing the slope of the descending section of the operator, and realizes the effect of the shape of the improved play operator changing with frequency by introducing a derivative with respect to the standard input signal. In the present invention, since the improved PI model has asymmetric and frequency-related characteristics, it can more accurately describe the hysteresis phenomenon of piezoelectric ceramics, thereby improving the compensation accuracy and adaptability of the piezoelectric ceramic system to standard input signals; in addition, since the proposed ILC-MPC composite control method combines the advantages of iterative learning and model predictive control, it can effectively suppress steady-state errors while ensuring rapid response, thereby further improving the stability and control accuracy of the system.

[0041] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 A schematic flow chart of a piezoelectric ceramic composite control method based on an improved PI model provided in an embodiment of the present invention;

[0043] Figure 2 The schematic diagram of the structure of the improved play operator is shown exemplarily;

[0044] Figure 3 The schematic diagram of the structure of the classic play operator is shown as an example;

[0045] Figure 4 The schematic diagram of the fitting result corresponding to the improved PI model when the input frequency is 10 Hz is shown by way of example;

[0046] Figure 5The schematic diagram of the fitting result corresponding to the improved PI model when the input frequency is 50 Hz is shown by way of example;

[0047] Figure 6 The schematic diagram of the inverse model prediction output result when the input frequency is 1 Hz is shown by way of example;

[0048] Figure 7 The simulation results of the ILC-MPC control method of the present invention and the existing control method are compared by way of example;

[0049] Figure 8 A schematic structural diagram of a piezoelectric ceramic composite control device based on an improved PI model provided in an embodiment of the present invention;

[0050] Fig. 9 A schematic structural diagram of a piezoelectric ceramic composite control device based on an improved PI model provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0051] The present invention is further described in detail below with reference to specific embodiments, but the embodiments of the present invention are not limited thereto.

[0052] In order to improve the compensation accuracy and adaptability of a piezoelectric ceramic system to a standard input signal, an embodiment of the present invention provides a piezoelectric ceramic composite control method based on an improved PI model. Figure 1 The present invention provides a schematic flow chart of a piezoelectric ceramic composite control method based on an improved PI model. Figure 1 As shown, the method includes:

[0053] S101, obtaining a standard input signal.

[0054] In this embodiment, the standard input signal can be, for example, a standard triangle wave signal, a sine wave signal, a square wave signal, or a multi-frequency sine wave signal. The selection of the standard input signal is related to the actual application scenario, the spectral characteristics of the signal, the complexity and controllability of the signal, and the nonlinear characteristics of the system. For example, in a scanning probe microscope, a triangle wave signal is closer to the actual scanning motion; while in an ultrasonic generator, a sine wave signal may be more suitable. The embodiment of the present invention does not impose any fixed restrictions on the specific type of the input signal.

[0055] S102, inputting the standard input signal into the ILC-MPC control model to obtain a piezoelectric ceramic compensation result.

[0056] Among them, the ILC-MPC control model is established under the improved PI model using the ILC-MPC composite control method; the improved PI model is established using the improved play operator, and the cubic terms and initial offset terms about the standard input signal are added to the non-memory part function; the improved play operator realizes the asymmetric characteristics by changing the slope of the descending segment of the operator, and the derivative of the standard input signal is introduced to achieve the effect of the shape of the improved play operator changing with frequency.

[0057] Optionally, the improved play operator is expressed as:

[0058]

[0059] in, represents the output of the improved play operator with input u at time k, is the derivative of u, u is the standard input signal y s The vector corresponding to the voltage signal obtained by scaling transformation is the standard input signal y s Perform enlargement processing with a preset multiple; is the derivative of u at time k, u(k) represents the value of vector u at time k, r represents the threshold of the improved play operator, α represents the first frequency correlation coefficient, β represents the second frequency correlation coefficient, represents the output of the improved play operator with input u at time k-1, b represents the asymmetric factor, u(k-1) represents the value corresponding to the vector u at time k-1, the first frequency correlation coefficient is the frequency correlation coefficient of the improved play operator in the rising stage, and the second frequency correlation coefficient is the frequency correlation coefficient of the improved play operator in the falling stage.

[0060] In the embodiment of the present invention, in order to make the improved PI model have asymmetric characteristics and frequency-dependent characteristics, the memory part and non-memory part of the PI model are improved. In the memory part, since the piezoelectric ceramic hysteresis curve does not involve the negative half area, the negative part of the play operator is simplified, only the first quadrant part is retained, and the asymmetric factor is introduced to change the slope of the play operator. Figure 2 The schematic diagram of the structure of the improved play operator is shown as an example. Figure 3 The schematic diagram of the structure of the existing play operator is exemplarily shown. Figure 2 The curve has obvious asymmetry. Figure 3 The curve can only realize the symmetric characteristics. Since the shape of the piezoelectric ceramic hysteresis curve is asymmetric in actual scenes, the improved play operator of the present invention is more suitable for practical applications.

[0061] In addition, in order to realize the frequency-related characteristics, the play operator is divided into two parts: the rising stage and the falling stage. The derivative of the standard input signal is introduced into the classic play operator. When the sampling frequency is the same, the input frequency and the rate of change of the input voltage are positively correlated. Therefore, the absolute value of the input voltage derivative changes with the input frequency, and the improved play operator shows a frequency-related characteristic.

[0062] Furthermore, on the basis of the improved play operator, the non-memory part function is added with cubic terms and initial offset terms about the input to enhance its nonlinear fitting ability, and an improved PI model can be obtained. By adding rate-related factors, the entire improved PI model can change with the change of frequency, so that the improved PI model has frequency-related characteristics.

[0063] Alternatively, the improved PI model is expressed as:

[0064]

[0065] P[u](k)=du 3 (k)+au(k)+e

[0066] Among them, H[u](k) represents the value of the improved PI model when the input is u at time k, represents the value of the memory function when the input is u at time k, P[u](k) represents the value of the non-memory function when the input is u at time k, and p(r i ) is the weight coefficient of the i-th improved play operator, r i is the threshold of the i-th improved play operator, F oi [u](k) is the value of the i-th improved play operator when the input is u at time k, d is the coefficient of the cubic term, and u 3 (k) represents the cubic term with respect to u(k), e represents the initial offset term, and N represents the total number of improved play operators.

[0067] The embodiment of the present invention provides a piezoelectric ceramic composite control method based on an improved PI model, including: obtaining a standard input signal; inputting the standard input signal into an ILC-MPC control model to obtain a piezoelectric ceramic compensation result; wherein the ILC-MPC control model is established under the improved PI model using an ILC-MPC composite control method; the improved PI model is established using an improved play operator, and a cubic term and an initial offset term about the standard input signal are added to the non-memory part function; the improved play operator realizes asymmetric characteristics by changing the slope of the operator's descending segment, and by introducing a derivative about the standard input signal to realize the effect of the shape of the improved play operator changing with frequency. In the embodiment of the present invention, since the improved PI model has asymmetric and frequency-related characteristics, it can more accurately describe the hysteresis phenomenon of piezoelectric ceramics, and improve the compensation accuracy and adaptability of the piezoelectric ceramic system for the standard input signal; in addition, since the proposed ILC-MPC composite control method combines the advantages of iterative learning and model predictive control, it can effectively suppress steady-state errors while ensuring rapid response, and further improve the stability and control accuracy of the system.

[0068] Optionally, the construction process of the ILC-MPC control model includes:

[0069] Obtaining an improved PI model;

[0070] The improved PI model is inversely transformed using the direct inverse method to obtain the inverse model;

[0071] Perform parameter identification on the inverse model to obtain the inverse model identification result;

[0072] The linear part of the Hammerstein model is used to construct the state space equation of the piezoelectric ceramic system;

[0073] The ILC-MPC control model is constructed by using state-space equations, inverse model identification results and ILC-MPC control method.

[0074] It should be noted that, in this embodiment, in order to eliminate the inherent hysteresis nonlinearity of piezoelectric ceramics, an inverse model is established to control and compensate the piezoelectric ceramics. Specifically, since the play operator of the improved PI model is improved in the above steps, the traditional analytical method for inverse formula is not applicable, so the direct inverse method is adopted to identify the inverse model according to the experimental data, and the inverse model is directly used to describe the relationship between displacement and voltage.

[0075] In the present invention, since the control algorithm adopts the ILC-MPC composite control method, the method combines the advantages of MPC (model prediction) control and learning control algorithms. Since the MPC control algorithm needs to obtain the transfer function of the system to calculate the algorithm parameters, the piezoelectric ceramic transfer function adopts the linear part transfer function of the Hammerstein model.

[0076] After obtaining the nominal transfer function of the system, the discrete state space equation of the piezoelectric ceramic is established. After making relevant transformations on the discrete space equation, the state vectors of other steps can be obtained by recursive method. The required control output u can be obtained by minimizing the objective function. M,k (t). In addition, since the model predictive control part of the ILC-MPC control model can be regarded as a proportional term, it may cause steady-state errors. In order to suppress the steady-state error, an integral term and a feedforward term composed of the above inverse model can be added. Finally, the idea of ​​iterative learning is introduced to construct the ILC-MPC control method, so that the system can show better performance in repeated scanning motion. The specific execution steps are as follows:

[0077] Optionally, performing parameter identification on the inverse model to obtain an inverse model identification result includes:

[0078] The parameters of the inverse model are identified by simulated annealing particle swarm optimization algorithm, and the inverse model identification result is obtained.

[0079] It should be noted that in order to identify the parameters of the hysteresis model, some optimization algorithms are needed to perform parameter identification. Since the traditional particle swarm optimization algorithm is prone to fall into the local optimum, especially when many parameters need to be identified, in order to avoid falling into the local optimum, the simulated annealing particle swarm optimization algorithm is used to perform parameter identification in the present invention, and the parameter identification results are obtained by continuously adjusting the optimization algorithm parameters. For example, Figure 4 The schematic diagram of the fitting result corresponding to the improved PI model when the input frequency is 10 Hz is exemplarily shown. Figure 5 The schematic diagram of the fitting result corresponding to the improved PI model when the input frequency is 50 Hz is exemplarily shown. Figure 6 The following is an example of the inverse model prediction output result when the input frequency is 1 Hz. Figure 4-Figure 6 It can be seen that the improved PI model and inverse model provided in the embodiment of the present invention can effectively fit the actual output and maintain a high degree of consistency with the curve of the actual output, which verifies the effectiveness of the improved PI model provided in the embodiment of the present invention.

[0080] Optionally, the linear part of the Hammerstein model is used to construct the state space equations of the piezoelectric ceramic system, including:

[0081] Generate the system nominal transfer function using the linear part of the Hammerstein model;

[0082] Discretize the system nominal transfer function to obtain the discrete state space equation;

[0083] The discrete state space equation is spatially transformed according to a preset transformation rule to obtain the state space equation.

[0084] In the embodiment of the present invention, the corresponding discrete state space equation can be obtained by Laplace transforming the system nominal transfer function, and the system nominal transfer function can be expressed as:

[0085]

[0086] Where G(z) represents the value of the system nominal transfer function and z represents the z-transformed variable.

[0087] After obtaining the nominal transfer function of the system, the nominal transfer function of the system can be discretized to obtain the discrete state space equation. The discrete state space equation is expressed as:

[0088]

[0089] Where y(k) represents the output of the piezoelectric ceramic system at time k. It should be noted that the output of the piezoelectric ceramic system is the actual displacement output of the piezoelectric ceramic system. x(k+1) is the state vector of the discrete state space equation at time k+1. x(k) is the state vector of the discrete state space equation at time k. u(k) represents the value corresponding to the vector u at time k. A d represents the first state matrix, B d represents the second state matrix, C d represents the third state matrix, A d ,B d ,C d The value of can be obtained based on the coefficient value of the system nominal transfer function.

[0090] The discrete state space equation is transformed as follows:

[0091] x s (k)=[y(k)…y(k-n+1)u(k-1)…u(k-m+1)] T ;

[0092] Among them, x s(k) represents the state vector of the discrete state space equation after transformation, y(k-n+1) represents the actual displacement output of the piezoelectric ceramic system at time k-n+1, ​​u(k-1) represents the value of the vector u at time k-1, u(k-m+1) represents the value of the vector u at time k-m+1, m and n are variables related to the order of the nominal transfer function of the system. In this embodiment, the values ​​of m and n can be 2.

[0093] Correspondingly, the transformed state space equation can be expressed as:

[0094]

[0095] Among them, A, B, and C represent the first coefficient matrix, the second coefficient matrix, and the third coefficient matrix respectively. A, B, and C can be obtained by A d ,B d ,C d After some transformation, it can be expressed as:

[0096]

[0097] B=[b10…0 1 0…0] T ;

[0098] C = [1 0…0];

[0099] Among them, a1-a n 、b1-b m Corresponding to A d ,B d ,C d The elements in .

[0100] Thus, the state vector after the current moment can be recursively obtained:

[0101]

[0102] Among them, x s|k (k+Np) is the state space vector after the Npth input interval after time k, u k (k+i) is the value of vector u after i input intervals after time k.

[0103] x s|k The matrix form corresponding to (k+Np) is as follows:

[0104] X F|k =Fx s (k)+HU F|k ;

[0105] in,

[0106] X F|k =[xs|k T (k+1) x s|k T (k+2) … x s|k T (k+Np)] T ;

[0107]

[0108] U F|k =[u(k) u k (k+1) … u k (k+Np-1)] T ;

[0109] u k (k+1) represents the value of vector u corresponding to the k+1th input interval after time k, u k (k+Np-1) represents the value of vector u corresponding to the k+Np-1th input interval after time k.

[0110] Based on the transformed state space equation, the displacement output matrix Y predicted by the piezoelectric ceramic system can be obtained:

[0111] Y=C m X F|k ;

[0112] Y=[y k T (k+1) y k T (k+2) … y k (k+Np)] T ;

[0113] Among them, y k (k+1) represents the predicted output of the piezoelectric ceramic system corresponding to the first input interval after time k, y k (k+2) represents the predicted output of the piezoelectric ceramic system corresponding to the second input interval after time k, y k (k+Np) represents the predicted output of the piezoelectric ceramic system corresponding to the Npth input interval after time k, Np represents the number of prediction steps, C m =(n+m-1)×N p The diagonal matrix of , where the diagonal element matrix is ​​C. Specifically, Y is used to construct the subsequent objective function.

[0114] Alternatively, the ILC-MPC control model can be expressed as:

[0115] W k (t) = k1u 1,k (t)-k2uM,k (t)+H[y s|k ](t);

[0116] Among them, W k (t) represents the piezoelectric ceramic compensation result at time t in the kth batch, k1 represents the first weight coefficient, k2 represents the second weight coefficient, H[y s|k ](t) means when the standard input signal is y in the kth batch s The value of the inverse model at time t, u 1,k (t) represents the output of the ILC control process at time t of the kth batch, u M,k (t) represents the control output of the kth batch based on the objective function at time t. Specifically, u M,k (t) represents the partial output of the model predictive control (MPC) based on the objective function at time t of the kth batch, and the objective function is constructed based on the quadratic form and the state space equation.

[0117] Optionally, the objective function is expressed as:

[0118] J=(Yy s ) T λ y (Yy s )+(U F|k -U s ) T λ u (U F|k -U s );

[0119] Among them, J represents the output of the objective function, Y represents the predicted output sequence, and y s represents the standard input signal, λ y represents the first positive definite coefficient matrix, λ u represents the second positive definite coefficient matrix, U F|k represents the predicted voltage sequence at time k, U s represents the supplementary matrix, which is used to make the control output u M,k (t) is more gentle. By minimizing J, the corresponding control output u can be obtained M,k The value of (t). M,k (t) is U F|k The first row element, u M,k The calculation process of (t) is implemented based on the MPC control method.

[0120] Since there may be errors in the process of identifying the inverse model and the nominal transfer function of the system, and there is uncertainty in the piezoelectric ceramic drive system, and in practical applications, piezoelectric ceramics always perform functions in a scanning motion, the idea of ​​iterative learning is introduced, and the ILC-MPC control method is designed to solve u 1,k (t):

[0121]

[0122] In the formula, u 1,k (t) is the output of the ILC part of the kth batch at time t, u 1,k-1 (t) is the output of the ILC part calculation at time t of the k-1th batch, is the derivative of the error at time t in the k-1th batch, is the derivative of the error at time t of the kth batch, γ is the learning coefficient corresponding to the batch before the current batch, η is the learning coefficient of the iterative error of the current batch, and the error represents the standard input signal y s The difference between the actual displacement output y of the piezoelectric ceramic system at the corresponding moment, Represents the standard input signal y at time t in the current batch s The derivative of the difference between the actual displacement output of the piezoelectric ceramic system at the current moment.

[0123] In order to verify the effectiveness of the piezoelectric ceramic composite control method based on the improved PI model provided in the embodiment of the present invention, a simulation experiment was also carried out as follows:

[0124] In order to compare the effects, the embodiment of the present invention uses the feedforward control and MPC control methods as the comparison methods of the present invention (ILC-MPC control) under the same experimental conditions. Furthermore, the program is written through simulink, and the triangle wave signal with an amplitude of 20μm and a frequency of 1HZ is input again. The ILC part 1 batch is a 1-cycle triangle wave signal to obtain the simulation results. The error comparison of feedforward control, MPC control, and ILC-MPC control (where the ILC-MPC control error is the error data after 100 seconds) is shown in the figure below. Figure 7 shown.

[0125] from Figure 7 It can be seen that under the input of a 20 μm amplitude triangle wave, the ILC-MPC control algorithm proposed in the present invention has better performance in the case of repetitive motion than the feedforward control and the traditional MPC control.

[0126] In summary, the piezoelectric ceramic composite control method based on the improved PI model provided in the embodiment of the present invention has the following technical innovations and technical advantages:

[0127] 1. Innovation of hysteresis asymmetric model:

[0128] The traditional PI model assumes that the hysteresis curve is symmetrical, which is inconsistent with the hysteresis behavior of actual piezoelectric ceramics, resulting in insufficient model accuracy. The improved PI model proposed in the present invention can more accurately reflect the actual hysteresis characteristics of piezoelectric ceramics, especially its asymmetry and frequency dependence. This improvement makes the improved PI model more in line with the actual situation and improves the accuracy of prediction and control.

[0129] 2. Introduction of rate-related factors:

[0130] The present invention adds a rate-dependent factor, which takes into account the effect of the output frequency on the shape of the hysteresis curve. This is a function that the traditional PI model does not have, and the addition of frequency dependence enables the improved PI model to adapt to dynamic changes under different working conditions, thereby reducing the output displacement error caused by frequency changes.

[0131] 3. Combining the advantages of model predictive control (MPC) and iterative learning control (ILC):

[0132] Model predictive control relies on accurate system transfer functions, but in nonlinear systems such as piezoelectric ceramics, the identification of transfer functions may have large errors, affecting the effect of MPC. Iterative learning control is good at handling errors in repetitive tasks, but its ability to compensate for random errors is limited. The composite control method combining ILC and MPC proposed in the present invention enhances the robustness and adaptability of the system and improves the control performance.

[0133] 4. Improve control accuracy and response speed:

[0134] Through the above improvements, the method of the present invention can accelerate the response speed of the piezoelectric ceramic system while maintaining high control accuracy and reduce the delay caused by hysteresis, which is particularly important for application scenarios that require high-precision positioning and fast response.

[0135] 5. Enhance the robustness and adaptability of the system:

[0136] Since the model and control strategy of the present invention are closer to actual working conditions, they have better robustness and adaptability and can better cope with uncertainties and environmental changes.

[0137] Therefore, the present invention proposes a more comprehensive, flexible and efficient solution through an in-depth understanding and modeling of the hysteresis characteristics of piezoelectric ceramics, as well as the integration and innovation of existing control methods, which significantly improves the control effect of the piezoelectric ceramic driver and embodies high creativity and practicality.

[0138] The method provided in the embodiment of the present invention can be applied to an electronic device. Specifically, the electronic device can be: a desktop computer, a portable computer, an intelligent mobile terminal, a server, etc., which is not limited in the embodiment of the present invention.

[0139] Based on the same inventive concept, an embodiment of the present invention further provides a piezoelectric ceramic composite control device based on an improved PI model. Figure 8 A schematic diagram of the structure of a piezoelectric ceramic composite control device based on an improved PI model provided by an embodiment of the present invention. Figure 8 As shown, it includes: an acquisition unit 801 and a compensation unit 802;

[0140] The acquisition unit 801 is used to: acquire a standard input signal;

[0141] The compensation unit 802 is used to: input the standard input signal into the ILC-MPC control model to obtain the piezoelectric ceramic compensation result; wherein, the ILC-MPC control model is established under the improved PI model using the ILC-MPC composite control method; the improved PI model is established using the improved play operator, and the cubic term and the initial offset term about the standard input signal are added to the non-memory part function; the improved play operator realizes the asymmetric characteristic by changing the slope of the descending section of the operator, and realizes the effect of the shape of the improved play operator changing with the frequency by introducing the derivative about the standard input signal.

[0142] Fig. 9 A structural diagram of a piezoelectric ceramic composite control device based on an improved PI model provided by an embodiment of the present invention includes: a processor 910, a storage medium 920 and a bus 930, wherein the storage medium 920 stores machine-readable instructions executable by the processor 910, and when the piezoelectric ceramic composite control device based on the improved PI model is running, the processor 910 communicates with the storage medium 920 through the bus 930, and the processor 910 executes the machine-readable instructions to execute the steps of the above method embodiment. The specific implementation method and technical effect are similar and will not be repeated here.

[0143] The storage medium may include a random access memory (RAM) or a non-volatile memory (NVM), such as at least one disk storage. Optionally, the storage medium may also be at least one storage device located away from the aforementioned processor.

[0144] The above-mentioned processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components.

[0145] It should be noted that the terms "first", "second", etc. are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchangeable where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. Instead, they are merely examples of devices and methods consistent with some aspects of the present invention.

[0146] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification.

[0147] Although the present invention is described herein in conjunction with various embodiments, in the process of implementing the claimed invention, those skilled in the art can understand and implement other changes of the above disclosed embodiments by viewing the drawings and the disclosed content. In the description of the present invention, the term "comprising" does not exclude other components or steps, "one" or "an" does not exclude multiple situations, and the meaning of "multiple" is two or more, unless otherwise clearly and specifically limited. In addition, certain measures are recorded in different embodiments, but this does not mean that these measures cannot be combined to produce good results.

[0148] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the scope of protection of the present invention.

Claims

1. A piezoelectric ceramic composite control method based on an improved PI model, characterized in that: include: Get standard input signal; The standard input signal is input into the ILC-MPC control model to obtain a piezoelectric ceramic compensation result; wherein, the ILC-MPC control model is established under the improved PI model by using the ILC-MPC composite control method; the improved PI model is established by using an improved play operator, and a cubic term and an initial offset term about the standard input signal are added to the non-memory part function; the improved play operator realizes asymmetric characteristics by changing the slope of the descending segment of the operator, and realizes the effect of the shape of the improved play operator changing with frequency by introducing a derivative about the standard input signal.

2. The piezoelectric ceramic composite control method based on the improved PI model according to claim 1, characterized in that: The improved play operator is expressed as: in, represents the output of the improved play operator with input u at time k, is the derivative of u, u is the standard input signal y s The vector corresponding to the voltage signal obtained by scaling transformation is s Perform enlargement processing with a preset multiple; is the derivative of u at time k, u(k) represents the value of vector u at time k, r represents the threshold of the improved play operator, α represents the first frequency correlation coefficient, β represents the second frequency correlation coefficient, represents the output of the improved play operator with input u at time k-1, b represents the asymmetric factor, u(k-1) represents the value corresponding to the vector u at time k-1, the first frequency correlation coefficient is the frequency correlation coefficient of the improved play operator in the rising stage, and the second frequency correlation coefficient is the frequency correlation coefficient of the improved play operator in the falling stage.

3. The piezoelectric ceramic composite control method based on the improved PI model according to claim 2, characterized in that: The improved PI model is expressed as: P[u](k)=du 3 (k)+au(k)+e Among them, H[u](k) represents the value of the improved PI model when the input is u at time k, represents the value of the memory function when the input is u at time k, P[u](k) represents the value of the non-memory function when the input is u at time k, and p(r i ) is the weight coefficient of the i-th improved play operator, r i is the threshold of the i-th improved play operator, F oi [u](k) is the value of the i-th improved play operator when the input is u at time k, d is the coefficient of the cubic term, and u 3 (k) represents the cubic term with respect to u(k), e represents the initial offset term, and N represents the total number of improved play operators.

4. The piezoelectric ceramic composite control method based on the improved PI model according to claim 1, characterized in that: The construction process of the ILC-MPC control model includes: Obtaining the improved PI model; Performing model inverse transformation on the improved PI model by using a direct inverse method to obtain an inverse model; Performing parameter identification on the inverse model to obtain an inverse model identification result; The linear part of the Hammerstein model is used to construct the state space equation of the piezoelectric ceramic system; The ILC-MPC control model is constructed by using the state space equation, the inverse model identification result and the ILC-MPC control method.

5. The piezoelectric ceramic composite control method based on the improved PI model according to claim 4 is characterized in that: The performing parameter identification on the inverse model to obtain an inverse model identification result includes: The parameters of the inverse model are identified by using a simulated annealing particle swarm optimization algorithm to obtain the inverse model identification result.

6. The piezoelectric ceramic composite control method based on the improved PI model according to claim 4, characterized in that: The linear part of the Hammerstein model is used to construct the state space equations of the piezoelectric ceramic system, including: Generate the system nominal transfer function using the linear part of the Hammerstein model; Discretizing the nominal transfer function of the system to obtain a discrete state space equation; The discrete state space equation is spatially transformed according to a preset transformation rule to obtain the state space equation.

7. The piezoelectric ceramic composite control method based on the improved PI model according to claim 4, characterized in that: The ILC-MPC control model is expressed as: W k (t)=k1u 1,k (t)-k2u M,k (t)+H[y s|k ](t); Among them, W k (t) represents the piezoelectric ceramic compensation result at time t in the kth batch, k1 represents the first weight coefficient, k2 represents the second weight coefficient, H[y s|k ](t) means when the standard input signal is y in the kth batch s The value of the inverse model at time t, u 1,k (t) represents the output of the ILC control process at time t of the kth batch, u M,k (t) represents the control output of the kth batch at time t based on the objective function, and the objective function is constructed based on the quadratic form and the state space equation.

8. The piezoelectric ceramic composite control method based on the improved PI model according to claim 7, characterized in that: The objective function is expressed as: J=(Yy s ) T λ y (Yyy s )+(U F|k -U s ) T λ u (U F|k -U s ); Among them, J represents the output of the objective function, Y represents the predicted output sequence, and y s represents the standard input signal, λ y represents the first positive definite coefficient matrix, λ u represents the second positive definite coefficient matrix, U F|k represents the predicted voltage sequence at time k, U s represents a supplementary matrix, which is used to make the control output u M,k (t) is more gentle, where Y and U F|k Constructed based on the state space equation; And=[and k T (k+1) and k T (k+2) … and k T (k+Np)] T ; Among them, y k (k+1) represents the predicted output of the piezoelectric ceramic system corresponding to the first input interval after time k, y k (k+2) represents the predicted output of the piezoelectric ceramic system corresponding to the second input interval after time k, y k (k+Np) represents the predicted output of the piezoelectric ceramic system corresponding to the Npth input interval after time k, and Np represents the number of prediction steps.

9. A piezoelectric ceramic composite control device based on an improved PI model, characterized in that: include: Acquisition unit and compensation unit; The acquisition unit is used to: acquire a standard input signal; The compensation unit is used to: input the standard input signal into the ILC-MPC control model to obtain a piezoelectric ceramic compensation result; wherein the ILC-MPC control model is established under the improved PI model using the ILC-MPC composite control method; the improved PI model is established using an improved play operator, and a cubic term and an initial offset term with respect to the standard input signal are added to the non-memory part function; the improved play operator realizes asymmetric characteristics by changing the slope of the descending segment of the operator, and realizes the effect of the shape of the improved play operator changing with frequency by introducing a derivative with respect to the standard input signal.

10. A piezoelectric ceramic composite control device based on an improved PI model, characterized in that: include: A processor, a storage medium and a bus, wherein the storage medium stores machine-readable instructions executable by the processor, and when the piezoelectric ceramic composite control device based on the improved PI model is running, the processor communicates with the storage medium through the bus, and the processor executes the machine-readable instructions to perform the steps of the piezoelectric ceramic composite control method based on the improved PI model as described in any one of claims 1 to 8.

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