CN112327627B - Nonlinear switching system self-adaptive sliding mode control method based on composite learning - Google Patents

Nonlinear switching system self-adaptive sliding mode control method based on composite learning Download PDF

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CN112327627B
CN112327627B CN202011274007.4A CN202011274007A CN112327627B CN 112327627 B CN112327627 B CN 112327627B CN 202011274007 A CN202011274007 A CN 202011274007A CN 112327627 B CN112327627 B CN 112327627B
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sliding mode
switching system
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CN112327627A (en
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许斌
程怡新
马波
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Northwestern Polytechnical University
AVIC Chengdu Aircraft Design and Research Institute
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AVIC Chengdu Aircraft Design and Research Institute
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Abstract

The invention relates to a nonlinear switching system self-adaptive sliding mode control method based on composite learning, which is used for solving the technical problem of poor practicability of the existing nonlinear switching system control method. Considering the existence of external interference and input nonlinearity of a nonlinear switching system, and obtaining an input dead zone model of the switching system; respectively estimating unknown nonlinear functions and complex interference of the system by using a neural network and a switching disturbance observer, constructing a prediction error representing the learning performance based on a parallel estimation model, and adjusting the neural network weight updating law and the disturbance observer by the prediction error; designing a self-adaptive sliding die cutting controller based on a dynamic inverse technology framework and a composite learning strategy; a sliding mode time-varying gain function is constructed by utilizing the prediction error, the amplitude of the sliding mode switching buffeting is reduced, and the performance of sliding mode control is improved; the invention combines the control characteristics of a nonlinear switching system and effectively improves the control performance by designing the self-adaptive sliding mode controller based on the composite learning.

Description

Nonlinear switching system self-adaptive sliding mode control method based on composite learning
Technical Field
The invention relates to a nonlinear switching system control method, in particular to a nonlinear switching system self-adaptive sliding mode control method based on composite learning, and belongs to the field of flight control.
Background
In practical engineering, many control objects such as a variant aircraft, a variable frequency motor, a robot and the like can be described by using a nonlinear switching system, so that the nonlinear switching system control technology attracts wide attention and is researched and applied in many industries such as automobiles, electric power, chemical engineering and the like.
The nonlinear switching system has strong uncertainty and is easily influenced by external interference and an input dead zone, the existing control method mostly adopts an intelligent system such as a neural network or fuzzy logic to approximate the uncertainty, and a disturbance observer is adopted to estimate the external interference. The control methods only consider the approaching effect of an intelligent system, ignore the essence of an intelligent learning strategy, and do not effectively evaluate the uncertain learning performance, and the intelligent approaching system and the disturbance observer do not have information interaction, so the robustness is poor, and the engineering realization is not facilitated. Therefore, the research of the advanced control method for improving the learning performance has great significance and urgent need for the control research of the nonlinear switching system.
Disclosure of Invention
Technical problem to be solved
In order to overcome the defect that the existing nonlinear switching system control method is poor in practicability, the invention provides a nonlinear switching system self-adaptive sliding mode control method based on composite learning. According to the method, uncertainty, external interference and input nonlinearity of a nonlinear switching system are considered, and an input dead zone model is obtained through model conversion. Meanwhile, the neural network and the disturbance observer are adopted to estimate the nonlinear function and the composite interference respectively, the learning effect is evaluated by constructing a prediction error, and then the neural network weight self-adaptive updating law and the disturbance observer are adjusted. A self-adaptive sliding mode controller is designed based on a dynamic inverse technology frame and a composite learning strategy, and a time-varying sliding mode gain function improves the robustness of the controller and facilitates engineering realization.
Technical scheme
A nonlinear switching system self-adaptive sliding mode control method based on composite learning is characterized by comprising the following steps:
step 1: single-input single-output non-linear energy control standard type switching system
Figure BDA0002778558790000021
Wherein,
Figure BDA0002778558790000022
is a system state vector;uσ(t)e R is system input, y e R is system output; the function σ (t) [ [0, ∞) → M ═ 1,2, …, M } is the switching signal, and σ (t) → k indicates that the kth subsystem is active;
Figure BDA0002778558790000023
is about
Figure BDA0002778558790000024
Is determined by the unknown smoothing function of (a),
Figure BDA0002778558790000025
is about
Figure BDA0002778558790000026
An unknown non-zero smoothing function of (a); dσ(t)(t) is external unknown interference;
step 2: describing system input nonlinearity as
Figure BDA0002778558790000027
Wherein u isv,kE R is an input with a dead zone,
Figure BDA0002778558790000028
br,kand bl,kIs an unknown normal number;
can be further described as (2)
Figure BDA0002778558790000029
Wherein
Figure BDA00027785587900000210
Signal ukThere are the following relationships
Figure BDA00027785587900000211
Wherein
Figure BDA00027785587900000212
Is uv,kThe upper bound value of (d);
the system (1) can be further written as
Figure BDA0002778558790000031
Wherein,
Figure BDA0002778558790000032
and step 3: for unknown functions
Figure BDA0002778558790000033
And
Figure BDA0002778558790000034
approximation by neural networks
Figure BDA0002778558790000035
Figure BDA0002778558790000036
Wherein,
Figure BDA0002778558790000037
and
Figure BDA0002778558790000038
is the optimal weight vector of the neural network,
Figure BDA0002778558790000039
and
Figure BDA00027785587900000310
is a vector of basis functions of the neural network, epsilonf,kAnd epsilonG,kIs a neural network residual and exists
Figure BDA00027785587900000311
And
Figure BDA00027785587900000312
and
Figure BDA00027785587900000313
is a normal number;
then
Figure BDA00027785587900000314
And
Figure BDA00027785587900000315
can be written as
Figure BDA00027785587900000316
Figure BDA00027785587900000317
Wherein,
Figure BDA00027785587900000318
and
Figure BDA00027785587900000319
is the optimal weight vector estimation value of the neural network;
definition of Δ uk＝uv,k-uc,kThen xnCan be written as
Figure BDA00027785587900000320
Wherein,
Figure BDA00027785587900000321
Figure BDA00027785587900000322
and 4, step 4: aiming at a nonlinear switching system (1), designing an adaptive sliding mode controller based on a composite learning strategy;
defining output tracking error
Figure BDA00027785587900000323
Wherein e ═ x1-yd，ydIs a control reference command;
the slip form surface is designed as
s＝[ΛT 1]E (11)
Wherein Λ ═ τn-1,(n-1)τn-2,…,(n-1)τ]T，τ>0；
The derivative of the slip form surface s is
Figure BDA0002778558790000041
Wherein,
Figure BDA0002778558790000042
the design controller is
Figure BDA0002778558790000043
Wherein
Figure BDA0002778558790000044
Figure BDA0002778558790000045
Figure BDA0002778558790000046
Wherein,
Figure BDA0002778558790000047
is DkEstimate of (t), βkIs a positive design parameter, mkIs a sliding mode gain function;
construction prediction error znNNIs composed of
Figure BDA0002778558790000048
Wherein,
Figure BDA0002778558790000049
can be obtained by parallel estimation model
Figure BDA00027785587900000410
Wherein,
Figure BDA00027785587900000411
λn,kis a positive design parameter;
designing a sliding mode gain function of
mk＝-γz,kλkznNN (19)
Wherein, γz,kIs a positive design parameter;
design neural network weight update law as
Figure BDA0002778558790000051
Figure BDA0002778558790000052
Wherein,γf,k，γG,k，δf,kand deltaG,kIs a positive design parameter;
design a switching disturbance observer as
Figure BDA0002778558790000053
Wherein ξnIs an intermediate variable, LkIs a positive design parameter;
and 4, step 4: according to the control amount u obtained in step 3 (13)c,kReturning to the system model (1), the system output y is subjected to tracking control.
Advantageous effects
The invention provides a nonlinear switching system self-adaptive sliding mode control method based on composite learning. According to the method, uncertainty, external interference and input nonlinearity of a nonlinear switching system are considered, and an input dead zone model is obtained through model conversion. And simultaneously, a neural network and a disturbance observer are adopted to estimate the nonlinear function and the composite interference respectively, and the learning effect is evaluated by constructing a prediction error, so that the weight adaptive updating law of the neural network and the disturbance observer are adjusted. A self-adaptive sliding mode controller is designed based on a dynamic inverse technology frame and a composite learning strategy, and a time-varying sliding mode gain function improves the robustness of the controller and facilitates engineering realization. The beneficial effects are as follows:
(1) a prediction error is constructed based on a parallel estimation model, a neural network weight updating law is designed based on the error, the uncertainty learning precision is improved, and engineering application is facilitated;
(2) a nonlinear switching disturbance observer is designed, and effective estimation compensation is carried out on the adverse effects caused by external time-varying interference and an input unknown dead zone;
(3) based on the prediction error, an improved time-varying gain sliding mode is adopted for controller design, and buffeting during control switching is reduced;
(4) and introducing the sliding mode surface signal into the design of a neural network and a disturbance observer, and realizing effective estimation on an unknown nonlinear function and external time-varying interference through the interactive cooperation of the neural network and the disturbance observer.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention.
Detailed Description
The invention will now be further described with reference to the following examples and drawings:
referring to fig. 1, the adaptive sliding mode control method of the nonlinear switching system based on the composite learning comprises the following specific steps:
step 1: consider morphing aircraft wing rock model
Figure BDA0002778558790000061
Wherein phi is,
Figure BDA0002778558790000062
And
Figure BDA0002778558790000063
roll angle, roll angle rate and roll angle acceleration, respectively, u is the control input;
the various coefficients in the model are defined as
Figure BDA0002778558790000064
Wherein, a1To a5Is a variable related to angle of attack, c1And c2Is a constant determined by the sweep angle;
defining a state quantity x (t) ═ x1,x2]T∈R2Wherein x is1＝φ，
Figure BDA0002778558790000065
The sweep-back angle is used as a switching signal, and the morphing aircraft wing rock model can be converted into a 2-order single-input single-output nonlinear switching system
Figure BDA0002778558790000066
Wherein,
Figure BDA0002778558790000067
is a system state vector; u. ofσ(t)E R is system input, y e R is system output; the function σ (t) e {1,2} is the switching signal;
Figure BDA0002778558790000068
is an unknown nonlinear function; d1(t)＝0.1cos(t2)，d2(t) ═ 0.1sin (t) is the introduced external interference;
step 2: describing system input nonlinearity as
Figure BDA0002778558790000071
Wherein u isv,kE R is an input with a dead zone,
Figure BDA0002778558790000072
bl,1＝0.5，br,1＝0.1，
Figure BDA0002778558790000073
bl,2＝0.8，br,2＝0.3；
can be further described as (2)
Figure BDA0002778558790000074
Wherein
Figure BDA0002778558790000075
Signal ukThere is the following relationship
Figure BDA0002778558790000076
Wherein
Figure BDA0002778558790000077
Is uv,kThe upper bound value of (d);
the system (1) can be further written as
Figure BDA0002778558790000078
And step 3: for unknown functions
Figure BDA0002778558790000079
Approximation by neural networks
Figure BDA00027785587900000710
Wherein,
Figure BDA00027785587900000711
is the optimal weight vector of the neural network,
Figure BDA00027785587900000712
is a vector of basis functions of the neural network, epsilonf,kIs a neural network residual and exists
Figure BDA00027785587900000713
Is a normal number;
then
Figure BDA00027785587900000714
Can be written as
Figure BDA00027785587900000715
Wherein,
Figure BDA0002778558790000081
and
Figure BDA0002778558790000082
is the optimal weight vector estimation value of the neural network;
definition of Δ uk＝uv,k-uc,kThen x2Can be written as
Figure BDA0002778558790000083
Wherein,
Figure BDA0002778558790000084
and 4, step 4: aiming at a nonlinear switching system (1), designing an adaptive sliding mode controller based on a composite learning strategy;
defining output tracking error
Figure BDA0002778558790000085
Wherein e ═ x1-yd，ydIs a control reference command;
the slip form surface is designed as
s＝[ΛT 1]E (10)
Wherein Λ τ > 0;
the derivative of the slip form surface s is
Figure BDA0002778558790000086
Wherein,
Figure BDA0002778558790000087
the design controller is
Figure BDA0002778558790000088
Wherein
Figure BDA0002778558790000089
Figure BDA00027785587900000810
Figure BDA00027785587900000811
Wherein,
Figure BDA00027785587900000812
is Dk(t) estimated value, βkIs a positive design parameter, mkIs a sliding mode gain function;
construction prediction error z2NNIs composed of
Figure BDA0002778558790000091
Wherein,
Figure BDA0002778558790000092
can be obtained by a parallel estimation model
Figure BDA0002778558790000093
Wherein,
Figure BDA0002778558790000094
λkis a positive design parameter;
designing a sliding mode gain function as
mk＝-γz,kλkz2NN (18)
Wherein, γz,kIs a positive design parameter;
design neural network weight update law as
Figure BDA0002778558790000095
Wherein, gamma isf,kAnd deltaf,kIs a positive design parameter;
design a switching disturbance observer as
Figure BDA0002778558790000096
Wherein ξ2Is an intermediate variable, LkIs a positive design parameter;
and 4, step 4: according to the control amount u obtained in step 3 (12)c,kAnd returning to the wing rock-roll model (1) of the morphing aircraft, and performing tracking control on the roll angle phi.
The invention is not described in detail and is part of the common general knowledge of a person skilled in the art.

Claims (1)

1. A nonlinear switching system self-adaptive sliding mode control method based on composite learning is characterized by comprising the following steps:
step 1: single-input single-output non-linear energy control standard type switching system
Figure FDA0003531039510000011
Wherein,
Figure FDA0003531039510000012
is a system state vector; u. ofσ(t)E R is system input, y e R is system output; the function σ (t): 0, ∞ → M ═ 1,2, · M } is the switching signal, and σ (t) → k indicates that the kth subsystem is active;
Figure FDA0003531039510000013
is about
Figure FDA0003531039510000014
Is determined by the unknown smoothing function of (a),
Figure FDA0003531039510000015
is about
Figure FDA0003531039510000016
An unknown non-zero smoothing function of (a); dσ(t)(t) is external unknown interference;
step 2: describing system input nonlinearity as
Figure FDA0003531039510000017
Wherein u isv,kE R is an input with a dead zone,
Figure FDA0003531039510000018
br,kand bl,kIs an unknown normal number;
can be further described as (2)
Figure FDA00035310395100000112
Wherein
Figure FDA0003531039510000019
Signal ukThere are the following relationships
Figure FDA00035310395100000110
Wherein
Figure FDA00035310395100000111
Is uv,kThe upper bound value of (d);
the system (1) can be further written as
Figure FDA0003531039510000021
Wherein,
Figure FDA0003531039510000022
and step 3: for unknown functions
Figure FDA00035310395100000222
And
Figure FDA0003531039510000023
approximation by neural networks
Figure FDA0003531039510000024
Figure FDA0003531039510000025
Wherein,
Figure FDA0003531039510000026
and
Figure FDA0003531039510000027
is the optimal weight vector of the neural network,
Figure FDA00035310395100000223
and
Figure FDA0003531039510000028
is a vector of basis functions of the neural network, epsilonf,kAnd epsilonG,kIs a neural networkResidual error and existence
Figure FDA0003531039510000029
And
Figure FDA00035310395100000210
and
Figure FDA00035310395100000211
is a normal number;
then
Figure FDA00035310395100000212
And
Figure FDA00035310395100000213
can be written as
Figure FDA00035310395100000214
Figure FDA00035310395100000215
Wherein,
Figure FDA00035310395100000216
and
Figure FDA00035310395100000217
is the optimal weight vector estimation value of the neural network;
definition of Δ uk＝uv,k-uc,kThen xnCan be written as
Figure FDA00035310395100000218
Wherein,
Figure FDA00035310395100000219
Figure FDA00035310395100000220
and 4, step 4: aiming at a nonlinear switching system (1), designing an adaptive sliding mode controller based on a composite learning strategy;
defining output tracking error
Figure FDA00035310395100000221
Wherein e ═ x1-yd，ydIs a control reference command;
the slip form surface is designed as
s＝[ΛT 1]E (11)
Wherein Λ ═ τn-1,(n-1)τn-2,...,(n-1)τ]T，τ＞0；
The derivative of the slip form surface s is
Figure FDA0003531039510000031
Wherein,
Figure FDA0003531039510000032
the design controller is
Figure FDA0003531039510000033
Wherein
Figure FDA0003531039510000034
Figure FDA0003531039510000035
Figure FDA0003531039510000036
Wherein,
Figure FDA0003531039510000037
is DkEstimate of (t), βkIs a positive design parameter, mkIs a sliding mode gain function;
construction prediction error znNNIs composed of
Figure FDA0003531039510000038
Wherein,
Figure FDA0003531039510000039
can be obtained by a parallel estimation model
Figure FDA00035310395100000310
Wherein,
Figure FDA00035310395100000311
λkis a positive design parameter;
designing a sliding mode gain function of
mk＝-γz,kλkznNN (19)
Wherein, γz,kIs a positive design parameter;
design neural network weight update law as
Figure FDA0003531039510000041
Figure FDA0003531039510000042
Wherein, γf,k，γG,k，δf,kAnd deltaG,kIs a positive design parameter;
design a switching disturbance observer as
Figure FDA0003531039510000043
Wherein ξnIs an intermediate variable, LkIs a positive design parameter;
and 4, step 4: according to the control amount u obtained in step 3 (13)c,kReturning to the system model (1), the system output y is subjected to tracking control.
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