CN116644301A - High-precision model identification method, equipment and medium for piezoelectric ceramic system - Google Patents
High-precision model identification method, equipment and medium for piezoelectric ceramic system Download PDFInfo
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Abstract
The invention discloses a method, equipment and medium for identifying a high-precision model of a piezoelectric ceramic system, which are characterized in that a static hysteresis nonlinear model is constructed, updated output data is obtained according to the trained static hysteresis nonlinear model, a Hankel matrix correlation analysis method is adopted to identify the dynamic characteristics of the piezoelectric ceramic system, a transfer function model of the high-order dynamic characteristics of the piezoelectric ceramic is obtained, and the trained static hysteresis nonlinear model is connected with the transfer function model in series to obtain the high-precision model of the piezoelectric ceramic. By separating the hysteresis characteristic of the piezoelectric ceramic from the hysteresis rate-related characteristic, the static hysteresis characteristic of the piezoelectric ceramic is accurately described, and the rate-related characteristic of the hysteresis characteristic of the material is highly restored by adopting a Hankel matrix correlation analysis method, so that the identification process and calculation become simple, and the Hankel matrix method can be used for fitting the high-order dynamic characteristic of the system with high precision, thereby overcoming the defects of low model bandwidth, poor precision and difficult calculation in the traditional method.
Description
Technical Field
The invention relates to the field of automation, in particular to a high-precision model identification method, equipment and medium for a piezoelectric ceramic system.
Background
The intelligent materials such as piezoelectric ceramics and the like are widely applied in the fields of precise positioning, precise manufacturing and micro-amplitude active vibration control, but the intelligent devices of the piezoelectric materials have obvious hysteresis nonlinearity in the input-output relation, and the nonlinearity also has obvious first-pass characteristic. This not only reduces the control accuracy of the system, but may even lead to instability or oscillations of the closed loop system; the high-frequency resonance mode of the piezoelectric material actuator/driver is difficult to describe accurately, so that the established mathematical model is low in bandwidth and far from accurate. Therefore, the high-precision modeling method is a key for realizing ultra-high precision tracking and high-performance micro-nano vibration control.
Disclosure of Invention
The invention aims to provide a high-precision model identification method, equipment and medium for a piezoelectric ceramic system, which are used for separating the hysteresis characteristic of the piezoelectric ceramic from the hysteresis rate-related characteristic, accurately describing the static hysteresis characteristic of the piezoelectric ceramic, and highly reducing the rate-related characteristic of the hysteresis characteristic of the material by adopting a Hankel matrix correlation analysis method.
The invention is realized by the following technical scheme:
the invention provides a high-precision model identification method of a piezoelectric ceramic system, which comprises the following specific steps:
s1, acquiring input and output data of a piezoelectric ceramic system, constructing an input and output characteristic curve, and obtaining a static nonlinear part in the input and output characteristic curve;
s2, constructing a static hysteresis nonlinear model, and training the static hysteresis nonlinear model by adopting a low-frequency sinusoidal driving signal which enables the piezoelectric ceramic to show static nonlinearity;
s3, obtaining updated output data according to the trained static hysteresis nonlinear model, and carrying out model identification on the dynamic characteristics of the piezoelectric ceramic system by adopting a Hankel matrix correlation analysis method to obtain a transfer function model of the high-order dynamic characteristics of the piezoelectric ceramic;
and S4, connecting the trained static hysteresis nonlinear model with a transfer function model with high-order dynamic characteristics in series to obtain the piezoelectric ceramic high-precision model.
According to the invention, the static hysteresis characteristic of the piezoelectric ceramic is accurately described by separating the hysteresis characteristic from the hysteresis rate-related characteristic of the piezoelectric ceramic, and the rate-related characteristic of the material hysteresis characteristic is highly reduced by adopting a Hankel matrix correlation analysis method, so that the separation design enables the identification process and calculation to be simple, and the Hankel matrix method can be used for fitting the high-order dynamic characteristic of the system with high precision, thereby overcoming the defects of low model bandwidth, poor precision and difficult calculation in the traditional method.
Further, the acquiring the input/output data of the piezoelectric ceramic system specifically includes:
aiming at a piezoelectric ceramic system, an experimental platform is built;
generating sinusoidal input signals with different frequencies within the working frequency range through an experiment platform, wherein the sinusoidal input signals are used for acting on a piezoelectric actuator through a driver to cause piezoelectric effect and deformation of the piezoelectric actuator;
the deformation is measured by a sensor and the data acquisition of the output signal is performed by a power amplifier.
Further, training the static hysteresis nonlinear model by using a low-frequency sinusoidal driving signal for making the piezoelectric ceramic exhibit static nonlinearity specifically includes:
introducing a hysteresis operator model into a neural network expansion input operator EHO;
inputting an input signal into an operator EHO to obtain an output sequence of a hysteresis operator model;
taking the output sequence and the input signal of the operator EHO as input sample data of the neural network to be trained, and taking the output signal as output sample data of the neural network to be trained;
determining the number of layers and the number of nodes of the neural network, and training the BP neural network by using sample input data and sample output data;
and (3) connecting an operator EHO with the trained neural network in series to obtain the trained static hysteresis nonlinear model.
Further, the obtaining updated output data according to the trained static hysteresis nonlinear model includes:
and solving the analytic inverse of the trained static hysteresis nonlinear model, and connecting the hysteresis inverse compensation controller in series before the test system as an inverse compensation controller, so as to input pseudo-random signals into the whole system and obtain updated output data.
Further, the obtaining updated output data includes:
the pseudo-random signal comprises two periods, and the third period of the pseudo-random signal is set to zero;
and biasing the input signal to make the amplitude of the input signal greater than 0.
Further, the step S3 specifically includes:
acquiring a pseudo-random signal and updated output data, and determining a pseudo-random signal correlation sequence and an updated output data correlation sequence, wherein the updated data correlation sequence adopts a pseudo-random sequence with two periods and an all-0 sequence with one period as input data in calculation;
estimating impulse response of the discrete linear system model when the initial state is zero according to the two obtained correlation sequences;
constructing a Hankel matrix according to the impulse response, performing singular value decomposition on the Hankel matrix, determining the system order and obtaining a relational expression between the linear dynamic system state space description and the Hankel matrix;
and obtaining a transfer function model of the high-order dynamic characteristic of the piezoelectric ceramic according to the relational expression.
Further, the singular value decomposition of the Hankel matrix includes: and determining the system order according to the singular value characteristics, and decomposing the Hankel matrix singular value into an input matrix and an output matrix of the linear system state space description.
Further, the method further comprises the following steps: and constructing a new Hankel matrix, and decomposing the singular values of the Hankel matrix to obtain a system matrix of the state space model.
A second aspect of the present invention provides an electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor when executing the program being for implementing a method for high precision model identification of a piezo-ceramic system.
A third aspect of the present invention provides a computer-readable storage medium having stored thereon a computer program for implementing a high-precision model identification method of a piezoelectric ceramic system when executed by a processor.
Compared with the prior art, the invention has the following advantages and beneficial effects:
1. the dynamic hysteresis nonlinear characteristic is divided into two parts of static nonlinear link and dynamic linear link which are connected in series, so that the model identification of the hysteresis nonlinear complex dynamic characteristic is greatly simplified, the model accuracy is high, the two parts can be realized separately, and the separation characteristic not only simplifies the model identification and calculation process, but also is beneficial to the design of system control;
2. after separation design, the static hysteresis characteristic of the piezoelectric ceramic is accurately described by using an extended artificial neural network. Based on the method, the rate correlation of the hysteresis characteristic of the material is highly restored by adopting a Hankel matrix correlation analysis method, the high-order dynamic characteristic of the system can be fitted with high precision, and the problems of low model bandwidth, poor precision and difficult calculation in the traditional method are solved.
Drawings
In order to more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the drawings that are needed in the examples will be briefly described below, it being understood that the following drawings only illustrate some examples of the present invention and therefore should not be considered as limiting the scope, and that other related drawings may be obtained from these drawings without inventive effort for a person skilled in the art. In the drawings:
FIG. 1 is a flow chart of an embodiment of the present invention;
FIG. 2 is a schematic diagram of a piezoelectric ceramic system platform in an embodiment of the invention;
FIG. 3 is a schematic diagram of a static hysteresis model of a BP neural network of a series EHO in an embodiment of the present invention;
FIG. 4 is a schematic block diagram of linear dynamic model identification in an embodiment of the invention;
FIG. 5 is a pseudo-random input signal in an embodiment of the invention;
FIG. 6 is a correlation sequence of a piezoelectric system in an embodiment of the present invention;
FIG. 7 is an impulse response estimate of a piezoelectric system in an embodiment of the invention;
FIG. 8 is a singular value decomposition result in an embodiment of the present invention;
FIG. 9 illustrates a comparison of the model frequency response in an embodiment with the actual system frequency response;
FIG. 10 is a graph of the comparison of model output with actual piezoelectric ceramic system output (20 Hz, 100Hz, 30/60/90 Hz) at different inputs in an embodiment of the present invention.
Detailed Description
For the purpose of making apparent the objects, technical solutions and advantages of the present invention, the present invention will be further described in detail with reference to the following examples and the accompanying drawings, wherein the exemplary embodiments of the present invention and the descriptions thereof are for illustrating the present invention only and are not to be construed as limiting the present invention.
Example 1
As shown in fig. 1 and 2, a first aspect of the present embodiment provides a method for identifying a high-precision model of a piezoelectric ceramic system, which includes the following specific steps:
s1, acquiring input and output data of a piezoelectric ceramic system, constructing an input and output characteristic curve, and obtaining a static nonlinear part in the input and output characteristic curve;
s2, constructing a static hysteresis nonlinear model, and training the static hysteresis nonlinear model by adopting a low-frequency sinusoidal driving signal which enables the piezoelectric ceramic to show static nonlinearity;
s3, obtaining updated output data according to the trained static hysteresis nonlinear model, and carrying out model identification on the dynamic characteristics of the piezoelectric ceramic system by adopting a Hankel matrix correlation analysis method to obtain a transfer function model of the high-order dynamic characteristics of the piezoelectric ceramic;
and S4, connecting the trained static hysteresis nonlinear model with a transfer function model with high-order dynamic characteristics in series to obtain the piezoelectric ceramic high-precision model.
By separating the hysteresis characteristic of the piezoelectric ceramic from the hysteresis rate-related characteristic, the static hysteresis characteristic of the piezoelectric ceramic is accurately described, the rate-related characteristic of the hysteresis characteristic of the material is highly reduced by adopting a Hankel matrix correlation analysis method, the separation design enables the identification process and calculation to be simple, and the Hankel matrix method can be used for fitting the high-order dynamic characteristic of the system with high precision, so that the defects of low model bandwidth, poor precision and difficult calculation in the traditional method are overcome.
In some possible embodiments, acquiring input and output data of the piezoelectric ceramic system specifically includes:
aiming at a piezoelectric ceramic system, an experimental platform is built;
sinusoidal input signals with different frequencies in the working frequency range are generated through an experimental platform, and the sinusoidal input signals are used for acting on a piezoelectric actuator through a driver to cause piezoelectric effect and deformation of the piezoelectric actuator;
the deformation is measured by a sensor and the data acquisition of the output signal is performed by a power amplifier.
Wherein the working frequency range is 1-300Hz.
In some possible embodiments, as shown in fig. 3, training the static hysteresis nonlinear model with a low frequency sinusoidal drive signal that causes the piezoelectric ceramic to exhibit static nonlinearity specifically includes:
introducing a classical PI operator model into a neural network expansion input operator EHO;
inputting an input signal into an operator EHO to obtain an output sequence of a hysteresis operator model;
taking the output sequence and the input signal of the operator EHO as input sample data of the neural network to be trained, and taking the output signal as output sample data of the neural network to be trained;
determining the number of layers and the number of nodes of the neural network, determining the number of layers of the neural network to be 2 and the number of nodes to be 40, and training the BP neural network by using sample input data and sample output data;
and (3) connecting an operator EHO with the trained neural network in series to obtain the trained static hysteresis nonlinear model.
In some possible embodiments, as shown in fig. 4 and 5, the trained static hysteresis nonlinear model is subjected to analytic inversion, and is used as an inverse compensation controller, the hysteresis inverse compensation controller is connected in series before the test system, a pseudo-random signal is input to the whole system, the pseudo-random signal is divided into two periods, and the third period is set to zero, and because the working voltage of the piezoelectric material is positive, the input signal is biased to have the amplitude of the input signal all greater than 0, and the output data is measured again on the basis.
In some possible embodiments, S3 specifically includes:
the method adopts a Hankel matrix correlation analysis method to carry out model identification on the dynamic characteristics of the piezoelectric ceramic system, and comprises the following steps:
(1) As shown in fig. 6, the pseudo-random signal correlation sequence and the updated output data correlation sequence are determined by using the input pseudo-random signal u (k) and the measured output data y (k) of the system after the inverse compensation controller is connected in series:
where N is the sequence length of one period of the input pseudo-random signal, u represents the input sequence of the system, and y represents the output sequence of the system.
According to the scheme, the updated output data correlation sequence optimizes a calculation formula of a correlation function, a pseudo-random sequence with two periods and a full 0 sequence with one period are adopted when data are selected, and experiments show that accuracy is greatly improved, and a place with mutation in the correlation sequence is avoided, so that the problem of correlation caused by data period selection is avoided.
(2) By using the correlation sequence, the impulse response g (k) of the discrete linear system model when the initial state is zero is estimated, and the calculation formula is as follows:
when N is sufficiently large, g (n+l) ≡0, (l=0, 1,2, …), the following equation in matrix form can be obtained:
as shown in fig. 7, for the matrix arrangement, according to the impulse response of the discrete linear system model when the initial state is zero, the expression of the impulse response estimation value can be obtained as follows:
(3) A Hankel matrix of the form:
(4) Singular value decomposition is performed on the Hankel matrix:
H＝Udiag{σ 1 …σ n }V T
wherein sigma 1 ≥σ 2 ≥…≥σ r ＞＞σ r+1 ≥…≥σ n Not less than 0, and U, V is an orthogonal matrix, U T U＝I,V T V=i. The Hankel matrix calculated using experimental data is typically a non-singular matrix, i.e. all singular values are larger than 0, but only the first r singular values are larger and the remaining majority of singular values become smaller, which are caused by measurement noise. The order of the system can be determined by the suddenly decreasing position, i.e. the linear dynamic model order is r.
As shown in fig. 8, the singular values are more pronounced at the 3, 4, 5, 6 th data, and the singular values are nearly 0 from the 7 th data, so the system may take 3, 4, 5, 6 th order. However, comparing the results of each order, the frequency response diagram of the observation system finds that the system takes 6 orders as appropriate. The system order is finally determined to be r=6.
(5) Further decomposing the result of Hankel matrix singular value decomposition into the following two parts:
H＝Udiag{σ 1 …σ n }V T
＝[U 1 U 2 ]diag{∑ 1 ，∑ 2 }[V 1 V 2 ] T
＝U 1 ∑ 1 V 1 T +U 2 ∑ 2 V 2 T ≈U 1 ∑ 1 V 1 T
wherein:
U 1 ＝[u 1 …u r ],∑ 1 ＝diag{σ 1 ,…,σ r }，V 1 ＝[v 1 …v r ]
the linear dynamic system state space description and the Hankel matrix have the following relation:
therefore, the input matrix B and the output matrix C of the linear dynamic link state space model are taken as follows:
first row
First column
(6) StructureConstruction of a novel Hankel matrix H 1 Obtaining a system matrix of a state space model through singular value decomposition of the system matrix:
therefore, the system matrix A of the linear dynamic link state space model is taken as follows:
(7) The direct transfer matrix D of the state space model of the general engineering system is 0
(8) From the above matrix A, B, C, D, a transfer function model G of the high-order dynamic characteristics of the piezoelectric ceramic can be obtained h (s)：
In some possible embodiments, the high-precision model of the piezoelectric ceramic finally obtained is H (·) series G h (s). Comparing the model identification result with the frequency response of the actual system, the result is shown in fig. 9 and 10. The following two model test error performance indexes are defined, and the errors of the models under different input frequencies are shown in table 1;
root mean square error:
relative error:
wherein N is the length of the output sequence, y (t) is the actual output of the piezoelectric ceramic system,for the output of the built model.
TABLE 1 model test errors
A second aspect of the present embodiment provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor, where the processor is configured to implement a method for identifying a high-precision model of a piezoelectric ceramic system when the processor executes the program.
A third aspect of the present embodiment provides a computer-readable storage medium having stored thereon a computer program for implementing a high-precision model identification method of a piezoelectric ceramic system when executed by a processor.
The foregoing description of the embodiments has been provided for the purpose of illustrating the general principles of the invention, and is not meant to limit the scope of the invention, but to limit the invention to the particular embodiments, and any modifications, equivalents, improvements, etc. that fall within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (10)
1. The high-precision model identification method of the piezoelectric ceramic system is characterized by comprising the following specific steps of:
s1, acquiring input and output data of a piezoelectric ceramic system, constructing an input and output characteristic curve, and obtaining a static nonlinear part in the input and output characteristic curve;
s2, constructing a static hysteresis nonlinear model, and training the static hysteresis nonlinear model by adopting a low-frequency sinusoidal driving signal which enables the piezoelectric ceramic to show static nonlinearity;
s3, obtaining updated output data according to the trained static hysteresis nonlinear model, and carrying out model identification on the dynamic characteristics of the piezoelectric ceramic system by adopting a Hankel matrix correlation analysis method to obtain a transfer function model of the high-order dynamic characteristics of the piezoelectric ceramic;
and S4, connecting the trained static hysteresis nonlinear model with a transfer function model with high-order dynamic characteristics in series to obtain the piezoelectric ceramic high-precision model.
2. The method for identifying a high-precision model of a piezoelectric ceramic system according to claim 1, wherein the acquiring the input/output data of the piezoelectric ceramic system specifically comprises:
aiming at a piezoelectric ceramic system, an experimental platform is built;
generating sinusoidal input signals with different frequencies within the working frequency range through an experiment platform, wherein the sinusoidal input signals are used for acting on a piezoelectric actuator through a driver to cause piezoelectric effect and deformation of the piezoelectric actuator;
the deformation is measured by a sensor and the data acquisition of the output signal is performed by a power amplifier.
3. The method for identifying a high-precision model of a piezoelectric ceramic system according to claim 1, wherein the training of the static hysteresis nonlinear model by using a low-frequency sinusoidal driving signal for making the piezoelectric ceramic exhibit static nonlinearity specifically comprises:
introducing a hysteresis operator model into a neural network expansion input operator EHO;
inputting an input signal into an operator EHO to obtain an output sequence of a hysteresis operator model;
taking the output sequence and the input signal of the operator EHO as input sample data of the neural network to be trained, and taking the output signal as output sample data of the neural network to be trained;
determining the number of layers and the number of nodes of the neural network, and training the BP neural network by using sample input data and sample output data;
and (3) connecting an operator EHO with the trained neural network in series to obtain the trained static hysteresis nonlinear model.
4. The method of claim 1, wherein obtaining updated output data from the trained static hysteresis nonlinear model comprises:
and solving the analytic inverse of the trained static hysteresis nonlinear model, and connecting the hysteresis inverse compensation controller in series before the test system as an inverse compensation controller, so as to input pseudo-random signals into the whole system and obtain updated output data.
5. The method of claim 4, wherein obtaining updated output data comprises:
the pseudo-random signal comprises two periods, and the third period of the pseudo-random signal is set to zero;
and biasing the input signal to make the amplitude of the input signal greater than 0.
6. The method for identifying a high-precision model of a piezoelectric ceramic system according to claim 1, wherein S3 specifically comprises:
acquiring a pseudo-random signal and updated output data, and determining a pseudo-random signal correlation sequence and an updated output data correlation sequence, wherein the updated data correlation sequence adopts a pseudo-random sequence with two periods and an all-0 sequence with one period as input data in calculation;
estimating impulse response of the discrete linear system model when the initial state is zero according to the two obtained correlation sequences;
constructing a Hankel matrix according to the impulse response, and carrying out singular value decomposition on the Hankel matrix to obtain a relational expression between the state space description of the linear dynamic system and the Hankel matrix;
and obtaining a transfer function model of the high-order dynamic characteristic of the piezoelectric ceramic according to the relational expression.
7. The method of claim 6, wherein the singular value decomposition of the Hankel matrix comprises: and determining the system order according to the singular value characteristics, and decomposing the Hankel matrix singular value into an input matrix and an output matrix of the linear system state space description.
8. The method for high-precision model identification of a piezoelectric ceramic system according to claim 6, further comprising: and constructing a new Hankel matrix, and decomposing the singular values of the Hankel matrix to obtain a system matrix of the state space model.
9. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements a method for high precision model identification of a piezo-ceramic system according to any one of claims 1 to 8 when executing the program.
10. A computer-readable storage medium, on which a computer program is stored, characterized in that the program, when executed by a processor, implements a method for high-precision model identification of a piezoceramic system as claimed in any one of claims 1 to 8.
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