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外文翻译--三维桥式起重机的建模与控制 英文版【优秀】.pdf

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外文翻译--三维桥式起重机的建模与控制 英文版【优秀】.pdf

HoHoonLeeDepartmentofMechanicalEngineering,UniversityofSuwon,SuwcnP.0.Box77,Seoul440600,KoreaModelingandControlofaThreeDimensionalOverheadCraneInthispaper,anewdynamicmodelofathreedimensionaloverheadcraneisderivedbasedonanewlydefinedtwodegreeoffreedomswingangle.Thedynamicmodeldescribesthesimultaneoustraveling,traversing,andhoistingmotionsofthecraneandtheresultingloadswing.Forantiswingcontrol,thispaperproposesadecoupledcontrolschemebasedonthedynamicmodellinearizedaroundthestableequilibrium.Thedecoupledschemeguaranteesnotonlyrapiddampingofloadswingbutalsoaccuratecontrolofcranepositionandloadhoistingforthepracticalcaseofsimultaneoustraveling,traversing,andslowhoistingmotions,whichisalsoprovenbyexperiments.1IntroductionOverheadcranesarewidelyusedinindustryfortransportationofheavyloads.However,thecraneacceleration,requiredformotion,alwaysinducesundesirableloadswing.Largeraccelerationusuallyinduceslargerloadswing.Loadhoistingalsotendstoaggravatetheloadswing.Thisunavoidableloadswingfrequentlycausesefficiencydrop,loaddamages,andevenaccidents.Forsafety,overheadcranesareusuallysetinmotionwiththeirloadshoistedhigherthananypossibleobstaclesandthelengthofhoistingropesiskeptconstantorslowlyvaryingwhilethecranesareinmotion.Variousattemptshavebeenmadetocontroltheloadswing.Thenumberofthecontrolinputsforacranesystemisbynaturelessthanthatofthesystemoutputs,whichmakestherelatedcontrolproblemscomplicated.Thecranecontrolconsistsofcranemotioncontrol,loadhoistingcontrol,andloadswingsuppression.MitaandKanai1979solvedaminimumtimecontrolproblemforswingfreevelocityprofilesofacraneundertheconstraintofzeroloadswingatthestartandendofacceleration.Ohnishietal.1981proposedanantiswingcontrolbasedontheswingdynamicsoftheload.Starr1985proposedanopenloopcontrolalgorithm,whichrequirestheconstraintofzeroinitialloadswing.Ridout1987designedafeedbackcontrollawusingtherootlocusmethod.Yuetal.1995proposedanonlinearcontrolbasedonasingularperturbationmethod,whichisvalidonlyiftheloadmassismuchlargerthanthecranemass.MoustafaandAbouElYazid1996discussedthestabilityofacranecontrolsystemforhoistingmotionsoftheload.Leeetal.1997proposedanantiswingcontrollawthatguaranteedbothrapiddampingofloadswingandaccuratecontrolofcraneposition.Alltheaboveresearchershavefocusedonthecontroloftwodimensionaloverheadcranesthatallowonlythetravelingandhoistingmotionshowever,inmostfactoriesandwarehousesthreedimensionaloverheadcranesarenormallyused.MoustafaandEbeid1988derivedadynamicmodelofathreedimensionaloverheadcranebasedonthesphericalcoordinatesMeirovitch,1970andGreenwood,1988,andthendesignedatrajectorydependentcontrolbasedonthedynamicmodellinearizedalongadesiredtrajectory.TheirlinearizedmodeliscoupledanditsparametersaredependentoncranetrajectoriesthiscompUcatestherelatedcontroldesignsandapplications.TheirconContributedbytheDynamicSystemsandControlDivisionforpublicationintheJOURNALOFDYNAMICSYSTEMS,MEASUREMENT,ANDCONTROL.ManuscriptreceivedbytheDynamicSystemsandControlDivisionDecember2,1996.AssociateTechnicalEditorR.Redfield.troladdressesonlythesuppressionofloadswingconsequently,theircontrolresultsinconsiderablepositionerrorsincranemotionandloadhoisting.Thispaperpresentsapracticalsolutiontothemodelingandcontrolofthreedimensionaloverheadcranes,wheretheloadswing,cranemotion,andloadhoistingareconsideredalltogetherinthemodelingandcontrol.First,anewtwodegreeoffreedomswingangleisdefinedassociatedwiththetravelandtraverseaxesofathreedimensionaloverheadcrane.Thenanewnonlineardynamicmodelforthecraneisderivedbasedonthenewswingangledefinition.Thenewdynamicmodelisequivalenttothatofathreelinkflexiblerobothavingthefirstflexiblemode.Next,thenewdynamicmodelislinearizedaroundtheverticalstableequilibrium.Thentheresultingdynamicmodelisdecoupledandsymmetricwithrespecttothetravelingandtraversingmotionsofthecraneandthemodelparametersareindependentofcranetrajectory,whichsignificantlysimplifiesthecontrolproblems.Withthisresult,thispaperproposesanewdecoupledantiswingcontrolschemethatguaranteesaccuratecontrolofcranepositionandloadhoistingaswellasrapiddampingofloadswingforthepracticalcaseofsimultaneoustraveling,traversing,andslowhoistingmotions.Theremainderofthispaperisorganizedasfollows.InSection2,anonlineardynamicmodelisderivedbasedonanewtwodegreeoffreedomswingangle,forathreedimensionaloverheadcrane.InSection3,thenonlineardynamicmodelislinearized,andthenanewdecoupledantiswingcontrolschemeisdesignedusingtheloopshaping,rootlocus,andgainschedulingmethods.InSection4,thedecoupledcontrolschemeisappliedtoathreedimensionalprototypeoverheadcraneforperformanceevaluation.InSection5,theconclusionsaredrawnforthisstudy.2ModelingofaThreeDimensionalOverheadCrane2.1DefinitionofGeneralizedCoordinates.Figure1showsthecoordinatesystemsofathreedimensionaloverheadcraneanditsload.XYZisthefixedcoordinatesystemandXjYjZristhetrolleycoordinatesystemwhichmoveswiththetrolley.Theoriginofthetrolleycoordinatesystemisx,y,0inthefixedcoordinatesystem.Eachaxisofthetrolleycoordinatesystemisparalleltothecounterpartofthefixedcoordinatesystem.Yrisdefinedalongthegirderwhichisnotshowninthefigure.ThetrolleymovesonthegirderintheYjtraversedirectionandthegirderandYjaxismoveintheXTtraveldirection,distheswingangleoftheloadinanarbitrarydirectioninspaceandhastwocomponents9andOy,where9isJournalofDynamicSystems,Measurement,andControlCopyright©1998byASMEDECEMBER1998,Vol.120/471Downloaded18Mar2009to202.198.46.187.RedistributionsubjecttoASMElicenseorcopyrightseehttp//www.asme.org/terms/Terms_Use.cfmLoadFig.1CoordinatesystemsofathreedimensionaloverheadcranetheswingangleprojectedontheXrZrplaneand9yistheswinganglemeasuredfromtheXTZTplane.ThepositionoftheloadXm,ymZminthefixedcoordinatesystemisgivenbyx„XIsin6cos6y,y„,ylsinOy,ZmICOS0cos9y,123where/denotestheropelength.Thepurposeofthisstudyistocontrolthemotionofboththecraneanditsload.Hencex,y,I,9,and9yaredefinedasthegeneralizedcoordinatestodescribethemotion.2.2DynamicModelofaThreeDimensionalOverheadCrane.Inthissection,theequationsofmotionofacranesystemarederivedusingLagrangesequationMeirovitch,1970.Inthisstudy,theloadisconsideredasapointmass.Themassandstiffnessoftheropearealsoneglected.K,thekineticenergyofthecraneanditsload,andP,thepotentialenergyoftheload,aregivenas1»/KM,xMyfM,lvl,4Pmgl{\cos9xcos6y,5whereM,,My,andMiarethextraveling,ytraversing,and/hoistingdowncomponentsofthecranemassandtheequivalentmassesoftherotatingpartssuchasmotorsandtheirdrivetrains,respectivelym,g,andu„denotetheloadmass,thegravitationalacceleration,andtheloadspeed,respectivelyIm{xnyl,ZmISobtainedasvlxft/cos9y9l/ej2sin9,cos9yi/cos9cos9ydIsin9sin9y9yx2ism9yilcos9y9yy.6LagrangianLandRayleighsdissipationfunctionFaredefinedas1ttiL{M,xMyfM,Pvimglcos9„cosy17F\D,xDyfD,h,8where£,D,,andD,denotetheviscousdampingcoefficientsassociatedwiththex,y,and/motions,respectively.TheequationsofmotionofthecranesystemareobtainedbyinsertingLandFintoLagrangesequationsassociatedwiththegeneralizedcoordinatesx,9,y,6y,and/,respectivelyM,Imxmlcos9cos9y9,mlsin9sin9y9ymsin9cos9ylDx2mcos9cos9yi92msin9sin9yWymlsin9cos9ydl2mlcos9Jsin9y9jymlsincos9y9y/,,9mPcos9y9xmlcos9cos9yX2mlcos9yi6x2mlsin9ycos9y9t9ymglsin9cos9y0,10{Mymymlcos9y9ymsin9yiDyy2OTcos9yi9ymlsin9y9yfy,11m/ymlcosyymlsin0sin5j,jfc2mll9ymlcos9ysinmg/cos6sin50,12{Mlmlmsin9cosAmsinyAmlcos„imlbmgcos9cos9yfi,13where,/j,,andarethedrivingforcesforthex,y,and/motions,respectively.2.3RemarksontheDynamicModel.Thedynamicmodelforathreedimensionaloverheadcranehasthefollowingfeaturesthankstothecharacteristicsoftheproposedswingangledescription.Whenyy9y9y9y0,thedynamicmodelofathreedimensionaloverheadcraneisreducedtothatofatwodimensionaloverheadcraneLeeetal.,1997movingalongtheXaxis.ThesameistruefortheYaxiswhenxx99.h0.ThedynamicmodelisequivalenttothatofathreelinkflexiblerobothavingthefirstflexiblemodeLucaandSiciliano,1991.Thatis,thedynamicmodel913canberepresentedbythefollowingmatrixvectorformMqqIZqFC0and\9y\K0sl{KpSHK,isadoptedonpurposetocancel{KpSKilsofKsis.ThenKg{sbecomesalagcompensatorwhentheoutputofKD{SisdirectlyinputtedtothevelocityservosystemGis.Inthisway,theswingangleandcranemotioncanbeseparatelycontrolled.Figure5showstherootlocusoftheoverallcontrolsystemfor/1m,K,24.0,Kp1.6,K,0.08,K„1.5,andK0.6.TheoptimumvalueofKacanbedeterminedfromtherootlocus.TheoverallcontrolsystemisshowntobestableregardlessofthevalueofK,,.However,thesystemmaybecomeunstableforalargevalueofK,,sincethenonlineardynamicswereneglectedinthelinearizationprocess.3.2.4RemarksontheControlPerformance.TheperformanceoftheoverallcontrolsystemcanbeanalyzedusingthetransferfunctionsfromeachinputtoeachoutputinFig.4.ThetransferfunctionsforZ1mandKa3.55withthecontrolgainsobtainedaboveareasfollowsX38.4s0.05s0.6j9.838.4j0.05s0.6Gcisss0.6s24s9.80XrAGAs©_s\s0.652433343536whereGdsisdefinedasG,.ss0.05sO.S2s3.1Xsn.26s1.691.47.37Asexpected,theclosedlooppolesshowninGsareallstablewithsufficientdampingaccordingly,soarethetransferfunctions3336.X/XshowsexcellentcommandtrackingrealaxisFig.5Rootlocusoftheoverallcontrolsysteminthelowfrequencyregion.0/X,showsthatthesteadystateswingangleiszeroforramppositioncommands.AccordingtoX/Dand/D„,thesteadystatecranepositionisnotinfluencedbystepdisturbancesandthesteadystateswingangleisnotaffectedbyparaboladisturbances.3.3AntiSwingControlforSlowlyVaryingRopeLength.Anewdecoupledantiswingcontrollawhasbeendesignedaboveforthecaseofconstantropelength.Inpractice,however,theropelengthsometimesneedstobesetslowlyvaryingforloadhoistingwhilecranesareinmotion.Accordingly,thispracticalcasewillbeconsideredhere.3.3.DesignofaRopeLengthServoController.Aswiththecranedynamics21,theloadhoistingdynamics19canbewrittenasMlmlD/lmgK,iU,i,38whereu,iistheinputtothetorqueservocontrollerofthehoistingmotorandKiisthecranedependentconstant.Asabove,aprecompensatorisdesignedfirst.Thatis,u,iinEq.38isselectedasu„u,mglK,i39whereUiisthenewcontrolinputtobedetermined.Thentheloadhoistingdynamics38becomesAf,mlD,lK,,u,.40Fig.4SchematicdiagramoftheoverallcontrolsystemThedynamics24and40areofthesamestructure.Thereforearopelengthservocontrolsystemcanbereadilydesignedbyfollowingthedesignproceduresforthecranepositionservocontrolsystem30.Thehoistingmotorsaresometimescontrolledbyvelocityservocontrollersinsteadofthetorqueservocontrollers.ThenthedesignmethodproposedbyLeeetal.1997canbereadilyapplied.3.3.2GainSchedulingforSlowlyVaryingRopeLength.Thevelocityandpositionservocontrolgainsaredeterminedindependentlyoftheropelength.However,theanglegainsK„,K„,andKjneedtobeadjustedtochangesinropelength.Inthisstudy,againschedulingmethodisadoptedtocopewithslowlyvaryingropelength.Thatis,foreachselectedropelengthI,theoptimumvaluesofK,K„,andKaredeterminedfromtherootlocusoftheoverallcontrolsystem,andthentheanglegainfunctionsKl,K„il,andKlareobtainedfromtheoptimumvaluesusingthecurvefittingtechnique.Theyarefunctionsoftheropelength/hencetheyareusedinrealtimecontrolaccordingtorealtimeropelength.3.4StabilityAnalysisforSlowlyVaryingRopeLength.Theropelengthisindependentlycontrolledsincetheloadhoistingdynamics19isindependentofcranemotionandloadswing.Asaresult,thecranecontrolsystemisstableiftheoverallcontrolsystemshowninFig.4isstableforslowlyvaryingropelength.474/Vol.120,DECEMBER1998TransactionsoftheASMEDownloaded18Mar2009to202.198.46.187.RedistributionsubjecttoASMElicenseorcopyrightseehttp//www.asme.org/terms/Terms_Use.cfm

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