Quasilinear control : performance analysis and design of feedback systems with nonlinear sensors and actuators

300 Pages·2010·5.49 MB·English

by  ShiNung Ching, et al

QUASILINEARCONTROL
PerformanceAnalysisandDesignofFeedbackSystemswith
NonlinearSensorsandActuators
Thisisatextbookonquasilinearcontrol(QLC).QLCisasetofmethodsforperformance
analysisanddesignoflinearplant/nonlinearinstrumentation(LPNI)systems.Theapproach
ofQLCisbasedonthemethodofstochasticlinearization,whichreducesthenonlinearities
of actuators and sensors to quasilinear gains. Unlike the usual – Jacobian linearization –
stochasticlinearizationisglobal.Usingthisapproximation,QLCextendsmostofthelinear
controltheorytechniquestoLPNIsystems.Inaddition,QLCincludesnewproblems,specific
fortheLPNIscenario.ExamplesincludeinstrumentedLQR/LQG,inwhichthecontrolleris
designedsimultaneouslywiththeactuatorandsensor,andpartialandcompleteperformance
recovery,inwhichthedegradationoflinearperformanceiseithercontainedbyselectingthe
rightinstrumentationorcompletelyeliminatedbythecontrollerboosting.
ShiNungChingisaPostdoctoralFellowattheNeurosciencesStatisticsResearchLaboratory
atMIT,sincecompletinghisPh.D.inelectricalengineeringattheUniversityofMichigan.His
researchinvolvesasystemstheoreticapproachtoanesthesiaandneuroscience,lookingtouse
mathematicaltechniquesandengineeringapproaches–suchasdynamicalsystems,modeling,
signalprocessing,andcontroltheory–tooffernewinsightsintothemechanismsofthebrain.
YongsoonEunisaSeniorResearchScientistatXeroxInnovationGroupinWebster, New
York.Since2003,hehasworkedonanumberofsubsystemtechnologiesinthexerographic
markingprocessandimageregistrationtechnologyfortheinkjetmarkingprocess.Hisinterests
arecontrolsystemswithnonlinearsensorsandactuators, cyclicsystems, andtheimpactof
multitaskingindividualsonorganizationalproductivity.
Cevat Gokcek was an Assistant Professor of Mechanical Engineering at Michigan State
University.HisresearchintheControlsandMechatronicsLaboratoryfocusedonautomo-
tive,aerospace,andwirelessapplications,withcurrentprojectsinplasmaignitionsystemsand
resonance-seekingcontrolsystemstoimprovecombustionandfuelefficiency.
PierreT.KabambaisaProfessorofAerospaceEngineeringattheUniversityofMichigan.
Hisresearchinterestsareintheareaoflinearandnonlineardynamicsystems,robustcontrol,
guidanceandnavigation,andintelligentcontrol.Hisrecentresearchactivitiesareaimedatthe
developmentofaquasilinearcontroltheorythatisapplicabletolinearplantswithnonlinear
sensorsoractuators.Hehasalsodoneworkinthedesign,scheduling,andoperationofmulti-
spacecraft interferometric imaging systems, in analysis and optimization of random search
algorithms,andinsimultaneouspathplanningandcommunicationschedulingforUAVsunder
theconstraintofradaravoidance.Hehasmorethan170publicationsinrefereedjournalsand
conferencesandnumerousbookchapters.
SemyonM.MeerkovisaProfessorofElectricalEngineeringattheUniversityofMichigan.
HereceivedhisPh.D.fromtheInstituteofControlSciencesinMoscow,whereheremained
until 1977. He then moved to the Department of Electrical and Computer Engineering at
theIllinoisInstituteofTechnologyandtoMichiganin1984.Hehasheldvisitingpositionsat
UCLA(1978–1979);StanfordUniversity(1991);Technion,Israel(1997–1998and2008);and
Tsinghua,China(2008).Hewastheeditor-in-chiefofMathematicalProblemsinEngineering,
department editor for Manufacturing Systems of IIE Transactions, and associate editor of
severalotherjournals.Hisresearchinterestsareinsystemsandcontrolwithapplicationsto
productionsystems, communicationnetworks, andthetheoryofrationalbehavior. Heisa
LifeFellowofIEEE.Heistheauthorofnumerousresearchpublicationsandbooks,including
ProductionSystemsEngineering(withJingshangLi,2009).
http://ebooks.cambridge.org/ebook.jsf?bid=CBO9780511976476

Quasilinear Control
Performance Analysis and Design of Feedback
Systems with Nonlinear Sensors and Actuators
ShiNung Ching
MassachusettsInstituteofTechnology
Yongsoon Eun
XeroxResearchCenterWebster
Cevat Gokcek
MichiganStateUniversity
Pierre T. Kabamba
UniversityofMichigan
Semyon M. Meerkov
UniversityofMichigan
CAMBRIDGE UNIVERSITY PRESS
Cambridge,NewYork,Melbourne,Madrid,CapeTown,Singapore,
SãoPaulo,Delhi,Dubai,Tokyo,MexicoCity
CambridgeUniversityPress
32AvenueoftheAmericas,NewYork,NY10013-2473,USA
www.cambridge.org
Informationonthistitle:www.cambridge.org/9781107000568
©ShiNungChing,YongsoonEun,CevatGokcek,PierreT.Kabamba,
andSemyonM.Meerkov2011
Thispublicationisincopyright.Subjecttostatutoryexception
andtotheprovisionsofrelevantcollectivelicensingagreements,
noreproductionofanypartmaytakeplacewithoutthewritten
permissionofCambridgeUniversityPress.
Firstpublished2011
PrintedintheUnitedStatesofAmerica
AcatalogrecordforthispublicationisavailablefromtheBritishLibrary.
LibraryofCongressCataloginginPublicationdata
Quasilinearcontrol:performanceanalysisanddesignoffeedbacksystems
withnonlinearsensorsandactuators/ShiNungChing...[etal.].
p. cm.
Includesbibliographicalreferencesandindex.
ISBN978-1-107-00056-8(hardback)
1. Stochasticcontroltheory. 2. Quasilinearization. I. Ching,ShiNung.
QA402.37.Q372010
(cid:1)
629.8312–dc22 2010039407
ISBN978-1-107-00056-8Hardback
CambridgeUniversityPresshasnoresponsibilityforthepersistenceor
accuracyofURLsforexternalorthird-partyInternetWebsitesreferredtoin
thispublicationanddoesnotguaranteethatanycontentonsuchWebsitesis,
orwillremain,accurateorappropriate.
Tomyparents,withlove,
SHINUNG CHING
TomywifeHaengju,mysonDavid,andmymotherAhnYoung,
withloveandgratitude,
YONGSOON EUN
Tomyfamily,withloveandgratitude,
PIERRE T. KABAMBA
TomydearwifeTerryandtoourchildren,Meera,Meir,Leah,
andRachel,withdeepestloveandadmiration,
SEMYON M. MEERKOV

Brief Contents
Preface page xiii
1 Introduction 1
2 StochasticLinearizationofLPNISystems 20
3 AnalysisofReferenceTrackinginLPNISystems 66
4 AnalysisofDisturbanceRejectioninLPNISystems 114
5 DesignofReferenceTrackingControllersforLPNISystems 134
6 DesignofDisturbanceRejectionControllersforLPNISystems 167
7 PerformanceRecoveryinLPNISystems 204
8 Proofs 225
Epilogue 275
AbbreviationsandNotations 277
Index 281
vii

Contents
Preface .................................................. page xiii
1 Introduction ............................................... 1
1.1 LinearPlant/NonlinearInstrumentationSystems
andQuasilinearControl 1
1.2 QLCProblems 3
1.3 QLCApproach:StochasticLinearization 4
1.4 QuasilinearversusLinearControl 5
1.5 OverviewofMainQLCResults 9
1.6 Summary 14
1.7 AnnotatedBibliography 14
2 StochasticLinearizationofLPNISystems ...................... 20
2.1 StochasticLinearizationofOpenLoopSystems 20
2.1.1 StochasticLinearizationofIsolatedNonlinearities 20
2.1.2 StochasticLinearizationofDirectPathsofLPNISystems 29
2.2 StochasticLinearizationofClosedLoopLPNISystems 30
2.2.1 NotationsandAssumptions 30
2.2.2 ReferenceTrackingwithNonlinearActuator 31
2.2.3 DisturbanceRejectionwithNonlinearActuator 36
2.2.4 ReferenceTrackingandDisturbanceRejectionwith
NonlinearSensor 37
2.2.5 ClosedLoopLPNISystemswithNonlinearActuators
andSensors 40
2.2.6 MultipleSolutionsofQuasilinearGainEquations 46
2.2.7 StochasticLinearizationofStateSpaceEquations 50
2.3 AccuracyofStochasticLinearizationinClosedLoopLPNI
Systems 53
2.3.1 Fokker-PlanckEquationApproach 53
2.3.2 FilterHypothesisApproach 55
ix
x Contents
2.4 Summary 57
2.5 Problems 57
2.6 AnnotatedBibliography 64
3 AnalysisofReferenceTrackinginLPNISystems ................ 66
3.1 TrackableDomainsandSystemTypesforLPNISystems 67
3.1.1 Scenario 67
3.1.2 TrackableDomainsandSteadyStateErrors 67
3.1.3 SystemTypes 74
3.1.4 Application:ServomechanismDesign 75
3.2 QualityIndicatorsforRandomReference
TrackinginLinearSystems 79
3.2.1 Scenario 79
3.2.2 RandomReferenceModel 79
3.2.3 RandomSensitivityFunction 81
3.2.4 TrackingQualityIndicators 86
3.2.5 Application:LinearHardDiskServoDesign 88
3.3 QualityIndicatorsforRandomReferenceTrackinginLPNI
Systems 90
3.3.1 Scenario 90
3.3.2 SaturatingRandomSensitivityFunction 92
3.3.3 TrackingQualityIndicators 98
3.3.4 Application:LPNIHardDiskServoDesign 101
3.4 Summary 105
3.5 Problems 106
3.6 AnnotatedBibliography 112
4 AnalysisofDisturbanceRejectioninLPNISystems ............. 114
4.1 BasicRelationships 114
4.1.1 SISOSystems 115
4.1.2 MIMOSystems 116
4.2 FundamentalLimitationsonDisturbanceRejection 124
4.3 LPNISystemswithRate-SaturatedActuators 125
4.3.1 ModelingRate-SaturatedActuators 126
4.3.2 BandwidthofRate-SaturatedActuators 127
4.3.3 DisturbanceRejectioninLPNISystemswith
Rate-SaturatedActuators 128
4.4 Summary 130
4.5 Problems 132
4.6 AnnotatedBibliography 133
5 DesignofReferenceTrackingControllersforLPNISystems ...... 134
5.1 AdmissiblePoleLocationsforRandomReferenceTracking 134
5.1.1 Scenario 134