Fuzzy-+-PID-Controller-for-Robot-Manipulator

Fuzzy+PIDControllerforRobotManipulatorS.G.AnavattiandS.A.SalmanJ.Y.ChoiSchoolofAerospace,Civil&SchoolofElectricalEngineeringMechanicalEngineeringSeoulNationalUniversityAustralianDefenceForceAcademyKwanak,P.O.Box34(#048)UNSW@ADFA,Canberra,ACT2600Seoul,151600AUSTRALIASOUTHKOREA{a.sreenatha,s.salman}@[e-mail]lityanalysisforahybridfuzzylogiccontrollerispresentedinthepresentworkforarobotmanipulator.ThePD-typefuzzycontrolleriscombinedwithaconventionalPIDcontrollertoenhancetheperformanceandrobustnessofthecontroller.Asimplestabilityanalysisispresentedforthehybridcontroller.Numericalsimulationresultsarepresentedtovalidatethecontrollerdesign.1.IntroductionInthelasttwodecades,theproblemofcontrollingrobotmanipulatorshasattractedandchallengedmanyresearchers[1-4].Generally,Robotmanipulatordynamicsischaracterizedbynonlinearityandparametervariationsduetovariationsinload,frictionandexternaldisturbances,etc[2,3].Theconventionalcontrollersforsuchasystemmaynotgivedesirableresults[4].OntheotherhandtheconventionalcontrollerssuchasPIDareverywidelyusedintheindustryduetotheirreliabilityandeaseofimplementation.Althoughthesecontrollersareveryeffectiveandeasytousewithlinearsystem,theyarenothighlysuitablefornonlinear,complex,timevariantsystemswithdelay.Thefuzzylogiccontrollersareshowntobeefficienttoolsforcontrolofnonlinearanduncertainparameterssystems.Acombinationofthefuzzylogicandconventionalcontroller(hybrid)willbeafarmoreappropriatesolutionforcontrollingtherobotmanipulators.InrecentyearshybridfuzzyandconventionalcontrollersarecombinedtodesignacontrollersuchasfuzzyP+ID[5,6].Thisisshowntoimprovethetransientaswellassteadystateresponse.Inthepresentwork,aconventionalPIDcontrolleristunedinparallelwiththefuzzyPDtypecontroller.Numericalsimulationresultstodemonstratetheeffectivenessofthishybridcontrollerarepresented.Asimplestabilityanalysisisalsoinvestigated.Section2givesabriefdescriptionofthefuzzylogiccontrollerwhereassection3givesabriefdescriptionofrobotmanipulatordynamics.Insection4,fuzzyPDcontrollerforthesystemisdescribedandnumericalsimulationforthesystemisshowninsection5.Insection6and7stabilityanalysisandconcludingremarksarepresentedrespectively.2.FuzzylogiccontrollerThebasicconfigurationoffuzzysystemisshowninFigure1.Therearefourcomponentsinafuzzysystem:1)Fuzzifierwhichmapscrisppointsintheinputspaceintofuzzysets.2)FuzzyinferenceenginewhichusestechniquesinapproximatereasoningtodetermineamappingfromthefuzzysetsintheinputspacenRU⊂tothefuzzysetsintheoutputspacemRV⊂.3)Fuzzyrulebasewhichcomprisesfuzzyrulesdescribinghowthefuzzysystemperforms;itistheheartofthewholesysteminthesensethatotherthreecomponentsareusedtointerpretandcombinetheserulestoformthefinalsystem.4)Defuzzifierwhichmapsfuzzysetsintheoutputspaceintocrisppoints.ThereareseveralformsforfuzzycontrollerP-likefuzzycontroller,PD-likefuzzycontroller,PI-likefuzzycontrollerandPID-likefuzzycontroller.Inthepresentwork,PD-likefuzzycontrollerisapplied.InthefuzzyPDcontrollerthecontrolvariablesaretheerror(e)andthechangeoftheerror(∆e).Therulebaseis;InternationalConferenceonComputationalIntelligenceforModellingControlandAutomation,andInternationalConferenceonIntelligentAgents,WebTechnologiesandInternetCommerce(CIMCA-IAWTIC'06)0-7695-2731-0/06$20.00©2006ifeis(propertysymbol)and∆eis(propertysymbol)thenuis(propertysymbol)3.RobotmanipulatordynamicsThelinearrobotmanipulatordynamicsfora6-axisindustrialrobotmodeledasthefollowingfourthorderSISOisgivenby[8];[]1111122220100001+,00010000010,CKKJJJJxxuCKKJJJyx−−=−−=where1Jand2Jaretheinertiaofthemassconnectedtothemotorandthelinkrespectively,Kisthetorsionalspringconstant,and1Cand2Caretherotarydampingconstantsforthemotorandthelinkrespectively.Table1showsthesystemparameters.nn1andnn2arethefractionsofthevariationsinmomentofinertiaforthemodelandthelinkrespectively.Figure5representstheblockdiagramforthesystemunderstudywherethecoulombfrictionsforthemotorandthelinkaretakenintotheaccountandthismakesthesystemunderstudynonlinear.4.FuzzyPDcontrollerforrobotmanipulatorInthepresentwork,thefuzzyPDcontrollerwasdesignedasfollows:theinputstofuzzyPDcontrollerarethepositionofencoder1(Pos_ENC1)andvelocityoftheencoder1(Vel_ENC1).Theoutputfromthecontrolleristhemotortorque.Figure2,3and4representthefuzzymembershipsforthesystem.Threemembershipsareused(Negative,Zero,Positive).Table1Systemparameters1J0.0108+nn1*0.01082J0.0108+nn2*0.01081C0.0072.C0.001K1.37Arulebaseconsistingofninerulesiswrittentoprovidethecontrolinput.Therulebaseisgivenby;IfeisNegativeand∆eisNegativethenuisNegativeIfeisNegativeand∆eisZerothenuisNegativePlantControlvariables(e,∆e)Controlinput(u)DefuzzifierFuzzifierFuzzyRuleBaseFuzzyInferenceEngineFuzzysetsinVCrispUєFigure1.Basicconfigurationoffuzzysystem.05-10-510NegativeZeroPositive1Figure2.FuzzymembershipsforPos_ENC1.08-10-810NegativeZeroPositive1Figure3.FuzzymembershipsforVel_ENC1.030-40-3040NegativeZeroPositive1Figure4.Fuzzymembershipsforoutput.InternationalConferenceonComputationalIntelligenc