Operator-Based Nonlinear Control Systems: Design and Applications

274 Pages·2014·7.514 MB·English

by  Mingcong Deng

OPERATOR-BASED NONLINEAR
CONTROL SYSTEMS
IEEEPress
445HoesLane
Piscataway,NJ08854
IEEEPressEditorialBoard
TariqSamad,EditorinChief
LindaShafer MengChuZhou GeorgeZobrist
GeorgeW.Arnold RayPerez DmitryGoldgof
EkramHossain MaryLanzerotti Pui-InMak
KennethMoore,DirectorofIEEEBookandInformationServices(BIS)
TechnicalReviewers
Prof.XinkaiChen,DepartmentofElectronicInformationSystems,ShibauraInstituteofTechnology
Prof.HongWang,ControlSystemsCentre,TheUniversityofManchester
OPERATOR-BASED
NONLINEAR CONTROL
SYSTEMS
Design and Applications
Mingcong Deng
TokyoUniversityofAgricultureandTechnology
Copyright(cid:2)C 2014byTheInstituteofElectricalandElectronicsEngineers,Inc.
PublishedbyJohnWiley&Sons,Inc.,Hoboken,NewJersey.
PublishedsimultaneouslyinCanada.
Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmittedinanyformor
byanymeans,electronic,mechanical,photocopying,recording,scanning,orotherwise,exceptas
permittedunderSection107or108ofthe1976UnitedStatesCopyrightAct,withouteithertheprior
writtenpermissionofthePublisher,orauthorizationthroughpaymentoftheappropriateper-copyfeeto
theCopyrightClearanceCenter,Inc.,222RosewoodDrive,Danvers,MA01923,[phone],
fax[phone],oronthewebatwww.copyright.com.RequeststothePublisherforpermission
shouldbeaddressedtothePermissionsDepartment,JohnWiley&Sons,Inc.,111RiverStreet,
Hoboken,NJ07030,[phone],fax[phone].
LimitofLiability/DisclaimerofWarranty:Whilethepublisherandauthorhaveusedtheirbesteffortsin
preparingthisbook,theymakenorepresentationsorwarrantieswithrespecttotheaccuracyor
completenessofthecontentsofthisbookandspecificallydisclaimanyimpliedwarrantiesof
merchantabilityorfitnessforaparticularpurpose.Nowarrantymaybecreatedorextendedbysales
representativesorwrittensalesmaterials.Theadviceandstrategiescontainedherinmaynotbesuitable
foryoursituation.Youshouldconsultwithaprofessionalwhereappropriate.Neitherthepublishernor
authorshallbeliableforanylossofprofitoranyothercommercialdamages,includingbutnotlimitedto
special,incidental,consequential,orotherdamages.
ForgeneralinformationonourotherproductsandservicespleasecontactourCustomerCare
DepartmentwiththeU.S.at877-762-2974,outsidetheU.S.at317-572-3993orfax317-572-4002.
Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappearsinprint,
however,maynotbeavailableinelectronicformat.
LibraryofCongressCataloging-in-PublicationData:
Deng,Mingcong.
Operator-basednonlinearcontrolsystemsdesignandapplications/MingcongDeng.–Firstedition.
pagescm.–(IEEEPressseriesonsystemsscienceandengineering)
ISBN978-1-118-13122-0(hardback)
1.Automaticcontrol. 2.Nonlinearcontroltheory. I.Title.
TJ213.D4352013
629.8(cid:3)36–dc23
2013026695
PrintedintheUnitedStatesofAmerica
10 9 8 7 6 5 4 3 2 1
CONTENTS
1 Introduction 1
1.1 DefinitionofNonlinearSystems 1
1.2 NonlinearSystemDynamicsAnalysisandControl 1
1.3 WhyOperator-BasedNonlinearControlSystem? 2
1.4 OverviewoftheBook 2
Acknowledgments 3
2 RobustRightCoprimeFactorizationforNonlinearPlants
withUncertainties 5
2.1 Preliminaries 5
2.1.1 DefinitionofSpaces 5
2.1.2 DefinitionofOperators 6
2.2 OperatorTheory 11
2.2.1 RightCoprimeFactorization 11
2.2.2 RobustRightCoprimeFactorization 12
2.2.3 Isomorphism-BasedRobustRightPrimeFactorization 16
3 RobustStabilityofOperator-BasedNonlinearControlSystems 27
3.1 ConceptofOperator-BasedRobustStability 27
3.2 DesignMethodsofNonlinearSystemswithUncertainties 27
3.2.1 RobustRightCoprimeFactorizationCondition 27
3.2.2 TrackingControlDesignScheme 32
3.3 Operator-BasedRobustAnti-WindupNonlinearFeedbackControl
SystemsDesign 41
3.3.1 Introduction 41
3.3.2 DesignDescription 42
3.3.3 IllustrativeExamples 47
3.3.4 Discussion 55
3.4 Operator-BasedMulti-Input–Multi-OutputNonlinearFeedback
ControlSystemsDesign 55
3.4.1 Introduction 55
3.4.2 DefinitionsandNotation 56
v
vi CONTENTS
3.4.3 DifferentiableOperator-BasedNonlinearRobust
ControlforMIMONonlinearSystemsUsing
ControllerFactorization 60
3.4.4 NonlinearRobustControlforMIMONonlinearSystemsby
ConsideringCouplingEffectsasUncertaintiesofPlants 70
3.4.5 NonlinearRobustControlforMIMONonlinearSystemsby
RightFactorizingCouplingOperators 75
3.4.6 Operator-BasedNonlinearRobustControlforMIMO
NonlinearSystemswithUnknownCouplingEffects 85
3.4.7 Summary 106
3.5 Operator-BasedTime-VaryingDelayedNonlinearFeedback
ControlSystemsDesign 106
3.5.1 NetworkedExperimentalSystem 107
3.5.2 NetworkedNonlinearFeedbackControlDesign 110
3.5.3 ExperimentalResult 112
3.5.4 Summary 115
4 TrackingandFaultDetectionIssuesinNonlinearControlSystems 117
4.1 Operator-BasedTrackingCompensatorinNonlinearFeedback
ControlSystemsDesign 117
4.1.1 Introduction 117
4.1.2 TrackingControllerDesignSchemeUsing
UnimodularOperator 118
4.1.3 Simulation 121
4.1.4 Summary 124
4.2 RobustControlforNonlinearSystemswithUnknown
PerturbationsusingSimplifiedRobustRightCoprimeFactorization 125
4.2.1 Introduction 125
4.2.2 RobustDesignofTrackingController 126
4.2.3 IllustrativeExamples 132
4.2.4 Summary 140
4.3 Operator-BasedActuatorFaultDetectionMethods 140
4.3.1 Introduction 140
4.3.2 ActuatorFaultDetetionMethodinNonlinearSystems 141
4.3.3 AlgorithmofFaultDetectionSystem 145
4.3.4 ExperimentsandDiscussion 147
4.3.5 Summary 152
4.4 Operator-BasedInputCommandFaultDetectionMethodin
NonlinearFeedbackControlSystems 152
4.4.1 Introduction 152
4.4.2 ModelingandProblemSetup 154
4.4.3 RobustInputCommandFaultDetectionMethod 158
CONTENTS vii
4.4.4 SimulationandExperimentalResults 161
4.4.5 Summary 167
5 Operator-BasedNonlinearControlSystemswithSmartActuators 169
5.1 Operator-BasedRobustNonlinearFeedbackControlSystems
DesignforNonsymmetricBacklash 169
5.1.1 Introduction 169
5.1.2 ProblemStatement 170
5.1.3 NonsymmetricBacklashControlDesignScheme 173
5.1.4 SimulationResults 177
5.1.5 Summary 182
5.2 Operator-BasedRobustNonlinearFeedbackControlSystems
DesignforSymmetricandNonsymmetricHysteresis 182
5.2.1 Introduction 182
5.2.2 ProblemSetup 183
5.2.3 NonsymmetricPrandtl–IshlinskiiHysteresisModel 185
5.2.4 DesignofRobustStableControlSystem 190
5.2.5 NumericalExample 192
5.2.6 Summary 193
5.3 Operator-BasedNonlinearFeedbackSystemsApplicationfor
SmartActuators 194
5.3.1 NonlinearControlofPiezoelectricActuator 194
5.3.2 NonlinearControlofShapeMemoryAlloyActuator 203
5.3.3 NonlinearControlofIPMC 216
5.3.4 Summary 234
6 ApplicationofOperator-BasedNonlinearFeedbackControlto
Large-ScaleSystemsusingDistributedControlSystemDevice 235
6.1 Introduction 235
6.2 MultitankProcessModeling 237
6.3 RobustRightCoprimeFactorizationDesignand
ControllerRealization 242
6.4 ExperimentalResults 248
6.5 Summary 252
References 253
Index 261

CHAPTER 1
Introduction
1.1 DEFINITIONOFNONLINEARSYSTEMS
Ingeneral,anonlinearsystemisonethatdoesnotsatisfythesuperpositionprinciple
orwhoseoutputisnotdirectlyproportionaltoitsinput.Thatis,anonlinearsystem
is any problem where the variable(s) to be solved for cannot be written as a linear
combination of independent components. Since most economic, social, and many
industrialsystemsareinherentlynonlinearinnature,wheremathematicalanalysisis
unabletoprovidegeneralsolutions,nonlinearsystemproblems,especiallynonlinear
systemsdynamicsanalysisandcontrolproblemsforindustrialsystems,areofinterest
tomathematicians,physicists,andengineers.
1.2 NONLINEARSYSTEMDYNAMICSANALYSISANDCONTROL
Nonlinearsystemscontrolisthedisciplinethatappliescontroltheorytodesignsys-
tems with desired behaviors. It can be broadly defined or classified as nonlinear
control theory and application. It seeks to understand nonlinear systems dynamics,
using mathematical modeling, in terms of inputs, outputs, and various components
with different behaviors and to use nonlinear control systems design schemes to
develop controllers for those systems in one or many time, frequency, and com-
plex domains, depending on the nature of the design problem. As a result, control
of nonlinear systems is a multidisciplinary research field involving the synergistic
integrationofmechanicalandelectricalengineering,computerscience,andevenbio-
logicalengineering.Controlofnonlinearsystemswillbecomemainstreamconsumer
products withinthenext decade, providingasignificantgrowthopportunityforthe
above-mentionedengineeringsystems.Sofar,thereareseveralsignificanttechniques
for analyzing nonlinear systems, for example, describing the function method, the
phaseplanemethod,Lyapunov-basedanalysis,thesingularperturbationmethod,the
Popovcriterion,thecentermanifoldtheorem,thesmall-gaintheorem,andpassivity
analysis.Basedontheabovetechniques,significantresultswereintroducedextend-
ing to nonlinear feedback systems design and control. Some cornerstone control
Operator-BasedNonlinearControlSystems:DesignandApplications,FirstEdition.MingcongDeng.
©2014TheInstituteofElectricalandElectronicsEngineers,Inc.Published2014byJohnWiley&Sons,Inc.
1