【導讀】倒立擺系統(tǒng)是一種廣泛應用的實驗平臺，在該平臺上，可以采用反饋控制理論鎮(zhèn)定不穩(wěn)定的開環(huán)系統(tǒng)使之達到穩(wěn)定狀態(tài)。這個問題的第一個的解決方法是在Roberge[1]的一篇名為《機械密封》的論文中做出了描述。隨后，它作為一種不穩(wěn)定系統(tǒng)的范例被用于許多報刊書籍。雖然正確，但這種做法是不必要的?？紤]倒立擺系統(tǒng)如圖1所示。在垂直方向產生的擺角θ的角重力加速度值等于，而小車在方向產生的角加速度為。該傳遞函數有一個在右半邊，和我們對不穩(wěn)定系統(tǒng)所預期一致的極點。包括常見的運動傳遞函數：。Siebert指出，這種正反饋會使電機最初在有嚴重的偏差，但這種行為是理想的效果。力度必須被嚴格地應用以保持系統(tǒng)的完整性。通常倒立擺系統(tǒng)建模成一個線形系統(tǒng)，因此模型只對小幅度擺動的擺才有效?！暗沽[、分析、設計和執(zhí)行”是由一個MATLAB方程和內容的收藏的，還有SIMULINK模型，對分析倒立 擺系統(tǒng)和設計控制系統(tǒng)是很有用的。這個報道MATLAB文件收藏是由少量的控制系統(tǒng)分析的實際任務而發(fā)

　　

【正文】 e.Intheparticular caseofaswitchingline separatingthephase planeintooneregion where thecontrol ispositivewhereasintheotheritis negative,thefuzzy controllermaybeseen as a variable structure controller.Thiskindofafuzzy controllercanbeassimilatedtoa variablestructurecontrollerwithboundarylayersuchasin,forwhichstabilitytheoremsexist,butwithanonlinearswitchingsurface. Wewillbeginwithsystemdesign。analyzingcontrolbehaviorofatwostageinvertedpendulum. We willthenshowhowtodesignafuzzy controllerforthesystem.We willdescribea controlcurveand howitdiffersfromthatofconventional controllerswhenusinga fuzzy controller. Finally,wewill discusshowtousethiscurvetodefine labelsandmembership functions forvariables, aswellashowtocreaterulesforthecontroller.Intheformulationofanycontrolproblemtherewilltypicallybediscrepanciesbetweenthe actualplantandthemathematicalmodeldevelopedforcontrollermismatchmaybe dueto unmodelleddynamics,variationinsystem parametersortheapproximation ofplexplant behaviorbyastraightforward engineermust ensurethatthe resulting controller has theabilityto producetherequiredperformance levelsinpractice despitesuchplant/model mismatches. Thishasledtoanintenseinterest inthedevelopment ofsocalledrobust controlmethodswhichseektosolvethis problem.Oneparticular approachtorobustcontrolcontrollerdesignisthesocalledslidingmode controlmethodology. SlidingmodecontrolisaparticulartypeofVariableStructureControlSystem(VSCS).A VSCSischaracterizedbyasuiteoffeedbackcontrollawsandadecisionrule.Thedecisionrule,termedthe switchingfunction,hasasitsinputsomemeasureofthecurrentsystem behaviorandproducesasan outputtheparticularfeedbackcontroller whichshouldbe usedatthat instantin time.Avariable structuresystem,whichmayberegarded asabinationof subsystemswhere eachsubsystemhasa fixedcontrolstructureandis validforspecified regionsof systembehavior,results.Oneofthe advantagesofintroducingthis additional plexity into thesystemistheabilitytobineuseful propertiesofeach oftheposite structuresof thesystem.Furthermore,thesystemmaybedesigned topossessnewproperties notpresentinany ofthepositestructuresalone.Utilizationofthese naturalideas beganinthe SovietUnioninthelate195039。s. Inslidingmodecontrol,theVSCSisdesignedtodriveandthenconstrainthesystemstatetolie withinaneighborhoodoftheswitchingfunction. Therearetwomain advantagesto this approach. Firstly,thedynamicbehaviorofthesystemmaybe tailoredby the particular choiceofswitching function.Secondly,theclosedloopresponse beestotallyinsensitive to a particular classof uncertainty.Thelatterinvariancepropertyclearly makesthemethodologyan appropriate candidatefor robustcontrol.Inaddition,theabilitytospecify performancedirectly makes slidingmodecontrol attractivefromthedesignperspective.Theslidingmodedesignapproachconsistsoftwoponents.Thefirstinvolvesthedesignofa switchingfunctionsothattheslidingmotion satisfiesdesignspecifications. The second is concerned withtheselectionofacontrollawwhichwill maketheswitching functionattractive to the system state. Notethatthiscontrollawisnotnecessarilydiscontinuous.Wewillprovidethereaderwithathoroughgroundingintheslidingmodecontrolareaandassuchisappropriateforthegraduatewithabasicknowledgeofclassicalcontroltheoryandsome knowledge ofstatespacemethods.Fromthisbasis, moreadvancedtheoretical results are developed. Resulting designproceduresareemphasizedusingMatlab files.Fullyworked designexamplesareanadditional tutorialfeature. Industrial case studies, which present the results of sliding mode controller implementations, areusedtoillustratethesuccessful practical application ofthetheory.