倒立摆英文文献

Investigationonthecaroftheinvertedpendulumpendulumcontrolsystemisacomplex,uncertain,nonlinearsystems,controltheoryteachingandvariouscontrolexperimentisidealexperimentplatform.Studyoninvertedpendulumsystemcaneffectivelyreflectincontrolofmanyofthetypicalissues:suchasnonlinearproblems,robustness,stabilization,servoandtrackingproblems.Throughthecontrolofinvertedpendulum, usedtoverifythatthenewcontrolmethodofstrongabilitytohandlenonlinearandinstabilityproblems.Atthesametime,itscontrolmethodintherobotformilitary,aerospace,andGeneralinthefieldofindustrialprocesseshaveawiderangeofuses,suchasintheprocessofwalkingrobotbalancecontrol,verticalcontrolintherocketandsatelliteattitudecontrolinflight.Keywords:nonlinear,pendulum,balancecontrol,1.Invertedpendulumisinmultipleareasofrobotics,controltheory,computer-controlled,multi-technologyorganicCombination,thecontrolledsystemisanabsoluteinstability,higher-order,multivariable,stronglycouplednonlinearSystemcanbeusedasatypicalcontrolobjecttostudyit.Theinitialstudybeganinthetwentiethcentury1950s,theMassachusettsInstituteofTechnology(MIT),cyberneticsexperts,basedontheprincipleofrocketlaunchboosterdesigntheequipmentofaninvertedpendulum.Inrecentyears,anewcontrolmethod,peoplearetryingtotestnewcontrolmethodshaveastronghandlemultivariate,nonlinear,andabsolutelyunstablesystemcapacitythroughatypicalinvertedpendulumcontrolobject,andthusfromwhichtofindthebestcontrolmethods.Invertedpendulumsystemasacontroltheoreticalresearchinanidealexperimentaltoolfortheteachingofautomaticcontroltheory,experimentandresearchtobuildanexperimentalplatformtosomekindofcontroltheoryormethodusedtotestatypicalprogramtopromotecontrolsystemtheory,thedevelopmentofnewideas.Duetotheextensiveapplicationofcontroltheory,thusthesystemofmethodsandtechniquesinthesemiconductorandprecisioninstrumentprocessing,robotcontroltechnology,artificialintelligence,missileinterceptcontrolsystem,aviationdockingcontroltechnology,rocketlaunchersverticalcontrolthesatelliteflightattitudecontrol,andgeneralindustrialapplications,hasabroaddevelopmentprospects.Planarinvertedpendulumcanbemorerealisticsimulationoftherocketflightcontrolandwalkingrobotstabilitycontrol.2.ControlInvertedpendulumswing-upproblemisaclassicexperimentinthecontroltheory,theessenceoftheinvertedpendulumsystemfromastableequilibriumstateintheroleofexternalforcesautomaticallytransferredtoanotherstateofequilibrium.Inthisprocess,wedemandfromtheswingfast,butnottoomuchovershoot.Mainslidingmodecontrolforinvertedswing-upcontrolmethod,Dicolorpredictivecontrol,partialstatefeedbackcontrol,optimalcontrol,energycontrol,supervisionandcontrolofanthropomorphiccontrol,neuralnetworkcontrol,evolutionarycontrol,butthemainfocusIntheenergycontrol,optimalcontrol,intelligentcontrol.Donotapplytonon-linearinputandoutput,andmanycommonlyusedlinearcontroltheorybasedonnonlineartheory,theheadljifthefollowingseveralmethodshavebeensuccessfullyinvertedpendulumstartingtoswingcontrol.1976,MoiltIJ,whoproposedacontrolsystemcontainstwocontrollers,onecontrollertoautomaticallyswing,andtheothertostabilizeintotheinvertedpendulumsystemnearequilibrium.Ingeneral,theswing-upcontrollerbyshakingtheinvertedpendulummovementtoaspecifiedrange,thenthecontrollerswitchestoanotherresponsibleforthestablepart.1996,Torres.PomalesJdesignasimpleslidingmodecontrollerforinvertedpendulumswing-up.Basedonthesimplecontroloftheenergytermsistocontroltheenergyofthependulumratherthancontrolthepositionandvelocityofthependulum.Yoshidausingtheenergyofthelinearinvertedpendulumswing-upcontrol,theFantoniE41energycontrol,butthecontrolledobjectthecontrolledobjectisaplanemotionofapendulum.TheAstromdetailedaccountoftheenergycontroltheory,thecontrolobjectisastraightlineaninvertedpendulum.FuYing,ZhangGuanglienergyfeedbackmethodtocompletetheinvertedpendulumswing-upcontrol,similartotheabovemethod,relativelyspeaking,moreexperienced,andsuccessfulimplementationofakindofastraightlineforinvertedpendulumswing-upcontrol.Numericalalgorithmsforoptimalcontrol,thecalculationoftheoptimalcontrollawinthestatevariableswhentherearefewer,butmoreforthestatevariables,especiallytheproblemwithendpointconstraintsaredifficulttoachieve.HouXianglin[71basedontheoptimalmethodoffastswing-principlesstudyofinvertedpendulumendpointconstraints,thevectorofeachtimeperiodonthecontrollawasthedesignvariables,objectivefunction,theestablishmentoftheoptimizationprocedurecalculationoftheoptimalcontrollawandappliedtothecircularsingle-stageinvertedpendulumswing-upprocesscontrol.TheZhujiangBin,etc.~kindsofpredictivecontrol,real-timenonlinearsystemsbasedonexpertsystemandvariablestepsizecontrolmethod,toavoidthecomplexnon-linearderivation,combinedwithexpertsystemcontrolparametercorrectionsteppredictionwithvariablestepsize,thusultimaterealizationofthelineardoubleinvertedpendulumswing-upandstabilitycontrol.Swing-upalgorithmbasedonintelligentcontrol,therearetwocategories:oneisdirectlythroughthestraight-linemanualcontrolaswing-upinvertedprocessofparsing,basedonthehumanoidintelligentcontroltheorysuchasfuzzycontrol,neuralnetworkdesignforswing-swingcontroloftheintelligentcontrollerinverted,singledegreeoffreedominthecaseofoperatingunderlimitedtorqueLiZushuovercastgooduseofsuchmethods,simulationandreal-timetestresultsaswellasbetweenfullagreementprovedhumanoidintelligentcontrolmethodsvalidity,butthecontrollergaincoefficientbyexperiment,andswing-upsuccesstohaveagreatimpact.Theother,theintelligentcontrolalgorithmwithothercontrolalgorithms,suchasoptimizationmethods,acombinationofenergyfeedbackmethod,suchasHouXianglinfirstopen-loopcontrollawoptimizationalgorithmtodeterminetheidealcontrollawandthestatevariablematrix,theestablishmentofthestandardsample,andthenbytheartificialneurale-learningstandardsamples,expressionofthestatevariablesandcontroltheamountofneuralnetworkweightsandthreshold,theestablishmentoftheswing-upcontroloftheneuralnetworkstatevariables,andthendetectedintheclosed-loopcontrol,decidedtoimplementswing-upcontrolorstabilitycontrol,intelligentcontrolandoptimalcontroltoachievetheinvertedpendulumswing-up.3.invertedWhatisanInvertedPendulum?Rememberwhenyouwereachildandyoutriedtobalancea broom-stickorbaseballbatonyourindexfingerorthepalmofyourhand?Youhadtoconstantlyadjustthepositionofyourhandtokeeptheobjectupright.AnInvertedPendulumdoesbasicallythesamething.However,itislimitedinthatitonlymovesinonedimension,whileyourhandcouldmoveup,down,sideways,etc.CheckoutthevideoprovidedtoseeexactlyhowtheInvertedPendulumAninvertedpendulumisaphysicaldeviceconsistinginacylindricalbar(usuallyofaluminum)freetooscillatearoundafixedpivot.Thepivotismountedonacarriage,whichinitsturncanmoveonahorizontaldirection.Thecarriageisdrivenbyamotor,whichcanexertonitavariableforce.Thebarwouldnaturallytendtofalldown omthetopverticalposition,whichisapositionofunsteadyequilibrium.Thegoaloftheexperimentistostabilizethependulum(bar)onthetopverticalposit-ion.Thisispossiblebyexertingonthecarriagethroughthemotoraforcewhichtendstocontrastthe'free'pendulumdynamics.Thecorrectforcehastobecalculatedmeasuringtheinstantvaluesofthehorizontalpositionandthependulumangle(obtainede.g.throughtwoThesystempendulum+cart+motorcanbemodeledasalinearsystemifalltheparametersareknown(masses,lengths,etc.),inordertofindacontrollertostabilizeit.Ifnotalltheparametersareknown,onecanhowevertryto'reconstruct'thesystemparametersusingmeasureddataonthedynamicsofthependulum.Whatisitusedfor?Justlikethebroom-stick,anInvertedPendulumisaninherentlyunstablesystem.Forcemustbeproperlyappliedtokeepthesystemintact.Tovethis,propercontroltheoryisrequired.TheInvertedPendulumisessentialintheevaluatingandcomparingofvariouscontroltheories.Theinvertedpendulumisatraditionalexample(neitherdifficultnortrivial)ofac-ontrolledsystem.Thusitisusedinsimulationsandexperimentstoshowtheperformanceofdifferentcontrollers(e.g.PIDcontrollers,statespacecontrollers,fuzzycontrollers.).TheReal-TimeInvertedPendulumisusedasabenchmark,totestthevalidityandtheperformanceofthesoftwareunderlyingthestate-spacecontrolleralgorithm,i.e.theusedoperatingsystem.Actuallythealgorithmisimplementformthenumericalpointofviewasasetofmutuallyco-operatingtasks,whichareperiodicallyactivatedbythekernel,andwhichperformdifferentcalculations.Thewayhowthesetasksareactive-ted(e.g.theactivationorder)iscalledschedulingofthetasks.Itisobviousthatacor-rectschedulingofeachtaskiscrucialforagoodperformanceofthecontroller,an henceforaneffectivependulumstabilization.Thustheinvertedpendulumisveryusefulindeterminingwhetheraparticularschedulingchoiceisbetterthananotherone,inwhichcases,towhichextent,andsoon.Modelinganinvertedpendulum.Generallytheinvertedpendulumsystemismodeledasalinearsystem,andhencethemodelingisvalidonlyforsmalloscillationsofthependulum.Prescribedtrajectorytrackingwithcertainaccuracyisamaintaskofroboticcontrol.Thecontrolisoftenbasedonamathematicalmodelofthesystem.Thismodelisnev-eranexactrepresentationofreality,sincemodelingerrorsareinevitable.Moreover,onecanuseasimplifiedmodelonpurpose.Inthispaper,thestructuredandunstructureduncertaintiesareofprimaryinterest,i.e.,themodelingerrorduetotheparametersvariationandunmodeledmodes,especiallythefrictionandsensordynamics,neglectedtimedelays,etc.Theerroneousmodelandthedemandforhighperformancerequirethecontrollertoberobust.Theslidingmodecontrollers(SMC)basedonvariablestructurecontrolcanbeusediftheinaccuraciesinthemodelstructureareboundedwithknownbounds.However,anSMChassomedisadvantages,relatedtochatteringofthecontroltsignal.Oftenthisphenomenonisundesirable,sinceitcausesexcessivecontrolactionleadingtoincreasewearoftheactuatorsandtoexcitationofunmodeleddynamics.Theattemptstoattenuatethisundesirableeffectresultinthedeteriorationoftherobustnesscharacteristics.Thisisawell-knownproblemandwidelytreatedintheliterature.Inordertoobtainsmoothinginthebang-bangtypeddiscontinuitiesofthengmodecontrollerdifferentschemeshavebeenAnotherimportantissuelimitingthepracticalapplicabilityofSMCistheovercon-servativecontrollawduetotheupperboundsoftheuncertainties.Inpracticemostoftentheworstcaseimplementedincontrollawdoesnottakeplaceandtheresultinglar-gecontrolinputsbecomeunnecessaryanduneconomical.Inthispaperwesuggestanapproachtothedesignofdecentralizedmotioncontrollersforelectromechanicalsystemsbesidestheslidingmodemotioncontrollerstructureanddisturbancetorqueestimation.Theaccuracyoftheestimationisthecriticalparam-eterforrobustnessinthisscheme,asopposedtotheupperboundsoftheperturbationsthemselves.Consequently,thedrivingtermsoftheerrordynamicsarereducedfromtheuncertainties(asintheconventionalSMC)totheaccuracyintheirestimates.TheresultisamuchbettertrackingaccuracywithoutbeingoverconservativeincontExperimentalrobustnesspropertiesoffuzzycontrollersremaintheoreticallydiffic-ulttoproveandtheirsynthesisisstillanopenproblem.Thenon-linearstructureofthefinalcontrollerisderivedfromallcontrollersatthedifferentstagesoffuzzycontrol,particularlyfromcommondefuzzificationmethods(suchasCentreofArea).Ingeneral,fuzzycontrollershavearegion-wisestructuregiventhepartitionofitsinputspacebythefuzzificationstage.Localcontrolsdesignedintheseregionsarethencombinedintosetstomakeupthefinalglobalcontrol.Apartitionofthestatespacecanbefoundforwhichthecontrollerhasregion-wiseconstantparameters.Moreover,eachfuzzycontrollertuningparameter(i.e.theshapesandthevaluesofinputoroutputvariablesmembershipfunctions)influencesthevaluesofparametersinseveralreg-ionsatthesametime.Intheparticularcaseofaswitchinglineseparatingthephaseplaneintooneregionwherethecontrolispositivewhereasintheotheritisnegative,thefuzzycontrollermaybeseenasavariablestructurecontroller.Thiskindofafuzzycontrollercanbeassimilatedtoavariablestructurecontrollerwithboundarylayersuchasin,forwhichstabilitytheoremsexist,butwithanon-linearswitchingsurface.Withtheuseoftrapezoidalinputmembershipfunctionsandappropriatecompositionandinferencemethods,itwillbeshownthatitispossibletoobtainrulemembershipfunctionswhichareregion-wiseaffinefunctionsofthecontrollerinputvariable.Weproposealineardefuzzificationalgorithmthatkeepsthisregion-wiseaffinestructureandyieldsapiece-wiseaffinecontroller.Aparticularandsystematicparametertuningmethodwillbegivenwhichallowsturningthiscontrollerintoavariablestructure-likecontroller.Wewillcomparethisregion-wiseaffinecontrollerwithaFuzzyandVariableStructureControllerthroughtheapplicationtoaninvertedpendulumcontrol.Sofar,intheapplicationnoteseries,wehaveprovidedseveralexamplesshowinghowtocreatefuzzycontrollerswithFIDE.However,theseexamplesdonotprovidetopicsonimplementationofthedesignedsystem.Inthisapplicationnote,weuseanexampleofaninvertedpendulumtoprovidedetailsonallaspectsoffuzzylogicbasedsystemdesign.Wewillbeginwithsystemdesign;analyzingcontrolbehaviorofatwo-stageertedpendulum.Wewillthenshowhowtodesignafuzzycontrollerforthesystem.Wewilldescribeacontrolcurveandhowitdiffersfromthatofconventionalcontrollerswhenusingafuzzycontroller.Finally,wewilldiscusshowtousethiscurvetodefinelabelsandmembershipfunctionsforvariables,aswellashowtocreaterulesforthecontroller.Intheformulationofanycontrolproblemtherewilltypicallybediscrepanciesbetweentheactualplantandthemathematicalmodeldevelopedforcontrollerdesign.Thismismatchmaybeduetounmodelleddynamics,variationinsystemparametersortheapproximationofcomplexplantbehaviorbyastraightforwardmodel.Theengineermustensurethattheresultingcontrollerhastheabilitytoproducetherequiredperformancelevelsinpracticedespitesuchplant/modelmismatches.Thishasledtoanintenseinterestinthedevelopmentofso-calledrobustcontrolmethodswhichseektosolvethisproblem.Oneparticularapproachtorobustcontrolcontrollerdesignistheso-alledslidingmodecontrolSlidingmodecontrolisaparticulartypeofVariableStructureControlSystem(VSCS).AVSCSischaracterizedbyasuiteoffeedbackcontrollawsandadecisionrule.Thedecisionrule,termedtheswitchingfunction,hasasitsinputsomemeasureofthecurrentsystembehaviorandproducesasanoutputtheparticularfeedbackcontrollerwhichshouldbeusedatthatinstantintime.Avariablestructuresystem,whichmayberegardedasacombinationofsubsystemswhereeachsubsystemhasafixedcontrolstructureandisvalidforspecifiedregionsofsystembehavior,results.Oneoftheadvantagesofintroducingthisadditionalcomplexityintothesystemistheabilityto-mbineusefulpropertiesofeachofthecompositestructuresofthesystem.Furthermore,thesystemmaybedesignedtopossessnewpropertiesnotpresentinanyofthecompositestructuresalone.UtilizationofthesenaturalideasbeganintheSovietUnioninthelate1950's.Inslidingmodecontrol,theVSCSisdesignedtodriveandthenconstrainthesystemstatetoliewithinaneighborhoodoftheswitchingfunction.Therearetwomainadvantagestothisapproach.Firstly,thedynamicbehaviorrofthesystemmaybetailoredbytheparticularchoiceofswitchingfunction.Secondly,theclosed-loopresponsebecomestotallyinsensitivetoaparticularclassofuncertainty.Thelatterinvariancepropertyclearlymakesthemethodologyanappropriatecandidateforrobustcontrol.Inaddition,theabilitytospecifyperformancedirectlymakesslidingmodecontrolattractivefromthedesignperspective.Theslidingmodedesignapproachconsistsoftwocomponents.Thefirstinvolvesthedesignofaswitchingfunctionsothattheslidingmotionsatisfiesdesignspecifications.Thesecondisconcernedwiththeselectionofacontrollawwhichwillmaketheswitchingfunctionattractivetothesystemstate.Notethatthiscontrollawisnotnecessarilydiscontinuous.Wewillprovidethereaderwithathoroughgroundinginthesliding modecontrolareaandassuchisappropriateforthegraduatewithabasicknowledgeofclassicalc-ontroltheoryandsomeknowledgeofstate-spacemethods.Fromthisbasis,moreadvancedtheoreticalresultsaredeveloped.ResultingdesignproceduresareemphasizedusingMatlabfiles.Fullyworkeddesignexamplesareanadditionaltutorialfeature.Industrialcasestudies,whichpresenttheresultsofslidingmodecontrollerimplementations,areusedtoillustratethesuccessfulpracticalapplicationofthetheory.The“INVERTEDPENDULUM,ANALYSIS,DESIGNANDION”isacollectionofMATLABfunctionsandscripts,and