倒立摆外文翻译

电093 高小燕The inverted pendulumKey words: invertedpendulum, modeling, PIDcontrollers,Fuzzycontrollers,statespacecontrollersWhatisanInvertedPendulum?Rememberwhenyouwereachildandyoutriedtobalancea broom-stickorbaseballbatonyourindexfingerorthepalmofyourhand?Youhadtoconstantlyadjustthepositionofyourhandtokeeptheobjectupright.AnInvertedPendulumdoesbasicallythesamething.However,itislimitedinthatitonlymovesinonedimension,whileyourhandcouldmoveup,down,sideways,etc.CheckoutthevideoprovidedtoseeexactlyhowtheInvertedPendulumworks. Aninvertedpendulumisaphysicaldeviceconsistinginacylindricalbar(usuallyofaluminum)freetooscillatearoundafixedpivot.Thepivotismountedonacarriage,whichinitsturncanmoveonahorizontaldirection.Thecarriageisdrivenbyamotor,whichcanexertonitavariableforce.Thebarwouldnaturallytendtofalldownfromthetopverticalposition,whichisapositionofunsteadyequilibrium. Thegoaloftheexperimentistostabilizethependulum(bar)onthetopverticalposition.Thisispossiblebyexertingonthecarriagethroughthemotoraforcewhichtendstocontrastthefreependulumdynamics.Thecorrectforcehastobecalculatedmeasuringtheinstantvaluesofthehorizontalpositionandthependulumangle(obtainede.g.throughtwopotentiometers). Thesystempendulum+cart+motorcanbemodeledasalinearsystemifalltheparametersareknown(masses,lengths,etc.),inordertofindacontrollertostabilizeit.Ifnotalltheparametersareknown,onecanhowevertrytoreconstructthesystemparametersusingmeasureddataonthedynamicsofthependulum. Whatisitusedfor?Justlikethebroom-stick,anInvertedPendulumisaninherentlyunstablesystem.Forcemustbeproperlyappliedtokeepthesystemintact.Toachievethis,propercontroltheoryisrequired.TheInvertedPendulumisessentialintheevaluatingandcomparingofvariouscontroltheories. Theinvertedpendulumisatraditionalexample(neitherdifficultnortrivial)ofacontrolledsystem.Thusitisusedinsimulationsandexperimentstoshowtheperformanceofdifferentcontrollers(e.g.PIDcontrollers,statespacecontrollers,fuzzycontrollers.). TheReal-TimeInvertedPendulumisusedasabenchmark,totestthevalidityandtheperformanceofthesoftwareunderlyingthestate-spacecontrolleralgorithm,i.e.theusedoperatingsystem.Actuallythealgorithmisimplementformthenumericalpointofviewasasetofmutuallyco-operatingtasks,whichareperiodicallyactivatedbythekernel,andwhichperformdifferentcalculations.Thewayhowthesetasksareactivated(e.g.theactivationorder)iscalledschedulingofthetasks.Itisobviousthatacorrectschedulingofeachtaskiscrucialforagoodperformanceofthecontroller,andhenceforaneffectivependulumstabilization.Thustheinvertedpendulumisveryusefulindeterminingwhetheraparticularschedulingchoiceisbetterthananotherone,inwhichcases,towhichextent,andsoon. Modelinganinvertedpendulum.Generallytheinvertedpendulumsystemismodeledasalinearsystem,andhencethemodelingisvalidonlyforsmalloscillationsofthependulum. Prescribedtrajectorytrackingwithcertainaccuracyisamaintaskofroboticcontrol.Thecontrolisoftenbasedonamathematicalmodelofthesystem.Thismodelisneveranexactrepresentationofreality,sincemodelingerrorsareinevitable.Moreover,onecanuseasimplifiedmodelonpurpose.Inthispaper,thestructuredandunstructureduncertaintiesareofprimaryinterest,i.e.,themodelingerrorduetotheparametersvariationandunmodeledmodes,especiallythefrictionandsensordynamics,neglectedtimedelays,etc.Theerroneousmodelandthedemandforhighperformancerequirethecontrollertoberobust.Theslidingmodecontrollers(SMC)basedonvariablestructurecontrolcanbeusediftheinaccuraciesinthemodelstructureareboundedwithknownbounds.However,anSMChassomedisadvantages,relatedtochatteringofthecontrolinputsignal.Oftenthisphenomenonisundesirable,sinceitcausesexcessivecontrolactionleadingtoincreasewearoftheactuatorsandtoexcitationofunmodeleddynamics. Theattemptstoattenuatethisundesirableeffectresultinthedeteriorationoftherobustnesscharacteristics.Thisisawell-knownproblemandwidelytreatedintheliterature.Inordertoobtainsmoothinginthebang-bangtypeddiscontinuitiesoftheslidingmodecontrollerdifferentschemeshavebeensuggested. AnotherimportantissuelimitingthepracticalapplicabilityofSMCistheoverconservativecontrollawduetotheupperboundsoftheuncertainties.Inpracticemostoftentheworstcaseimplementedincontrollawdoesnottakeplaceandtheresultinglargecontrolinputsbecomeunnecessaryanduneconomical. Inthispaperwesuggestanapproachtothedesignofdecentralizedmotioncontrollersforelectromechanicalsystemsbesidestheslidingmodemotioncontrollerstructureanddisturbancetorqueestimation.Theaccuracyoftheestimationisthecriticalparameterforrobustnessinthisscheme,asopposedtotheupperboundsoftheperturbationsthemselves.Consequently,thedrivingtermsoftheerrordynamicsarereducedfromtheuncertainties(asintheconventionalSMC)totheaccuracyintheirestimates.Theresultisamuchbettertrackingaccuracywithoutbeingoverconservativeincontrol. Experimentalrobustnesspropertiesoffuzzycontrollersremaintheoreticallydifficulttoproveandtheirsynthesisisstillanopenproblem.Thenon-linearstructureofthefinalcontrollerisderivedfromallcontrollersatthedifferentstagesoffuzzycontrol,particularlyfromcommondefuzzificationmethods(suchasCentreofArea).Ingeneral,fuzzycontrollershavearegion-wisestructuregiventhepartitionofitsinputspacebythefuzzificationstage.Localcontrolsdesignedintheseregionsarethencombinedintosetstomakeupthefinalglobalcontrol.Apartitionofthestatespacecanbefoundforwhichthecontrollerhasregion-wiseconstantparameters.Moreover,eachfuzzycontrollertuningparameter(i.e.theshapesandthevaluesofinputoroutputvariablesmembershipfunctions)influencesthevaluesofparametersinseveralregionsatthesametime.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-stageinvertedpendulum.Wewillthenshowhowtodesignafuzzycontrollerforthesystem.Wewilldescribeacontrolcurveandhowitdiffersfromthatofconventionalcontrollerswhenusingafuzzycontroller.Finally,wewilldiscusshowtousethiscurvetodefinelabelsandmembershipfunctionsforvariables,aswellashowtocreaterulesforthecontroller. Intheformulationofanycontrolproblemtherewilltypicallybediscrepanciesbetweentheactualplantandthemathematicalmodeldevelopedforcontrollerdesign.Thismismatchmaybeduetounmodelleddynamics,variationinsystemparametersortheapproximationofcomplexplantbehaviorbyastraightforwardmodel.Theengineermustensurethattheresultingcontrollerhastheabilitytoproducetherequiredperformancelevelsinpracticedespitesuchplant/modelmismatches.Thishasledtoanintenseinterestinthedevelopmentofso-calledrobustcontrolmethodswhichseektosolvethisproblem.Oneparticularapproachtorobustcontrolcontrollerdesignistheso-calledslidingmodecontrolmethodology. SlidingmodecontrolisaparticulartypeofVariableStructureControlSystem(VSCS).AVSCSischaracterizedbyasuiteoffeedbackcontrollawsandadecisionrule.Thedecisionrule,termedtheswitchingfunction,hasasitsinputsomemeasureofthecurrentsystembehaviorandproducesasanoutputtheparticularfeedbackcontrollerwhichshouldbeusedatthatinstantintime.Avariablestructuresystem,whichmayberegardedasacombinationofsubsystemswhereeachsubsystemhasafixedcontrolstructureandisvalidforspecifiedregionsofsystembehavior,results.Oneoftheadvantagesofintroducingthisadditionalcomplexityintothesystemistheabilitytocombineusefulpropertiesofeachofthecompositestructuresofthesystem.Furthermore,thesystemmaybedesignedtopossessnewpropertiesnotpresentinanyofthecompositestructuresalone.UtilizationofthesenaturalideasbeganintheSovietUnioninthelate1950s. Inslidingmodecontrol,theVSCSisdesignedtodriveandthenconstrainthesystemstatetoliewithinaneighborhoodoftheswitchingfunction.Therearetwomainadvantagestothisapproach.Firstly,thedynamicbehaviorofthesystemmaybetailoredbytheparticularchoiceofswitchingfunction.Secondly,theclosed-loopresponsebecomestotallyinsensitivetoaparticularclassofuncertainty.Thelatterinvariancepropertyclearlymakesthemethodologyanappropriatecandidateforrobustcontrol.Inaddition,theabilitytospecifyperformancedirectlymakesslidingmodecontrolattractivefromthedesignperspective. Theslidingmodedesignapproachconsistsoftwocomponents.Thefirstinvolvesthedesignofaswitchingfunctionsothattheslidingmotionsatisfiesdesignspecifications.Thesecondisconcernedwiththeselectionofacontrollawwhichwillmaketheswitchingfunctionattractivetothesystemstate.Notethatthiscontrollawisnotnecessarilydiscontinuous. Wewillprovidethereaderwithathoroughgroundingintheslidingmodecontrolareaandassuchisappropriateforthegraduatewithabasicknowledgeofclassicalcontroltheoryandsomeknowledgeofstate-spacemethods.Fromthisbasis,moreadvancedtheoreticalresultsaredeveloped.ResultingdesignproceduresareemphasizedusingMatlabfiles.Fullyworkeddesignexamplesareanadditionaltutorialfeature.Industrialcasestudies,whichpresenttheresultsofslidingmodecontrollerimplementations,areusedtoillustratethesuccessfulpracticalapplicationofthetheory. The“INVERTEDPENDULUM,ANALYSIS,DESIGNANDIMPLEMENTATION”isacollectionofMATLABfunctionsandscripts,andSIMULINKmodels,usefulforanalyzingInvertedPendulumSystemanddesigningControlSystemforit.Thisreport&MATLAB-filescollectionaredevelopedasapartofpracticalassignmentonControlSystemAnalysis,Design&Developmentpracticalproblem.TheassignedproblemofINVERTEDPENDULUMisapartofLabWorkofControlSystem. TheInvertedPendulumisoneofthemostimportantclassicalproblemsofControlEngineering.BroomBalancing(InvertedPendulumonacart)isawellknownexampleofnonlinear,unstablecontrolproblem.Thisproblembecomesfurthercomplicatedwhenaflexiblebroom,inplaceofarigidbroom,isemployed.Degreeofcomplexityanddifficultyinitscontrolincreaseswithitsflexibility.Thisproblemhasbeenaresearchinterestofcontrolengineers. ControlofInvertedPendulumisaControlEngineeringprojectbasedontheFLIGHTSIMULATIONOFROCKETORMISSILEDURINGTHEINITIALSTAGESOFFLIGHT.TheAIMOFTHISSTUDYistostabilizetheInvertedPendulumsuchthatthepositionofthecarriageonthetrackiscontrolledquicklyandaccuratelysothatthependulumisalwayserectedinitsinvertedpositionduringsuchmovements. Thispracticalexerciseisapresentationoftheanalysisandpracticalimplementationoftheresultsofthesolutionspresentedinthepapers,“RobustControllerforNonlinear&UnstableSystem:InvertedPendulum”and“FlexibleBroomBalancing”,inwhichthiscomplexproblemwasanalyzedandasimpleyeteffectivesolutionwaspresented. 倒立摆系统关键词：倒立摆，建模，PID控制器，模糊控制器，状态空间控制器什么是倒立摆？记得你在儿童时期用你的食指或者掌心试图去平衡一扫帚柄或者棒球棍吗？你需要不停地动你手的位置来让对象垂直。一倒立摆实质上就是做一样的事。但是，因为受限制它只能在一定的范围内动，即使你的手可以往上、往下、往斜等等。看录象里的画面来观察倒立摆的工作。 倒立摆是一个物理设备。它包括一个圆柱形的棒子（通常是铝的）在一个支点附近振荡。这个支点是安装在一个车架上的，它是水平方向偏转的。小车是由一个马达控制，它可以用在一个变力上。棒子自然的趋势从最高的竖直的地方开始下落，这是一个不稳定的平衡位置。 实验的目的是使摆（棒球棍）稳定在最高的竖直位置。这是有可能会实现的，只要运用通过带有马达的小车的一个力，该力可以抵消“自由”摆的动力学。这正确的力必须用计算来测量水平偏转的瞬时值和摆的角度（获得两个电位计）。系统摆+小车+马达可以建成一个线性系统。如果所有的参数都已知（质量、长度等），要寻找一个控制器来稳定它。如果不是所有的参数都是已知的，那就可以用多种方法去“推理”系统参数，比如摆的动力学的测量数据。 实时倒立摆作为一个基准，去测试软件在状态空间控制器的运算法则下的有效性和功能，也就是实用操作系统。实际上运算法则是通过把数值点来实现的该数值点看作一组互助操作的任务，它是有周期的通过核心的活动，它是执行不同计算的。这些如何活动任务的方法（例如激活命令）被称作任务的时序安排。对于每个任务的时序安排很明显这是对控制器的性能来说是至关紧要的，因此这对于摆的稳定性是有用的。如此来说倒立摆是很有用的决定是否一个特殊的时序安排的选择比另一个好，在什么情况下，在哪种程度等等。 倒立摆是干什么的呢？它就象是扫帚柄，一个倒立摆是一个注定的不稳定系统。力度须被精准地应用来保持系统的完整性。为了来实现它，严格的控制理论是必须要有的。倒立摆有必要用于在求数值和各种控制理论的比较中。倒立摆是控制器系统中的一个比较传统的例子（既不是很困难也不是没有价值）。尽管它是用仿真和实验来显示不同的控制器的性能（例如PID控制器，状态空间控制器，模糊控制器）。 倒立摆的建模。一般倒立摆系统建模成一个线形系统，因此模型只有对小幅度内的摆动的摆才有效。 轨道通过的精确性是机器控制的一个首要任务。控制通常是基于系统的数学模型。模型不是一个准确的实际表现，模型出现误差是不可避免的。此外，我们可以特意建一个简单的模型。在这篇论文中，构造好的和未构造好的不确定性因素是主要的，简单来说就是模型的误差导致参数的变化和还没有模型化的模式，特别是摩擦力和元件的力，被忽略的时间延迟等等。错误的模型和高性能的需求要求控制器很坚固。如果模型中结构的错误在已知的范围内跨越滑模控制器(SMC)是基于变结构控制使用的。但是，一个SMC有一些缺点，涉及输入控制信号的振荡。通常这个现象是不好的，它会引起多余的控制作用，从而导致激励者穿戴的增加和未建模动力学的刺激。削弱这个令人不快的效果的尝试导致固有特性的变化。这是一个众所周知的难题并且广泛的在文献中被处理。已经提出了为了在继电器控制中获得滤波中断滑模控制器的方案。另外一个重要论点限制了SMC的实际应用就是创新的控制定律导致上面不确定因素的范围。在实践中通常大部分最差的案例在控制定律下执行却没有发生并且作为结果的大控制输入变得不必要和不经济。在这篇论文中除了滑模震动控制器结构和干扰转矩的估算我们提出一个机电系统中分散振动控制器的设计方法。估算的准确性是这个计划中最中坚的评定参数，与上面不确定的范围正好相反。因此，在评估的准确性中控制一些误差动力学的条件减少了一些不确定性（就如同在传统的SMC中）。结果在没有超越传统控制的控制中是一个较好的跟踪精度。 模糊控制装置实验健全的性质难以用理论去证明它们仍然是一个未解决的问题。最终控制器的非线性性质来源于各级模糊控制的控制器，显著地逆模糊化方法（诸如中心区）。通常，模糊控制器有一个区域劝导的模糊化级数给的输入空间的性质。本地控制设计这些区域结成集来实现最终的全球控制。一个级数空间的划分可以在控制器中有区域劝导的常数参数中找到。此外，每个模糊控制器调整参数（即形状以及输入输出的变量值的隶属函数）会在同一时间在某些区域影响参数值。在特殊情况下开关线会将相平面分成一个区域，那个区域中控制是正的反之另一边是负的，模糊控制器可视为一个可变结构的控制器。这类模糊控制器可以吸收到可变结构控制器的边界层，其中稳定性定理存在，是一个非线形开关面。 通过梯形输入隶属函数的使用和适当的作图法和推论方法，将说明那是可能遵循规则的区域劝导的输入变量仿射函数的隶属函数。我们提出线形逆模糊化算法它能在这个区域劝导仿射结构和产生一个块仿射控制器。一个特殊系统的参数调节方法会被给定允许把这个控制器调节成一个可变的结构相似的控制器。我们可以通过应用一个倒立摆控制比较这个区域劝导仿射控制器和一个模糊的可变结构的控制器。 迄今为止，在应用笔记系列中，我们已经提供许多展示如何用FIDE创造模糊控制装置的例子。但是这些例子不能提供设计系统执行的话题。在这应用笔记中，我们可以用一个倒立摆的例子来提供