毕业设计(论文)外文参考资料及译文封面.doc

毕 业 设 计（论 文）外 文 参 考 资 料 及 译 文译文题目： Inverted Pendulum学生姓名： 徐飞马 学 号： 0704111030 专 业： 07自动化 所在学院： 机电学院 指导教师： 陈丽换 职 称： 讲师 2011 年 2月 24日The inverted pendulumKey words: invertedpendulum, modeling, PIDcontrollers,LQRcontrollersWhatisanInvertedPendulum?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. 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. Withtheuseoftrapezoidalinputmembershipfunctionsandappropriatecompositionandinferencemethods,itwillbeshownthatitispossibletoobtainrulemembershipfunctionswhichareregion-wiseaffinefunctionsofthecontrollerinputvariable.Weproposealineardefuzzificationalgorithmthatkeepsthisregion-wiseaffinestructureandyieldsapiece-wiseaffinecontroller.Aparticularandsystematicparametertuningmethodwillbegivenwhichallowsturningthiscontrollerintoavariablestructure-likecontroller.Wewillcomparethisregion-wiseaffinecontrollerwithaFuzzyandVariableStructureControllerthroughtheapplicationtoaninvertedpendulumcontrol. Wewillbeginwithsystemdesign;analyzingcontrolbehaviorofatwo-stageinvertedpendulum.Wewillthenshowhowtodesignafuzzycontrollerforthesystem.Wewilldescribeacontrolcurveandhowitdiffersfromthatofconventionalcontrollerswhenusingafuzzycontroller.Finally,wewilldiscusshowtousethiscurvetodefinelabelsandmembershipfunctionsforvariables,aswellashowtocreaterulesforthecontroller. Intheformulationofanycontrolproblemtherewilltypicallybediscrepanciesbetweentheactualplantandthemathematicalmodeldevelopedforcontrollerdesign.Thismismatchmaybeduetounmodelleddynamics,variationinsystemparametersortheapproximationofcomplexplantbehaviorbyastraightforwardmodel.Theengineermustensurethattheresultingcontrollerhastheabilitytoproducetherequiredperformancelevelsinpracticedespitesuchplant/modelmismatches.Thishasledtoanintenseinterestinthedevelopmentofso-calledrobustcontrolmethodswhichseektosolvethisproblem.Oneparticularapproachtorobustcontrolcontrollerdesignistheso-calledslidingmodecontrolmethodology. TheInvertedPendulumisoneofthemostimportantclassicalproblemsofControlEngineering.BroomBalancing(InvertedPendulumonacart)isawellknownexampleofnonlinear,unstablecontrolproblem.Thisproblembecomesfurthercomplicatedwhenaflexiblebroom,inplaceofarigidbroom,isemployed.Degreeofcomplexityanddifficultyinitscontrolincreaseswithitsflexibility.Thisproblemhasbeenaresearchinterestofcontrolengineers. ControlofInvertedPendulumisaControlEngineeringprojectbasedontheFLIGHTSIMULATIONOFROCKETORMISSILEDURINGTHEINITIALSTAGESOFFLIGHT.TheAIMOFTHISSTUDYistostabilizetheInvertedPendulumsuchthatthepositionofthecarriageonthetrackiscontrolledquicklyandaccuratelysothatthependulumisalwayserectedinitsinvertedpositionduringsuchmovements. Thispracticalexerciseisapresentationoftheanalysisandpracticalimplementationoftheresultsofthesolutionspresentedinthepapers,“RobustControllerforNonlinear&UnstableSystem:InvertedPendulum”and“FlexibleBroomBalancing”,inwhichthiscomplexproblemwasanalyzedandasimpleyeteffectivesolutionwaspresented.Prescribedtrajectorytrackingwithcertainaccuracyisamaintaskofroboticcontrol.Thecontrolisoftenbasedonamathematicalmodelofthesystem.Thismodelisneveranexactrepresentationofreality,sincemodelingerrorsareinevitable.Moreover,onecanuseasimplifiedmodelonpurpose.Inthispaper,thestructuredandunstructureduncertaintiesareofprimaryinterest,i.e.,themodelingerrorduetotheparametersvariationandunmodeledmodes,especiallythefrictionandsensordynamics,neglectedtimedelays,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. 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. 倒立摆关键词：倒立摆，模型，PID控制，LQR控制倒立摆是什么？还记得当你是个孩子时你曾用你的食指或者掌心设法去平衡一把扫帚柄或者棒球棍吗？你必须不断地调整你的手的位置以保持对象的垂直。一个倒立摆在本质上就是做相同的事情。然而，它会受限制因为它只能在一定范围内移动，虽然你的手可以上升、下降、斜向一边等等。检查录象提供的画面来观察倒立摆是如何确切地工作的。一个倒立摆是个物理设备它包括一个圆柱体的棒子（通常是铝的）可以在一个支点周围振荡。这个支点是安在一个车架上，它的转动方向是水平的偏转。小车是由一个马达控制的，它可以运用于一个变力。棒子会有自然的趋势从最高的竖直位置下落，那是一个不稳定的平衡位置。实验的目标是使摆（棒子）稳定在最高的竖直位置。这是有可能的只要运用通过马达的小车一个力该力可以与“自由”摆的动力学抵消。这个正确的力必须通过计算测量水平偏转的瞬时值和摆的角度（获得两个电位计）。倒立摆是干什么的？就好象扫帚柄，一个倒立摆是一个天生的不稳定系统。力度必须被严格地应用以保持系统的完整性。为了实现它，严格的控制理论是必须的。倒立摆在求数值和各种控制理论的比较中是必要的。倒立摆是一个控制器系统中的一个传统的例子（既不困难也不是没有价值）。尽管它是仿真和实验来显示不同控制器的性能（举例来说PID控制器，状态空间控制器，模糊控制器）。实时倒立摆被作为一个基准，去测试软件在状态空间控制器运算法则下的有效性和性能，也就是实用的操作系统。事实上运算法则是通过数值点实现的该数值点看作一组互助的协同操作的任务，它是周期性的通过核心的活动，它执行不同的计算。这些任务如何活动的方法（举例来说激活命令）被称作任务的时序安排。很明显每个任务的时序安排对控制器的一个好的性能是至关紧要的，因此对一个摆的稳定性是有效的。如此倒立摆是非常有用的在决定是否一个特殊的时序安排的选择比另一个好，在哪个情形下，在什么程度内等等。为倒立摆建模。通常倒立摆系统建模成一个线形系统，因此模型只对小幅度摆动的摆才有效。 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，这将说明那是有可能遵循规则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。一个特殊的系统的参数调节方法将会被给定它允许把这个控制器调节成一个可变的结构相似的控制器。我们将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通过应用一个倒立摆控制。 我们将从系统设计开始；分析二级倒立摆的控制行为。随后我们将展示如何为系统设计一个模糊控制装置。我们将描绘一个控制曲线当使用模糊控制装置时它与一个常规控制器是如何的不同。最后，我们将讨论如何使用这个曲线去定义标志还有变量的隶属函数，还有就是如何为控制器创立一套规则。“倒立摆、分析、设计和执行”是由一个MATLAB方程和内容的收藏的，还有SIMULINK模型，对分析倒立摆系统和设计控制系统是很有用的。这个报道MATLAB文件收藏是由少量的控制系统分析的实际任务而发展的，设计和发展实际问题。这分派的倒立摆的问题是一个控制系统的实验室工作的一部分。倒立摆是最重要最经典的控制工程问题中的一个。帚平衡（车载的倒立摆）是一个著名的非线形例子，不稳定的控制问题。这个问题越来越复杂当一个柔韧的帚代替一个刚硬的帚被使用。复杂的问题的真实度和难度在控制中随着弹性而增长。这个问题已经引起调度工程师的兴趣并展开研究。倒立摆的控制是一个控制工程的方案基于火箭的飞行模拟或者导弹飞行的初始状态。这个学习的目的是稳定倒立摆这样小车的位置在轨道上被控制得快速和准确以使摆在这一装置下始终垂直在它的倒立位置。 这个实际的运动是一个分析的表现还有实际的执行在解决问题的结果中在本文中，“非线形和不稳定系统的坚固的控制器：倒立摆”和“柔韧的帚平衡”，其中这个复杂问题分析和一个简单的有效的解决方案被引出法定轨道通过确定的精确性是机器控制的一个主要任务。控制通常是基于一个系统的数学模型。模型不是一个准确的实体表现，模型的误差是不可避免的。此外，我们可以特意使用一个简化的模型。在这篇论文中，构造好的和未构造好的不确定因素是主要的兴趣所在，也就是说模型的误差导致参数变化和未模型化的模式，尤其是摩擦力和敏感元件的力度，被忽视的时间延迟等等。不正确的模型和高性能的需求要求控制器非常坚固。滑模控制器(SMC)是基于变结构控制使用的如果模型结构中的错误在已知的范围内跃进。然而，一个SMC有一些缺点，涉及控制输入信号的振动。通常这个现象是令人不快的，它会引起额外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坚固的特性的变化。这是一个众所周知的难题并且广泛的在文献中经过处理。为了在继电器控制中获得滤波中断滑模控制器的方案已经被提出了。另外一个重要的论点限定了SMC的实际应用性就是创新的控制定律导致上面的不确定因素的范围。在实践中通常大部分最差的案例在控制定律下执行确没有发生并且作为结果的大的控制输入变得不必要和不经济的。在这篇论文中我们提出一个