CN102998973B - The multi-model Adaptive Control device of a kind of nonlinear system and control method - Google Patents

The multi-model Adaptive Control device of a kind of nonlinear system and control method Download PDF

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CN102998973B
CN102998973B CN201210496139.0A CN201210496139A CN102998973B CN 102998973 B CN102998973 B CN 102998973B CN 201210496139 A CN201210496139 A CN 201210496139A CN 102998973 B CN102998973 B CN 102998973B
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CN102998973A (en
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王昕�
黄淼
牟金善
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Shanghai Jiaotong University
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Abstract

The present invention discloses multi-model Adaptive Control device and the control method of a kind of nonlinear system, use a non linear robust Indirect adaptive control device and a nonlinear neural network Indirect adaptive control device, be switched to optimal controller based on performance indications in each sampling instant and realize control.Compared with traditional non-linear multi-model Adaptive Control device and control method, the boundary of the nonlinear terms of nonlinear system is loosened to zeroth order close to bounded by the present invention, can effectively expand the adaptability of multi-model Adaptive Control device.

Description

The multi-model Adaptive Control device of a kind of nonlinear system and control method
Technical field
The present invention relates to the controlled device of various reality in every profession and trade production process, be specifically related to the non-of a class zeroth order bounded One class multi-model Adaptive Control device of linear complex control system and control method thereof.
Background technology
Owing to modern industry changes to technology-intensive type, occur in that and be made up of miscellaneous subsystem and element and internal The complicated Complex Industrial Systems process of relation.This system often has the features such as strong nonlinearity, fast time variant, model be uncertain. Although existing non-linear processing methods has some to apply, but imperfection in theory, and the requirement to controlled device is high, and not There is generality.
Due to the adaptive parameter features such as the unknown in a large number, classical control theory and the method in modern control theory are difficult to solve These features, Self Adaptive Control can process the control problem of to a certain degree uncertain system and be widely used in non-linear In the control of system.By to System Discrimination, Self Adaptive Control can automatically compensate for model order, parameter and input signal side The change in face, can preferably be controlled effect.But very fast for time-varying, parameter has the controlled device of saltus step, self adaptation The poor effect of control system identification, thus cause the situation that dynamic property is poor, transient error is excessive of system.Multi-model is certainly Suitable solution develops on the basis of Self Adaptive Control, can effectively reduce the transient error of system.It is proposed that it is a kind of The model structure of new nonlinear system, this model structure be made up of linear segment and nonlinear terms part have more general Property, for fast time variant, parameter saltus step object, use multiple identification model, it is thus achieved that preferably control effect.But, traditional many Model self-adapted control method requires the nonlinear terms part global bounded of controlled device, and it is adaptive that this condition limits multi-model Answer control method application in systems in practice.
Content of the invention
The present invention is directed to technical problem present in above-mentioned prior art, the multi-model providing a kind of nonlinear system is adaptive Answer controller and control method.Relax the restrictive condition of nonlinear system, expand the use model of multi-model Adaptive Control method Enclose.Nonlinear terms global bounded condition has not only been loosened to zeroth order close to bounded by the method, and it is adaptive to reduce multi-model Answer the steady-state error of control system, improve control accuracy.
For reaching above-mentioned purpose, the technical solution used in the present invention is:
The multi-model Adaptive Control device of a kind of nonlinear system, this controller is by a non linear robust indirect self-adaptive Controller, a nonlinear neural network adaptive controller and switching mechanism three part composition, wherein, a controller is non- Linear robust Indirect adaptive control device, another is nonlinear neural network Indirect adaptive control device, controlled device defeated Enter and selected between the two controllers by switching mechanism to produce, between the output of controlled device and two controllers, have a closed loop to bear Feedback, is set to subtract each other relation between the model output of controlled device and two Indirect adaptive control devices, and model error is used for Adjust the parameter of model and the weights of neutral net.
Described non linear robust Indirect adaptive control device includes a non linear robust adaptive model and a non-thread Property controller, non linear robust adaptive model is made up of linear processes two parts, linear segment correspondence system linearize After linear segment, non-linear partial is represented by the norm of the regression vector with coefficient, after compensating system linearization Non-linear partial.Regression vector is made up of input and the output variable of system last time.Adaptive parameter is linear regression The coefficient of vector, adaptive law uses projection adaptive law.Gamma controller uses a step advancing controller.
Described nonlinear neural network adaptive controller includes a nonlinear neural network adaptive model and one Nonlinear neural network adaptive controller.Nonlinear neural network adaptive model is by linear segment and nonlinear neural network Part composition.The coefficient of linear segment can be updated in any way as auto-adaptive parameter.Nonlinear neural network is adopted Use BP network, utilize error back propagation method to train.
In described switching mechanism, first one performance indications of design, this performance indications comprise an accumulated error part With a transient error part.Control the moment at each, calculate the performance indications of each controller, select performance indications less Controller produce subsequent time control input, it is possible to achieve switch smoothly, and improve system transient performance.
The step that the control method of the multi-model Adaptive Control device of above-mentioned nonlinear system is comprised is as follows:
S1: system initialization: the parameter of random initializtion non linear robust adaptive model, the non-linear god of random initializtion Through the weights of the parameter of network model and neutral net, these parameters can be determined by certain priori;
In the S2:k=0 moment, object is output as 0;In k ≠ 0 moment, object is output as the real output value of system, and is System setting value makees the control error e that difference obtains systemc;Actual output makees poor obtaining with the output of non linear robust adaptive model Model error e1, make difference with nonlinear neural network model and obtain model error e2
S3: error e will be controlledcAs non linear robust adaptive controller and nonlinear neural network adaptive controller Input, two controllers are produced controlled quentity controlled variable u respectively1And u2
S4: according to model error e1And e2Carry out calculation of performance indicators C1And C2Value, select the less control of performance index value The input u that device producesi, as the control input u of controlled device and two models;
S5: utilize model error e1And e2Update non linear robust adaptive model respectively and nonlinear neural network is adaptive Answer parameter and the weights of model;
S6: forward step S2 to.
Compared with prior art, beneficial effects of the present invention is as follows:
From the multi-model Adaptive Control method of the present invention it can be seen that non linear robust adaptive controller comprises one Individual non linear robust adaptive model, this model increase on the basis of former linear adaption model one adaptive non-linear Compensation term, thus the restrictive condition of the nonlinear terms of controlled device has been loosened to zeroth order close to bounded by Bounded Linear, significantly The scope of application having widened multi-model Adaptive Control device.By non linear robust adaptive controller individually control non-linear System can be proved to have stability and convergence.
Nonlinear neural network adaptive controller comprises a nonlinear neural network model of system, according to nerve The almighty approaching theorem of network, this model can be with the true output of arbitrary accuracy approximation system, and this makes the control of the present invention Method has higher precision compared with conventional multi-mode type self-adaptation control method.Controller is designed with a step controls in advance to be thought Thinking, amount of calculation is little, can improve the calculating speed of system.
By the design of switching mechanism so that the controller of system is non linear robust adaptive controller and non-linear god Switch between network self-adapting controller, controller that performance index value is less can be selected as the control of current system System input, so can reduce the transient error of system.Performance indications comprise the accumulation item of an error, is possible to prevent system Frequently switch between the two controllers, and make system output more smooth.Due to non linear robust Self Adaptive Control system System has stability, and the present invention uses non linear robust adaptive controller to carry out with nonlinear neural network adaptive controller Switching, may certify that the multi-model Adaptive Control utensil of the present invention has stability and convergence.
Brief description
Fig. 1 closes feedback control system block diagram for what the present invention designed multi-model neural network adaptive controller;
Fig. 2 is non linear robust Indirect adaptive control device structured flowchart;
Fig. 3 is nonlinear neural network Indirect adaptive control device structured flowchart;
Fig. 4 is the structured flowchart of neutral net;
Fig. 5 is the flow chart of switching mechanism;
Fig. 6 (1) and Fig. 6 (2) is respectively curve of output and the input curve of controller of the present invention.
Concrete implementation method
Below in conjunction with accompanying drawing and example, further illustrate the present invention.
As it is shown in figure 1, in the controller designed by multi-model Adaptive Control method of the present invention, by a non-linear Shandong Rod adaptive controller, a nonlinear neural network adaptive controller and a switching mechanism composition.In figure, r (t+1) is The tracking reference signal of system, u (t) is the input of controlled device, and y (t+1) is the output of controlled device.Non linear robust is indirect Adaptive controller comprises non linear robust adaptive modelWith non linear robust adaptive controllerIt is controllerOutput,It is modelOutput.Nonlinear neural network Indirect adaptive control device comprises nonlinear neural network Adaptive modelWith nonlinear neural network adaptive controllerIt is controllerOutput,It is model Output.U (t) is existed by switching mechanismWithBetween select produce.
The present invention is directed to the nonlinear discrete time system of following structure
Σ : x ( t + 1 ) = F ( x ( t ) , u ( t ) ) y ( t ) = G ( x ( t ) ) - - - ( 1 )
In formula, u (t), y (t) ∈ R is input and the output of system respectively, x (t) ∈ RnIt is n dimension state vector, F (), G () is smooth nonlinear function.
In a neighborhood of initial point, system can be represented by following nonlinear model:
y ( t + 1 ) = Σ i = 0 n a - 1 a i y ( t - i ) + Σ j = 0 n b b j u ( t - j ) + f ( w ( t ) ) - - - ( 2 )
In formula, ai, i=0 ..., na-1;bj,j=0,…,nbFor the parameter that system is unknown, na,nbFor the order of system, w (t)=[y(t),…,y(t-na+1),u(t),…,u(t-nb)]TThe regression vector being made up of system data.
Carry out following hypothesis to said system (2):
A1. the order n of systemaAnd nbIt is known;
A2. parameter ai, i=0 ..., na-1,bj,j=0,…,nb, compact in Ω at one and change;
A3. system has the Zero-dynamics system of global consistent asymptotic stability so that the growth of arbitrary list entries of system Speed is less than the growth rate of its corresponding output sequence;
A4. there is known constant 0≤μ < ∞ so that function f (w (t)) forBe zeroth order close to bounded, i.e. full FootWherein w &OverBar; ( t ) = [ y ( t ) , . . . , y ( t - n a + 1 ) , u ( t - 1 ) , . . . , u ( t - n b ) ] T , g ( w &OverBar; ( t ) ) = &lambda; | | w &OverBar; ( t ) | | For nonlinear function, λ is unknown arbitrary constant.
The structure chart of non linear robust Indirect adaptive control shown in Fig. 2.This controller includes non linear robust adaptive mode Type and nonlinear autoregressive device two parts composition.First, the non linear robust adaptive model designing controlled device is designated as
y 1 ( t + 1 ) = &theta; 1 T ( t ) w ( t ) + &lambda; 1 ( t ) | | w &OverBar; ( t ) | |
(3)
= &delta; 1 T ( t ) &psi; ( t )
In formula &theta; 1 ( t ) = [ a 0 1 ( t ) , . . . , a n a - 1 1 ( t ) , b 0 1 ( t ) , . . . , b n b 1 ( t ) ] T WithIt is modelIn the parameter of t, order I.e. can get (2) formula.At any system time t, by modelBe given The estimate of system output isPoor with the actual value of system output by estimate, non linear robust can be obtained certainly The model error of adaptive modelI.e.According to model errorUse following Model parameter is updated by the robust adaptive identification algorithm with dead band:
&delta; 1 ^ ( t ) = &delta; 1 ^ ( t - 1 ) + h 1 ( t ) e 1 ( t ) &psi; ( t - 1 ) 1 + | | w ( t - 1 ) | | 2 - - - ( 4 )
In formula, h 1 ( t ) = 1 2 | e 1 ( t ) | &GreaterEqual; 2 &mu; 0 otherwise .
At each system time t, according to a step controls in advance thought, by the parameter of non linear robust adaptive modelDesign nonlinear autoregressive device
u 1 ( t ) = 1 b ^ 0 ( t ) 1 [ r ( t + 1 ) - &delta; &OverBar; 1 ^ T ( t ) &psi; &OverBar; ( t ) ] - - - ( 5 )
In formula, &delta; &OverBar; 1 ^ ( t ) = [ &theta; &OverBar; 1 ^ T ( t ) , &lambda; 1 ^ ( t ) ] T , &theta; &OverBar; 1 ^ ( t ) = [ a ^ 0 1 ( t ) , . . . , a ^ n a - 1 1 ( t ) , b ^ 1 1 ( t ) , . . . , b ^ n b 1 ( t ) ] T , &psi; &OverBar; ( t ) = [ w &OverBar; T ( t ) , | | w &OverBar; ( t ) | | ] T .
The device structure chart of nonlinear neural network Indirect adaptive control shown in Fig. 3.This controller includes non-linear neural net Network adaptive model and nonlinear neural network controller two parts.
Design a nonlinear neural network identification model to non-linear controlled device
y 2 ( t + 1 ) = &theta; 2 T ( t ) w ( t ) + f 2 ( W ( t ) , w &OverBar; ( t ) ) - - - ( 6 )
In formula, &theta; 2 ( t ) = [ a 0 2 ( t ) , . . . , a n a - 1 2 ( t ) , b 0 2 ( t ) , . . . , b n b 2 ( t ) ] T It is modelParameter,It is with god Approaching through the nonlinear function of the bounded of network representation, W (t) is the weight coefficient of neutral net, coefficientWith W (t) at one Predefined compact in S.It is t pairDebate knowledge,It is updated in the following manner:
&theta; 2 ^ ( t ) = &theta; 2 ^ ( t - 1 ) + h 2 ( t ) e 2 ( t ) w ( t - 1 ) 1 + | | w ( t - 1 ) | | 2 - - - ( 7 )
In formula, e 2 ( t ) = y ( t ) - y 2 ^ ( t ) , h 2 ( t ) = 1 2 | e 2 ( t ) | &GreaterEqual; 2 &mu; 0 otherwise . If b ^ 0 2 ( t ) < b min , Then make b ^ 0 2 ( t ) = b min .
According to nonlinear neural network modelThe Nonlinear control law of available system is:
u 2 ( t ) = 1 b ^ 0 2 ( t ) [ r ( t + 1 ) - &theta; &OverBar; 2 ^ T ( t ) w &OverBar; ( t ) - f 2 ( W ( t ) , w &OverBar; ( t ) ) ] - - - ( 8 )
In formula, &theta; &OverBar; 2 ^ ( t ) = [ a ^ 0 2 ( t ) , . . . , a ^ n a - 1 2 ( t ) , b ^ 1 2 ( t ) , . . . , b ^ n b 2 ( t ) ] T .
The structure chart of neutral net shown in Fig. 4, this neutral net is the BP neutral net with three layers of neuron, including defeated Enter layer, hidden layer and output layer.Each neuron between levels connects entirely, does not connect with between layer neuron.Input layer is extremely Connection weight l in intermediate layerij, i=1,2 ..., na+nb-2,j=1,2,…,p;Hidden layer is to connection weight v of output layerj1,j=1, 2,…,p;The output threshold tau of hidden layer each unitj,j=1,2,…,p;The output threshold value of output layer unit is γ1;Parameter k=1, 2,…,m.Input is w &OverBar; ( t ) = [ y ( t ) , . . . , y ( t - n a + 1 ) , u ( t - 1 ) , . . . , u ( t - n b ) ] T .
The input s of each neuron of hidden layerjFor: s j = &Sigma; i = 1 n l ij w &OverBar; i - &tau; j , j = 1,2 , . . . , p . Use sjHidden by transferometer The output b of each neuron of layerjFor: bj=g(sj), j=1,2 ..., p. utilizes the output b of hidden layerj, connection weight vj1And threshold gamma1Meter Calculate the output L of output layer neurontFor:Then the response of output layer neuron is calculated by transferometerFor:Utilize connection weight vj1, errorOutput b with hidden layerj, calculate hidden layer Error d of each neuronj(t)。
d j ( t ) = [ e 2 ( t ) v j 1 ] b j ( 1 - b j )
Utilize output errorThe output b of each neuron with hidden layerjRevise connection weight vj1And threshold gamma1:
v j 1 = v j 1 + &kappa; e 2 ( t ) b j
&gamma; 1 = &gamma; 1 + &kappa; e 2 ( t )
j=1,2,…,p,0<κ<1
Utilize error d of hidden neuronj(t), the input of input layer
w &OverBar; ( t ) = [ y ( t ) , . . . , y ( t - n a + 1 ) , u ( t - 1 ) , . . . , u ( t - n b ) ] T Revise connection weight lijAnd threshold tauj:
τjj+σdj(t).
I=1,2 ..., na+nb-2,j=1,2,…,p,0<σ<1
It is the flow chart of switching mechanism shown in Fig. 5, be first non linear robust Indirect adaptive control and non-linear neural Network Indirect adaptive control separately designs performance indicationsWithIts computational methods are as follows:
J s ( t ) = &Sigma; i = 1 t h s ( i ) [ e s 2 ( i ) - 4 &mu; 2 ] 2 [ 1 + | | w ( i - 1 ) | | 2 ] + c &Sigma; j = t - 1 - N t [ 1 2 - h s ( j ) ] e s 2 ( j ) , s = 1,2 - - - ( 10 )
In formula e s ( t ) = y ( t ) - y s ^ ( t ) , h s ( t ) = 1 2 | e s ( t ) | > 2 &mu; 0 otherwise , μ >=0, N are predefined integers, c >=0 It is a constant.Judge that two controller performances refer to the size of target value, controller less for performance index value is assigned to be Control input u (t) of system, it may be assumed that
u ( t ) = u 1 ( t ) J 1 ( t ) &le; J 2 ( t ) u 2 ( t ) J 1 ( t ) > J 2 ( t )
From the discussion above, the concrete real-time online rate-determining steps of the multi-model Adaptive Control method of the present invention is such as Under:
S1: system initialization: random initializtion modelWithParameter and neutral net, can come really according to priori Fixed;(neutral net is set to single hidden layer, and hidden neuron number is typically set to 6-10);
In the S2:t=0 moment, system is output as zero, i.e. y (0)=0;When t ≠ 0 moment, be given by the controlled device of system and be True output y (t) of system, by modelWithProvide the estimation output of model respectivelyWithThe estimation of computation model Error is respectivelyWith e 2 ( t ) = y ( t ) - y 2 ( t ) ;
S3: calculated control error e (t) of system by true output y (t) of reference input r (t) of system and system;
S4: utilize modelWithParameter design controllerWithAccording to formula (5) (8), by the control error of system E (t) calculates the output valve of Nonlinear Robust Controller and nonlinear neural network controller respectivelyWith
S5: calculated the performance indications of each controller by model evaluated errorWithBy the choosing of switching mechanism (11) formula Select the less controller u of the value of performance indicationsiT () is as control input u (t) of controlled device;
S6: by model evaluated errorWithAccording to respective adaptive law (4) and (7), more new model respectivelyWithParameter and the weights of neutral net;
S7: return to step S2.
Fig. 6 (1) and (2) are respectively input and the curve of output of the control system of the present invention.It can be seen that multi-model is adaptive Answer controller can well track reference sine curve, control input ratio shallower, it is easy to accomplish.

Claims (7)

1. the multi-model Adaptive Control device of a nonlinear system, it is characterised in that this controller is by two indirect self-adaptives Controller and a switching mechanism composition, wherein, a controller is non linear robust Indirect adaptive control device, and another is Nonlinear neural network Indirect adaptive control device, the input of controlled device is selected by switching mechanism to produce between the two controllers Raw, there are a close loop negative feedback, controlled device and two Indirect adaptive controls between the output of controlled device and two controllers Being set to subtract each other relation between the model output of device, model error is for adjusting the parameter of model and the weights of neutral net;
Non linear robust Indirect adaptive control device and nonlinear neural network Indirect adaptive control device separately design performance and refer to MarkWithIts computational methods are as follows:
In formulaμ >=0, N are predefined integers, and c >=0 is One constant, y (t) is the output signal of system,Being the estimate of system output signal, w (i-1) is system input and output The regression vector of signal composition;
The controller that the value of performance indications is less is selected to input as the control of controlled device by switching mechanism.
2. the multi-model Adaptive Control device of nonlinear system according to claim 1, it is characterised in that described non-linear Robust Indirect adaptive control device includes a non linear robust adaptive model and a gamma controller, non linear robust Adaptive model is by increasing a compensation term to mission nonlinear item on the basis of linear model, it is ensured that when system non-thread When the restrictive condition of property item is loosened to zeroth order close to bounded, the Identification Errors of this model also asymptotic can be less than a normal number.
3. the multi-model Adaptive Control device of nonlinear system according to claim 1, it is characterised in that described non-linear Neutral net Indirect adaptive control device includes a nonlinear neural network adaptive model and a nonlinear neural network Controller, nonlinear neural network adaptive model passes through on-line tuning neural network weight, it is thus achieved that the estimation to controlled device Output.
4. the multi-model Adaptive Control device of nonlinear system according to claim 2, it is characterised in that described nerve Network self-adapting model contains an input layer, a hidden layer and an output layer.
5. the multi-model Adaptive Control device of nonlinear system according to claim 4, it is characterised in that described nerve Containing 6-10 neuron in the hidden layer of network self-adapting model, output layer has a neuron.
6. the control method for described multi-model Adaptive Control device arbitrary in claim 1 to 5, its feature exists In the step of this control method is as follows:
S1: system initialization: the parameter of random initializtion non linear robust adaptive model, random initializtion non-linear neural net The parameter of network model and the weights of neutral net, these parameters can be determined by certain priori;
In the S2:k=0 moment, object is output as 0;In k ≠ 0 moment, object is output as the real output value of system, sets with system Definite value makees the control error e that difference obtains systemc;Actual output obtains model with the output work difference of non linear robust adaptive model Error e1, make difference with nonlinear neural network model and obtain model error e2
S3: error e will be controlledcDefeated as non linear robust adaptive controller and nonlinear neural network adaptive controller Enter, two controllers are produced controlled quentity controlled variable u respectively1And u2
S4: according to model error e1And e2Carry out calculation of performance indicators C1And C2Value, select the less controller of performance index value to produce Raw input ui, as the control input u of controlled device and two models,
S5: utilize model error e1And e2Update non linear robust adaptive model and nonlinear neural network adaptive mode respectively The parameter of type and weights;
S6: forward step S2 to.
7. the control method of the multi-model Adaptive Control device of nonlinear system according to claim 6, it is characterised in that In described step S4, in switching mechanism, first one performance indications of design, this performance indications comprise an accumulated error part With a transient error part, control the moment at each, calculate the performance indications of each controller, select performance indications relatively Little controller produces the control input of subsequent time.
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