A high-precision model identification method, device and medium for piezoelectric ceramic system

Abstract

The present invention discloses a high-precision model identification method, device, and medium for a piezoelectric ceramic system. A static hysteresis nonlinear model is constructed, updated output data is obtained based on the trained static hysteresis nonlinear model, and the Hankel matrix correlation analysis method is used to perform model identification on the dynamic characteristics of the piezoelectric ceramic system to obtain a transfer function model of the high-order dynamic characteristics of the piezoelectric ceramic. The trained static hysteresis nonlinear model and the transfer function model are connected in series to obtain a high-precision model of the piezoelectric ceramic. The static hysteresis characteristics of the piezoelectric ceramic are accurately described by separating the hysteresis characteristics from the rate-dependent characteristics of the hysteresis. The Hankel matrix correlation analysis method is used to highly restore the rate-dependence of the hysteresis characteristics of the material, simplifying the identification process and calculation. The Hankel matrix method can accurately fit the high-order dynamic characteristics of the system, overcoming the shortcomings of traditional methods such as low model bandwidth, poor accuracy, and computational difficulties.

Description

Technical Field

[0001] The present invention relates to the field of automation, and in particular to a high-precision model identification method, equipment and medium for a piezoelectric ceramic system. Background Art

[0002] Smart materials such as piezoelectric ceramics are widely used in precision positioning, precision manufacturing, and micro-amplitude active vibration control. However, piezoelectric smart devices exhibit significant hysteresis nonlinearity in the input-output relationship, along with a pronounced lead-off characteristic. This not only reduces system control accuracy but can also lead to instability or oscillation in closed-loop systems. The high-frequency resonant modes of piezoelectric actuators / drivers are difficult to accurately describe, resulting in low bandwidth and inadequate accuracy in the established mathematical models. Therefore, high-precision modeling methods are crucial for achieving ultra-high-precision tracking and high-performance micro- and nano-scale vibration control. Summary of the Invention

[0003] The technical problem to be solved by the present invention is that the existing piezoelectric ceramic system modeling method is difficult to accurately describe the rate-dependent nonlinearity of smart materials, the established mathematical model has low bandwidth and the model accuracy is far from enough. The purpose is to provide a high-precision model identification method, equipment and medium for a piezoelectric ceramic system, which separates the hysteresis characteristics of the piezoelectric ceramic from the rate-dependent characteristics of the hysteresis, accurately describes the static hysteresis characteristics of the piezoelectric ceramic, and uses the Hankel matrix correlation analysis method to highly restore the rate correlation of the hysteresis characteristics of the material. This separation design simplifies the identification process and calculation, and the Hankel matrix method can fit the high-order dynamic characteristics of the system with high precision, overcoming the shortcomings of the traditional method of low model bandwidth, poor accuracy and difficulty in calculation.

[0004] The present invention is achieved through the following technical solutions:

[0005] A first aspect of the present invention provides a high-precision model identification method for a piezoelectric ceramic system, comprising the following specific steps:

[0006] S1. Obtain input and output data of the piezoelectric ceramic system, construct an input-output characteristic curve, and obtain a static nonlinear portion of the input-output characteristic curve;

[0007] S2. Constructing a static hysteresis nonlinear model and training the static hysteresis nonlinear model using a low-frequency sinusoidal driving signal that causes the piezoelectric ceramic to exhibit static nonlinearity;

[0008] S3. Obtain updated output data based on the trained static hysteresis nonlinear model, use Hankel matrix correlation analysis method to perform model identification on the dynamic characteristics of the piezoelectric ceramic system, and obtain a transfer function model of the high-order dynamic characteristics of the piezoelectric ceramic;

[0009] S4. Connect the trained static hysteresis nonlinear model and the transfer function model of high-order dynamic characteristics in series to obtain a high-precision model of piezoelectric ceramics.

[0010] The present invention separates the hysteresis characteristics of piezoelectric ceramics from the rate-dependent characteristics of the hysteresis, accurately describes the static hysteresis characteristics of piezoelectric ceramics, and uses the Hankel matrix correlation analysis method to highly restore the rate-dependence of the hysteresis characteristics of the material. This separation design simplifies the identification process and calculation, and the Hankel matrix method can fit the high-order dynamic characteristics of the system with high precision, overcoming the shortcomings of traditional methods such as low model bandwidth, poor accuracy, and difficult calculations.

[0011] Furthermore, the obtaining of input and output data of the piezoelectric ceramic system specifically includes:

[0012] Build an experimental platform for piezoelectric ceramic systems;

[0013] Generating sinusoidal input signals of different frequencies within the operating frequency range through the experimental platform, wherein the sinusoidal input signals act on the piezoelectric actuator through the driver, causing the piezoelectric effect and generating deformation;

[0014] The deformation is measured by a sensor and data of the output signal is collected through a power amplifier.

[0015] Furthermore, the training of the static hysteresis nonlinear model by using a low-frequency sinusoidal driving signal that causes the piezoelectric ceramic to exhibit static nonlinearity specifically includes:

[0016] The hysteresis operator model is introduced to extend the input operator EHO of the neural network;

[0017] Input the input signal into the operator EHO to obtain the output sequence of the hysteresis operator model;

[0018] The output sequence and input signal of the operator EHO are used as the input sample data of the neural network to be trained, and the output signal is used as the output sample data of the neural network to be trained;

[0019] Determine the number of layers and nodes of the neural network, and use sample input data and sample output data to train the BP neural network;

[0020] The operator EHO is connected in series with the trained neural network to obtain the trained static hysteresis nonlinear model.

[0021] Furthermore, obtaining updated output data according to the trained static hysteresis nonlinear model includes:

[0022] The analytical inverse of the trained static hysteresis nonlinear model is obtained as an inverse compensation controller. The hysteresis inverse compensation controller is connected in series before the test system, and a pseudo-random signal is input to the entire system to obtain updated output data.

[0023] Furthermore, obtaining the updated output data includes:

[0024] The pseudo-random signal includes two cycles, and the third cycle of the pseudo-random signal is set to zero;

[0025] Add a bias to the input signal so that its amplitude is greater than 0.

[0026] Furthermore, the S3 specifically includes:

[0027] Acquire a pseudorandom signal and updated output data, determine a pseudorandom signal correlation sequence and an updated output data correlation sequence, wherein the updated data correlation sequence is calculated using a two-cycle pseudorandom sequence and a one-cycle all-0 sequence as input data;

[0028] According to the two obtained correlation sequences, the impulse response of the discrete linear system model when the initial state is zero is estimated;

[0029] Constructing a Hankel matrix based on the impulse response, performing singular value decomposition on the Hankel matrix, determining the system order and obtaining a relationship between the state space description of the linear dynamic system and the Hankel matrix;

[0030] The transfer function model of the high-order dynamic characteristics of the piezoelectric ceramic is obtained according to the relationship.

[0031] Furthermore, performing singular value decomposition on the Hankel matrix includes: determining the system order according to the singular value characteristics, and decomposing the Hankel matrix singular values into an input matrix and an output matrix described in the linear system state space.

[0032] Furthermore, the method further includes: constructing a new Hankel matrix and performing singular value decomposition on the new Hankel matrix to obtain a system matrix of the state space model.

[0033] A second aspect of the present invention provides an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor is used to implement a high-precision model identification method for a piezoelectric ceramic system when executing the program.

[0034] A third aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, is used to implement a high-precision model identification method for a piezoelectric ceramic system.

[0035] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0036] 1. The dynamic hysteresis nonlinear characteristics are divided into two parts, the static nonlinear link and the dynamic linear link, which greatly simplifies the model identification of the complex dynamic characteristics of the hysteresis nonlinearity. The model accuracy is high and the two parts can be realized separately. This separation feature not only simplifies the model identification and calculation process, but also facilitates the design of system control.

[0037] 2. After separation design, an extended artificial neural network was used to accurately describe the static hysteresis characteristics of piezoelectric ceramics. Based on this, the Hankel matrix correlation analysis method was used to highly restore the rate dependence of the material's hysteresis characteristics. This method can accurately fit the system's high-order dynamic characteristics, solving the problems of low model bandwidth, poor accuracy, and computational difficulties encountered by traditional methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] In order to more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the following briefly introduces the drawings required for use in the examples. It should be understood that the following drawings only illustrate certain embodiments of the present invention and should not be considered as limiting the scope. A person of ordinary skill in the art can also derive other relevant drawings based on these drawings without inventive effort. In the drawings:

[0039] Figure 1 is a flow chart in an embodiment of the present invention;

[0040] Figure 2 This is a diagram of the piezoelectric ceramic system platform in an embodiment of the present invention;

[0041] Figure 3 It is the BP neural network static hysteresis model structure of the series EHO in the embodiment of the present invention;

[0042] Figure 4 This is a block diagram of the linear dynamic model identification principle in an embodiment of the present invention;

[0043] Figure 5 is a pseudo-random input signal in an embodiment of the present invention;

[0044] Figure 6 is a correlation sequence of the piezoelectric system in an embodiment of the present invention;

[0045] Figure 7 Estimation of the impulse response of the piezoelectric system in an embodiment of the present invention;

[0046] Figure 8 is the singular value decomposition result in the embodiment of the present invention;

[0047] Figure 9 Comparison of the model frequency response in the embodiment with the actual system frequency response;

[0048] Figure 10 1 is a comparison chart of the model output and the actual piezoelectric ceramic system output under different inputs in an embodiment of the present invention (20 Hz, 100 Hz, 30 / 60 / 90 Hz). DETAILED DESCRIPTION

[0049] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with examples and drawings. The exemplary embodiments of the present invention and their descriptions are only used to explain the present invention and are not intended to limit the present invention.

[0050] Example 1

[0051] like Figure 1 and Figure 2 As shown, the first aspect of this embodiment provides a high-precision model identification method for a piezoelectric ceramic system, comprising the following specific steps:

[0052] S1. Obtain input and output data of the piezoelectric ceramic system, construct an input-output characteristic curve, and obtain a static nonlinear portion of the input-output characteristic curve;

[0053] S2. Constructing a static hysteresis nonlinear model and training the static hysteresis nonlinear model using a low-frequency sinusoidal driving signal that causes the piezoelectric ceramic to exhibit static nonlinearity;

[0054] S3. Obtain updated output data based on the trained static hysteresis nonlinear model, use Hankel matrix correlation analysis method to perform model identification on the dynamic characteristics of the piezoelectric ceramic system, and obtain a transfer function model of the high-order dynamic characteristics of the piezoelectric ceramic;

[0055] S4. Connect the trained static hysteresis nonlinear model and the transfer function model of high-order dynamic characteristics in series to obtain a high-precision model of piezoelectric ceramics.

[0056] By separating the hysteresis characteristics of piezoelectric ceramics from the rate-dependent characteristics of the hysteresis, the static hysteresis characteristics of piezoelectric ceramics are accurately described, and the Hankel matrix correlation analysis method is used to highly restore the rate-dependence of the hysteresis characteristics of the material. This separation design simplifies the identification process and calculation, and the Hankel matrix method can fit the high-order dynamic characteristics of the system with high precision, overcoming the shortcomings of traditional methods such as low model bandwidth, poor accuracy and difficulty in calculation.

[0057] In some possible embodiments, obtaining input and output data of the piezoelectric ceramic system specifically includes:

[0058] Build an experimental platform for piezoelectric ceramic systems;

[0059] The experimental platform generates sinusoidal input signals of different frequencies within the operating frequency range. The sinusoidal input signals act on the piezoelectric actuator through the driver, causing its piezoelectric effect and deformation.

[0060] The deformation is measured by the sensor and the output signal is collected through the power amplifier.

[0061] Among them, the operating frequency range is 1-300Hz.

[0062] In some possible embodiments, such as Figure 3 As shown, the training of the static hysteresis nonlinear model using a low-frequency sinusoidal driving signal that causes the piezoelectric ceramic to exhibit static nonlinearity specifically includes:

[0063] The classic PI operator model is introduced to extend the input operator EHO of the neural network;

[0064] Input the input signal into the operator EHO to obtain the output sequence of the hysteresis operator model;

[0065] The output sequence and input signal of the operator EHO are used as the input sample data of the neural network to be trained, and the output signal is used as the output sample data of the neural network to be trained;

[0066] Determine the number of layers and nodes of the neural network, determine the number of layers of the neural network to be 2 and the number of nodes to be 40, and use sample input data and sample output data to train the BP neural network;

[0067] The operator EHO is connected in series with the trained neural network to obtain the trained static hysteresis nonlinear model.

[0068] In some possible embodiments, such as Figure 4 and Figure 5 As shown in the figure, the analytical inverse of the trained static hysteresis nonlinear model is obtained. As the inverse compensation controller, the hysteresis inverse compensation controller is connected in series in front of the test system, and a pseudo-random signal is input to the entire system. The signal has two cycles and the third cycle is set to zero. Because the working voltage of the piezoelectric material is positive, a bias should be added to the input signal so that its amplitude is all greater than 0. On this basis, the output data is remeasured.

[0069] In some possible embodiments, S3 specifically includes:

[0070] The Hankel matrix correlation analysis method is used to identify the dynamic characteristics of the piezoelectric ceramic system model. The specific steps are as follows:

[0071] (1) Figure 6As shown, using the input pseudo-random signal u(k) and the measured output data y(k) of the system after the series inverse compensation controller, the pseudo-random signal correlation sequence and the updated output data correlation sequence are solved:

[0072]

[0073]

[0074] Where N is the sequence length of one cycle of the input pseudo-random signal, u represents the input sequence of the system, and y represents the output sequence of the system.

[0075] The updated output data correlation sequence in this scheme optimizes the calculation formula of the correlation function. When selecting data, a two-cycle pseudo-random sequence plus a one-cycle all-0 sequence is used. Experimental results show that the accuracy is greatly improved, and there will be no mutations in the correlation sequence. This is because the correlation problem caused by the data cycle selection is avoided.

[0076] (2) Using the above correlation sequence, the impulse response g(k) of the discrete linear system model when the initial state is zero is estimated. The calculation formula is:

[0077]

[0078] When N is large enough, g(N+l)≈0, (l=0,1,2,…), so the following matrix equation can be obtained:

[0079]

[0080] like Figure 7 As shown, by arranging the above matrix, according to the impulse response of the discrete linear system model when the initial state is zero, the expression of the impulse response estimate can be obtained as follows:

[0081]

[0082] (3) Construct the Hankel matrix of the following form:

[0083]

[0084] (4) Perform singular value decomposition on the Hankel matrix:

[0085] H=Udiag{σ1…σ n}V T

[0086] where σ1≥σ2≥…≥σ r >>σ r+1 ≥…≥σ n≥0, and U and V are orthogonal matrices, that is, U T U=I,V T V = I. The Hankel matrix calculated from experimental data is typically nonsingular, meaning all its singular values are greater than 0. However, only the first r singular values are large, while the majority of the remaining singular values are very small. These are caused by measurement noise. Therefore, the order of the system can be determined from the location of the sudden decrease, meaning that the order of the linear dynamic model is r.

[0087] like Figure 8 As shown, the singular values jump significantly at the 3rd, 4th, 5th, and 6th data points, and from the 7th data point onwards, they approach zero, so the system can be of order 3, 4th, 5th, or 6. However, comparing the results of each order and observing the system's frequency response, we find that order 6 is more appropriate. Therefore, the final system order is r = 6.

[0088] (5) The result of the singular value decomposition of the Hankel matrix is further decomposed into the following two parts:

[0089] H=Udiag{σ1…σ n}V T

[0090] =[U1 U2]diag{∑1,∑2}[V1 V2] T

[0091] =U1∑1V1 T +U2∑2V2 T ≈U1∑1V1 T

[0092] in:

[0093] U1=[u1…u r ],∑1=diag{σ1,…,σ r}, V1=[v1…v r ]

[0094] The state space description of a linear dynamic system has the following relationship with the Hankel matrix:

[0095]

[0096]

[0097] Therefore, the input matrix B and output matrix C of the linear dynamic link state space model are taken as:

[0098] First row

[0099] First column

[0100] (6) Construct a new Hankel matrix H1 and perform its singular value decomposition to obtain the system matrix of the state space model:

[0101]

[0102] Therefore, the system matrix A of the linear dynamic link state space model is taken as:

[0103]

[0104] (7) The direct transfer matrix D of the general engineering system state space model is 0

[0105] (8) From the above matrices A, B, C, and D, we can get the transfer function model G of the high-order dynamic characteristics of piezoelectric ceramics. h (s):

[0106]

[0107] In some possible embodiments, the final high-precision model of the piezoelectric ceramic is H(·) in series with G h (s). Comparing the model identification results with the frequency response of the actual system, the results are as follows Figure 9 and Figure 10 The following two model test error performance indicators are defined. The model errors under different input frequencies are shown in Table 1.

[0108] Root mean square error:

[0109] Relative error:

[0110] Where N is the output sequence length, y(t) is the actual output of the piezoelectric ceramic system, is the output of the established model.

[0111] Table 1 - Model testing error

[0112]

[0113]

[0114] A second aspect of this embodiment provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it is used to implement a high-precision model identification method for a piezoelectric ceramic system.

[0115] A third aspect of this embodiment provides a computer-readable storage medium having a computer program stored thereon. When the program is executed by a processor, the program is used to implement a high-precision model identification method for a piezoelectric ceramic system.

[0116] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A high-precision model identification method for a piezoelectric ceramic system, characterized in that: The specific steps include: S1. Obtain input and output data of the piezoelectric ceramic system, construct an input-output characteristic curve, and obtain a static nonlinear portion of the input-output characteristic curve; S2. Constructing a static hysteresis nonlinear model and training the static hysteresis nonlinear model using a low-frequency sinusoidal driving signal that causes the piezoelectric ceramic to exhibit static nonlinearity; S3. Obtain updated output data based on the trained static hysteresis nonlinear model, use Hankel matrix correlation analysis method to perform model identification on the dynamic characteristics of the piezoelectric ceramic system, and obtain a transfer function model of the high-order dynamic characteristics of the piezoelectric ceramic; S4, connecting the trained static hysteresis nonlinear model with the transfer function model of high-order dynamic characteristics in series to obtain a high-precision model of the piezoelectric ceramic; The training of the static hysteresis nonlinear model by using a low-frequency sinusoidal driving signal that causes the piezoelectric ceramic to exhibit static nonlinearity specifically includes: The hysteresis operator model is introduced to extend the input operator EHO of the neural network; the input signal is input into the operator EHO to obtain the output sequence of the hysteresis operator model; The output sequence and input signal of the operator EHO are used as the input sample data of the neural network to be trained, and the output signal is used as the output sample data of the neural network to be trained; Determine the number of layers and nodes of the neural network, and use sample input data and sample output data to train the BP neural network; The operator EHO is connected in series with the trained neural network to obtain the trained static hysteresis nonlinear model; The S3 specifically includes: Acquire a pseudorandom signal and updated output data, determine a pseudorandom signal correlation sequence and an updated output data correlation sequence, wherein the updated data correlation sequence is calculated using a two-cycle pseudorandom sequence and a one-cycle all-0 sequence as input data; Estimate the impulse response of the discrete linear system model when the initial state is zero based on the two obtained correlation sequences; construct a Hankel matrix based on the impulse response, perform singular value decomposition on the Hankel matrix, and obtain a relationship between the state space description of the linear dynamic system and the Hankel matrix; The transfer function model of the high-order dynamic characteristics of the piezoelectric ceramic is obtained according to the relationship.

2. The high-precision model identification method for a piezoelectric ceramic system according to claim 1, characterized in that: The obtaining of input and output data of the piezoelectric ceramic system specifically includes: Build an experimental platform for piezoelectric ceramic systems; Generating sinusoidal input signals of different frequencies within the operating frequency range through the experimental platform, wherein the sinusoidal input signals act on the piezoelectric actuator through the driver, causing the piezoelectric effect and generating deformation; The deformation is measured by a sensor and data of the output signal is collected through a power amplifier.

3. The high-precision model identification method for a piezoelectric ceramic system according to claim 1, characterized in that: Obtaining updated output data according to the trained static hysteresis nonlinear model includes: The analytical inverse of the trained static hysteresis nonlinear model is obtained as an inverse compensation controller. The hysteresis inverse compensation controller is connected in series before the test system, and a pseudo-random signal is input to the entire system to obtain updated output data.

4. The high-precision model identification method for a piezoelectric ceramic system according to claim 3, characterized in that: The updated output data obtained includes: The pseudo-random signal includes two cycles, and the third cycle of the pseudo-random signal is set to zero; Add a bias to the input signal so that its amplitude is greater than 0.

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