非線性系統(tǒng)線性化綜述_英文_程代展

1、第39卷 第2期 Vol.39 No.2 山 東 大 學(xué) 學(xué) 報(bào) (工 學(xué) 版)JOURNALOFSHANDONGUNIVERSITY(ENGINEERINGSCIENCE) 2009年4月Apr.2009文章編號(hào):167223961(2009)0220026211AsurveyonlinearizationofnonlinearsystemsCHENGDai2zhan,LIZhi2qiang(InstituteofSystemsScience,ChineseAcademyofSciences,Beijing100190,China)Abstract:Linearizationisoneoft

2、hemostpowerfultoolsincontrolofnonlinearsystems.Ithasobtainedvariousapplicationsinaircraftpilotcontrol,safetycontrolofpowersystems,chemicalreactorcontrol,economicalsystem,biologicalsystem,robotcon2troletc.Thissurveyoutlinesthelonghistoryandtherecentdevelopmentoflinearization,includingdifferenttechniq

3、uesandusefulresults.Wefirstrecallthedevelopmentofthelinearizationfromapproximatedonetoexactone.Poincare.slinearizationisre2viewed.Thenecessaryandsufficientconditionsandalgorithmsofthestatefeedbacklinearizationarementioned.Thenvariouskindsoflinearizationsaresurveyed,whichincludesthegloballinearizatio

4、n,fulllinearization,input2outputlinearization,non2reg2ularfeedbacklinearization.Partiallinearizationanditsrelationshipwithrelativedegreesaresequentiallydiscussed.Someotherlinearizationtechniquessuchasdynamicfeedbacklinearization,approximatelinearization,CarlemanLinearizationetc.arealsobrieflyintrodu

5、ced.Thepaperisexpectedtoprovideacompletepictureoflinearization:itspast,presentandkeyissuesforfurtherinvestigation.Keywords:linearization;Poincare.stheorem;statefeedback;non2regular;partiallinearization非線性系統(tǒng)線性化綜述程代展,李志強(qiáng)(中國(guó)科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院,北京100190)摘要:非線性系統(tǒng)的線性化是設(shè)計(jì)非線性系統(tǒng)控制的強(qiáng)有力工具.這一方法已經(jīng)在飛行器控制、電力系統(tǒng)的安全控制、化學(xué)反應(yīng)

6、器控制、經(jīng)濟(jì)系統(tǒng)、生物學(xué)系統(tǒng)和機(jī)器人控制等領(lǐng)域得到廣泛應(yīng)用.本文闡述了非線性系統(tǒng)線性化的發(fā)展歷史以及有深刻意義的結(jié)果.首先回顧從非線性系統(tǒng)的近似線性化到精確線性化的發(fā)展.主要內(nèi)容包括Poincare線性化、系統(tǒng)能通過(guò)狀態(tài)反饋線性化的充要條件和算法.然后介紹各種不同的線性化方法:動(dòng)態(tài)反饋線性化,近似線性化,Carleman線性化等.本文主要目的是對(duì)非線性系統(tǒng)線性化的歷史,現(xiàn)狀和一些重要問(wèn)題進(jìn)行一個(gè)較完整全面的介紹,從而提供從事線性化理論與應(yīng)用研究的基礎(chǔ).關(guān)鍵詞:線性化;Poincare定理;狀態(tài)反饋;非正則;部分線性化中圖分類(lèi)號(hào):N941.1 文獻(xiàn)標(biāo)志碼:A1 IntroductionLinea

7、rizationofnonlinearsystemsisoneofthemostpowerfulmethodindealingwithnonlinear(control)systems.Ithasbeenstudiedwidelyforalongtime,andmanyvaluabletheoreticalresultshavebeeoobtained.Linearizationhasalsobeenusedwidelytovariousengineeringproblems.Forinstance,aircraftcontrol122,powersystems,chemicalreactor

8、,34Receiveddate:2009203207Foundationitem:ThisworkwassupportedpartlybyNNSF60674022,60736022and60821091ofChinaBiography:CHENGDai2zhan(19462),male,professor,IEEEFellow,IFACFellow,hisresearchinterestsincludenonlinearsystemandcontrol,numericalmethodetc.E2mail:dcheng第2期5CHENGDai2zhan,etal:ASurveyonLineari

9、zationofNonlinearSystems678927economicalsystems,biologicalsystems,neuralnetworks,airconditioningsystems,ecologicalsystems,robot10controlsystems,etc.ThemodelofVTOLaircraftisnotlinearizablebystaticstatefeedbackbutlinearizablebydynamicstatefeedback.Aflightcontrollerisdesignedforthetwinrotorhelicoptermo

10、del.Thedesignmethodaccomplishespartiallinearizationby1applyingstaticfeedbacklinearizationtothemainandthelowersubsystemshierarchically.Input2outputfeedbacklin2earizationmethodologyisusedtodesignadecentralizednonlinearcontrollerforlarge2scalepowersystems.Itisprovedthataninput2outputlinearizingtypefeed

11、backcantakethetrajectoriesofthereactorarbitrarilyclosetothesetpoint,de24spiteofparameteruncertainties.Statespaceexactlinearizationmethodisappliedtodesignanonlinearfeedbackcontrol11125lawtocontroltheKaldorandtheBonhoeffer2VanDerPohlnonlinearsystems.Applicationsofthelinearizationareillustratedforthean

12、alysisoftwobiologicalsystemsandthesynthesisofaphysicalsystem.ThedynamicmodelofaVAVACplantisderivedandformulatedasaMIMObilinearsystem.Feedbacklinearizationisappliedfordecoupling8andlinearizationofthenonlinearmodel.Stabilizationviafeedbacklinearizationoftwo2speciescompetitionmodelsbasedinthechemostatisconsideredin.Nonregularstaticfeedbacklinearizationisappliedtoaclassofflexiblejoint10robots,andthecontrollerconstructedisgloballyasymptoticallystabilizing. AlinearsystemisnxÛ=Ax, xIR.(111)Itmaybecalledthesimplestdynamicsystem.Itsdynamicbehaviorsarecomplete