Alpha-Beta-Gamma-Filter-for-Cascaded-PID-Motor-Pos

ProcediaEngineering41(2012)244–2501877-7058©2012PublishedbyElsevierLtd.doi:10.1016/j.proeng.2012.07.169InternationalSymposiumonRoboticsandIntelligentSensors2012(IRIS2012)AlphaBetaGammaFilterforCascadedPIDMotorPositionControlKhinHooiNg*,CheFaiYeong,EileenLeeMingSu,LiangXuanWongFacultyofElectricalEngineering,UniversitiTeknologiMalaysia,81310Skudai,Johor,MalaysiaAbstractPIDcontrollerisnormallyusedinpositioncontrole.g.motorpositioncontrol.However,inrealapplication,amotorisnon-linearduetofactorslikefrictionandpowersaturation.Therefore,inthispaper,cascadedPIDcontrollerisproposedtoreducethesenonlinearities.ThecascadedPIDcontrollerwasusedbecauseofthefastresponseandbetterdisturbancerejection.TheerrorfromthemotorpositionisfedintothefirstPID,andtheoutputfromthePIDcontrollerisusedasvelocityreferenceforthesecondPID.Withthesecharacteristicsofacascadedcontrol,thenonlinearityinamotorcanbereduced.ImplementationofPIDcontrollerisdoneinadigitalformandusually,thederivativeelementsaresubjecttonoisefromsamplingtimeerrorandquantizationerror.Tosolvethisproblem,thealphabetagammafilterisusedtoestimatethevelocityofthemotor.Experimentwasconductedusingamicrocontrollertoshowtheeffectivenessofcascadedcontrolinreducingnonlinearityofamotor,andthealphabetagammafilterwasimplementedtoreducesamplingtimeandquantizationerror.Resultsshowanoverdampedsystemwithnosteadystateerrorwasproduced.©2012TheAuthors.PublishedbyElsevierLtd.Selectionand/orpeer-reviewunderresponsibilityoftheCentreofHumanoidRobotsandBio-Sensor(HuRoBs),FacultyofMechanicalEngineering,UniversitiTeknologiMARA.Keywords:CascadedPIDcontroller,alphabetagammafilter1.IntroductionThepermanentmagnetdirectcurrentmotorispopularbecauseoftheeaseofcontrolandgoodtorqueregulation[1,2].Inapplicationslikerobotics,thedirectcurrentmotorisusedtomanipulatearoboticarm.Thedcmotorcancomesinmanyshapesandsizes,makesthedevelopmentofdcmotorforroboticsapplicationquiteeasyandflexible.Inamateurrobotics,thedcmotorisoftenusedbecauseitiseasilycontrolwithaH-bridge.BychangingthepolarityoftheH-bridge,themotordirectioncanbechanged.Andbymanipulatingtheappliedvoltage,thespeedofmotorcanbevaried.Inthefieldofamateurrobotics,alltherobotsareusuallyself-fabricated.Thismakestheloadofthemotorishighlynonlinearmainlyduetothefriction.Asexampleofroboticsapplication,intheAsiaPacificBroadcastingUnionRobotContest(ABUROBOCON),mobilerobotswereconstructedtocompletegiventasksinspecifictime[3].Theproblemofmotorpositioncontrolisnontrivialinthepresenceofsuchnonlinearities.Givenexampleofmotorinpaperlike[2,4],theseplantsweremanufacturedwithhighaccuracy,thusreducingthenonlinearities.Besides,theloadisnon-varyingandthefrictioncanbeeasilyobserved.ComparedittoaroboticarmmanipulatorinFig.5,differentpositionoftheslidermightgivedifferentvalueoffriction.Besides,theloadmightdifferentbecauseofpickandplaceoperation.ThismakeslinearcontrollerlikethePIDcontrollerdoesnotperformwellingeneral.*Correspondingauthor.Tel.:[phone]E-mailaddress:[e-mail](2012)244–250Besides,thewholemobilerobottaskhastobeprogrammedinmicrocontrollers.Advancenonlinearcontrollerlike[5]mightnotbeanattractivesolutionduetoitscomplexity.Thesolutionforthisproblemmustbecomputationalcheapintermsofmemoryspaceandexecutiontime.Inthispaper,thecascadedcontrollerwasproposedtoovercomethehighnonlinearityintheprocessplant.Byclosinginternaldynamicswithadditionalfeedbackloop,thewholesystemcanbeimproved.Besidesthat,PIDcontrollercanbeeasilyimplementedinamicrocontrollerbecauseofitssimplealgorithm.Buttoaddanotherfeedbacklooprequiresadditionalsensor.Fortunatelyforthenatureofadcmotor,thevelocitycanbeusedtoclosetheloopoftheinternaldynamics.Byestimatingthevelocityfromthemotorpositionreading,anotherPIDcanbeimplementedincascade.Butbydifferentiatingthepositionnumericallyusuallycausenoises.Tosolvethis,thealphabetagammafilterwasused[6–8].Alphabetafilterwasdevelopedinthe1960’sandithasbeenusedwidelyinradartrack-while-scantask.ItisfamousintheearlyagesbecausecomplexcomputationalfacilitiesandtheKalmanfilterhavenotyetbeeninvented[9].Themodifiedalphabetagammafilterisusedtoestimatethemotorvelocitybecauseofadditionalaccelerationstatethatgivesbetterestimationthananalphabetafilter.Section2describesthedirectcurrentmotormodelandtheinternaldynamicswhichenablesthecascadedcontroltobeapplied.Section3describesthealphabetagammafilterandtheestimationproblemitcanovercome.Section4describesthecascadedPIDcontrollerwherethepositioncontrolleriscascadedwithavelocitycontroller.Section5describestheexperimentsetup.Section6describestheexperimentsetupandresultsfromthoseexperiments.ThispaperisconcludedinSection7.2.DirectCurrentMotorModelFig.1.MotorschematicsThemodelusedforthePMDCmotorispresentedhere.Fig.1showsthemotorschematic.Thesecondordermodelisusedforthecontrollerdesignforthispaper.Becausetheinductanceofthearmatureisgenerallymuchsmallerthantheresistance,aaRL,itcanbeassumedzero[10].ByusingKirc