A First Course in Control System Design Book

324 Pages·2·29.736 MB·English

by  Kamran Iqbal

River Publishers Series in A utomation, Control and Robotics
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Control systems are pervasive in our lives. Our homes have 2n
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process control systems. The recent drive toward automation has
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This book discusses control systems design from a model-based t
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perspective for dynamic system models of single-input single-output m
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controller design for both continuous-time and discrete-time
systems. MATLAB© and its Control Systems Toolbox are extensively
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∙ Mathematical models of physical systems K ∫ Ki
∙ Analysis of transfer function and state variable models a
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∙ Control systems design objectives udt
∙ Control system design with root locus ra Crddθt r+θrR− θa =qi.
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∙ Control system design in the state-space

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Foreword by
Professor Emeritus Hooshang Hemami,
River Publishers River Ohio State University River Publishers
A First Course in
Control System Design
2nd Edition
RIVERPUBLISHERSSERIESINAUTOMATION,
CONTROLANDROBOTICS
SeriesEditors:
ISHWARK.SETHI
OaklandUniversity
USA
TAREKSOBH
UniversityofBridgeport
USA
QUANMINZHU
UniversityoftheWestofEngland
UK
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The “River Publishers Series in Automation, Control and Robotics” is a series of
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from the theory and use of control systems, automation engineering, robotics and
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Books published in the series include research monographs, edited volumes,
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andadvancedstudentsinthefieldwithaninvaluableinsightintothelatestresearch
anddevelopments.
Topics covered in the series include, but are by no means restricted to the
following:
• RobotsandIntelligentMachines
• Robotics
• ControlSystems
• ControlTheory
• AutomationEngineering
Foralistofotherbooksinthisseries,visitwww.riverpublishers.com
A First Course in
Control System Design
2nd Edition
Kamran Iqbal
UniversityofArkansas
LittleRock,USA
River Publishers
Published,soldanddistributedby:
RiverPublishers
Alsbjergvej10
9260Gistrup
Denmark
www.riverpublishers.com
ISBN:978-87-7022-152-8(Hardback)
978-87-7022-151-1(Ebook)
©2020RiverPublishers
Allrightsreserved.Nopartofthispublicationmaybereproduced,storedin
aretrievalsystem,ortransmittedinanyformorbyanymeans,mechanical,
photocopying,recordingorotherwise,withoutpriorwrittenpermissionof
thepublishers.
Contents
Foreword xi
Preface xiii
Acknowledgement xxi
ListofFigures xxiii
ListofTables xxix
ListofAbbreviations xxxi
1 MathematicalModelsofPhysicalSystems 1
1.1 ModelingofPhysicalSystems . . . . . . . . . . . . . . . . 2
1.1.1 ModelVariablesandElementTypes . . . . . . . . . 3
1.1.2 First-OrderODEModels . . . . . . . . . . . . . . . 4
1.1.3 SolvingFirst-OrderODEModelswithStepInput . . 8
1.1.4 Second-OrderODEModels . . . . . . . . . . . . . 10
1.1.5 SolvingSecond-OrderODEModels . . . . . . . . . 12
1.2 TransferFunctionModels . . . . . . . . . . . . . . . . . . . 15
1.2.1 DCMotorModel . . . . . . . . . . . . . . . . . . . 16
1.2.2 IndustrialProcessModels . . . . . . . . . . . . . . 20
1.3 StateVariableModels . . . . . . . . . . . . . . . . . . . . . 21
1.4 LinearizationofNonlinearModels . . . . . . . . . . . . . . 24
1.4.1 LinearizationAboutanOperatingPoint . . . . . . . 25
1.4.2 LinearizationofaGeneralNonlinearModel . . . . . 27
SkillAssessmentQuestions . . . . . . . . . . . . . . . . . . . . . 29
2 AnalysisofTransferFunctionModels 31
2.1 CharacterizationofTransferFunctionModels . . . . . . . . 32
2.1.1 SystemPolesandZeros . . . . . . . . . . . . . . . 32
2.1.2 SystemNaturalResponse . . . . . . . . . . . . . . 34
v
vi Contents
2.2 SystemResponsetoInputs . . . . . . . . . . . . . . . . . . 36
2.2.1 TheImpulseResponse . . . . . . . . . . . . . . . . 36
2.2.2 TheStepResponse . . . . . . . . . . . . . . . . . . 38
2.2.3 CharacterizingtheSystemTransientResponse . . . 44
2.2.4 SystemStability . . . . . . . . . . . . . . . . . . . 46
2.3 SinusoidalResponseofaSystem . . . . . . . . . . . . . . . 49
2.3.1 SinusoidalResponseofLow-OrderSystems . . . . . 50
2.3.2 VisualizingtheFrequencyResponse . . . . . . . . . 52
SkillAssessmentQuestions . . . . . . . . . . . . . . . . . . . . . 59
3 AnalysisofStateVariableModels 63
3.1 StateVariableModels . . . . . . . . . . . . . . . . . . . . . 64
3.1.1 SolutiontotheStateEquations . . . . . . . . . . . . 65
3.1.2 LaplaceTransformSolutionandTransferFunction . 66
3.1.3 TheState-TransitionMatrix . . . . . . . . . . . . . 68
3.1.4 HomogenousStateEquationandAsymptotic
Stability . . . . . . . . . . . . . . . . . . . . . . . . 70
3.1.5 SystemResponseforStateVariableModels . . . . . 74
3.2 StateVariableRealizationofTransferFunctionModels . . . 77
3.2.1 SimulationDiagrams . . . . . . . . . . . . . . . . . 78
3.2.2 ControllerFormRealization . . . . . . . . . . . . . 80
3.2.3 Dual(ObserverForm)Realization . . . . . . . . . . 83
3.2.4 ModalRealization . . . . . . . . . . . . . . . . . . 83
3.2.5 DiagonalizationandDecoupling . . . . . . . . . . . 85
3.3 LinearTransformationofStateVariables . . . . . . . . . . . 86
3.3.1 TransformationintoControllerForm . . . . . . . . 86
3.3.2 TransformationintoModalForm . . . . . . . . . . 88
SkillAssessmentQuestions . . . . . . . . . . . . . . . . . . . . . 90
4 FeedbackControlSystems 93
4.1 StaticGainController . . . . . . . . . . . . . . . . . . . . . 95
4.2 DynamicControllers . . . . . . . . . . . . . . . . . . . . . 96
4.2.1 First-OrderPhase-LeadandPhase-Lag
Controllers . . . . . . . . . . . . . . . . . . . . . . 97
4.2.2 ThePIDController . . . . . . . . . . . . . . . . . . 99
4.2.3 RateFeedbackControllers . . . . . . . . . . . . . . 103
SkillAssessmentQuestions . . . . . . . . . . . . . . . . . . . . . 108
Contents vii
5 ControlSystemDesignObjectives 111
5.1 StabilityoftheClosed-LoopSystem . . . . . . . . . . . . . 112
5.1.1 Closed-LoopCharacteristicPolynomial . . . . . . . 112
5.1.2 StabilityDeterminationbyAlgebraicMethods . . . 114
5.1.3 StabilityDeterminationfromtheBodePlot . . . . . 116
5.2 TransientResponseImprovement. . . . . . . . . . . . . . . 117
5.2.1 SystemDesignSpecifications . . . . . . . . . . . . 119
5.2.2 TheDesiredCharacteristicPolynomial . . . . . . . 121
5.2.3 OptimalPerformanceIndices . . . . . . . . . . . . 123
5.3 Steady-StateErrorImprovement . . . . . . . . . . . . . . . 124
5.3.1 TheSteady-StateError . . . . . . . . . . . . . . . . 124
5.3.2 SystemErrorConstants . . . . . . . . . . . . . . . 125
5.3.3 Steady-StateErrortoRampInput . . . . . . . . . . 126
5.4 DisturbanceRejection . . . . . . . . . . . . . . . . . . . . . 128
5.5 SensitivityandRobustness . . . . . . . . . . . . . . . . . . 130
SkillAssessmentQuestions . . . . . . . . . . . . . . . . . . . . . 132
6 ControlSystemDesignwithRootLocus 133
6.1 TheRootLocus . . . . . . . . . . . . . . . . . . . . . . . . 135
6.1.1 RootsoftheCharacteristicPolynomial . . . . . . . 135
6.1.2 RootLocusRules . . . . . . . . . . . . . . . . . . . 136
6.1.3 ObtainingRootLocusPlotinMATLAB . . . . . . . 138
6.1.4 StabilityfromtheRootLocusPlot . . . . . . . . . . 139
6.1.5 AnalyticRootLocusConditions . . . . . . . . . . . 141
6.2 StaticControllerDesign . . . . . . . . . . . . . . . . . . . 143
6.3 DynamicControllerDesign . . . . . . . . . . . . . . . . . . 144
6.3.1 TransientResponseImprovement . . . . . . . . . . 145
6.3.2 Steady-StateErrorImprovement . . . . . . . . . . . 151
6.3.3 Lead–LagandPIDDesigns . . . . . . . . . . . . . 152
6.3.4 RateFeedbackCompensation . . . . . . . . . . . . 156
6.3.5 ControllerDesignsCompared . . . . . . . . . . . . 161
6.4 ControllerRealization . . . . . . . . . . . . . . . . . . . . . 163
6.4.1 Phase-Lead/Phase-LagControllers . . . . . . . . . . 164
6.4.2 PD,PI,PIDControllers . . . . . . . . . . . . . . . 164
SkillAssessmentQuestions . . . . . . . . . . . . . . . . . . . . . 165
7 DesignofSampled-DataSystems 167
7.1 ModelsofSampled-DataSystems . . . . . . . . . . . . . . 169
7.1.1 Z-transform . . . . . . . . . . . . . . . . . . . . . . 169
viii Contents
7.1.2 Zero-OrderHold . . . . . . . . . . . . . . . . . . . 171
7.1.3 PulseTransferFunction . . . . . . . . . . . . . . . 172
7.2 Sampled-DataSystemResponse . . . . . . . . . . . . . . . 175
7.2.1 DifferenceEquationSolutionbyIteration . . . . . . 175
7.2.2 Unit-PulseResponse . . . . . . . . . . . . . . . . . 176
7.2.3 Unit-StepResponse . . . . . . . . . . . . . . . . . . 179
7.2.4 ResponsetoArbitraryInputs . . . . . . . . . . . . . 183
7.3 StabilityintheCaseofSampled-DataSystems . . . . . . . 184
7.3.1 Jury’sStabilityTest . . . . . . . . . . . . . . . . . . 184
7.3.2 StabilityThroughBilinearTransform . . . . . . . . 185
7.4 Closed-LoopSampled-DataSystems . . . . . . . . . . . . . 186
7.4.1 Closed-LoopSystemStability . . . . . . . . . . . . 186
7.4.2 Unit-StepResponse . . . . . . . . . . . . . . . . . . 187
7.4.3 Steady-StateTrackingError . . . . . . . . . . . . . 190
7.5 ControllersforSampled-DataSystems . . . . . . . . . . . . 192
7.5.1 RootLocusDesignofDigitalControllers . . . . . . 193
7.5.2 AnalogandDigitalControllerDesignCompared . . 196
7.5.3 DigitalControllerDesignbyEmulation . . . . . . . 200
7.5.4 EmulationofAnalogPIDController . . . . . . . . . 203
SkillAssessmentQuestions . . . . . . . . . . . . . . . . . . . . . 206
8 ControllerDesignforStateVariableModels 211
8.1 StateFeedbackControllerDesign . . . . . . . . . . . . . . 212
8.1.1 PolePlacementwithStateFeedback . . . . . . . . . 213
8.1.2 PolePlacementintheControllerForm . . . . . . . . 215
8.1.3 PolePlacementusingBass–GuraFormula . . . . . . 217
8.1.4 PolePlacementusingAckermann’sFormula . . . . 218
8.1.5 PolePlacementusingSylvester’sEquation . . . . . 220
8.2 TrackingSystemDesign . . . . . . . . . . . . . . . . . . . 222
8.2.1 TrackingSystemDesignwithFeedforward
Gain . . . . . . . . . . . . . . . . . . . . . . . . . . 222
8.2.2 TrackingPIControllerDesign . . . . . . . . . . . . 225
8.3 StateVariableModelsofSampled-DataSystems . . . . . . 230
8.3.1 DiscretizingtheStateEquations . . . . . . . . . . . 230
8.3.2 SolutiontotheDiscreteStateEquations . . . . . . . 232
8.3.3 PulseTransferFunctionfromStateEquations . . . . 234
8.4 ControllersforDiscreteStateVariableModels . . . . . . . . 235
8.4.1 EmulatinganAnalogController . . . . . . . . . . . 235
8.4.2 PolePlacementDesignofDigitalController. . . . . 236
Contents ix
8.4.3 DeadbeatControllerDesign . . . . . . . . . . . . . 238
8.4.4 TrackingPIControllerDesign . . . . . . . . . . . . 241
SkillAssessmentQuestions . . . . . . . . . . . . . . . . . . . . . 244
9 FrequencyResponseDesignofCompensators 247
9.1 FrequencyResponseRepresentation . . . . . . . . . . . . . 248
9.1.1 TheBodePlot . . . . . . . . . . . . . . . . . . . . 248
9.1.2 TheNyquistPlot . . . . . . . . . . . . . . . . . . . 250
9.2 MeasuresofPerformance . . . . . . . . . . . . . . . . . . . 254
9.2.1 RelativeStability . . . . . . . . . . . . . . . . . . . 254
9.2.2 PhaseMarginandtheTransientResponse . . . . . . 256
9.2.3 ErrorConstantsandSystemType . . . . . . . . . . 259
9.2.4 SystemSensitivity . . . . . . . . . . . . . . . . . . 260
9.3 FrequencyResponseDesign . . . . . . . . . . . . . . . . . 261
9.3.1 GainCompensation . . . . . . . . . . . . . . . . . . 261
9.3.2 Phase-LagCompensation. . . . . . . . . . . . . . . 262
9.3.3 Phase-LeadCompensation . . . . . . . . . . . . . . 264
9.3.4 Lead-LagCompensation . . . . . . . . . . . . . . . 267
9.3.5 PICompensator . . . . . . . . . . . . . . . . . . . . 269
9.3.6 PDCompensator . . . . . . . . . . . . . . . . . . . 271
9.3.7 PIDCompensator . . . . . . . . . . . . . . . . . . . 273
9.3.8 CompensatorDesignsCompared . . . . . . . . . . . 275
9.4 Closed-LoopFrequencyResponse . . . . . . . . . . . . . . 276
SkillAssessmentQuestions . . . . . . . . . . . . . . . . . . . . . 280
Appendix 281
Index 285
AbouttheAuthor 289