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当前位置:首页 > 行业资料 > 冶金工业 > 基于NARX神经网络的磁悬浮仿真模型(IJISA-V5-N5-4)
I.J.IntelligentSystemsandApplications,2013,05,25-32PublishedOnlineApril2013inMECS()DOI:10.5815/ijisa.2013.05.04Copyright©2013MECSI.J.IntelligentSystemsandApplications,2013,05,25-32SimulationModelofMagneticLevitationBasedonNARXNeuralNetworksDraganAntić,MiroslavMilovanović,SašaNikolić,MarkoMilojković,StanišaPerićUniversityofNiš,FacultyofElectronicEngineering,DepartmentofControlSystems,AleksandraMedvedeva14,18000Niš,RepublicofSerbia,Phone:(+381)18529363,Fax:(+381)18588399E-mails:{dragan.antic,miroslav.milovanovic2,sasa.s.nikolic,marko.milojkovic,stanisa.peric}@elfak.ni.ac.rsAbstract—Inthispaper,wepresentanalysisofdifferenttrainingtypesfornonlinearautoregressiveneuralnetwork,usedforsimulationofmagneticlevitationsystem.First,themodelofthishighlynonlinearsystemisdescribedandafterthattheNonlinearAutoRegressiveeXogenous(NARX)ofneuralnetworkmodelisgiven.Also,numericaloptimizationtechniquesforimprovednetworktrainingaredescribed.ItisverifiedthatNARXneuralnetworkcanbesuccessfullyusedtosimulaterealmagneticlevitationsystemifsuitabletrainingprocedureischosen,andthebesttwotrainingtypes,obtainedfromexperimentalresults,aredescribedindetails.IndexTerms—NeuralNetwork,MagneticLevitationSystem,NonlinearModel,NeuralNetworkTrainingI.IntroductionMagneticlevitationingeneralreferstotheprocessofobjectfloatingintheairundertheinfluenceofelectromagneticforce.Thatforceiscausedbythecurrentflowingthroughmagneticcoiloflevitationsystem.Levitatorisusedinpracticeasadevicewithonedegreeoffreedomwhichiscontrollingverticaltranslationofmetalball(SISOsystem).Ontheotherhand,magneticlevitatorcanbealsousedasmultiple-inputmultiple-output(MIMO)systemwithtwodegreesoffreedom,verticaltranslationandrotation[1].Magneticlevitationisusedintransportsector(highspeedtrains)wheremovementwithoutfrictionisobtained,formoltenmetallevitationininductionfurnaces,aswellasinmetalprocessingindustries.In[2],magneticlevitationisusedforcontrolofextremelyhightemperatureplasmasinfusionreactor.Magneticlevitationusageforvibrationisolatingduringworkofsensitivemachinesisalsodescribedinthispaper.Neuralnetworkscanbesuccessfullyappliedincomplexandnonlinearsystems,systemswithdisturbancesandinsufficientlyknownparameters,unpredictableanduncoordinatedsystems[3]-[5].Inthecaseofmagneticlevitationsystems,firstassignmentofneuralnetworkison-linelearningandthensuccessfulsimulationofmagneticlevitationbehaviour.Thesimilarapproachwasgivenin[6],whereneuralnetworkwithbuilt-innominallinearmodelisshown.Linearmodelisprovidedbysettingsomenetworkweightstodesiredandinadvancedefinedvalues.Otherweightsarefreeatstartandtheyarechangingtheirvaluesduringlearningprocess.Initialstabilityisprovidedbythelinearmodelcontrolatthestartofthetrainingprocess.ThemainobjectiveofthispaperistosimulateworkingprocessofmagneticlevitationsystembyimplementingNARXmodelofneuralnetworkusingMATLABsoftware.NARXmodelrepresentsnonlinearautoregressivenetworkwithexternalinputs,anditisbasedonlinearautoregressivemodel.NARXrepresentsrecurrentdynamicalfeedbacknetworkwithpredictivestructure.Maingoalofthispredictivemodelistopredictfuturesystembehaviourforknownandunknowninputvectors.Modelpredictionaccuracydirectlydeterminesqualityandefficiencyofthecontrollaw.Primaryconsiderationofworkaccuracyduringimplementationprocessisofagreatimportance.Thepaperisorganizedasfollows.InSectionII,themathematicalmodelofmagneticlevitationsystemisgiven.ThestructureofneuralnetworkbasedonNARXmodelispresentedinSectionIII.InnextSection,differenttrainingtypesofneuralnetworkaredescribed.TheexperimentalresultsareillustratedanddiscussedinSectionV.ItisshownthatthebestsimulationperformancesareobtainedusingBasicQuasi–NewtonandBackpropagationmethod.TheconcludingremarksaregiveninSectionVI.II.MathematicalModelofMagneticLevitationSystemMainpartsoflaboratorymagneticlevitationsystemareelectromagneticcoil,positionsensor,steelballandsteelframethatcanbedividedintothreeparts.Onthetopoftheframetheelectromagneticcoilisinstalled.26SimulationModelofMagneticLevitationBasedonNARXNeuralNetworksCopyright©2013MECSI.J.IntelligentSystemsandApplications,2013,05,25-32Fig.1:MagneticlevitationsystemOneofitsmagnetpolesispointingtothemiddlepartofframe.Sensorfortrackingballpositionisinstalledinwallofthemiddleframepart.Ballholder(wheretheballispositionedwhensystemisinactive)isinstalledonbottompartoftheframe.Therearealsomagneticlevitatorswithtwoelectromagneticcoilsandinthatcase,insteadofballholder,secondelectromagneticcoilisinstalled.Inthispaperweusedmagneticlevitationsystem[7]withoneelectromagneticcoil(Fig.1),sothesecondtypeoflevitationsystemwillnotbedescribedfurther.Magneticlevitatorcanbedividedintotwosubsystems,mechanicalandelectrical[8]-[10].ForelectricalsubsystemitisimportanttosingleoutelectromagneticcoilinductanceLHanditsresistancelR.Electricalsubsystemcanbedescribedwiththefollowingwell-knowndifferentialequation:ldiURiLdt.(1)Inordertodeterminethecurrentincoil,theresistorSRisserialconnectedtothecoil.InthatwayvoltageSUcanbemeasuredacrossresistorSR,byusingA/Dconvertorformeas
本文标题:基于NARX神经网络的磁悬浮仿真模型(IJISA-V5-N5-4)
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