CN110866218A - Hysteresis system compensation method and system - Google Patents
Hysteresis system compensation method and system Download PDFInfo
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- CN110866218A CN110866218A CN201911111489.9A CN201911111489A CN110866218A CN 110866218 A CN110866218 A CN 110866218A CN 201911111489 A CN201911111489 A CN 201911111489A CN 110866218 A CN110866218 A CN 110866218A
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- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
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Abstract
The invention discloses a hysteresis system compensation method and a hysteresis system compensation system. The method comprises the steps of obtaining a plurality of sample points to be selected; determining a first support vector according to any one sample point to be selected; determining a least squares support vector model according to the first support vector; predicting all sample points to be selected according to the least square support vector model to obtain a first prediction result; determining the prediction error of each sample point to be selected according to the first prediction result and the actual result; judging whether the maximum prediction error is within an error range, and determining the maximum prediction error as a sparse least square support vector model; and compensating the hysteresis system according to the sparse least square support vector model. The invention provides a hysteresis system compensation method and a hysteresis system compensation system, which solve the problems that the prior art has low adaptivity to hysteresis change and cannot realize effective control on a hysteresis system.
Description
Technical Field
The present invention relates to the field of hysteresis system compensation, and in particular, to a hysteresis system compensation method and system.
Background
With the development of nanotechnology, the development of nano positioning systems and sensing systems has also been widespread. However, the materials used in the above system have the problems of low positioning accuracy, poor repeated positioning performance, slow positioning speed, etc. due to hysteresis and creep characteristics, the above system is also called as a hysteresis system. Since the hysteresis system has the hysteresis nonlinearity phenomenon, the controller cannot be designed by using the classical control theory.
For the hysteresis nonlinear phenomenon existing in the hysteresis system, a preisac model, a PI hysteresis model or a least square support vector and other hysteresis nonlinear models are adopted for solving the hysteresis nonlinear phenomenon. The Preisach model models hysteresis by using multiple hysteresis operators; the PI hysteresis model is modeled by using a hysteresis operator with a slope function characteristic; in the modeling process of the model, model calculation is complex, parameter identification is difficult, and the change of the hysteresis nonlinear system is difficult to adapt. The hysteresis model of the least square support vector is modeled by directly using all samples and then pruned according to the contribution degree of the support vector; and the complexity of the algorithm of each modeling is O (n)3) And (n is the number of the support vectors) the solving algorithm is complex, and the online adaptation to the change of the hysteresis system cannot be carried out, so that the effective control of the hysteresis system cannot be realized.
Disclosure of Invention
The invention aims to provide a hysteresis system compensation method and a hysteresis system compensation system, and solves the problems that in the prior art, the adaptability to hysteresis change is low, and the hysteresis system cannot be effectively controlled.
In order to achieve the purpose, the invention provides the following scheme:
a hysteresis system compensation method, comprising:
obtaining a plurality of sample points to be selected; the sample points to be selected are sample experimental data, and the sample experimental data comprises input voltage data and output displacement data of the hysteresis system;
determining a first support vector according to any one sample point to be selected;
determining a least squares support vector model according to the first support vector;
predicting all sample points to be selected according to the least square support vector model to obtain a first prediction result;
determining the prediction error of each sample point to be selected according to the first prediction result and the actual result;
determining a maximum prediction error;
judging whether the maximum prediction error is within an error range or not to obtain a first judgment result;
when the first judgment result shows that the maximum prediction error is not in the error range, determining a second support vector according to a sample point to be selected corresponding to the maximum prediction error;
updating the least square support vector model according to the first support vector and the second support vector, and returning to the step of predicting all sample points to be selected according to the least square support vector model to obtain a first prediction result;
when the first judgment result shows that the maximum prediction error is within the error range, determining the least square support vector model as a sparse least square support vector model;
and compensating the hysteresis system according to the sparse least square support vector model.
Optionally, the obtaining a plurality of sample points to be selected further includes:
and performing form conversion on the sample points to be selected by adopting a nonlinear adaptive regression model to obtain a training data set.
Optionally, the compensating the hysteresis system according to the sparse least squares support vector model further includes:
and optimizing the sparse least square support vector model according to the sample experimental data at the historical moment.
Optionally, the optimizing the sparse least squares support vector model according to the sample experimental data at the historical time specifically includes:
acquiring sample experimental data at historical time;
taking the sample experimental data of the historical moment as a historical moment sample point, and predicting the historical moment sample point according to the sparse least square support vector model to obtain a second prediction result;
calculating sample experiment data according to the second prediction result and the historical moment, and determining a historical error;
and optimizing the sparse least square support vector model according to the historical errors.
A hysteresis system compensation system comprising:
the device comprises a sample point acquisition module, a selection module and a selection module, wherein the sample point acquisition module is used for acquiring a plurality of sample points to be selected; the sample points to be selected are sample experimental data, and the sample experimental data comprises input voltage data and output displacement data of the hysteresis system;
the first support vector determining module is used for determining a first support vector according to any one sample point to be selected;
a least squares support vector model determining module for determining a least squares support vector model according to the first support vector;
the first prediction result determining module is used for predicting all sample points to be selected according to the least square support vector model to obtain a first prediction result;
the prediction error determining module is used for determining the prediction error of each sample point to be selected according to the first prediction result and the actual result;
a maximum prediction error determination module for determining a maximum prediction error;
the first judgment module is used for judging whether the maximum prediction error is within an error range to obtain a first judgment result;
a second support vector determining module, configured to determine a second support vector according to the sample point to be selected corresponding to the maximum prediction error when the first determination result indicates that the maximum prediction error is not within the error range;
the updating module is used for updating the least square support vector model according to the first support vector and the second support vector, and returning to the step of predicting all sample points to be selected according to the least square support vector model to obtain a first prediction result;
a sparse least squares support vector model determining module, configured to determine the least squares support vector model as a sparse least squares support vector model when the first determination result indicates that the maximum prediction error is within the error range;
and the compensation module is used for compensating the hysteresis system according to the sparse least square support vector model.
Optionally, the method further includes:
and the conversion module is used for performing form conversion on the sample points to be selected by adopting a nonlinear adaptive regression model to obtain a training data set.
Optionally, the method further includes:
and the optimization module is used for optimizing the sparse least square support vector model according to the sample experiment data at the historical moment.
Optionally, the optimization module specifically includes:
the data acquisition unit is used for acquiring sample experiment data at historical time;
the second prediction result determining unit is used for taking the sample experiment data at the historical moment as a sample point at the historical moment, predicting the sample point at the historical moment according to the sparse least square support vector model and obtaining a second prediction result;
a historical error determination unit, configured to calculate sample experimental data according to the second prediction result and the historical time, and determine a historical error;
and the optimization unit is used for optimizing the sparse least square support vector model according to the historical errors.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
according to the hysteresis system compensation method and system provided by the invention, the sparse least square support vector model is established through a small number of sample points, the complexity and the overfitting phenomenon of the model are reduced, the precision of the model is improved, the least square support vector model is updated in real time according to the sample points, the hysteresis system is adapted to the change of the hysteresis system, and the effective control of the hysteresis system is realized.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a schematic flow chart illustrating a compensation method for a hysteresis system according to the present invention;
FIG. 2 is a schematic diagram of a hysteresis system compensation system according to the present invention;
fig. 3 is a schematic diagram illustrating a compensation principle of a hysteresis system according to the present invention.
Description of reference numerals: 201-a sample point obtaining module, 202-a first support vector determining module, 203-a least square support vector model determining module, 204-a first prediction result determining module, 205-a prediction error determining module, 206-a maximum prediction error determining module, 207-a first judging module, 208-a second support vector determining module, 209-an updating module, 210-a sparse least square support vector model determining module, 211-a compensating module.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a hysteresis system compensation method and a hysteresis system compensation system, and solves the problems that in the prior art, the adaptability to hysteresis change is low, and the hysteresis system cannot be effectively controlled.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
On the basis of the least square support vector machine, considering that a large number of sample points have certain redundancy, and a sample with a small error has small contribution to the least square support vector machine, a cyclic iteration method is used, a least square support vector machine model established by a small number of sample points is used for predicting all sample points, the sample point with the largest error is selected and added into the support vector, a new model is continuously established until the error reaches a set level, compared with the method of directly using all samples for modeling, and the calculation amount of an algorithm for reducing the support vector through the contribution degree is smaller, as shown in fig. 3.
Fig. 1 is a schematic flow chart of a hysteresis system compensation method provided by the present invention, and as shown in fig. 1, the hysteresis system compensation method provided by the present invention includes:
s101, obtaining a plurality of sample points to be selected; the sample points to be selected are sample experimental data, and the sample experimental data comprises input voltage data and output displacement data of the hysteresis system.
S102, determining a first support vector according to any one sample point to be selected.
S103, determining a least square support vector model according to the first support vector.
And S104, predicting all sample points to be selected according to the least square support vector model to obtain a first prediction result.
And S105, determining the prediction error of each sample point to be selected according to the first prediction result and the actual result.
And S106, determining the maximum prediction error.
S107, judging whether the maximum prediction error is in an error range or not, and obtaining a first judgment result.
And S108, when the first judgment result shows that the maximum prediction error is not in the error range, determining a second support vector according to the sample point to be selected corresponding to the maximum prediction error.
And S109, updating the least square support vector model according to the first support vector and the second support vector, and returning to S104.
And S110, when the first judgment result shows that the maximum prediction error is in the error range, determining the least square support vector model as a sparse least square support vector model.
And S111, compensating the hysteresis system according to the sparse least square support vector model.
In a specific embodiment, the obtaining a plurality of sample points to be selected further includes: and performing form conversion on the sample points to be selected by adopting a nonlinear adaptive regression model to obtain a training data set.
And converting the sample points to be selected into the following forms by adopting a nonlinear autoregressive model:
yk＝f(xk)+ξk；
wherein, ykFor compensating voltage values for hysteresis systems, xkVector of input voltage data and output displacement data, ξkIs a prediction error; x is the number ofk＝[uk,uk-1,...,uk-n,yk-1,yk-2,...,yk-m]。
Determining a least squares support vector model according to the first support vector, specifically comprising:
using formulas
Determining an optimization function and constraint conditions, wherein omega is a weight vector, ξ is a prediction error, ξiFor the ith prediction error, C is the fault tolerance coefficient, xiFor the support vector of the ith time,
represents mapping the ith support vector to a high-dimensional space; n is the number of the support vectors, T is the transposition symbol, s.t. is the constraint condition, yi is the compensation voltage value corresponding to the support vectors,
indicating when the minimum of the function needs to be solved.
The original optimization problem can be converted into a dual problem by using a formula
Go on differentiation, wherein αiIs a lagrange multiplier.
Transforming optimization problems into
Where e represents a vector of all 1 s, Ω is a kernel matrix, Ωi,j＝K(xi,xj) Y is the actual result of the support vector, α is the vector composed of Lagrange multipliers, INIs an N-dimensional identity matrix.
Finally converting into a model of least squares support vector:
And predicting all the samples to be selected by using the obtained least square support vector model.
The prediction result is as follows:
determining the prediction error of each sample point to be selected according to the first prediction result and the actual result; and adding the sample point corresponding to the maximum absolute error obtained by the error calculation module into the support vector.
In order to further adapt to the change of the system, the compensation of model errors to the hysteresis system according to the sparse least squares support vector model is reduced, and the method also comprises the following steps: and optimizing the sparse least square support vector model according to the sample experimental data at the historical moment.
The optimizing the sparse least squares support vector model according to the sample experimental data at the historical moment specifically comprises:
and acquiring sample experimental data at historical time.
And taking the sample experimental data of the historical moment as a historical moment sample point, and predicting the historical moment sample point according to the sparse least square support vector model to obtain a second prediction result.
And calculating sample experiment data according to the second prediction result and the historical time, and determining a historical error.
And optimizing the sparse least square support vector model according to the historical errors.
In a specific embodiment, historical input and output of a hysteresis system are used to form a historical sample point x (k) at time k, and then a prediction result is obtained by a least squares support vector machine:
calculating an error using the obtained predicted value and the true value: err (k) ═ y*(k)-y(k)；
And optimizing the sparse least square support vector model by using the obtained error, wherein the specific process is as follows:
αi(k)＝αi(k)-2μ1err(k)K(xi,x(k))；
b(k+1)＝b(k)-2μ2err(k)。
fig. 2 is a schematic structural diagram of a hysteresis system compensation system provided in the present invention, and as shown in fig. 2, the present invention further provides a hysteresis system compensation system, including: the method comprises a sample point obtaining module 201, a first support vector determining module 202, a least squares support vector model determining module 203, a first prediction result determining module 204, a prediction error determining module 205, a maximum prediction error determining module 206, a first judging module 207, a second support vector determining module 208, an updating module 209, a sparse least squares support vector model determining module 210 and a compensating module 211.
The sample point obtaining module 201 is configured to obtain a plurality of sample points to be selected; the sample points to be selected are sample experimental data, and the sample experimental data comprises input voltage data and output displacement data of the hysteresis system.
The first support vector determining module 202 is configured to determine a first support vector according to any one sample point to be selected.
The least squares support vector model determining module 203 is configured to determine a least squares support vector model according to the first support vector.
The first prediction result determining module 204 is configured to predict all sample points to be selected according to the least square support vector model, so as to obtain a first prediction result.
The prediction error determining module 205 is configured to determine a prediction error of each sample point to be selected according to the first prediction result and the actual result.
The maximum prediction error determination module 206 is configured to determine the maximum prediction error.
The first determining module 207 is configured to determine whether the maximum prediction error is within an error range, so as to obtain a first determining result.
The second support vector determining module 208 is configured to determine a second support vector according to the sample point to be selected corresponding to the maximum prediction error when the first determination result indicates that the maximum prediction error is not within the error range.
The updating module 209 is configured to update the least squares support vector model according to the first support vector and the second support vector, and return to the step of predicting all sample points to be selected according to the least squares support vector model to obtain a first prediction result.
The sparse least square support vector model determining module 210 is configured to determine the least square support vector model as a sparse least square support vector model when the first determination result indicates that the maximum prediction error is within the error range.
The compensation module 211 is configured to compensate the hysteresis system according to the sparse least squares support vector model.
The invention provides a hysteresis system compensation system, which further comprises: the device comprises a conversion module and an optimization module.
And the conversion module is used for performing form conversion on the sample points to be selected by adopting a nonlinear adaptive regression model to obtain a training data set.
The optimization module is used for optimizing the sparse least square support vector model according to the sample experiment data at the historical moment.
The optimization module specifically comprises: the device comprises a data acquisition unit, a second prediction result determination unit, a historical error determination unit and an optimization unit.
The data acquisition unit is used for acquiring sample experimental data of historical time.
And the second prediction result determining unit is used for predicting the historical time sample points according to the sparse least square support vector model by taking the historical time sample experiment data as the historical time sample points to obtain a second prediction result.
And the historical error determining unit is used for calculating sample experimental data according to the second prediction result and the historical time, and determining a historical error.
The optimization unit is used for optimizing the sparse least square support vector model according to the historical errors.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (8)
1. A hysteresis system compensation method, comprising:
obtaining a plurality of sample points to be selected; the sample points to be selected are sample experimental data, and the sample experimental data comprises input voltage data and output displacement data of the hysteresis system;
determining a first support vector according to any one sample point to be selected;
determining a least squares support vector model according to the first support vector;
predicting all sample points to be selected according to the least square support vector model to obtain a first prediction result;
determining the prediction error of each sample point to be selected according to the first prediction result and the actual result;
determining a maximum prediction error;
judging whether the maximum prediction error is within an error range or not to obtain a first judgment result;
when the first judgment result shows that the maximum prediction error is not in the error range, determining a second support vector according to a sample point to be selected corresponding to the maximum prediction error;
updating the least square support vector model according to the first support vector and the second support vector, and returning to the step of predicting all sample points to be selected according to the least square support vector model to obtain a first prediction result;
when the first judgment result shows that the maximum prediction error is within the error range, determining the least square support vector model as a sparse least square support vector model;
and compensating the hysteresis system according to the sparse least square support vector model.
2. The hysteresis system compensation method of claim 1, wherein the obtaining a plurality of candidate sample points further comprises:
and performing form conversion on the sample points to be selected by adopting a nonlinear adaptive regression model to obtain a training data set.
3. The hysteresis system compensation method as claimed in claim 1, wherein the compensating the hysteresis system according to the sparse least squares support vector model further comprises:
and optimizing the sparse least square support vector model according to the sample experimental data at the historical moment.
4. The hysteresis system compensation method according to claim 3, wherein the optimizing the sparse least squares support vector model according to the sample experimental data at the historical time specifically comprises:
acquiring sample experimental data at historical time;
taking the sample experimental data of the historical moment as a historical moment sample point, and predicting the historical moment sample point according to the sparse least square support vector model to obtain a second prediction result;
calculating sample experiment data according to the second prediction result and the historical moment, and determining a historical error;
and optimizing the sparse least square support vector model according to the historical errors.
5. A hysteresis system compensation system, comprising:
the device comprises a sample point acquisition module, a selection module and a selection module, wherein the sample point acquisition module is used for acquiring a plurality of sample points to be selected; the sample points to be selected are sample experimental data, and the sample experimental data comprises input voltage data and output displacement data of the hysteresis system;
the first support vector determining module is used for determining a first support vector according to any one sample point to be selected;
a least squares support vector model determining module for determining a least squares support vector model according to the first support vector;
the first prediction result determining module is used for predicting all sample points to be selected according to the least square support vector model to obtain a first prediction result;
the prediction error determining module is used for determining the prediction error of each sample point to be selected according to the first prediction result and the actual result;
a maximum prediction error determination module for determining a maximum prediction error;
the first judgment module is used for judging whether the maximum prediction error is within an error range to obtain a first judgment result;
a second support vector determining module, configured to determine a second support vector according to the sample point to be selected corresponding to the maximum prediction error when the first determination result indicates that the maximum prediction error is not within the error range;
the updating module is used for updating the least square support vector model according to the first support vector and the second support vector, and returning to the step of predicting all sample points to be selected according to the least square support vector model to obtain a first prediction result;
a sparse least squares support vector model determining module, configured to determine the least squares support vector model as a sparse least squares support vector model when the first determination result indicates that the maximum prediction error is within the error range;
and the compensation module is used for compensating the hysteresis system according to the sparse least square support vector model.
6. The hysteresis system compensation system of claim 5, further comprising:
and the conversion module is used for performing form conversion on the sample points to be selected by adopting a nonlinear adaptive regression model to obtain a training data set.
7. The hysteresis system compensation system of claim 5, further comprising:
and the optimization module is used for optimizing the sparse least square support vector model according to the sample experiment data at the historical moment.
8. The hysteresis system compensation system of claim 7, wherein the optimization module specifically comprises:
the data acquisition unit is used for acquiring sample experiment data at historical time;
the second prediction result determining unit is used for taking the sample experiment data at the historical moment as a sample point at the historical moment, predicting the sample point at the historical moment according to the sparse least square support vector model and obtaining a second prediction result;
a historical error determination unit, configured to calculate sample experimental data according to the second prediction result and the historical time, and determine a historical error;
and the optimization unit is used for optimizing the sparse least square support vector model according to the historical errors.
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