Adaptive Control Based On Neural Network System .
Recent Researches in Communications, Electronics, Signal Processing and Automatic ControlAdaptive Control Based on Neural Network System IdentificationHassan E. A. IbrahimDept. of Electrical and Computer Control EngineeringArab Academy for Science and Technology, Cairo, Egypt.e-mail: hibrahim eg@yahoo.comAbstract:- In adaptive control and system identification the self tuning regulator has wide range ofapplications. Neural network and artificial intelligence have big role in this area. This paperpresents adaptive neural network control based on self tuning regulator (STR) scheme. The paperpresents neural network block for on line system identification and discrete PID block controller.Analysis for the whole scheme is presented and simulated for different systems. Adequate desiredperformance is obtained by comparison with the nominal methods for using self tuning regulator.Key-Words:Adaptive Control, Self Tuning Regulator, System Identification, Neural Network, Neuro Controldifferent neural networks schemes foridentification and control for such system. Thefirst scheme is designed to control the rotorangular speed by establish three hidden layerfeedforward neural network. The second schemeis designed to control the stator current by usingpredetermined control law as a function of theestimated states. The second scheme hasestablished three feedforward neural networktrained online using Levenberg-Marquardtalgorithm. The neural network control strategyadapts to the uncertainties of the motor loaddynamics and nonlinearities. System simulationconcluded that, neuro controller in conjunctionwith adaptive control scheme is flexible andreliable which can have wide utilization andapplication in the real lifeIn [5] authors propose a new adaptivecontrol scheme, composed of a neural identifierand a nonlinear controller and applied it to alinear induction motor (LIM). In order tocompare the performance of LIM, they use α βand d q models. A neural identifier oftriangular form is proposed for both models as anonlinear block controllable form (NBC). Then,a reduced order observer is designed in order toestimate measured variables. Learning law forneural network weights ensure that theidentification error converges to zeroexponentially.The effect of sampling period on theidentification process is very important; it has1. IntroductionThe purpose of adaptive controllers is toadapt control law parameters of control law tothe changes of the controlled system. Manytypes of adaptive controllers are known. In [1]the adaptive self-tuning LQ controller isdescribed. The design and implementation ofadaptive linear optimal controller (LQ) based ona pseudo-space model into PLC. Foridentification of the controlled system analgorithm based on artificial neural network isused. In [2] an adaptive neural network controlscheme for thermal power system is described.The online tuning algorithm and neural networkarchitecture are described. The performance ofthe controller is illustrated via simulation fordifferent changes in process parameters.Performance of neural network controller iscompared with conventional proportionalintegral control scheme for frequency control inthermal power systems. In [3] neural networkadaptive force controller is proposed for ahydraulic system. The dynamic model of thissystem is highly non-linear and very complex toobtain. The neural network parameters areupdated online according to an adaptationalgorithm obtained via stability analysis. Theperformance of the proposed neural networkcontroller is validated on an experimental plant.In [4] the paper presents adaptivecontroller with online identification block forbrushless dc motor. The paper presents twoISBN: 978-1-61804-069-584
Recent Researches in Communications, Electronics, Signal Processing and Automatic Controlbig effect on the identification accuracy andstability. It is a kind of trading off i.e. rapidsampling causes a problem of stability andmakes advantage of disturbance cancelation andgood overshoot. Short sampling causes aproblem of aliasing and makes advantage ofgood numerical stability.For classical methods of identificationslike RLS (recursive least square method) orLSM (least square method), short samplingperiod done for real time system identificationfails even though the disturbance have beentaken into account. This fact happens due to thequantization in A/D converter. So, thequantization,noiseeffectandothernonlinearities accompanied by real planets makeonline identification more complex than it couldbe expected. [6, 7] show that a possible solutionof this problem is using of an identificationmethod based on neural networks.The schemes of these types of controllerare separated into the two main parts:identification and controller. In this work,identification based on neural network approachis used and the control algorithm is based onself tuning regulator as an adaptive controllerusing PID controller as an adaptive controller.system u(t) and the corresponding system outputy(t) we are able to find the vector of systemparameters θ. For computing of the identifiedsystem output we can use the linear model inequation (1) which represents the standard formof the actual process (plant).((1)The above model can be written invector form as follows, where equation (2)represents the estimated output( at) sample kfrom the model (neural network) which will becompared with the plant output ( a)t the samesample k and ( )represents the vector of allinputs and outputs samples for prespecifiedsampling period, and finally ( )represents thevector of all the plant parameters which isneeded to be identified.( ) ( ) ( )(2)Where( ) [ ( 1) ( 1 ) ( 1) ( 1 ] )(3)is the vector of measured inputs and outputs and( ) [ ( ) ( ) ( ) ( )] (4)is the vector of estimated system parameters andk denotes discrete time.u2. On-Line IdentificationOn-line identification of process parameters isthe key element in adaptive control. The basicidea of on line identification is to compare theoutput of estimated system with the output ofmodel during some time. The model isdescribable as a parameter vector. The aim is toadjust parameter until the model output issimilar to the observed system output. Theclassical Recursive Least Square (RLS)identification method [8] and gradient methodcompares only actual model output to systemoutput, while the identification method based onneural network approaches compares outputover some interval time defined by length of atraining set.Fig. 1 shows the principle ofidentification of system using neural network. Avery fast algorithm for training neural networksis the Levenberg-Marquardt (LM) algorithm.The main idea of on-line identification is thataccording to the measured input to the identifiedISBN: 978-1-61804-069-5) yPlantz-1z-1z-1NeuralNetworkBasedIdentification- z-1z-1z-1Fig. 1 The principle of identification of systemusing neural networkAs it has been mentioned above, theLevenberg– Marquardt [7] method can be usedfor training of the neural network. The newvector of parameters is in each step given byequation (5).( 1) ( ) ( )( ) (5)Where j is the jacobian matrix as shown inequation (6).85
Recent Researches in Communications, Electronics, Signal Processing and Automatic Control ( ) ( ) ( )chosen measured error (required accuracy). Theproperties of the forgetting factor λ and its bigeffect on the RLS algorithm accuracy speed andeven convergence to the right values of theestimated parameters has taken a lot ofconcentration and studies previously, thesestudies are summarized and presented in [8].Where, most of authors, used to choose descentrandom value for λ in the range of (0-1), byexperience authors conclude that choosing highvalue for λ (closet to 1) yields to slowest speed(but provide the best robustness toward noise)and decreasing values of λ result in increasingspeed of parameter convergence at the expenseof increased noise influence. In [8], the authorpresented new algorithm called adaptive RLS,to choose the optimum value of λ which givethe best convergence to the system parameters.This algorithm has been used and implementedin our work for on-line identification.Intensive simulation has been done usingMATLAB, for the RLS algorithm. Thesimulation has been done for different processeshave different orders such as the process shownin equation (1).The simulation has been rerun fordifferent values of λ and every time thesimulation shows the estimated parameters andthe instantaneous error. The optimum value forλ is (0.53) which shows robust convergence ofthe estimated parameters to their right valuesand zero error at the iteration number 200.Fig. 2 shows the system identificationresults during on-line mode for random input forboth original system (plant) and neural networksystem identification block. It is clear that theneural network output is very close to the plantoutput which means small accepted error.Fig. 3 shows the error signal between theplant output and the neural network systemidentification block output during on-line modefor random. As shown the error signal tends tozero value after 20 input. This means smallaccepted value.The neural network block has beentested for another input to make sure of itsaccuracy and performance. Fig. 4 shows thesystem identification results during on-linemode for sinusoidal input for both originalsystem (plant model) and neural network system(6)(7)Where ε is the vector of errors, itmeasures the difference between the output ofthe system and the output of the model for alltraining sets. The parameter i denotes thenumber of training patterns and j denotes thenumber of estimated parameters.One of the most important reasons whyneural network approach, when used as anidentification block, is preferable than the RLSand LSM approaches is that, it can adapt itselffor different systems orders and even fornonlinearity which could be included in somesystems which leads to better controllerperformance i.e. the controller could be morereliable and faster.3. Simulation Results Of On-LineIdentificationThe Recurrent neural network with tapdelay is chosen and implemented usingMATLAB neural network toolbox, the networkcould be designated in different ways, manyassumptions exits in the literature [9,10] for thenumber of hidden layers, number of neurons ineach layer and type of activation function foreach layer. Fig. 1 shows schematic diagram forthe recurrent neural network for single input,single output system with delays on each.Initially, the training input vectors and targetvectors of the recurrent network have beenfound from many simulation results for theoriginal plant model represented in equation (1).The network has been designed with input biasat each neuron; the gain and the system stabilityhave been checked and designed during thetraining process. The neural network has beentrained and checked for specified accuracyduring the off-line mode.From the description above, theimplementation of the neural network systemidentification block consists of just iterating thefive equations (2 to 7) at every time instant k,that is described as in Fig. 1., where ε is theISBN: 978-1-61804-069-586
Recent Researches in Communications, Electronics, Signal Processing and Automatic Controlidentification block. It is clear that the neuralnetwork output is very close to the plant outputwhich means small accepted error.law synthesis. Many of control law synthesisapproaches are based on two methods – poleplacement and inversion of dynamics. Both ofthe methods are numerically sensitive to thegood estimation of the plant.The requirement for correctly computedsystem parameters vector θ is not often fulfilledduring controlling of real system with a higherorder. Therefore, we use simple synthesis basedon modified Zeigler –Nichole method. Thebasic architecture of adaptive controller (STR)we discussed is shown in Fig. 5.The system (adaptive PID controllerbased on STR scheme, with neural networkidentification block) presents adaptive PIDcontroller designed using Zeigler –Nicholemethod.0.30.25Plant (solid) NN Output (dotted)0.20.150.10.050-0.05-0.1050100150Random Input200250300Fig. 2 neural network system identification forrandom input-4x 10State MachineYR5Step ResponseGenerator4T10% T90% Y100%3θ2Error1Neural Network-BasedIdentificationModified Z-NMethod0-1-2KP TI TD-3-4r-5050100150200250300Random inputDiscrete PIDControlleruPlantyFig. 3 Error for random inputFig.5 Block diagram of Recursive parameterestimate10Plant (solid) NN Output (dotted)86420-2-4050100150200250300Sinusoidal Input350400450500Fig. 4 neural network system identification forsinusoidal input4. Adaptive ControlThe idea of adaptive controllers (selftuning controller’s scheme STR) is to combinean on-line identification with on-line controlISBN: 978-1-61804-069-5Fig.6 the characteristics points used for a tuningof the adaptive heuristics controller based onmodified Ziegler-Nichols open loop method87
Recent Researches in Communications, Electronics, Signal Processing and Automatic ControlThe step response generator generatesthe sequence YR of a step response of theestimated model θ. Then, the state machinefinds characteristic points T10% , T90% and Y100%in the sequence YR Fig. 6. These values are usedto design PID discrete controller according to[9,11]. As shown in equations (8, 9). 0.8 . ,%, 3 ,%% 0.5 Fig. 9 shows the plant step responseafter the PID controller adapted its parametersto fit the design requirements, the figure showsthe plant output versus the time, as shown theoutput reaches its final value (1) at time 30 secin a critical damping mode (i.e. zero overshoot),which gives error value of zero%.(8)Step Response Without Controler0.50.45(9)0.40.35Where KP, TI and TD are the parameters thatof the PID controller needed to find the PIDgain.Output0.30.250.20.155. Simulation ResultsFrom the description above, theimplementation of the adaptive PID controllerbased on neural network on line identificationshown in Fig. 5 has been implemented andsimulated using MATLAB.Intensive simulation has been done usingMATLAB. The simulation has been done fordifferent plants have different orders follows thestandard form shown in equation (1).The following simulation results have beenpresented for a plant shown in equation (10)( ) (10)0.10.05012345Time678910Fig.7 Step response for 2nd order plant withoutcontrol10x 10-3Error Versus Iterations8Output Error6Theassumeddesiredcontrolrequirements have been chosen to get 30 secsettling time, critical damping performance (i.e.damping ratio 1) and zero steady state errorfor all cases of changing the plant parameters ororder.First the simulation has been run for thefollowing plant parameters (a1 0.909, a2 0.206, a3 1, b1 0.0909), Fig. 7 shows thestep response for the plant without control (i.e.the PID controller is switched off), the figureshows the plant output versus the time, asshown the output reaches its final value (0.5) attime 6 sec in a critical damping modes, whichgives error value of 50%.Fig. 8 shows the error between the plant outputand the neural network output versus theiteration number. As shown the error reacheszero at iteration number 18 which means fastidentification which leads to better adaptivecontrol system.ISBN: 978-1-61804-069-50420-2020406080100IterationsFig.8 Error Versus iterationStep Response With Non Adaptive PID 202530354045TimeFig.9 Step response for 2nd order plant withAdaptive PID (STR Scheme) control88
Recent Researches in Communications, Electronics, Signal Processing and Automatic ControlTo check the adaptive PID controllersystem, first, we started to change the plantparameters to the following (a1 0.909, a2 0.02, a3 1, b1 0.0909), and then first checkthe controller performance before adapting itsparameters.Fig. 10 shows the plant step responsebefore the PID controller start adapting itsparameters to fit the new changing in the plantparameters (i.e. the neural network block for online identification is switched off). The figureshows the plant output versus the time, asshown the output reaches its final value (1) attime 36 sec in an under damping mode withovershoot of 35%, and gives error value ofzero%. So, the comment on this result says thatthe performance of the PID controller is not bad,but it deviated from the desired designrequirements, where the change in the plantparameters was not too large.Fig. 11 shows the error between theplant output and the neural network outputversus the iteration number. As shown the errorreaches zero at iteration number 17 whichmeans fast identification which leads to betteradaptive control system.To continue checking the adaptive PIDcontroller system, second, we started to changethe plant order and parameters (i.e. new plant)to the following (a1 0.909, a2 0.02, a3 1,b1 0.0909), and then first check the controllerperformance before adapting its parameters. Asshown in Fig. 13, the step response of the plantstep response before the PID controller startadapting its parameters to fit the new changingin the plant parameters (i.e. the neural networkblock for on line identification is switched off).The figure shows the plant output versus thetime, as shown the output goes to infinity attime 170 sec which indicates unstable responseand gives error value of infinity. So, thecomment on this result says that the PIDcontroller has failed to control such system andhas to be redesigned to control the new plant,where the plant has been fully changed.10Error Versus Iterations-38Output Error6Step Response With Non Adaptive PID Controler1.4x 10421.201-202040Output6080100Iterations0.8Fig.11 Error Versus iteration after changingplant parameters0.60.4Step Response With Non Adaptive PID .10 Step response for 2 order plant withPID control after changing plant parametersOutput0.60.50.4Fig. 12 shows the plant step responseafter the PID controller adapted its parametersto fit the design requirements, the figure showsthe plant output versus the time, as shown theoutput reaches its final value (1) at time 23 secin a critical damping mode (i.e. zero overshoot),which gives error value of zero%.ISBN: 2 Step response for 2nd order plant withAdaptive PID (STR Scheme) control afterchanging plant parameters89
Recent Researches in Communications, Electronics, Signal Processing and Automatic ControlSo, the first step is to turn on the neuralnetwork identification block to start identifyingthe plant parameters and dominant poles. Fig.14 shows the error between the plant output andthe neural network output versus the iterationnumber. As shown the error reaches zero atiteration number 19 which means fastidentification which leads to better adaptivecontrol system.in a critical damping mode (i.e. zero overshoot),which gives error value of zero%.Step Response With Non Adaptive PID Controler10.90.80.7Output0.651.5Step Response With Non Adaptive PID Controlerx 500Fig.15 Step response for 2nd order plant withAdaptive PID (STR Scheme) control afterchanging plant order and recovering the eFig.14 Error Versus iteration after changingplant parameters6. ConclusionAdaptive discrete PID controller analysis, asa self tuning regulator scheme, has beenpresented with artificial neural network as online system identification in mind. On linesystem identification block using neuralnetwork has been presented. Recurrent neuralnetwork type for system identification has beenpresented and analyzed. Neural network hasbeen designed and trained for identifying plantparameters. Modified zeigler –Nichole methodfor designing PID controller has been presentedand simulated using MATLB. Analysis for thewhole scheme model is presented and
Adaptive Control, Self Tuning Regulator, System Identification, Neural Network, Neuro Control 1. Introduction The purpose of adaptive controllers is to adapt control law parameters of control law to the changes of the controlled system. Many types of adaptive controllers are known. In [1] the adaptive self-tuning LQ controller is described.
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Adaptive Control - Landau, Lozano, M'Saad, Karimi Adaptive Control versus Conventional Feedback Control Conventional Feedback Control System Adaptive Control System Obj.: Monitoring of the "controlled" variables according to a certain IP for the case of known parameters Obj.: Monitoring of the performance (IP) of the control
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Chapter Two first discusses the need for an adaptive filter. Next, it presents adap-tation laws, principles of adaptive linear FIR filters, and principles of adaptive IIR filters. Then, it conducts a survey of adaptive nonlinear filters and a survey of applica-tions of adaptive nonlinear filters. This chapter furnishes the reader with the necessary
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