Piezoelectric ceramic composite control method and device based on improved pi model

Abstract

The application provides a piezoelectric ceramic composite control method and device based on an improved PI model. The method comprises the following steps: 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 by using an ILC-MPC composite control method under an improved PI model; 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 in a 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 that the shape of the improved play operator changes with the frequency by introducing the derivative about the standard input signal; based on the method, the steady-state error can be effectively suppressed while ensuring fast response, and the stability and control precision of the piezoelectric ceramic system are improved.

Description

Technical Field

[0001] This invention relates to the field of precision drive and control technology, specifically to a piezoelectric ceramic composite control method and device based on an improved PI model. Background Technology

[0002] In precision manufacturing, optical positioning, and micro / nano manipulation, piezoelectric ceramic-driven micro-motion platforms have become indispensable precision drive components due to their high precision, frictionless operation, and compact structure. However, the inherent hysteresis nonlinearity of piezoelectric ceramics severely affects the accuracy of their displacement output. This characteristic can cause errors of up to 50% of the platform's travel, significantly limiting their performance in high-precision applications. To improve system performance, a displacement amplification mechanism is typically used to increase the output displacement of the piezoelectric ceramic. However, this further exacerbates the hysteresis nonlinearity effect, not only reducing system accuracy but also potentially leading to instability in the control system, severely impacting the positioning accuracy and dynamic response capability of the micro-motion platform. Therefore, effectively compensating for the hysteresis nonlinearity of piezoelectric ceramics has become a key technical challenge for improving the performance of micro-motion platforms.

[0003] For the hysteresis nonlinearity problem of piezoelectric ceramics, both academia and industry generally adopt a strategy combining modeling and compensation control. Among these, phenomenological models have become the mainstream research and application direction due to their accurate prediction of hysteresis effects. Within phenomenological models, the Prandtl-Ishlinskii (PI) model is favored for its simple structure and high modeling efficiency. The PI model, through a series of weighted threshold functions, can effectively describe the hysteresis behavior of piezoelectric ceramics, providing a foundation for designing effective hysteresis compensation controllers. By combining PI-based inverse model feedforward control with other feedback control methods (such as PID control, fuzzy control, and neural network control), the displacement error caused by hysteresis can be significantly reduced, improving the system's control accuracy.

[0004] While the PI model has achieved significant 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 exhibits asymmetry, causing traditional PI models to fail to accurately fit actual hysteresis behavior, thus affecting the compensation effect. Furthermore, as the output frequency of the piezoelectric ceramic increases, the hysteresis curve changes, and traditional PI models lack dynamic adaptability, failing to automatically adjust model parameters according to changes in output frequency, leading to increased displacement errors at high-frequency outputs. Regarding control strategies, although Model Predictive Control (MPC) is widely used as an optimal control method for piezoelectric ceramic control, its performance is highly dependent on the accuracy of the system transfer function. When there are errors in the identification of the piezoelectric ceramic transfer function, the optimal control performance of MPC is difficult to guarantee, limiting its application in complex dynamic environments. Therefore, exploring more accurate and adaptive hysteresis modeling and control methods is of great significance for improving the performance of piezoelectric ceramic-driven micro-motion platforms. Summary of the Invention

[0005] To address the aforementioned problems in the prior art, this invention provides a piezoelectric ceramic composite control method and apparatus based on an improved PI model.

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

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

[0008] Obtain the standard input signal;

[0009] The standard input signal is input into the ILC-MPC control model to obtain the piezoelectric ceramic compensation result. The ILC-MPC control model is established by using the ILC-MPC composite control method under the improved PI model. The improved PI model is established using the 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 achieves asymmetric characteristics by changing the slope of the operator's falling segment, and the shape of the improved play operator changes with frequency by introducing the derivative with respect to the standard input signal.

[0010] Alternatively, the improved play operator can be represented as:

[0011]

[0012] in, Let represent the output of the improved play operator with input u at time k. Let y be the derivative of u, where u is the standard input signal y.s The voltage signal vector obtained by scaling is the vector corresponding to the standard input signal y. s Perform a pre-defined multiplier amplification process; Let u(k) be the derivative of u at time k, where 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, and β represents the second frequency correlation coefficient. Let represent the output of the improved play operator with input u at time k-1, b represent the asymmetric factor, u(k-1) represent the value of vector u at time k-1, the first frequency correlation coefficient is the frequency correlation coefficient of the improved play operator in the rising phase, and the second frequency correlation coefficient is the frequency correlation coefficient of the improved play operator in the falling phase.

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

[0014]

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

[0016] Where H[u](k) represents the value of the improved PI model at time k when the input is u. P[u](k) represents the value of the memory function when the input is u at time k, and P[u](k) represents the value of the non-memory function when the input is u at time k. i ) represents the weight coefficients of the i-th improved play operator, r i For the threshold of the i-th improved play operator, F oi [u](k) represents the value of the i-th improved play operator when the input is u at time k, and d represents the coefficient of the cubic term. 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] Obtain an improved PI model;

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

[0020] Parameter identification is performed on the inverse model to obtain the inverse model identification results;

[0021] The state-space equations of the piezoelectric ceramic system are constructed using the linear part of the Hammerstein model;

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

[0023] Optionally, parameter identification is performed on the inverse model to obtain the inverse model identification result, including:

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

[0025] Optionally, the state-space equations of the piezoelectric ceramic system are constructed using the linear part of the Hammerstein model, including:

[0026] The nominal transfer function of the system is generated using the linear part of the Hammerstein model;

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

[0028] The discrete state-space equations are transformed according to a preset transformation rule to obtain the state-space equations. Optionally, the ILC-MPC control model is represented as follows:

[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 k-th batch, where k1 represents the first weighting coefficient, k2 represents the second weighting coefficient, and H[y s|k ](t) represents the standard input signal y in the k-th batch. s The value of the inverse model at time t, u 1,k (t) represents the output of the ILC partial control process at time t in the kth batch, u M,k (t) represents the control output based on the objective function at time t of the kth batch. The objective function is constructed based on the quadratic form and the state-space equation.

[0031] Alternatively, the objective function can be 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] Where J represents the output of the objective function, Y represents the predicted output sequence, and y s λ represents the standard input signal. y Let λ represent the first positive definite coefficient matrix. u U represents the second positive definite coefficient matrix. F|k U represents the predicted voltage sequence at time k. s This represents the supplementary matrix, which is used to adjust the control output u. M,k (t) is more gradual, where Y and U F|k It is constructed based on the state-space equations;

[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 Np-th input interval after time k, where Np represents the prediction step.

[0036] Secondly, 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 the 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 by using the ILC-MPC composite control method under the improved PI model; the improved PI model is established using the 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 achieves asymmetric characteristics by changing the slope of the falling segment of the operator, and achieves the effect of the improved play operator's shape changing with frequency by introducing the derivative with respect to the standard input signal.

[0039] Thirdly, 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. 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 communicates with the storage medium 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 described in the first aspect above.

[0040] This invention provides a piezoelectric ceramic composite control method and apparatus based on an improved PI model. The piezoelectric ceramic composite control method based on the improved PI model includes: acquiring a standard input signal; inputting the standard input signal into an ILC-MPC control model to obtain piezoelectric ceramic compensation results; wherein the ILC-MPC control model is established using the ILC-MPC composite control method under the improved PI model; 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 of the function; the improved play operator achieves asymmetric characteristics by changing the slope of the falling segment of the operator, and the shape of the improved play operator changes with frequency by introducing a derivative with respect to the standard input signal. In this invention, the improved PI model, with its asymmetric and frequency-dependent characteristics, 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. Furthermore, the proposed ILC-MPC composite control method combines the advantages of iterative learning and model predictive control, effectively suppressing steady-state errors while ensuring fast response, 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. Attached Figure Description

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

[0043] Figure 2 A schematic diagram of the improved play operator is shown as an example;

[0044] Figure 3 An exemplary schematic diagram of the classic play operator is shown;

[0045] Figure 4 An exemplary diagram of the fitting results for the improved PI model when the input frequency is 10Hz is shown.

[0046] Figure 5An exemplary diagram shows the fitting results of the improved PI model when the input frequency is 50Hz.

[0047] Figure 6 An exemplary diagram of the inverse model prediction output is shown when the input frequency is 1Hz.

[0048] Figure 7 An exemplary comparison of simulation results between the ILC-MPC control method of the present invention and existing control methods is shown;

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

[0050] Figure 9 This is a schematic diagram of a piezoelectric ceramic composite control device based on an improved PI model, provided as an embodiment of the present invention. Detailed Implementation

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

[0052] To improve the compensation accuracy and adaptability of piezoelectric ceramic systems to standard input signals, this invention provides a piezoelectric ceramic composite control method based on an improved PI model. Figure 1 This is a schematic flowchart illustrating a piezoelectric ceramic composite control method based on an improved PI model, provided as an embodiment of the present invention. Figure 1 As shown, the method includes:

[0053] S101, Obtain the standard input signal.

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

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

[0056] The ILC-MPC control model is established by using the ILC-MPC composite control method under the improved PI model. The improved PI model is established using the 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 achieves asymmetric characteristics by changing the slope of the falling segment of the operator, and the shape of the improved play operator changes with frequency by introducing the derivative with respect to the standard input signal.

[0057] Alternatively, the improved play operator can be represented as:

[0058]

[0059] in, Let represent the output of the improved play operator with input u at time k. Let y be the derivative of u, where u is the standard input signal y. s The voltage signal vector obtained by scaling is the vector corresponding to the standard input signal y. s Perform a pre-defined multiplier amplification process; Let u(k) be the derivative of u at time k, where 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, and β represents the second frequency correlation coefficient. Let represent the output of the improved play operator with input u at time k-1, b represent the asymmetric factor, u(k-1) represent the value of vector u at time k-1, the first frequency correlation coefficient is the frequency correlation coefficient of the improved play operator in the rising phase, and the second frequency correlation coefficient is the frequency correlation coefficient of the improved play operator in the falling phase.

[0060] In this embodiment of the invention, to give the improved PI model asymmetric and frequency-dependent characteristics, the memory and non-memory parts of the PI model are improved. Regarding the memory part, since the piezoelectric ceramic hysteresis curve does not involve the negative half-region, the negative part of the play operator is simplified, retaining only the first quadrant portion. An asymmetric factor is introduced to change the slope of the play operator. Figure 2 A schematic diagram of the improved play operator is shown as an example. In contrast, Figure 3 An exemplary schematic diagram of the structure of an existing play operator is shown. Figure 2 The curve exhibits significant asymmetry, while Figure 3 The curve can only achieve symmetrical characteristics. Since the hysteresis curve of piezoelectric ceramics has an asymmetrical shape in real-world scenarios, the improved play operator of this invention is more suitable for practical applications.

[0061] Furthermore, to achieve frequency-dependent characteristics, the play operator is divided into two parts: a rising phase and a falling phase. 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 derivative of the input voltage changes with the input frequency, and the improved play operator exhibits frequency-dependent characteristics.

[0062] Furthermore, based on the improved play operator, a cubic term with respect to the input and an initial offset term are added to the non-memory part function to enhance its nonlinear fitting ability, resulting in an improved PI model. By adding a rate correlation factor, the entire improved PI model can change with frequency, giving it frequency-dependent characteristics.

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

[0064]

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

[0066] Where H[u](k) represents the value of the improved PI model at time k when the input is u. P[u](k) represents the value of the memory function when the input is u at time k, and P[u](k) represents the value of the non-memory function when the input is u at time k. i ) represents the weight coefficients of the i-th improved play operator, r i For the threshold of the i-th improved play operator, F oi [u](k) represents the value of the i-th improved play operator when the input is u at time k, and d represents the coefficient of the cubic term. 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] This invention provides a piezoelectric ceramic composite control method based on an improved PI model, comprising: acquiring a standard input signal; inputting the standard input signal into an ILC-MPC control model to obtain piezoelectric ceramic compensation results; wherein, the ILC-MPC control model is established using the ILC-MPC composite control method under the improved PI model; 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 achieves asymmetric characteristics by changing the slope of the falling segment of the operator, and achieves the effect of the improved play operator's shape changing with frequency by introducing a derivative with respect to the standard input signal. In this invention, because the improved PI model has asymmetric and frequency-dependent characteristics, it can more accurately describe the hysteresis phenomenon of piezoelectric ceramics, improving the compensation accuracy and adaptability of the piezoelectric ceramic system to the standard input signal; in addition, because 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 fast response, further improving the stability and control accuracy of the system.

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

[0069] Obtain an improved PI model;

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

[0071] Parameter identification is performed on the inverse model to obtain the inverse model identification results;

[0072] The state-space equations of the piezoelectric ceramic system are constructed using the linear part of the Hammerstein model;

[0073] The ILC-MPC control model is constructed by combining state-space equations, inverse model identification results, and the 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 for the piezoelectric ceramics. Specifically, since the play operator of the improved PI model has been modified in the above steps, the traditional analytical method for finding the inverse formula is no longer applicable. Therefore, a direct inverse method is adopted to identify the inverse model based on experimental data, and the inverse model is directly used to describe the relationship between displacement and voltage.

[0075] In this invention, the control algorithm employs an ILC-MPC composite control method, which combines the advantages of MPC (Model Predictive) control and learning-based control algorithms. Since the MPC control algorithm requires the system's transfer function to calculate algorithm parameters, the piezoelectric ceramic transfer function uses the linear portion of the Hammerstein model.

[0076] After obtaining the nominal transfer function of the system, the discrete-form state-space equation of the piezoelectric ceramic is established. By performing relevant transformations on the discrete-space equation, the state vectors of other steps can be obtained using a recursive method. The desired control output u can be obtained by minimizing the objective function. M,k (t). Furthermore, since the model predictive control part of the ILC-MPC control model can be considered a proportional term, it may lead to steady-state error. To suppress this error, an integral term and a feedforward term composed of the aforementioned inverse model can be added. Finally, the idea of ​​iterative learning is introduced to construct the ILC-MPC control method, enabling the system to exhibit better performance in repetitive scanning motions. The specific execution steps are as follows:

[0077] Optionally, parameter identification is performed on the inverse model to obtain the inverse model identification result, including:

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

[0079] It should be noted that optimization algorithms are needed to identify the parameters of the hysteresis model. Since traditional particle swarm optimization algorithms are prone to getting trapped in local optima, especially when identifying a large number of parameters, this invention utilizes simulated annealing particle swarm optimization for parameter identification to avoid this trap. The parameter identification results are obtained by continuously adjusting the optimization algorithm parameters. For example, Figure 4 An exemplary diagram of the fitting results for the improved PI model when the input frequency is 10Hz is shown. Figure 5 An exemplary diagram of the fitting results for the improved PI model when the input frequency is 50Hz is shown. Figure 6 An exemplary diagram illustrating the inverse model prediction output when the input frequency is 1Hz is shown. Figures 4-6 As can be seen, the improved PI model and inverse model provided in this embodiment of the invention can effectively fit the actual output and maintain a high degree of consistency with the curve of the actual output, thus verifying the effectiveness of the improved PI model provided in this embodiment of the invention.

[0080] Optionally, the state-space equations of the piezoelectric ceramic system are constructed using the linear part of the Hammerstein model, including:

[0081] The nominal transfer function of the system is generated using the linear part of the Hammerstein model;

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

[0083] The discrete state-space equations are transformed according to the preset transformation rules to obtain the state-space equations.

[0084] In this embodiment of the invention, the corresponding discrete state-space equation can be obtained from the nominal transfer function of the system through the Laplace transform. The nominal transfer function of the system can be expressed as:

[0085]

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

[0087] After obtaining the nominal transfer function of the system, it can be discretized to obtain the discrete state-space equation, which 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, and u(k) represents the value of vector u at time k. d Let B represent the first state matrix. d Let C represent the second state matrix. d Let A represent the third state matrix. d B d C d The value can be obtained from the coefficients of the system's nominal transfer function.

[0090] The discrete state-space equations are transformed as follows, let:

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

[0092] Where, x s(k) represents the state vector of the transformed discrete state-space equation, 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 vector u at time k-1, u(k-m+1) represents the value of vector u at time k-m+1, and 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] Where 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 derived from A d B d C d After a certain transformation, it is obtained as follows:

[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] Therefore, the state vector after the current time step can be obtained recursively:

[0101]

[0102] Where, x s|k (k+Np) is the state-space vector after the Np-th input interval following time k, u k (k+i) represents the value of vector u after i input intervals following 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+1)th input interval after time k, u k (k+Np-1) represents the value of vector u corresponding to the (k+Np-1)th input interval after time k.

[0110] Based on the transformed state-space equations, the predicted displacement output matrix Y of 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 Np-th input interval after time k, where Np represents the prediction step number, and C... m (n+m-1)×N p The diagonal matrix is ​​denoted by C, 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 represented 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 k-th batch, where k1 represents the first weighting coefficient, k2 represents the second weighting coefficient, and H[y s|k ](t) represents the standard input signal y in the k-th batch. s The value of the inverse model at time t, u 1,k (t) represents the output of the ILC partial control process at time t in the kth batch, u M,k (t) represents the control output based on the objective function at time t of the k-th batch, specifically, u M,k (t) represents the output of the Model Predictive Control (MPC) part 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] Alternatively, the objective function can be 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] Where J represents the output of the objective function, Y represents the predicted output sequence, and y s λ represents the standard input signal. y Let λ represent the first positive definite coefficient matrix. u U represents the second positive definite coefficient matrix. F|k U represents the predicted voltage sequence at time k. s This represents the supplementary matrix, which is used to adjust the control output u. M,k (t) is more gradual. Minimizing J yields the corresponding control output u. M,k The value of (t). u M,k (t) is U F|k The first element, u M,k The calculation process of (t) is based on the MPC control method.

[0120] Because errors may exist in identifying the inverse model and the system's nominal transfer function, and because the piezoelectric ceramic drive system has uncertainties, and because in practical applications the piezoelectric ceramic always performs its function through scanning motion, the idea of ​​iterative learning is introduced to design the ILC-MPC control method to solve for u. 1,k (t):

[0121]

[0122] In the formula, u 1,k (t) represents the output of the ILC part calculated at time t in the kth batch, u 1,k-1 (t) represents the output of the ILC part calculated at time t in the (k-1)th batch. The derivative of the error at time t in the (k-1)th batch. Let γ be the derivative of the error at time t for the k-th batch, γ be the learning coefficients for batches prior to the current batch, η be the learning coefficients for the iteration error of the current batch, and the error represent the standard input signal y. s The difference between the actual displacement output y of the piezoelectric ceramic system at the corresponding moment and the value of the difference between the actual displacement output y of the piezoelectric ceramic system at the corresponding moment. This represents the standard input signal y at time t in the current batch. s The derivative of the difference between the current displacement output of the piezoelectric ceramic system and the actual displacement output at the current moment.

[0123] To verify the effectiveness of the piezoelectric ceramic composite control method based on the improved PI model provided in this embodiment of the invention, simulation experiments were also conducted, as follows:

[0124] To compare the effects, under the same experimental conditions, this embodiment of the invention uses feedforward control and MPC control methods as comparison methods for this invention (ILC-MPC control). Further, a program was written in Simulink, and a triangular wave signal with an amplitude of 20 μm and a frequency of 1 Hz was input again. The ILC part used a one-cycle triangular wave signal in one batch, and simulation results were obtained. The comparison graph of the errors of feedforward control, MPC control, and ILC-MPC control (where the error of ILC-MPC control is the error data after 100 seconds) is shown below. Figure 7 As shown.

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

[0126] In summary, the piezoelectric ceramic composite control method based on an improved PI model provided by this invention has the following technical innovations and advantages:

[0127] 1. Innovation of the hysteresis asymmetric model:

[0128] Traditional PI models assume a symmetrical hysteresis curve, which does not match the actual hysteresis behavior of piezoelectric ceramics, leading to insufficient model accuracy. The improved PI model proposed in this invention can more accurately reflect the actual hysteresis characteristics of piezoelectric ceramics, particularly their asymmetry and frequency dependence. This improvement makes the PI model more closely resemble reality, enhancing the accuracy of prediction and control.

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

[0130] This invention incorporates a rate dependence factor, which takes into account the influence of output frequency on the shape of the hysteresis curve. This is a feature not found in traditional PI models, and the addition of frequency dependence allows the improved PI model to adapt to dynamic changes under different operating conditions, thereby reducing output displacement errors caused by frequency variations.

[0131] 3. Combining the advantages of Model Predictive Control (MPC) and Iterative Learning Control (ILC):

[0132] Model predictive control relies on an accurate system transfer function, but in nonlinear systems such as piezoelectric ceramics, the identification of the transfer function can contain significant errors, affecting the performance of MPC. Iterative learning control excels at handling errors in repetitive tasks, but its ability to compensate for random errors is limited. This invention proposes a composite control method combining ILC and MPC, which enhances the robustness and adaptability of the system and improves control performance.

[0133] 4. Improve control precision 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 especially important for application scenarios that require high-precision positioning and fast response.

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

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

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

[0138] The method provided in this embodiment of the invention can be applied to electronic devices. Specifically, the electronic device can be a desktop computer, a portable computer, a smart mobile terminal, a server, etc., and this embodiment of the invention does not limit the application to such devices.

[0139] Based on the same inventive concept, embodiments of the present invention also provide a piezoelectric ceramic composite control device based on an improved PI model. Figure 8 This is a schematic diagram of a piezoelectric ceramic composite control device based on an improved PI model, provided as an embodiment of the present invention. Figure 8 As shown, it includes: an acquisition unit 801 and a compensation unit 802;

[0140] 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 by using the ILC-MPC composite control method under the improved PI model; the improved PI model is established by using the 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 achieves asymmetric characteristics by changing the slope of the falling segment of the operator, and achieves the effect of the shape of the improved play operator changing with frequency by introducing the derivative with respect to the standard input signal.

[0142] Figure 9 A schematic diagram of a piezoelectric ceramic composite control device based on an improved PI model, provided in an embodiment of the present invention, includes: a processor 910, a storage medium 920, and a bus 930. The storage medium 920 stores machine-readable instructions executable by the processor 910. When the piezoelectric ceramic composite control device based on the improved PI model is running, the processor 910 and the storage medium 920 communicate via the bus 930. The processor 910 executes the machine-readable instructions to perform the steps of the above-described method embodiment. Specific implementation methods and technical effects are similar and will not be repeated here.

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

[0144] The processors mentioned above can be general-purpose processors, including central processing units (CPUs), network processors (NPs), etc.; they can also be digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, or 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 such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders 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. Rather, they are merely examples of apparatuses and methods consistent with some aspects of the invention.

[0146] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions 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 suitable manner in one or more embodiments or examples. Furthermore, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0147] Although the invention has been described herein in conjunction with various embodiments, those skilled in the art, by reviewing the accompanying drawings and the disclosure, will understand and implement other variations of the disclosed embodiments in carrying out the claimed invention. In the description of the invention, the word "comprising" does not exclude other components or steps, "a" or "an" does not exclude a plurality, and "a plurality" means two or more, unless otherwise explicitly specified. Furthermore, while different embodiments may describe certain measures, this does not mean that these measures cannot be combined to produce good results.

[0148] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the inventive concept, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A piezoelectric ceramic compound control method based on an improved PI model, characterized by, The method comprises the following steps: acquiring a standard input signal; inputting the standard input signal into an ILC-MPC control model to obtain a piezoceramic compensation result; wherein the ILC-MPC control model is established by using an ILC-MPC compound control method under an improved PI model; 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 in a non-memory part function; the improved play operator realizes an asymmetric characteristic by changing the slope of a descending segment of the operator, and realizes the shape change effect of the improved play operator with frequency by introducing a derivative about the standard input signal; wherein the improved play operator is expressed as: ； wherein, denotes the output of the improved play operator at time , is the derivative of , is the vector corresponding to the voltage signal obtained by scaling transformation of the standard input signal , the scaling transformation is an expansion processing of the standard input signal by a preset multiple; is the derivative of at time , denotes the value corresponding to the vector at time denotes the threshold of the improved play operator, denotes a first frequency correlation coefficient, denotes a second frequency correlation coefficient, denotes the output of the improved play operator at time , denotes an asymmetry factor, denotes the value corresponding to the vector at time, the first frequency correlation coefficient is a frequency correlation coefficient of the improved play operator in the rising stage, and the second frequency correlation coefficient is a frequency correlation coefficient of the improved play operator in the falling stage. the construction process of the ILC-MPC control model comprises: acquiring the improved PI model; performing model inversion on the improved PI model by using a direct inversion method to obtain an inverse model; performing parameter identification on the inverse model to obtain an inverse model identification result; constructing a state space equation of a piezoceramic system by using a linear part of a Hammerstein model; constructing the ILC-MPC control model by using the state space equation, the inverse model identification result and an ILC-MPC control method.

2. The piezoceramic compound control method based on the improved PI model according to claim 1, characterized in that, The improved PI model is expressed as: ； wherein denotes the input at time the value of the improved PI model at time denotes the input at time the value of the memory function at time denotes the input at time the value of the non-memory function at time is the weight coefficient of the th improved play operator, is the threshold value of the th improved play operator, is the input at time is the value of the th improved play operator at time denotes the coefficient of the cubic term, denotes the cubic term with respect to denotes the initial offset term, denotes the total number of improved play operators.​ 3. The piezoceramic compound control method based on the improved PI model according to claim 1, characterized in that, the parameter identification on the inverse model to obtain the inverse model identification result comprises: performing parameter identification on the inverse model by using a simulated annealing particle swarm optimization algorithm to obtain the inverse model identification result.

4. The piezoceramic compound control method based on the improved PI model according to claim 1, characterized in that, constructing a state space equation of a piezoceramic system by using a linear part of a Hammerstein model comprises: generating a nominal transfer function of the system by using the linear part of the Hammerstein model; performing discretization processing on the nominal transfer function of the system to obtain a discrete state space equation; performing space transformation on the discrete state space equation according to a preset transformation rule to obtain the state space equation.

5. The piezoceramic compound control method based on the improved PI model according to claim 1, wherein, The ILC-MPC control model is expressed as: ； wherein, represents the first batch at the time instant t, represents the first weight coefficient, represents the second weight coefficient, represents the first batch when the standard input signal is the value of the inverse model at the time instant t, represents the first batch at the time instant t, represents the first batch at the time instant t, the control output based on an objective function constructed based on a quadratic form and the state space equation.

6. The piezoceramic compound control method based on the improved PI model according to claim 5, characterized in that, the objective function is expressed as: ； wherein denotes the output of the objective function, denotes the predicted output sequence, denotes the standard input signal, denotes a first positive definite coefficient matrix, denotes a second positive definite coefficient matrix, denotes the predicted voltage sequence at time instant t, denotes a supplementary matrix for making the control output more smooth, wherein and are constructed based on the state space equation; ； wherein, represents the predicted output of the piezoceramic system corresponding to the input interval after the time instant, represents the predicted output of the piezoceramic system corresponding to the input interval after the time instant, represents the predicted output of the piezoceramic system corresponding to the input interval after the time instant, represents the prediction step number.

7. A piezoelectric ceramic compound control device based on an improved PI model, characterized by, The method comprises the following steps: an acquisition unit and a compensation unit; the acquisition unit is configured to acquire a standard input signal; the compensation unit is configured to input the standard input signal into an ILC-MPC control model to obtain a piezoceramic compensation result; wherein the ILC-MPC control model is established by using an ILC-MPC compound control method under an improved PI model; 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 in a non-memory part function; the improved play operator realizes an asymmetric characteristic by changing the slope of a descending segment of the operator, and realizes the shape change effect of the improved play operator with frequency by introducing a derivative about the standard input signal; wherein the improved play operator is expressed as: ； wherein, denotes the derivative of the output of the improved play operator at time is is is the vector corresponding to the voltage signal obtained by scaling transformation of the standard input signal , the scaling transformation being an expansion of the standard input signal by a preset multiple; is the derivative of at time denotes the value of the vector at time denotes the threshold of the improved play operator, denotes a first frequency correlation coefficient, denotes a second frequency correlation coefficient, denotes the output of the improved play operator at time denotes an asymmetry factor, denotes the value of the vector at time , the first frequency correlation coefficient being a frequency correlation coefficient of the improved play operator in the rising phase, and the second frequency correlation coefficient being a frequency correlation coefficient of the improved play operator in the falling phase. the construction process of the ILC-MPC control model comprises: acquiring the improved PI model; performing model inversion on the improved PI model by using a direct inversion method to obtain an inverse model; Parameter identification is performed on the inverse model to obtain an inverse model identification result; A state space equation of the piezoceramic system is constructed using a linear part of a Hammerstein model; An ILC-MPC control model is constructed using the state space equation, the inverse model identification result, and an ILC-MPC control method.

8. A piezoelectric ceramic compound control device based on an improved PI model, characterized by, Comprise: A processor, a storage medium, and a bus, the storage medium storing machine readable instructions executable by the processor, when the piezoceramic composite control equipment based on the improved PI model is running, the processor and the storage medium communicate through the bus, and the processor executes the machine readable instructions to perform the steps of the piezoceramic composite control method based on the improved PI model in any one of claims 1-6.

Images