NEURAL NETWORK PROCESS CONTROL

8/7/2019 NEURAL NETWORK PROCESS CONTROL

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NEURAL NETWORK PROCESS CONTROLMichael J. Piovoso and Aaron J. OwensE.I. du Pent de Nemours 8ZCo.

Allen GuezDrexel University

Eva NilssenUniversity of Delaware

Abstract. Neural Networks are increasinglyfinding engineering applications. Most earlyapplications were in the areas of patternrecognition and modeling. This paper showshow neural network models can be used inprocess control. Two separate techniques areillustrated, each with a specific exampleapplication. One involves using the networkitself as the inverse model, by fixing the neuralnetwork weights and training on the inputs togive the desired output pattern. The othersuggests using the pattern recognition ability ofa neural network to identify an appropriatelower order linear model to use for controllerdesign.1. INTRODUCTION

A neural network is an interconnectedset of many neuron-like subsystems that aredynamically coupled and exhibit through theircollective behavior some useful computationalfeatures. These networks were extensivelystudied by many researchers over the past 40years. Of the many different neural networkmodels, we will focus on feed-forwardnetworks in which training is done using theback-propagation paradigm (BPN). Figure 1illustrates this network, which is particuladyuseful for model development [McClelland andRummelhart], [Piovoso and Owens].

Linear dynamic models are the basis ofmost modern control methods such as adaptivecontrol, Dynamic Matrix Control [Cutler andRarnaker] and Internal Model Control [Garciaand Morari]. Such dynamic models are used topredict system performance and to compare thatperformance with actual process outputs. Wesuggest the use of neural models in place of thelinear dynamic models. Control schemes thatPermission to copy without fee alt or part of this material is grantedprovided that the copies are not made or distributed for directcommercial advantage, the ACM copyright notice and the title of thepubli~tion and its date appear, and notice is given that co ying is by$ercussion of the Association for Computirrg Machinery. o copyotherwise, or to republish requi res a fee and/or speci fk permiss ion.@ 1991 ACM 089791-432-5/91/0005/0084 $1.50

incorporate neural networks are referred to asneuro-controllers [Guez et al.].The class of neurocontrollers is closelyrelated to other classical forms of control. Wefirst compare it to the adaptive and learningcontrollers and demonstrate their similarities.The problem of systems control can bedefined as follows. Given the system S where

S:x= f(x,u,t,p); X(to) = Xo; Y - 9(XNAP) (1.1)

and where the time t & R. The initial time is %,the state x & Sx & Rn, the control input u &Su & Rm, and the parameters vector p 8 Sp&R]. The sets Sx, Su and Sp are admissiblestate, control and parameter sets respectively,which account for general equality andinequality constraints, and where n, m and 1areappropriate integers. The control problem is tofind the system input; u(t) = c[v(t) ,z,z] foropen-loop control and U(t) = C[v(t) ,X ,z,z]for closed-loop control, such that certainterminal and optimality conditions for theoutput y are satisfied. The signal v(t) is thereference input vector, and z(t) is a vectordescribing the controller state variables.

Under the above general definition, it iseasy to classify the various controller classesaccording to the type of control function c thatthey are able to provide. If c is independent of zand Z, it defines the class of static controllers.

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In particular, if c is also linear in x and v, weobtain the class of linear state feedbackcontrollers. When c is a function of z and Z,we obtain a dynamic controller, where z(t)describes the controllers state variables. If z isa function of all or some of the systemparameters, p, we obtain the class of adaptivecontrollers. (As there is no unique definition ofadaptive control { [Astrom], ~andau] ), the onegiven above represents the authors choice.) Ifz(t) is related to the states of the inverse of theplant transfer function, then an Internal ModelControlla or derivative thereof is formed.

An important feature of most adaptivecontrollers, including Model ReferenceAdaptive Controllers (MRAC), Self TuningRegulators (STR) and Gain Schedulers (GS),is that they are pmle 1based. The control law cvaries according to the best estimate of somesystem model parameters, p. Usually anestimation scheme for some or all of the systemparameters is employed ([Astrom], [Landau]).The parameter estimates are used to modify the$tructu re of the control law (c) in an on-linefashion, automating in the process somecontrol design rules. A general block diagramis depicted in Figure 2.

In contrast is the class of learningController, ([Arimoto et al.] [Bondi et al.],[Kawamura et al.]) also called repetitivecontrol, or betterment control, which should bedistinguished from learning automata asdescribed in [Narendra and Thatachar],[Tsypkin], [Fu]. For a learning controller,typically it is assumed that the reference signalv(t) is periodic, the structure of the controller(i.e., the function c) is fixed, and learning isexhibited through the Iterative modification ofthe (open loop) Jime function u(t). A schematicblock diagram is given in Figure 3.

We define the class of neurocontrollersas the set of all controllers whosestructure (control law) c(x,v,z,Z) isbased on some neural network modelarchitecture and learning paradigm[Guez and Kam]. It should be emphasized thatthe neural network model and the learningalgorithm are defined independently from anyspecific process to be controlled (S).Neurocontrollers are, therefore, not model

w,, in the sense usually associated withadaptive controllers. Also, since the learningalgorithm employed by neurocontrollers doesnot require periodic input, but rather canaccommodate any temporal behavior, the classof learning controllers is a proper subset of theneurocontroller class.Although neurocontrollers are differentfrom the model based adaptive controllersdescribed above, they do perform real timeadaptation through their on-line learningcapabilities. The robustness of neurocontrollersstems from the fact that they are not modelbased. It is expected, however, that whencompared with classical controllers with thesame throughput (processing power) theiraccuracy may be inferior.Finally when some or all the nodes ofthe neural network employed in theneurocontroller are specifically allocated for theestimation and storage of all or a subset of thesystem parameters, p, we obtain a neuro-morphic realization of model-based adaptivecontrollers. In that sense the set of adaptivecontrollers may also be regarded as beingcontained in the class of neurocontrollers.Internal model control (IMC) [Garciaand Morari] is also a model based controlscheme. Here a model of the process is

developed that gives a prediction of the output.The controller Q(s) is the model inverse (F@re4). Unfortunately, for most problems ofpractical interest the model inverse is notphysically realizable. For example, if theprocess has a time delay, the inverse modelwould require a knowledge of the future input.Any system that has non-minimum phasecharacteristics would have either an unstable ornon-realizable inverse. The controller is chosento give the minimum squared error over theclass of linear controllers. However, such adesign is not robust in the sense that errors inthe assumed parameters may cause the controlto deteriorate significantly or possibly tobecome unstable. To overcome this problem, afilter Fe(s) is added to the model inverse so thatthe filter plus optimal controller has robustbehavior in the face of model uncertainties. Themodels typically used in IMC are linearapproximations of the typically nonlinear real

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system. Thus, a serious drawback occurs whenthe process changes operating conditions. Theparameters of the linear approximation at theprevious state are often inappropriate in thenew state. The resulting control, if stable, isstill less than optimal. A neural net model, onthe other hand, captures the nonlinearities ofthe process and should be valid over a largeroperating range than the linear IMC.

Neural networks can also be used togenerate models for doing process control.Like IMC, the neural network must be, in somesense, inverted to obtain the proper controlinputs to drive the output to desired result. Aconceptual problem exists with using a neuralnet for the model of the process: since this formof the model is nonlinear, the method forgenerating the inverse (as done in IMC) is notobvious. One approach would be to design aneural network that would predict the systeminput from measurement of the system output.(I.e., have the neural network model theinverse problem.) Care must be taken becauseit is again the problem of modeling the inverse.The system response time must be considered(see below). Rather than trying to predict theinput needed to drive the process output errorto zero at the earliest possible time, one woulduse an input to the system that would cause theerror to decrease in an acceptable way. Thedynamics for returning the setpoint plays therole of the fflter in the IMC approach.

A technique for choosing the inputsetpoint is to use the trained BPN model of theforward process and a variant of thebackpropagation algorithm. Suppose that theforward process has been modeled by thenetwork its weights have been fixed. Theinputs are manipulated to minimize the errorbetween the predicted response and the desiredresponse. The gives the input setpoint toproduce the desired response.Another method for using neuralnetworks to do control is by using their patternrecognition capability. Suppose that the systemto be controlled is modeled as a second ordersystem. Apply a step input and monitor theresponse. Characteristics of that response suchas rise time, settling time and peak overshootcan be noted. This data so generated can beassociated with a second-order system that

would have given a similar set of suchcharacteristics. The controller implementedwould then be one designed to control thatsecond order system. In this approach, theneural network is used only for identifying thesecond-order system needed to retune thecontroller and not for continuous operation.When the controller needs retuning, a step testwould be conducted and from that data, a newsecond-order model defined. From this model,a new controller is designed.2. IMC

In Figure 4, P(s) is the process transferfunction, Q(s) is the controller transferfunction, and ~(s) is the transfer function of themodel. Disturbances enter the system at theoutput of the plant. The closed-loop transferfunction between the reference input r and thecontrolled output y of this system can beshown to be:

P(S)Q(S) (2.1)I+ Q(s)(P(s) - F(S))

The transfer function between the disturbance dat the output and controlled output y is:

l-~(s)Q(s)1+Q(s)(P(s) - F(s))

This controller is guaranteedsteadv-state error to step inputs

(2.2)

to give zeroif the productof th~ DC gains of the ~on~oller Q(s) find themodel of the process P(s) is forced to be 1.Note also that if P(s) is a perfect model ofP(s) and Q(s) is the perfect inverse of ;(S)then the closed-loop transfer function of (2.1)is one and the disturbance transfer function of(2.2) is zero.

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Because of the nature of physicallyrealizable system, the inverse of the plant P(s)is seldom, if ever, realizable. Thus, theinverse Q(s) is generally not the true inverse ofthe plant. Sometimes Q(s) can be madephysically realizable by adding a filter Fe(s) tothe true non-physically realizable inverse togenerate a realizable one. For example, thesystem

P(s) = -& (2.3)is not physically realizable. By adding a filterFe(s) that is a simple RC integrator, thecombined idealized inverse plus the filter istdizable.

Q(s) = ~ (2.4)Note that the closed system transfer functionwill now be Fe(s) in this idealized case, asopposed to the value 1 for the case in which theplant inverse exists.

The implementation of this techniquewould generally be done digitally. Thecontroller and the plant models are digitalapproximations of the continuous-timesystems. The model is generally a linearapproximation of the actual nonlinear, typicallytime-delayed, system. From this linearapproximation, a controller is design to meetthe constraints of realizabil ity and robustness.There is no reason to restrict consideration to alinear time-invariant model of the process. Itcould be a nonlinear, neural net model. Thecontroller could be a nonlinear neural netsystem as well. The plant model would begenerated by taking present and past inputs andpast outputs to predict the present inputs. Theneural model would be a nonlinearapproximation of the real world system. Thecontroller model would take past plant outputs

and past plant inputs to predict the inversemodel or the pnxent plant input. Such trainingcould take place either on-line or off-line.This controller model would have allthe same problems as the linear, time-invariantmodel concerning realizability and operation.For example, if the plant has a time delay of 3seconds, then the controller inverse should bechoosing inputs for the present time that will beeffecting the output 3 seconds later in time.Also, to give robustness to the model, afiltering function ought to be added to neuralcontroller output. This will allow good controldespite dead time drift and plant parameteruncertainty.

3. NEURAL NETWORK CONTROLMany systems encountered in practicecan be modeled very accurately as a second-order system with dead time. This model ofthe system can then be used to design thecontroller needed. Such practices are quitecommon in industry and lead most often tosatisfactory controller design. The modelingcan be done using a step test or other signaltesting method followed by a statistical estimateof the model parameters ~jung].Neural Networks are good ways ofmodeling such a system. The modelsdeveloped are often determined by a feed-forward, three-layered BPN network. Thesenetworks can be trained in a number of ways.One could develop the model in an analogousfashion to the techniques of time seriesanalysis. Unfortunately, this can be a difficultway to train the network if the dynamics of the

system are complex. The differing speeds ofresponse and differing gains make the identifi-cation and training difficult. The heatexchanger example in Section 4 below showshow the BPN can be used as a generalizedmodel of time-series analysis.On the other hand, defining certainfeatures of the step response that define thegains and speeds of response for the varioussystems can produce more desirable results.These features include rise times, time to peak,percent overshoot, and settling times. Thesefeatures are easily measurable in a simple steptest. They are then applied to a network that

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produces the approximate second-order model.This model is then used for doing a pole-placement design.The pole-placement method is a designtechnique where the user defines the desiredlocation of the closed-loop poles (equivalentlythe desired closed-loop behavior). From thisinformation and the open-loop dynamics, acontroller is designed consisting of a feed-forward component from the reference inputand a feedback component from the controlledoutput [Astrom and Wittenmark].A control system designed in this waycan be retuned upon demand. When retuningis necessary, put the system into manual, inputa step disturbance, measure the performanceparameters, input them to the neural network todetermine the second-order model, and designa pole-placement controller. Such an approachcan guarantee a very well- controlled responsewithout the problems associated with on-lineparameter identification for doing adaptivecontrol.

4. EXAMPLESAs an example of capturing thedynamics of the system directly with a trainedBPN model, consider the heat exchangershown in Figure 5. Heat is applied by aresistive heater. The control objective is toadjust the voltage to the resistive heater to

maintain the outlet temperature constant. Thissystem is nonlinear and defined by thedifferential equation:

dy.. ~F(t)y (t) i&(t) T(t)+ -&*(t)dt V (4.1)

The differential euuation was exercised for ste~

and past values of u, F, T, and y, predict thefuture value of y.For the backward or inverse problem,you are given a desired output at the next timestep along with present and past values of y(t)and the control variables (u, F, T). With fixedweights and variable inputs, the neural networkis trained (on the inputs) to find the input setneeded now to produce the desired y(t+l) at thenext time step.An internal model controller was usedto control this system. The desired output wasthe output temperature value y desired. Nofilter was used; that is, Fe(s) was 1. Theforward model was used to predict the plantoutput. This predicted value was subtractedfrom the desired output to produce an errorsignal that was then fed back to network, andthe input was changed to minimize this error.Because no filter was used, the input changegenerated could be greater than is acceptable.Inputs that we~ too large were clipped at theirmaximum value. This produces a bang-banglike control actual that is shown, for single-variable (u) control, in figure 6. The actualresponse of the closed-loop system (y) is givenin figure 7.As a second example, consider the useof a neural network for system identification.A neural network was trained to output thedamping ratio, natural frequency and gain of a

second-order system. The inputs to the netwere several features that can be easilymeasured off a step test: peak overshoot, timeto peak, 10-90% and 0-50% rise times, andsettling time. From this data set, generatedwith many second order systems, the BPN wastrained to predict the parameters associated withthe time-series features. The technique wasapplied to a high order system with the transferfunction given by:

changes in the i~puts (F, T, and u), and th~ G(s)= 75000results were used to train a neural network in S5 + 162s4 + 6835ss + 65400s2 + 197500s + 75000 (4.2)the forward direction. That is, given present

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The neural network identified a second-ordersystem with natural frequency of 1.27 anddamping ratio of 1.420 Thestep response ofthe second-order system and of the systemdefined by equation 3.2 are shown in figure 8.The match is quite acceptable. A controller wasdesigned using a pole placement approach.The closed-loop poles were chosen so that theclosed-loop, reduced-order system would beoptimally damped. Figure 9 shows the stepresponse of the system given by equation(3.2), being controlled by the controllerdesigned for the second-order system. Theresults are essentially indistinguishable fromthose that would have been obtained if thesystem were actually the second-order approxi-mation. Figure 10 illustrates the control effortto achieve the step nxponse shown in Figure 9.5. CONCLUSIONS

Neural networks have become anincreasing popular technique for modelingproblems. Models can be generated without apriori assumptions of the model form. Thesemodels can then be used in various model-based process control techniques. Inparticular, internal model control (made popularby Morari) is well-suited for implementationusing neural networks. Both the processmodel and the inverse process model can belearned by a neural network. The primaryadvantage is that a complex process can bemodeled by the neural network without anexact knowledge of the form of thenonlinearities. An application to a nonlinearheat exchanger demonstrates the use of this useof this technique. A second example showshow a neural network can be used to identifysecond-order model parameters to be used incontroller design.

ReferencesArimoto, S., Kawarnura, S., Miyazaki, F. andTamaki. S. (1985) Learning Control Theoryfor Dynamical Systems, Proc. IEEE 24thCDC, Ft. Lauderdale, FL.

Astrom, K., J. (1988) Adaptive FeedbackControl, Proceedings of the IEEE, vol. 75,No. 2, pp. 185-217.Astrom, K., J., Wittenmark, B. (1990)Comrmter-Co ntrolled Svstems. Prentice Hall,Englewood Cliffs, New Jersey.Bondi, P., Casalino, G. and Gambardella, L.(1988) On the Iterative Learning ControlTheory, IEEE J. Rob. and Auto., Vol. 4,No. 1.Cutler, C., R. and Ramaker, B. L. (1979)Dynamic Matrix Control - A ComputerControl Algorithm, AICHE National Meeting,Houston, TX.Fu, K (1987) Learning Control Systems -Review and Outlook, IEEE Trans. AutomaticControl, AC-15, pp. 210-221.Garcia, C., E. and Morari, M. (1982) InternalModel Control - 1. A Unifying Review andSome New Results, Int. Eng. Chem. ProcessDes & Dev., Vol. 21, pp 308-323.Guez A., Elbert, J. and Kam, M. (1988)Neuromorphic Architecture for Control,IEEE Control System Magazine, Vol. 8, No.2.Guez, A. and Kam, M. (1988)Neurocomputing Architectures for IntelligentControl, A tutorial, Third IEEE InternationalSymposium on Intelligent Control, Alexandria,VA.Kawamura, S., Miyazaki, F. and Arimoto, S. (1984) Iterative Learning Control for RoboticSystems, Proc. of IECON 84, Tokyo, Japan.Landau, Y., D. (1979) Adaptive Control - ~Model Reference Adamive Control ADproac~,Marcel Dekker, New York.McClelland, J. L. and Rumelhart, D. E. (1986)Parallel Distributed Process ing, MIT Press,Cambridge, MA.Narendra, K., S. and Thatachar, M., A., L.(1974) Learning Automata - A Survey, IEEETrans. Syst., Man and Cybern., Vol SMC -4,pp. 323-334.

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Piovoso M. J. and Owens, A. J. (1991)Sensor Data Analysis Using NeuralNetworks, Proceedings of the FourthInternational Conference on Chemical ProcessControl, South Padre Island, TX.Tyspkin, Z. (1971) Adamation and Learning inUtomatic vste ms. Academic Press, NewYork.

Hidden Nodes3 2 1

inputs

w i(3)

o0q

q

q

i

,j(2)

outputs

FIGURE 1

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u(t) + SYSTEM SI I I

4wv(t)

Parameter estimatesADAPTIONMECHANISM* 4

FIGURE 2

MEMORY Uk SYSTEM S k

Auk+l + BETTERMENTPROCESS *+

-&

desired response

MEMORYf

1-Q(s)FIGURE 3

x(t)

w%e(s) P(s)

+

FIGURE 4

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Heat ExchangerVolume V

I IIncoming Fluid ~ R ~ mow Rate F(t)Temperature T(t) Temperature y(t)

Vokage u(t)

dy/dt = -(IN) F(t) y(t)+ (I/V) F(t) T(t)+ (URCV)W**2

FIGURE 5

Control StrategyHeat Exchanger Example

State

Time

FIGURE 6

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Dynamical ControlHeat Exchanger Example

0.3s I Temperature0.26.=al~.

:: OM~ki*a;E I;: 0.32 IInitialTemperature0.300 10 20

TimeFIGURE 7

TkneFIGURE 8

1.2 Stepresponseof cosmolkd system

1 -0.8 -a)

%!~ 0.6 -$ 0.4 -

0.2 -

FIGURE 9

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2 Corrlmller Output

1.8 -

1.6-1.41.21 -

0.8 Lo 2 4 6 8 10time

FIGURE 10

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NEURAL NETWORK PROCESS CONTROL

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