Feedback Control of Dynamic Systems

885 Pages·2014·24.13 MB·English

by  Gene F. Franklin, J. Da Powell, Abbas Emami-Naeini

Feedback Control
of Dynamic Systems
SeventhEdition
Gene F. Franklin
StanfordUniversity
J. David Powell
StanfordUniversity
Abbas Emami-Naeini
SCSolutions,Inc.
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LibraryofCongressCataloging-in-PublicationData
Franklin,GeneF.
Feedbackcontrolofdynamicsystems/GeneF.Franklin,J.DavidPowell,
AbbasEmami-Naeini.—Seventhedition.
pagescm
Includesbibliographicalreferencesandindex.
ISBN-13:978-0-13-349659-8
ISBN-10:0-13-349659-7
1. Feedbackcontrolsystems. I. Powell,J.David,1938– II. Emami-Naeini,Abbas.
III. Title.
TJ216.F723 2014
'
629.83—dc23 2014004059
(cid:2) (cid:2)
Matlab andSimulink areregisteredtrademarksofTheMathWorks,Inc.,4AppleHillDrive,Natick,MA.
10 9 8 7 6 5 4 3 21
ISBN:978-0-13-349659-8
ISBN: 0-13-349659-7
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To the memory of Gene F. Franklin
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Thispageintentionallyleftblank
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Contents
Preface xiii
1
AnOverviewandBriefHistoryofFeedbackControl 1
APerspectiveonFeedbackControl 1
ChapterOverview 2
1.1 ASimpleFeedbackSystem 3
1.2 AFirstAnalysisofFeedback 6
1.3 FeedbackSystemFundamentals 10
1.4 ABriefHistory 11
1.5 AnOverviewoftheBook 17
Summary 19
ReviewQuestions 19
Problems 20
2
DynamicModels 23
APerspectiveonDynamicModels 23
ChapterOverview 24
2.1 DynamicsofMechanicalSystems 24
2.1.1 TranslationalMotion 24
2.1.2 RotationalMotion 31
2.1.3 CombinedRotationandTranslation 39
2.1.4 ComplexMechanicalSystems(W)** 42
2.1.5 DistributedParameterSystems 42
2.1.6 Summary:DevelopingEquationsofMotion
forRigidBodies 44
2.2 ModelsofElectricCircuits 45
2.3 ModelsofElectromechanicalSystems 50
2.3.1 Loudspeakers 50
2.3.2 Motors 52
(cid:2) 2.3.3 Gears 56
(cid:2) 2.4 HeatandFluid-FlowModels 57
2.4.1 HeatFlow 58
2.4.2 IncompressibleFluidFlow 61
2.5 HistoricalPerspective 68
Summary 71
ReviewQuestions 71
Problems 72
**Sectionswith(W)indicatesthatadditionalmaterialislocatedonthewebatwww.FPE7e.com.
v
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vi Contents
3
DynamicResponse 84
APerspectiveonSystemResponse 84
ChapterOverview 85
3.1 ReviewofLaplaceTransforms 85
3.1.1 ResponsebyConvolution 86
3.1.2 TransferFunctionsandFrequencyResponse 91
3.1.3 TheL−LaplaceTransform 101
3.1.4 PropertiesofLaplaceTransforms 103
3.1.5 InverseLaplaceTransformbyPartial-Fraction
Expansion 105
3.1.6 TheFinalValueTheorem 107
3.1.7 UsingLaplaceTransformstoSolveDifferential
Equations 109
3.1.8 PolesandZeros 111
(cid:2)
3.1.9 LinearSystemAnalysisUsingMatlab 112
3.2 SystemModelingDiagrams 118
3.2.1 TheBlockDiagram 118
3.2.2 Block-DiagramReductionUsingMatlab 122
3.2.3 Mason’sRuleandtheSignalFlowGraph(W) 123
3.3 EffectofPoleLocations 123
3.4 Time-DomainSpecifications 131
3.4.1 RiseTime 132
3.4.2 OvershootandPeakTime 132
3.4.3 SettlingTime 134
3.5 EffectsofZerosandAdditionalPoles 137
3.6 Stability 146
3.6.1 BoundedInput–BoundedOutputStability 147
3.6.2 StabilityofLTISystems 148
3.6.3 Routh’sStabilityCriterion 149
(cid:2) 3.7 ObtainingModelsfromExperimentalData:
SystemIdentification(W) 156
(cid:2) 3.8 AmplitudeandTimeScaling(W) 156
3.9 HistoricalPerspective 156
Summary 157
ReviewQuestions 159
Problems 159
4
AFirstAnalysisofFeedback 180
APerspectiveontheAnalysisofFeedback 180
ChapterOverview 181
4.1 TheBasicEquationsofControl 182
4.1.1 Stability 183
4.1.2 Tracking 184
4.1.3 Regulation 185
4.1.4 Sensitivity 186
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Contents vii
4.2 ControlofSteady-StateErrortoPolynomialInputs:
SystemType 188
4.2.1 SystemTypeforTracking 189
4.2.2 SystemTypeforRegulationandDisturbance
Rejection 194
4.3 TheThree-TermController:PIDControl 196
4.3.1 ProportionalControl(P) 196
4.3.2 IntegralControl(I) 198
4.3.3 DerivativeControl(D) 201
4.3.4 ProportionalPlusIntegralControl(PI) 201
4.3.5 PIDControl 202
4.3.6 Ziegler–NicholsTuningofthePID
Controller 206
4.4 FeedforwardControlbyPlantModelInversion 212
(cid:2) 4.5 IntroductiontoDigitalControl(W) 214
(cid:2) 4.6 SensitivityofTimeResponsetoParameterChange(W) 215
4.7 HistoricalPerspective 215
Summary 217
ReviewQuestions 218
Problems 218
5
TheRoot-LocusDesign
Method 234
APerspectiveontheRoot-LocusDesignMethod 234
ChapterOverview 235
5.1 RootLocusofaBasicFeedbackSystem 235
5.2 GuidelinesforDeterminingaRootLocus 240
◦
5.2.1 RulesforDeterminingaPositive(180 )
RootLocus 242
5.2.2 SummaryoftheRulesforDetermininga
RootLocus 248
5.2.3 SelectingtheParameterValue 249
5.3 SelectedIllustrativeRootLoci 251
5.4 DesignUsingDynamicCompensation 264
5.4.1 DesignUsingLeadCompensation 266
5.4.2 DesignUsingLagCompensation 270
5.4.3 DesignUsingNotchCompensation 272
(cid:2) 5.4.4 AnalogandDigitalImplementations(W) 274
5.5 ADesignExampleUsingtheRootLocus 275
5.6 ExtensionsoftheRoot-LocusMethod 281
◦
5.6.1 RulesforPlottingaNegative(0 )
RootLocus 281
(cid:2) 5.6.2 ConsiderationofTwoParameters 284
(cid:2) 5.6.3 TimeDelay(W) 286
5.7 HistoricalPerspective 287
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viii Contents
Summary 289
ReviewQuestions 290
6 Problems 291
TheFrequency-Response
DesignMethod 308
APerspectiveontheFrequency-ResponseDesignMethod 308
ChapterOverview 309
6.1 FrequencyResponse 309
6.1.1 BodePlotTechniques 317
6.1.2 Steady-StateErrors 330
6.2 NeutralStability 331
6.3 TheNyquistStabilityCriterion 333
6.3.1 TheArgumentPrinciple 334
6.3.2 ApplicationofTheArgumentPrinciple
toControlDesign 335
6.4 StabilityMargins 348
6.5 Bode’sGain–PhaseRelationship 357
6.6 Closed-LoopFrequencyResponse 361
6.7 Compensation 363
6.7.1 PDCompensation 363
6.7.2 LeadCompensation(W) 364
6.7.3 PICompensation 374
6.7.4 LagCompensation 375
6.7.5 PIDCompensation 381
6.7.6 DesignConsiderations 387
(cid:2) 6.7.7 SpecificationsinTermsoftheSensitivity
Function 389
(cid:2) 6.7.8 LimitationsonDesigninTermsoftheSensitivity
Function 394
(cid:2) 6.8 TimeDelay 398
6.8.1 TimeDelayviatheNyquistDiagram(W) 400
(cid:2) 6.9 AlternativePresentationofData 400
6.9.1 NicholsChart 400
6.9.2 TheInverseNyquistDiagram(W) 404
6.10 HistoricalPerspective 404
Summary 405
ReviewQuestions 408
Problems 408
7
State-SpaceDesign 433
APerspectiveonState-SpaceDesign 433
ChapterOverview 434
7.1 AdvantagesofState-Space 434
7.2 SystemDescriptioninState-Space 436
7.3 BlockDiagramsandState-Space 442
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Contents ix
7.4 AnalysisoftheStateEquations 444
7.4.1 BlockDiagramsandCanonicalForms 445
7.4.2 DynamicResponsefromtheState
Equations 457
7.5 Control-LawDesignforFull-StateFeedback 463
7.5.1 FindingtheControlLaw 464
7.5.2 IntroducingtheReferenceInputwithFull-State
Feedback 473
7.6 SelectionofPoleLocationsforGoodDesign 477
7.6.1 DominantSecond-OrderPoles 477
7.6.2 SymmetricRootLocus(SRL) 479
7.6.3 CommentsontheMethods 488
7.7 EstimatorDesign 489
7.7.1 Full-OrderEstimators 489
7.7.2 Reduced-OrderEstimators 495
7.7.3 EstimatorPoleSelection 499
7.8 CompensatorDesign:CombinedControl
LawandEstimator(W) 501
7.9 IntroductionoftheReferenceInput
withtheEstimator(W) 514
7.9.1 GeneralStructurefortheReferenceInput 515
7.9.2 SelectingtheGain 524
7.10 IntegralControlandRobustTracking 525
7.10.1 IntegralControl 526
(cid:2) 7.10.2 RobustTrackingControl:TheError-Space
Approach 528
(cid:2) 7.10.3 Model-FollowingDesign 539
(cid:2) 7.10.4 TheExtendedEstimator 543
(cid:2) 7.11 LoopTransferRecovery 547
(cid:2) 7.12 DirectDesignwithRationalTransfer
Functions 552
(cid:2) 7.13 DesignforSystemswithPureTimeDelay 556
7.14 SolutionofStateEquations(W) 559
7.15 HistoricalPerspective 559
Summary 562
ReviewQuestions 565
Problems 566
8
DigitalControl 590
APerspectiveonDigitalControl 590
ChapterOverview 591
8.1 Digitization 591
8.2 DynamicAnalysisofDiscreteSystems 594
8.2.1 z-Transform 594
8.2.2 z-TransformInversion 595
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