This work deals with some practical aspects of fuzzy PID
controllers regarding multivariable non-linear feedforward
compensation. This contribution concerns to the task of
compensation for multivariable disturbances on the controlled
variable. The strategy consist in establishing a fuzzy rule base
for all disturbance variables and compensate the control
variable by feedforward action by means of a fuzzy rule base
properly adjuste

Ferreiro García, Ramón

Pérez Castelo, Francisco Javier

Vidal Paz, José

Repositorio da Universidade da Coruña

MULTIVARIABLE FUZZY FEEDFORWARDCOMPENSATIONR. Ferreiro García, F. J. Pérez Castelo, J. Vidal PazDep. Industrial Engineering. University of A CorunaE.S Marina Civil, Paseo de Ronda 51. 15011- A Coruna. Spain fax: 34 81 167101e-mail: ferreiro@udc.es†ECC2001 Conference e-mail: ecc2001@fe.up.pthttp://www.fe.up.pt/ecc2001/Keywords: Non-linear feedforward, multivariabledisturbances, multivariable feedforward compensation, fuzzyfeedforward compensationAbstractThis work deals with some practical aspects of fuzzy PIDcontrollers regarding multivariable non-linear feedforwardcompensation. This contribution concerns to the task ofcompensation for multivariable disturbances on the controlledvariable. The strategy consist in establishing a fuzzy rule basefor all disturbance variables and compensate the controlvariable by feedforward action by means of a fuzzy rule baseproperly adjusted.1 Feedforward control backgroundConventional feedforward control deals with the task ofcorrect the manipulated variable for a disturbance on thecontrolled process. Most common industrial processes aredisturbed by more than a variable. For instance, in heatexchangers, controlled temperature is disturbed from flow andtemperature variations of heated fluid. Furthermore, they aredisturbed also by variations of the operating point becausedissipation heat may depend on the ambient and operatingtemperatures and by process parameters.In conventional feedforward control [2,3], an error must bedetected in a controlled variable before the feedbackcontroller can act to change the manipulated variable.Therefore, disturbances must upset the system before thefeedback controller can do anything. It seems very reasonablethat if a disturbance entering a process could be detected, acontroller should begin to correct for it before it upsets theprocess. This is the basic idea of feedforward control. Ifdisturbance can be measured, this result will be used to send asignal through a feedforward control algorithm that makesappropriate changes in the manipulated variable so as to keepthe controlled variable near its desired value.Classical industrial controllers offer the possibility ofcompensation for only a disturbance variable entering theprocess, if such a disturbance can be measured. The realproblem concerning industrial control, in which a goodperformance is needed, requires the compensation task formore than a single disturbance variable. In such caseconventional controllers are not efficient and fuzzy logiccontrollers takes advantage. Furthermore, disturbancevariables are associated by non-linear functions. Non-linearfeedforward compensator can be designed for non-linearsystems.An alternative to implement feedforward control systems inorder to compensate multivariable disturbances, may beimplemented by means of a rule based controller, for whichthe use of fuzzy logic is a powerful tool.2 Rule based feedforward compensationIn complex systems, analytical methods to find non-linearfeedforward controllers become too complex. Alternativesolutions based in numerical techniques must be used to findthe required non-linear changes in manipulated variables. Oneof numerical techniques consists in apply rule basedcompensators. In Figure 1 it is shown the general structure if amultivariable feedforward compensator.Figure 1: Feedforward feedback control structure.SensorSensorsProcessmodelPIDMultivariableFeedforwardControllerDisturbancesDisturbancemodelIn Figure 2 it is shown the case of a system disturbed by twodifferent variables n1 and n2, which enter the fuzzy rule baseresponsible for generate a corrective output to be added to theoutput of the feedback controller.Figure 2: Multivariable feedforward compensation using afuzzy rule base.Given a closed loop system disturbed by a function consistingin a set of non-linear variables, its open loop model is definedas)()()()(sGsnsUsY=+∑ (1)where Y(s) is the system output or response, U(s) is the totalcontroller output, Σn(s) are the disturbances and G(s) is thesystem transfer function. (1) can be  expressed as)())()(()( sGsnsUsY ∑+= (2)The condition to ensure the steady state response due to theassociation of two exciting variables, which are the output of afeedback controller and the set of disturbance variables (U +Σn) is that(U + Σn) = constant (3)which implies that∆U + ∆Σn = constant (4)or∆Σn = -∆U (5)Expression (5) means that any variation of disturbancevariables ∆Σn, must be compensated by -∆U in order to keepthe controlled system in steady state. -∆U will be generated bya fuzzy rule base.Expression (5) will be implemented by means of a fuzzy rulebase [1].3 An applicationAccording Figure 3, for a heat exchanger, the first law can bewritten as)()(.. eTiF TTKTTCeqdtdTCeMQ −+−+= (6)rearranging (6) to separate disturbancesTKCeqdtdTCeMTKTCeqQ TFeTiF ).(... ++=++ (7)where M is the mass of fluid into the heat exchanger, Ce is thespecific heat of fluid, KT is the total transfer coefficientbetween exchanger and environment, qF is the fluid flow, Ti isthe input fluid temperature, Te is the environment temperatureand T is the output fluid temperature.In this study it is considered that only variations exist in fluidtemperature and flow, so that environment temperatureremains constant.Figure 3: Heat exchanger affected by disturbance variables(fluid flow and input fluid temperature).The block diagram for system simulation is shown in Figure4. According this figure, the feedback controller output isadded to the output of the fuzzy rule base responsible forcompensate the variations in the fluid flow and fluidtemperature. As it is shown in the left hand side of expression(7), fluid flow and fluid temperature are associated by meansof a product, which result in non-linear function formentioned disturbance variablesFigure 4: Block diagram for system simulation.The rule base is quite simple, provided that only nine rules aresufficient to compensate the disturbances studded. The Table1 shows the full rule base.The 3D rule base input/output relationship is shown in Figure5.Rule base adjusting task has been carried out off-line bysimulation. For several discrete values of the steady statevariables related with feedforward compensation (flow, inputtemperature and rule base output) stored into a data file, aPIDn2UFuzzyRule basen1eWYTdisturbances:flow, tempU TeQ10.947fluid-temp0.2989fluid-flowdist1distIn1Out1Valve1M*Ce.sTransfer Fcn20.266TaSum3Sum2Sum1SumStepScope2Scope1ScopeIn1In2In3In4In5Out1Process inputsIn1 Out1PIDMuxMux20GainFuzff2Ct21Ct1neuro fuzzy toolbox, the NeuroSys of Siemens is applied forsuch training procedure.If (flow is low) and (temp is low) then (output is Z)If (flow is low) and (temp is med) then (output is Vlow)If (flow is low) and (temp is high) then (output is Low)If (flow is med) and (temp is low) then (output is Vlow)If (flow is med) and (temp is med) then (output is Med)If (flow is med) and (temp is high) then (output is high)If (flow is high) and (temp is low) then (output is Med)If (flow is high) and (temp is med) then (output is high)If (flow is high) and (temp is high) then (output is Vhigh)Table1: Rule baseFigure 5: Block diagram for system simulation.Figure 6: The rule base layout.4 Simulation resultsSimulation is performed by setting the input set point in aspecified value, while disturbance variables (fluid flow andfluid temperature are varying according the curves shown inFigure 8. Fluid flow variations consist in a sine function of .2Kg/s amplitude and 0.002 rad/s. frequency. Fluid temperatureconsist in a sine function of 4.5 degrees amplitude andfrequency 0.004 rad/s.Results are shown in Figure 7. They show that disturbancesare compensated by means of the fuzzy controller withsatisfactory response values.Figure 7: Time response to a step set point input withdisturbances in fluid flow and fluid temperatureFigure 8: Variation of disturbance variables.(a) flow, (b) tempFigure 9: Control variables dynamics:(a) PID output. (b) Fuzy rule base output0              200            400             600            800     time (s)T40200ab0             200            400             600            800      time (s)qF,Ti2010 0ab0             200            400             600            800   time (s)10 0-105 ConclusionsMultivariable non-linear feedforward compensation by meansof a fuzzy rule base can be succefully achieved. To get thefuzzy rule base properly adjusted it is necessary to selectbetween two options: For the case of a dterministic math-model of disturbed process, simulation can be used to find theinput/output relationship. In other cases neuro-fuzzy adjustingprocedures must be performed. In any case disturbances musbe accessible to measurement.References[1] King R.E. “Computational Intellingence in ControlEngineering”, Chap.8, pp.105-118, Marcel Decker, Inc.New York, U.S.A. (1999).[2] Luyben W.L. “Process modeling, simulation, and controlfor chemical engineers”, Chap.11, pp.383-391,McGraw-Hill, Inc U.S.A. (1989).[3] Shinskey F.G.. “Process control systems. Applications,design and tuning”, Chap.7, pp.267-309, McGraw-Hill,Inc U.S.A. (1996).

Multivariable fuzzy feedforward compensation

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Multivariable fuzzy feedforward compensation

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