The inverted pendulum in control theory and robotics: from theory to new innovations

409 Pages·2017·11.317 MB·English

by  Boubaker, Olfa, Iriarte, Rafael

IETCONTROL,ROBOTICSANDSENSORSSERIES111
The Inverted Pendulum
in Control Theory and Robotics
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The Inverted Pendulum
in Control Theory and Robotics
From theory to new innovations
Edited by
Olfa Boubaker and Rafael Iriarte
The Institution of Engineering and Technology
PublishedbyTheInstitutionofEngineeringandTechnology,London,UnitedKingdom
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©TheInstitutionofEngineeringandTechnology2018
Firstpublished2017
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Contents
Foreword xiii
1 Theinvertedpendulum:historyandsurveyofopenandcurrent
problemsincontroltheoryandrobotics 1
OlfaBoubaker
Abstract 1
1.1 Introduction 1
1.2 Inverted-pendulumbenchmarks:anoverview 5
1.2.1 Notation 11
1.3 Experimentallaboratories 12
1.3.1 Commercialdevices 12
1.3.2 Universitiesplatforms 13
1.3.3 Virtualmodels 13
1.4 Advancesincontroltheory 14
1.4.1 Whytheinvertedpendulumisthemostpopular
benchmark? 14
1.4.2 Emergingcontrolproblems 14
1.4.3 Challengingcontrolproblems 16
1.5 Majoraccomplishmentsinrobotics 18
1.5.1 Modelingandcontrollingunder-actuatedmechanical
systems 18
1.5.2 Self-balancedmobile-wheeledrobots 19
1.5.3 Modelingandcontrollingwalkingpatterngeneration 19
1.6 Conclusion 20
References 20
PARTI Robuststateestimationandcontrol:application
topendulum-cartsystems 41
2 Stateestimationandparameteridentificationviasliding-mode
techniques:pendulum–cartsystem 43
DiegoGutiérrezandHéctorRíos
2.1 Introduction 43
2.2 Problemstatement 45
2.3 Preliminaries 47
vi Theinvertedpendulumincontroltheoryandrobotics
2.4 High-ordersliding-modeobservers 48
2.4.1 Super-twistingobserver 49
2.4.2 Fixed-timeobserver 51
2.4.3 Experimentalresults 54
2.5 Parameteridentificationalgorithms 58
2.5.1 Homogeneousalgorithm 59
2.5.2 Finite-timealgorithm 61
2.5.3 Experimentalresults 63
2.6 Conclusions 66
References 66
3 Higherordersliding-modestabilizationofinvertedcart–pendulum 71
JesusMendoza-AvilaandIsmaelCastillo
Abstract 71
3.1 Introduction 71
3.2 SingularLQslidingvariabledesign 72
3.2.1 MATLABfunction:SSLQ 75
3.3 Continuoushigherordersliding-modecontrollers 75
3.3.1 Integralsliding-modecontrol 76
3.3.2 Continuousintegralsliding-modecontrol 76
3.3.3 Arbitraryordercontrollersdesign 77
3.4 Cart–pendulumsystem 78
3.4.1 Mathematicalmodel 79
3.4.2 Linearmodel 81
3.5 Continuoushigherordersliding-modecontrollers:cart–pendulum
systemrealization 83
3.5.1 RelativedegreeoneSMC 86
3.5.2 RelativedegreetwoSMC 86
3.5.3 RelativedegreethreeSMC 87
3.5.4 RelativedegreefourSMC 87
3.6 Results 88
3.6.1 Accuracyanalysis 88
3.7 Conclusions 90
References 90
4 Stabilizationandtrackingcontroloftheinvertedpendulum
onacartviaamodifiedPSOfractionalorderPIDcontroller 93
HaifaMehdiandOlfaBoubaker
Abstract 93
4.1 Introduction 93
4.2 Thecart-invertedpendulumsystem 95
4.2.1 Systempresentation 95
4.2.2 Dynamicmodeling 97
Contents vii
4.3 Controlsystem 99
4.3.1 Super-twistingobserver 99
4.3.2 Fractionalcontroller 100
4.3.3 Tuningparametersoffractional-ordercontroller 102
4.4 Simulationresults 104
4.4.1 Simulationresultsandperformanceanalysis:casestudy1 106
4.4.2 Simulationresultsandperformanceanalysis:casestudy2 109
4.5 Conclusion 111
References 112
PARTII Controllersforunderactuatedmechanicalsystems 117
5 Model-freecontroloftheinertiawheelinvertedpendulum
withreal-timeexperiments 119
AhmedChemori
5.1 Introduction 119
5.2 Descriptionofthesystem:inertiawheelinvertedpendulum 120
5.2.1 Descriptionofthemechanicalpartofthesystem 120
5.2.2 Descriptionoftheelectronicpartofthesystem 121
5.2.3 DescriptionofthecontrolPCandsoftware 122
5.3 Aproposedcontrolsolutionforunderactuatedsystems 122
5.3.1 Briefbackgroundonmodel-freecontrol 122
5.3.2 Proposedcontrolsolution 123
5.4 Application:theinertiawheelinvertedpendulumsystem 128
5.4.1 Dynamicmodelingofthesystem 128
5.5 Numericalsimulations 129
5.6 Real-timeexperiments 131
5.6.1 Scenario1:Controlinnominalcase 132
5.6.2 Scenario2:Externaldisturbancerejection 132
5.7 Conclusion 134
References 134
6 Outputfeedbacksecond-ordersliding-modetrackingcontrol
forperturbedinertiawheelpendulum 137
LuisT.AguilarandRafaelIriarte
6.1 Introduction 137
6.2 Dynamicmodelandproblemstatement 138
6.2.1 Generatingdesiredtrajectoriescenteredattheupright
equilibriumpoint 139
6.3 Observerdesign 141
6.4 Controlsynthesis 142
6.5 Numericalresults 145
6.6 Conclusions 146
AppendixA 147
viii Theinvertedpendulumincontroltheoryandrobotics
Acknowledgments 149
References 149
7 Switchedintegralslidingmodecontrolforrobustgeneration
ofself-oscillationinpendulumsystems 151
JuanEduardoVelázquez-Velázquez,RosalbaGalván-Guerra,
andRafaelIriarte
Abstract 151
7.1 Introduction 151
7.2 Preliminariesandproblemformulation 153
7.2.1 Uncertainsystem 153
7.2.2 Generationofself-oscillations:two-relaycontroller 153
7.2.3 Motivationalexample 155
7.2.4 Problemstatement 157
7.3 Switchedintegralslidingmodes 158
7.3.1 Slidingvariabledesign 158
7.3.2 Controllerdesign 159
7.4 Simulationexample 161
7.5 Conclusion 162
Acknowledgment 162
References 162
8 Finite-timestabilizationofunderactuatedmechanicalsystemsin
thepresenceofuncertainties:applicationtothecart–polesystem 165
JawharGhommam,AhmedChemori,andFaiçalMnif
8.1 Introduction 165
8.2 Dynamicmodelingofunderactuatedmechanicalsystems:
Lagrangianformalism 167
8.3 Controlproblemformulation 173
8.4 Preliminaries 174
8.4.1 Notionsoffinitestability 174
8.5 Proposedcontroldesign 174
8.6 Numericalsimulations:thecaseofthecart–polesystem 182
8.7 Conclusion 187
References 187
PARTIII Nonlinearcontrollersformobile
invertedpendulumsystems 191
9 Advancesinrobustcontrolofmobilewheeledinvertedpendulum 193
JianHuangandToshioFukuda
Abstract 193
9.1 Introduction 193
Contents ix
9.2 Modelingofmobilewheeledinvertedpendulum 195
9.2.1 Derivationofdynamicmodel 195
9.2.2 Analysisofequilibriums 197
9.3 Slidingmodecontrollerdesignformobilewheeledinverted
pendulum 198
9.3.1 Type-IslidingmodecontrollerforMWIP 198
9.3.2 Type-IIslidingmodecontrollerforMWIP 202
9.4 Dynamicsurfacecontrollerwithnonlineardisturbanceobserver
forMWIP 205
9.4.1 NonlineardisturbanceobserverdesignforMWIP 205
9.4.2 Controllerdesign 207
9.5 Simulationstudy 217
9.5.1 SimulationofSMCforMWIP 217
9.5.2 SimulationofDSCNDOforMWIP 219
9.6 Conclusion 221
Acknowledgment 221
References 221
10 Casestudiesonnon-linearcontroltheoryofthe
invertedpendulum 225
XuXu,HongweiZhang,andGiuseppeCarbone
Abstract 225
10.1 Introduction 225
10.2 Modellingofthecart–pendulumsystems 227
10.3 Controlanalysis 232
10.3.1 Linearcontrolanalysis 232
10.3.2 Non-linearcontrolanalysis 233
10.4 Simulationsforsingleanddoublependulumcontrol 237
10.5 Casestudy1–LEGOEV3-basedinvertedpendulum 239
10.5.1 Introduction 239
10.5.2 LEGOMindstormsEV3 240
10.5.3 ConstructionofLEGOinvertedpendulum 243
10.5.4 ControllerdesignandSimulinkmodel 245
10.5.5 Experimentalresults 246
10.6 Casestudy2–aparallelmanipulatorasthecart 246
10.7 Conclusions 253
AppendixASolvingandimplementingcontrolsolutions
usingMATLAB® 254
AppendixA.1Non-linearcontrolofasinglependulumand
cartsystem 254
Acknowledgement 259
References 259