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 PDFInfo
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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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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
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
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:
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
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
(3)
In formula 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:
In formula,
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
In formula,
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
In formula, 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:
In formula, If Then make
According to nonlinear neural network modelThe Nonlinear control law of available system is:
In formula,
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
The input s of each neuron of hidden layerjFor: 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)。
Utilize output errorThe output b of each neuron with hidden layerjRevise connection weight vj1And threshold gamma1:
j=1,2,…,p,0<κ<1
Utilize error d of hidden neuronj(t), the input of input layer
τj=τj+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:
In formula 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
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
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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