CN111427266B - Nonlinear system identification method aiming at disturbance - Google Patents

Nonlinear system identification method aiming at disturbance Download PDF

Info

Publication number
CN111427266B
CN111427266B CN202010198543.4A CN202010198543A CN111427266B CN 111427266 B CN111427266 B CN 111427266B CN 202010198543 A CN202010198543 A CN 202010198543A CN 111427266 B CN111427266 B CN 111427266B
Authority
CN
China
Prior art keywords
output
disturbance
vector
linear
model
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202010198543.4A
Other languages
Chinese (zh)
Other versions
CN111427266A (en
Inventor
杨晓冬
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
North China Institute of Aerospace Engineering
Original Assignee
North China Institute of Aerospace Engineering
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by North China Institute of Aerospace Engineering filed Critical North China Institute of Aerospace Engineering
Priority to CN202010198543.4A priority Critical patent/CN111427266B/en
Publication of CN111427266A publication Critical patent/CN111427266A/en
Application granted granted Critical
Publication of CN111427266B publication Critical patent/CN111427266B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
    • G05B13/045—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance using a perturbation signal
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
    • Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Pure & Applied Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Software Systems (AREA)
  • Theoretical Computer Science (AREA)
  • Data Mining & Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Computational Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Medical Informatics (AREA)
  • Artificial Intelligence (AREA)
  • Operations Research (AREA)
  • Health & Medical Sciences (AREA)
  • Algebra (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Databases & Information Systems (AREA)
  • General Engineering & Computer Science (AREA)
  • Evolutionary Computation (AREA)
  • Feedback Control In General (AREA)

Abstract

The invention discloses a method for identifying a non-linear system with disturbance, which comprises the following steps: A. converting an industrial control system to be identified into a strip disturbanceThe nonlinear system model of (1), the nonlinear system is composed of a nonlinear link and a linear link, namely a Hammerstein system of an output error type; B. decomposing the non-linear system model with disturbance into two sub-models: the system has no noise output submodel and disturbance submodel; C. updating system parameters
Figure DDA0002418508890000011
Construction of P ζ (k) And e ζ (k) Updating the parameters
Figure DDA0002418508890000012
Let k = k +1, return to step a until the cutoff condition is satisfied
Figure DDA0002418508890000013
D. Identifying parameters and disturbances of the industrial control system. The invention can improve the defects of the prior art and has high convergence speed and identification precision.

Description

Nonlinear system identification method aiming at disturbance
Technical Field
The invention relates to the technical field of industrial control, in particular to a method for identifying a non-linear system with disturbance.
Background
Nonlinear systems are widely present in industrial systems, and identification and control problems of nonlinear systems are paid more and more attention by students and engineers, and become important in research. The nonlinear system can be divided into a hammerstein system, a wiener system and a hammerstein wiener system, and generally comprises a nonlinear link and a linear link, wherein the nonlinear link is in various forms, such as a dead zone, a set of a plurality of linear functions and the like, and the linear link is mainly an output error model. The hammerstein system, of which the type of output error is most widely studied. In an industrial process, measurement noise is widely existed, when an output error model is converted into a regression equation, white noise is converted into colored noise, a least square identification algorithm becomes biased estimation, and identification precision is reduced. In the identification process, the disturbance always pollutes the output data, the identification precision is reduced, and therefore the influence of the disturbance must be eliminated. There are few documents and patents mentioning a non-linear system identification method with disturbance at home and abroad, such as scholars y.mao et al in the document "a novel parameter separation based identification algorithm for Hammerstein systems", (brief translation: application of a new decoupling identification algorithm in Hammerstein system identification, published in Applied Mathematics Letters in the control field, vol.60,21-27,2016.) based on filtering technology and multiple innovation theory, a random gradient identification algorithm with parameter separation is provided, the complexity of calculation is reduced, the calculation of redundant parameters is avoided, meanwhile, the convergence rate and identification accuracy of the algorithm are improved by introducing the multiple innovation theory, but the method does not consider the influence of disturbance, the influence of disturbance on the identification algorithm cannot be eliminated, and the identification accuracy is reduced. Scholars M, poulique, et al in the document "Identification scheme for Hammerstein output error models with bound noise" (brief: an Identification mechanism of Hammerstein system for output error type of bounded noise, published in International journal IEEE Transactions on Automatic Control, vol.61, no.2,550-555, 2016.) provided an iterative Identification algorithm capable of identifying parameters of linear part and non-linear part of Hammerstein system of output error type at the same time, but this method did not consider the influence of disturbance on the Identification algorithm, when the output received disturbance, the Identification accuracy would be reduced, and this algorithm is an off-line algorithm and cannot be used on-line.
For the Hammerstein system with the output error type of disturbance, the existing method has the following defects: (1) The influence of measurement noise is not well processed, and when the output error model is converted into a regression equation, white noise can be converted into colored noise, so that the identification problem is more complicated; (2) The influence of disturbance is not considered, so that the disturbance pollutes output data in the identification process, the identification precision is reduced, or the system parameters and the disturbance are identified at the same time and are not distinguished; (3) The identification of system parameters adopts a single-information identification method, and only current data can be utilized. Identification of a hammerstein system for perturbed output error types has become a research hotspot.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a method for identifying a non-linear system with disturbance, which can solve the defects of the prior art and has high convergence rate and identification precision.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows.
A nonlinear system identification method aiming at disturbance comprises the following steps:
A. converting an industrial control system to be identified into a non-linear system model with disturbance, wherein the non-linear system consists of a non-linear link and a linear link, namely a Hammerstein system of an output error type; setting initial value
Figure BDA0002418508870000021
P(0)，P ξ (0)，
Figure BDA0002418508870000022
u(k)＝，p，γ 1 And gamma 2 Collecting system input and output data u (k) and y (k);
B. decomposing the non-linear system model with disturbance into two sub-models: a system noiseless output submodel and a disturbance submodel are used for constructing a system output vector Y (p, k) and an information vector
Figure BDA0002418508870000023
Information matrix
Figure BDA0002418508870000031
Disturbance vector
Figure BDA0002418508870000032
C. Updating system parameters
Figure BDA0002418508870000033
Construction of
Figure BDA0002418508870000034
And
Figure BDA0002418508870000035
updating parameters
Figure BDA0002418508870000036
Let k = k +1, return to step a until a cutoff condition is satisfied
Figure BDA0002418508870000037
Figure BDA0002418508870000038
Wherein δ is a non-negative number, or reaches a certain number of samples;
D. identifying parameters and disturbances of the industrial control system.
Preferably, in step A, u (k) is defined to represent system input, F (u (k)) represents a nonlinear element function, and F (q) represents a nonlinear element function -1 ) Representing a linear link function, x (k) representing the noise-free output of the system,
Figure BDA00024185088700000313
representing the system disturbance, v (k) representing the system output noise, and y (k) representing the system output, the non-linear discrete model with disturbance is as follows:
Figure BDA0002418508870000039
wherein the content of the first and second substances,
Figure BDA00024185088700000310
Figure BDA00024185088700000311
Figure BDA00024185088700000312
n a and n b For integer representation of the linear order of the elements, z represents a shifting factor, i.e.
Figure BDA0002418508870000041
The parameter vectors and information vectors defining the system model are as follows:
Figure BDA0002418508870000042
Figure BDA0002418508870000043
Figure BDA0002418508870000044
Figure BDA0002418508870000045
wherein n is s ＝n a +n b ×n c ；
The system noiseless output and the system output are respectively represented as,
Figure BDA0002418508870000046
Figure BDA0002418508870000047
preferably, in step B, the system noiseless output submodel and the disturbance submodel are expressed as,
y 1 (k)＝x(k)
Figure BDA0002418508870000048
the output of the system is represented as,
y(k)＝y 1 (k)+y 2 (k)+v(k)，
the prediction error function is expressed as,
Figure BDA0002418508870000049
a prediction error vector is defined which is,
Figure BDA0002418508870000051
wherein, p represents the length of the multiple news,
defining an information matrix, a noise vector, a disturbance vector and a system output vector,
Figure BDA0002418508870000052
Figure BDA0002418508870000053
Figure BDA0002418508870000054
Figure BDA0002418508870000055
the noiseless output submodel vector, the perturbation submodel vector and the system output vector are represented as,
Y 1 (p，k)＝Φ(p，k) T θ(k)
Figure BDA0002418508870000056
Y(p，k)＝Y 1 (p，k)+Y 2 (p，k)+V(p，k)，
a loss function is defined that is a function of,
Figure BDA0002418508870000057
since the non-linear system is decomposed into two submodels, the loss function is updated,
Figure BDA0002418508870000058
wherein, γ 1 ∈(0，1]And gamma 2 ∈(0，1]A forgetting factor is represented, which is,
Figure BDA0002418508870000061
represents an estimated value of phi (p, i),
Figure BDA0002418508870000062
an estimated value of theta (theta) is represented,
Figure BDA0002418508870000063
to represent
Figure BDA0002418508870000064
An estimate of (d).
Preferably, in step C, the loss function is updated to,
Figure BDA0002418508870000065
when calculating E (p, k), the last estimated value is used
Figure BDA0002418508870000066
Instead of the former
Figure BDA0002418508870000067
Calculating e 1 (k) Using the last estimated value
Figure BDA0002418508870000068
Substitute for
Figure BDA0002418508870000069
Establishing an auxiliary model, replacing an unknown variable x (k) with the output of the auxiliary model,
Figure BDA00024185088700000610
Figure BDA00024185088700000611
for is to
Figure BDA00024185088700000612
The first-order derivation is carried out,
Figure BDA00024185088700000613
Figure BDA00024185088700000614
Figure BDA00024185088700000615
Figure BDA00024185088700000616
Figure BDA00024185088700000617
Figure BDA0002418508870000071
ψ i (k)＝[f i (u(k-1))，L，f i (u(k-n b ))]
Figure BDA0002418508870000072
Figure BDA0002418508870000073
Figure BDA0002418508870000074
for is to
Figure BDA0002418508870000075
The first-order derivation is carried out,
Figure BDA0002418508870000076
Figure BDA0002418508870000077
Figure BDA0002418508870000078
wherein E (p, k) is multi-information,
Figure BDA0002418508870000079
is single information.
Preferably, in step C, before updating the loss function, the method is implemented
Figure BDA00024185088700000710
The pre-treatment is carried out, and the pretreatment,
Figure BDA00024185088700000711
Figure BDA00024185088700000712
wherein e is a natural base number, and F is a preprocessing function.
Adopt the beneficial effect that above-mentioned technical scheme brought to lie in:
the invention establishes a parameterized model of the Hammerstein system under disturbance conditions, and determines input variables, output variables, intermediate variables, measurement noise and disturbance noise. The parameterized model is decomposed into two sub-models: the system outputs a submodel and a disturbance submodel without noise, and divides the parameters to be identified into non-time-varying parameters and time-varying parameters. The noise-free output submodel consists of a nonlinear part and a linear part, the two parts are converted into a regression equation form of an input variable and a noise-free output, wherein the noise-free output is unknown. The noise-free output submodel of the system is deduced to be in a regression equation form, the system output is equal to the sum of the noise-free output, the disturbance and the measurement noise, wherein the disturbance is slow time-varying noise, and the measurement noise is white noise, so that the white noise is prevented from being converted into colored noise, and the least square is changed into biased estimation. And establishing a combined loss function of the noiseless output submodel and the disturbance submodel, and deducing a recursive least square algorithm, wherein the parameters of the noiseless output submodel adopt a multi-innovation theory, so that the convergence speed and the prediction precision of the identification algorithm are improved, and the parameters of the disturbance submodel adopt single innovation, so that the tracking performance of the algorithm is improved. Aiming at different characteristics of a noiseless output submodel and a disturbance submodel, two different forgetting factors are introduced, the introduction of forgetting can improve the convergence rate and the identification precision, and meanwhile, the tracking performance of slow time-varying disturbance is better.
The method for identifying various nonlinear industrial control systems has the advantages of high identification precision, high identification speed, strong robustness and wide applicable scenes.
Drawings
FIG. 1 is a schematic diagram of a Hammerstein system of the type with perturbed output errors of the present invention.
FIG. 2 is a schematic diagram of the aiding model of the present invention.
FIG. 3 is a flow chart of the identification method of the present invention.
Fig. 4 is a diagram of the input signals of the system of the present invention.
FIG. 5 is a graph of a perturbation signal according to the present invention.
Fig. 6 is a graph of the output signal of the present invention.
FIG. 7 is a comparison of the recognition effect of the least squares method of the present invention and the auxiliary model on the first parameter.
FIG. 8 is a comparison of the recognition effect of the least squares method of the present invention and the aided model on the second parameter.
FIG. 9 is a comparison of the identification effect of the least squares method of the present invention and the auxiliary model on the third parameter.
FIG. 10 is a comparison graph of the recognition effect of the least squares method of the present invention and the auxiliary model on the fourth parameter.
FIG. 11 is a comparison graph of the recognition effect of the least square method of the invention and the auxiliary model on the fifth parameter.
FIG. 12 is a comparison graph of the recognition effect of the least square method of the invention and the auxiliary model on the sixth parameter.
Detailed Description
Referring to fig. 1-3, one embodiment of the present invention includes the steps of:
A. converting an industrial control system to be identified into a non-linear system model with disturbance, wherein the non-linear system consists of a non-linear link and a linear link, namely a Hammerstein system of an output error type; setting initial value
Figure BDA0002418508870000091
P(0)，P ξ (0)，
Figure BDA00024185088700000912
u(k)＝0，p，γ 1 And gamma 2 Collecting system input and output data u (k) and y (k);
B. decomposing the non-linear system model with disturbance into two sub-models: the system noiseless output submodel and the disturbance submodel construct a system output vector Y (p, k) and an information vector
Figure BDA0002418508870000093
Information matrix
Figure BDA0002418508870000094
Disturbance vector
Figure BDA0002418508870000095
C. Updating system parameters
Figure BDA0002418508870000096
Construction of
Figure BDA0002418508870000097
And
Figure BDA0002418508870000098
updating parameters
Figure BDA0002418508870000099
Let k = k +1, return to step a until the cutoff condition is satisfied
Figure BDA00024185088700000910
Figure BDA00024185088700000911
Wherein δ is a non-negative number, or reaches a certain number of samples;
D. identifying parameters and disturbances of the industrial control system.
In the step A, u (k) is defined to represent system input, F (u (k)) represents a nonlinear link function, and F (q (k)) represents a nonlinear link function -1 ) Representing a linear element function, x (k) representing the noise-free output of the system,
Figure BDA0002418508870000101
representing the system disturbance, v (k) representing the system output noise, and y (k) representing the system output, the non-linear discrete model with disturbance is as follows:
Figure BDA0002418508870000102
wherein the content of the first and second substances,
Figure BDA0002418508870000103
Figure BDA0002418508870000104
Figure BDA0002418508870000105
n a and n b For integer representation of the linear order of the elements, z represents a shifting factor, i.e.
Figure BDA0002418508870000106
The parameter vector and the information vector defining the system model are as follows:
Figure BDA0002418508870000107
Figure BDA0002418508870000108
Figure BDA0002418508870000109
Figure BDA0002418508870000111
wherein n is s ＝n a +n b ×n c ；
The system noiseless output and the system output are respectively represented as,
Figure BDA0002418508870000112
Figure BDA0002418508870000113
in step B, the noise-free output submodel and the disturbance submodel of the system are expressed as,
y 1 (k)＝x(k)
Figure BDA0002418508870000114
the output of the system is represented as,
y(k)＝y 1 (k)+y 2 (k)+v(k)，
the prediction error function is expressed as,
Figure BDA0002418508870000115
a prediction error vector is defined which is,
Figure BDA0002418508870000116
wherein, p represents the length of the multiple information,
defining an information matrix, a noise vector, a disturbance vector and a system output vector,
Figure BDA0002418508870000117
Figure BDA0002418508870000118
Figure BDA0002418508870000121
Figure BDA0002418508870000122
the noiseless output submodel vector, the perturbation submodel vector and the system output vector are represented as,
Y 1 (p，k)＝Φ(p，k) T θ(k)
Figure BDA0002418508870000123
Y(p，k)＝Y 1 (p，k)+Y 2 (p，k)+V(p，k)，
a loss function is defined that is a function of,
Figure BDA0002418508870000124
since the non-linear system is decomposed into two submodels, the loss function is updated,
Figure BDA0002418508870000125
wherein, γ 1 ∈(0，1]And gamma 2 ∈(0，1]A forgetting factor is represented, which is,
Figure BDA0002418508870000126
represents an estimated value of phi (p, i),
Figure BDA0002418508870000127
represents an estimated value of theta (k),
Figure BDA0002418508870000128
represent
Figure BDA0002418508870000129
An estimate of (d).
In step C, the loss function is updated to,
Figure BDA00024185088700001210
when calculating E (p, k), the last estimated value is utilized
Figure BDA00024185088700001211
Substitute for
Figure BDA00024185088700001212
Calculating e 1 (k) Using the last estimated value
Figure BDA0002418508870000131
Instead of the former
Figure BDA0002418508870000132
Establishing an auxiliary model, replacing an unknown variable x (k) with the output of the auxiliary model,
Figure BDA0002418508870000133
Figure BDA0002418508870000134
to pair
Figure BDA0002418508870000135
The first-order derivation is carried out,
Figure BDA0002418508870000136
Figure BDA0002418508870000137
Figure BDA0002418508870000138
Figure BDA0002418508870000139
Figure BDA00024185088700001310
Figure BDA00024185088700001311
ψ i (k)＝[f i (u(k-1))，L，f i (u(k-n b ))]
Figure BDA00024185088700001312
Figure BDA00024185088700001313
Figure BDA0002418508870000141
to pair
Figure BDA0002418508870000142
The first-order derivation is carried out,
Figure BDA0002418508870000143
Figure BDA0002418508870000144
Figure BDA0002418508870000145
wherein E (p, k) is multi-information,
Figure BDA0002418508870000149
is single information.
In step C, before updating the loss function, the
Figure BDA0002418508870000146
The pre-treatment is carried out, and the pretreatment,
Figure BDA0002418508870000147
Figure BDA0002418508870000148
wherein e is a natural base number, and F is a preprocessing function.
After the system model is identified, the system model needs to be verified, the input and output data of the system needs to be collected again, the effectiveness of the identified model is verified by using new data, when the effect is not good, the initial value of the algorithm can be adjusted, and the identification is carried out again until the system model meeting the requirements is obtained.
The advantages of the method provided by the invention are illustrated by taking a hammerstein system model with disturbed output error types converted by a power plant reheater control system as an example. The system model is as follows:
Figure BDA0002418508870000151
wherein, the parameters to be identified are a = [ -1.22,0.93], B = [0.81,0.73], C = [0.51,0.22], and the input signal u (k) is shown in fig. 4 by using a gaussian random sequence with a mean value 0 and a variance of 1; the perturbation signal is shown in FIG. 5; the output signal y (k) is shown in fig. 6.
The initial value of the method is P (0) =10 6 I 8×8 ，
Figure BDA0002418508870000152
p =6,n =6000. The method provided by the invention and the scholars of Ding F, shi Y, chen T and the like are disclosed in the document "Auxiliary model-based least-squares identification methods for Hammerstein output-error systems [ J].Systems&The system model is identified by an auxiliary model least square method mentioned in Control Letters,2007,56 (5): 373-380', and FIGS. 7-12 prove that the method of the inventionEffectiveness.
The foregoing shows and describes the general principles and broad features of the present invention and advantages thereof. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (2)

1. A method for identifying a non-linear system with disturbance is characterized by comprising the following steps:
A. converting an industrial control system to be identified into a non-linear system model with disturbance, wherein the non-linear system consists of a non-linear link and a linear link, namely a Hammerstein system of an output error type; setting initial value
Figure FDA0003664079220000011
P(0)，
Figure FDA0003664079220000012
u(k)＝0，p，γ 1 And gamma 2 Collecting system input and output data u (k) and y (k);
B. decomposing the non-linear system model with disturbance into two sub-models: a system noiseless output submodel and a disturbance submodel are used for constructing a system output vector Y (p, k) and an information vector
Figure FDA0003664079220000013
Information matrix
Figure FDA0003664079220000014
Disturbance vector
Figure FDA0003664079220000015
C. Updating system parameters
Figure FDA0003664079220000016
Construction of
Figure FDA0003664079220000017
And
Figure FDA0003664079220000018
updating parameters
Figure FDA0003664079220000019
Let k = k +1, return to step a until a cutoff condition is satisfied
Figure FDA00036640792200000110
Figure FDA00036640792200000111
Wherein δ is a non-negative number, or reaches a certain number of samples;
D. identifying parameters and disturbances of the industrial control system;
in the step A, u (k) is defined to represent system input, F (u (k)) represents a nonlinear link function, and F (q) represents a nonlinear link function -1 ) Representing a linear element function, x (k) representing the noise-free output of the system,
Figure FDA00036640792200000112
representing the system disturbance, v (k) representing the system output noise, and y (k) representing the system output, the nonlinear discrete model with disturbance is as follows:
Figure FDA0003664079220000021
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003664079220000022
Figure FDA0003664079220000023
Figure FDA0003664079220000024
n a and n b For integer representation of the linear ring order, z represents a shifting factor, i.e.
Figure FDA0003664079220000025
The parameter vector and the information vector defining the system model are as follows:
Figure FDA0003664079220000026
Figure FDA0003664079220000027
Figure FDA0003664079220000028
Figure FDA0003664079220000029
wherein n is s ＝n a +n b ×n c ；
The system noiseless output and the system output are respectively represented as,
Figure FDA0003664079220000031
Figure FDA0003664079220000032
in the step B, the system noiseless output submodel and the disturbance submodel are expressed as,
y 1 (k)＝x(k)
Figure FDA0003664079220000033
the output of the system is represented as,
y(k)＝y 1 (k)+y 2 (k)+v(k)，
the prediction error function is expressed as,
Figure FDA0003664079220000034
a prediction error vector is defined which is,
Figure FDA0003664079220000035
wherein, p represents the length of the multiple news,
defining an information matrix, a noise vector, a disturbance vector and a system output vector,
Figure FDA0003664079220000036
Figure FDA0003664079220000037
Figure FDA0003664079220000038
Figure FDA0003664079220000041
the noiseless output sub-model vector, the perturbation sub-model vector and the system output vector are represented as,
Y 1 (p，k)＝Φ(p，k) T θ(k)
Figure FDA0003664079220000042
Y(p，k)＝Y 1 (p，k)+Y 2 (p，k)+V(p，k)，
a loss function is defined that is a function of,
Figure FDA0003664079220000043
since the non-linear system is decomposed into two submodels, the loss function is updated,
Figure FDA0003664079220000044
wherein, gamma is 1 ∈(0，1]And gamma 2 ∈(0，1]A forgetting factor is represented and a number of factors,
Figure FDA0003664079220000045
represents an estimated value of phi (p, i),
Figure FDA0003664079220000046
represents an estimated value of theta (k),
Figure FDA0003664079220000047
to represent
Figure FDA0003664079220000048
An estimated value of (d);
in the step C, the loss function is updated as,
Figure FDA0003664079220000049
when calculating E (p, k), the last estimated value is used
Figure FDA00036640792200000410
Substitute for
Figure FDA00036640792200000411
Calculating e 1 (k) Using the last estimated value
Figure FDA00036640792200000412
Substitute for
Figure FDA00036640792200000413
Establishing an auxiliary model, replacing an unknown variable x (k) with the output of the auxiliary model,
Figure FDA0003664079220000051
Figure FDA0003664079220000052
to pair
Figure FDA0003664079220000053
The first-order derivation is carried out,
Figure FDA0003664079220000054
Figure FDA0003664079220000055
Figure FDA0003664079220000056
Figure FDA0003664079220000057
Figure FDA0003664079220000058
Figure FDA0003664079220000059
ψ i (k)＝[f i (u(k-1))，L，f i (u(k-n b ))]
Figure FDA00036640792200000510
Figure FDA00036640792200000511
Figure FDA00036640792200000512
for is to
Figure FDA00036640792200000513
The first-order derivation is carried out,
Figure FDA0003664079220000061
Figure FDA0003664079220000062
Figure FDA0003664079220000063
wherein E (p, k) is multi-information,
Figure FDA0003664079220000064
is single information.
2. The method for non-linear system identification with disturbance according to claim 1, characterized in that: in step C, before updating the loss function, the pair
Figure FDA0003664079220000065
The pre-treatment is carried out, and the pretreatment,
Figure FDA0003664079220000066
Figure FDA0003664079220000067
wherein e is a natural base number, and F is a preprocessing function.
CN202010198543.4A 2020-03-20 2020-03-20 Nonlinear system identification method aiming at disturbance Active CN111427266B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202010198543.4A CN111427266B (en) 2020-03-20 2020-03-20 Nonlinear system identification method aiming at disturbance

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202010198543.4A CN111427266B (en) 2020-03-20 2020-03-20 Nonlinear system identification method aiming at disturbance

Publications (2)

Publication Number Publication Date
CN111427266A CN111427266A (en) 2020-07-17
CN111427266B true CN111427266B (en) 2022-10-11

Family

ID=71548225

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202010198543.4A Active CN111427266B (en) 2020-03-20 2020-03-20 Nonlinear system identification method aiming at disturbance

Country Status (1)

Country Link
CN (1) CN111427266B (en)

Families Citing this family (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110286332B (en) * 2019-06-17 2021-06-22 南通大学 Electric vehicle power battery SOC estimation method based on multiple innovation theory
CN111930014B (en) * 2020-08-13 2022-07-01 重庆邮电大学 Dynamic and static data hybrid-driven Hammerstein nonlinear industrial system simple grey box space identification method
CN112149274B (en) * 2020-08-19 2024-06-18 浙江工业大学 Online modeling method for multi-axis engraving machine system with dead zone input nonlinearity
CN112668120A (en) * 2020-12-30 2021-04-16 无锡商业职业技术学院 Online identification method for multi-innovation random gradient of nonlinear sandwich model auxiliary model of mechanical transmission system
CN113111505A (en) * 2021-04-08 2021-07-13 杭州电子科技大学 Variable forgetting factor recursive least square method and system based on nonlinear Hammerstein system
CN115167320A (en) * 2022-08-09 2022-10-11 浙江中控技术股份有限公司 Model identification method, device, equipment and storage medium of industrial control system
CN116400596B (en) * 2023-04-03 2024-04-09 中国矿业大学 Industrial time-varying system two-dimensional recursion identification modeling method for dead zone with input

Family Cites Families (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106227964B (en) * 2016-07-28 2019-01-22 华侨大学 Nonlinear systems with hysteresis parameter identification method based on extended state observer
CN109491251B (en) * 2018-12-18 2020-07-10 华中科技大学 AC servo system model identification method and equipment considering data disturbance compensation
CN109885807A (en) * 2019-01-22 2019-06-14 哈尔滨工业大学（深圳） Weighting latest estimated linear least squares method method of the Hammerstein system under white noise acoustic jamming

Also Published As

Publication number Publication date
CN111427266A (en) 2020-07-17

Similar Documents

Publication Publication Date Title
CN111427266B (en) Nonlinear system identification method aiming at disturbance
CN109766950B (en) Industrial user short-term load prediction method based on morphological clustering and LightGBM
Gao et al. New approach to mixed H/sub 2//H/sub/spl infin//filtering for polytopic discrete-time systems
CN113489014B (en) Quick and flexible full-pure embedded power system optimal power flow evaluation method
CN104537415A (en) Non-linear process industrial fault prediction and identification method based on compressed sensing and DROS-ELM
Duan et al. On the optimization landscape of dynamic output feedback linear quadratic control
Bardet et al. Monitoring procedure for parameter change in causal time series
CN114034486A (en) Unsupervised transfer learning-based bearing fault diagnosis method for pump mechanical equipment
CN108228978B (en) Xgboost time sequence prediction method combined with complementary set empirical mode decomposition
CN113627685B (en) Wind driven generator power prediction method considering wind power internet load limit
Elnaggar et al. Recursive estimation for system of unknown delay
CN115167320A (en) Model identification method, device, equipment and storage medium of industrial control system
WO2004090782A1 (en) Accurate linear parameter estimation with noisy inputs
CN117131022B (en) Heterogeneous data migration method of electric power information system
Xu et al. Finite-frequency fault estimation and accommodation for continuous-time Markov jump linear systems with imprecise statistics of modes transitions
Xie On robust H2 estimation
CN111399477B (en) Parameter separation-based Wiener nonlinear system identification method
Li et al. Integrated design of event-triggered closed-loop subspace predictive control scheme
CN116628524A (en) Community discovery method based on adaptive graph attention encoder
CN115473830A (en) Data center performance index abnormity detection method, device, system and medium
CN110244563B (en) Neural network internal model controller model mismatch identification and online updating method
CN115358473A (en) Power load prediction method and prediction system based on deep learning
CN113821419A (en) Cloud server aging prediction method based on SVR and Gaussian function
Han et al. Quantized optimal output feedback control and optimal triggering signal co‐design for unknown discrete‐time nonlinear systems
CN111258215A (en) Data driving controller of model unknown system

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant