Backstepping Control of Nonlinear Dynamical Systems (Advances in Nonlinear Dynamics and Chaos (ANDC))

531 Pages·2020·42.604 MB·English

by  Sundarapandian Vaidyanathan (editor), Ahmad Taher Azar (editor)

Backstepping Control of Nonlinear
Dynamical Systems
A volume in the Advances in Nonlinear
Dynamics and Chaos series
Serieseditors
AhmadTaherAzar
SundarapandianVaidyanathan
VisittheSerieswebpageathttps://www.elsevier.com/books/book-series/
advances-in-nonlinear-dynamics-and-chaos-andc
Backstepping Control of Nonlinear
Dynamical Systems
Edited by
Sundarapandian Vaidyanathan
ResearchandDevelopmentCentre,VelTechUniversity,Chennai,
TamilNadu,India
Ahmad Taher Azar
RoboticsandInternet-of-ThingsLab(RIOTU),PrinceSultanUniversity,
Riyadh,SaudiArabia
FacultyofComputersandArtificialIntelligence,BenhaUniversity,Benha,
Egypt
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Contents
Contributors xv
Preface xix
1. Anintroductiontobacksteppingcontrol
SundarapandianVaidyanathanandAhmadTaherAzar
1.1 Introduction 1
1.2 Backsteppingdesignfora2-Dlinearsystem 2
1.3 Backsteppingdesignfora2-Dnonlinearsystem 4
1.4 Backsteppingdesignfora3-Dlinearsystem 7
1.5 Backsteppingdesignforthe3-DVaidyanathanjerkchaotic
system 11
1.6 Backsteppingcontrolmethod 15
1.7 Examplesofbacksteppingcontroldesign 21
1.8 Conclusions 27
References 28
2. Anewchaoticsystemwithoutlinearterm,its
backsteppingcontrol,andcircuitdesign
Viet-ThanhPham,SundarapandianVaidyanathan,
AhmadTaherAzar,andVoHoangDuy
2.1 Introduction 33
2.2 Propertiesofthesystem 34
2.3 Dynamicsofthesystem 35
2.4 Backsteppingcontrolfortheglobalstabilizationofthenew
chaossystem 35
2.5 Backsteppingcontrolforthesynchronizationofthenewchaos
systems 40
2.6 Circuitdesign 45
2.7 Conclusions 48
Acknowledgment 48
References 48
v
vi Contents
3. Anewchaoticjerksystemwithegg-shapedstrange
attractor,itsdynamicalanalysis,backsteppingcontrol,
andcircuitsimulation
SundarapandianVaidyanathan,Viet-ThanhPham,and
AhmadTaherAzar
3.1 Introduction 53
3.2 Systemdetails 55
3.3 Backsteppingcontrolofthejerksystem 57
3.4 Backsteppingsynchronizationofthejerksystem 61
3.5 Circuitdesign 65
3.6 Conclusions 67
References 69
4. Anew4-Dchaotichyperjerksystemwithcoexisting
attractors,itsactivebacksteppingcontrol,and
circuitrealization
AcengSambas,SundarapandianVaidyanathan,SenZhang,
MohamadAfendeeMohamed,YichengZeng,and
AhmadTaherAzar
4.1 Introduction 73
4.2 Systemmodel 75
4.3 Dynamicanalysisofthenewhyperjerksystem 78
4.4 Activebacksteppingstabilizationofthenewhyperjerksystem 79
4.5 Activebacksteppingsynchronizationofthenewhyperjerk
system 82
4.6 Circuitsimulationofthenewhyperjerksystem 88
4.7 Conclusions 90
Acknowledgment 91
References 91
5. Anew3-Dchaoticjerksystemwithasaddle-focusrest
pointattheorigin,itsactivebacksteppingcontrol,and
circuitrealization
AcengSambas,SundarapandianVaidyanathan,SenZhang,
MohamadAfendeeMohamed,YichengZeng,and
AhmadTaherAzar
5.1 Introduction 95
5.2 Systemmodel 96
5.3 Dynamicanalysisofthenewjerksystem 99
5.4 Backsteppingcontrolofthejerksystem 100
5.5 Backsteppingsynchronizationofthejerksystem 103
Contents vii
5.6 Electroniccircuitsimulationofthechaoticjerksystem 108
5.7 Conclusions 110
Acknowledgments 111
References 111
6. Anew5-Dhyperchaoticfour-wingsystemwith
multistabilityandhiddenattractor,itsbackstepping
control,andcircuitsimulation
SundarapandianVaidyanathan,AcengSambas,AhmadTaherAzar,
K.P.S.Rana,andVineetKumar
6.1 Introduction 115
6.2 Systemmodel 116
6.3 Dynamicanalysisofthe5-Dhyperchaoticfour-wingmodel 119
6.3.1 Restpoints 119
6.3.2 Multistability 119
6.4 Activebacksteppingcontrolfortheglobalstabilizationdesign
ofthenew5-Dhyperchaoticfour-wingsystem 119
6.5 Activebacksteppingcontrolfortheglobalsynchronization
designofthenew5-Dhyperchaoticfour-wingsystems 124
6.6 Circuitsimulationofthenew5Dhyperchaoticfour-wing
system 130
6.7 Conclusions 132
References 134
7. Anew4-Dhyperchaotictemperaturevariationssystem
withmultistabilityandstrangeattractor,bifurcation
analysis,itsactivebacksteppingcontrol,andcircuit
realization
SundarapandianVaidyanathan,AcengSambas,AhmadTaherAzar,
K.P.S.Rana,andVineetKumar
7.1 Introduction 139
7.2 Systemmodel 140
7.3 Dynamicanalysisofthehyperchaotictemperaturevariations
model 144
7.3.1 Bifurcationanalysis 144
7.3.2 Restpoints 145
7.3.3 Multistability 146
7.4 Activebacksteppingcontrolfortheglobalstabilizationdesign
ofthenewhyperchaotictemperaturevariationssystem 148
7.5 Activebacksteppingcontrolfortheglobalsynchronization
designofthenewhyperchaostemperaturevariationsystems 150
7.6 Circuitsimulationofthenew4Dhyperchaotictemperature
variationsystem 155
viii Contents
7.7 Conclusions 159
References 160
8. Anewthermallyexcitedchaoticjerksystem,its
dynamicalanalysis,adaptivebacksteppingcontrol,and
circuitsimulation
SundarapandianVaidyanathan,AcengSambas,AhmadTaherAzar,
FernandoE.Serrano,andArezkiFekik
8.1 Introduction 165
8.2 Anewjerksystemwithtwononlinearities 167
8.3 Dynamicanalysisofthenewthermo-mechanicaljerkmodel 171
8.3.1 Restpointsofthenewjerkmodel 171
8.3.2 Bifurcationanalysis 171
8.3.3 Multistabilityandcoexistingattractors 172
8.4 Adaptivebacksteppingcontrolofthenewthermo-mechanical
jerksystem 173
8.5 Adaptivebacksteppingsynchronizationofthenew
thermo-mechanicaljerksystems 177
8.6 Electroniccircuitsimulationofthenewthermo-mechanical
chaoticjerksystem 181
8.7 Conclusions 184
References 185
9. Anewmultistableplasmatorchchaoticjerksystem,
itsdynamicalanalysis,activebacksteppingcontrol,
andcircuitdesign
SundarapandianVaidyanathan,AcengSambas,AhmadTaherAzar,
andShikhaSingh
9.1 Introduction 191
9.2 Anewplasmatorchchaoticjerksystemwithtwononlinearities 193
9.3 Dynamicanalysisofthenewplasmatorchchaoticjerkmodel 196
9.3.1 Restpointsofthenewchaoticjerkmodel 196
9.3.2 Bifurcationanalysis 198
9.3.3 Multistabilityandcoexistingattractors 198
9.4 Activebacksteppingcontrolfortheglobalstabilizationofthe
newplasmatorchchaoticjerksystem 200
9.5 Activebacksteppingcontrolfortheglobalsynchronizationof
thenewplasmatorchchaoticjerksystems 202
9.6 Electroniccircuitsimulationofthenewplasmatorchchaotic
jerksystem 205
9.7 Conclusions 208
References 210
Contents ix
10. Directpowercontrolofthree-phasePWM-rectifier
withbacksteppingcontrol
ArezkiFekik,HakimDenoun,AhmadTaherAzar,
NashwaAhmadKamal,MustaphaZaouia,NabilBenyahia,
MohamedLamineHamida,NacereddineBenamrouche,and
SundarapandianVaidyanathan
10.1 Introduction 215
10.2 MathematicalmodelofPWM-rectifier 216
10.2.1 Vectorrepresentation 218
10.2.2 Abriefreviewofdirectpowercontrol 219
10.3 Principleanddefinitionsofbacksteppingcontrol 220
10.4 ControlofDC-voltagebybackstepping 225
10.5 Simulationresults 225
10.6 Conclusion 230
References 232
11. AdaptivebacksteppingcontrollerforDFIG-basedwind
energyconversionsystem
IsmailDrhorhi,AbderrahimElFadili,ChakerBerrahal,
RachidLajouad,AbdelmounimeElMagri,FouadGiri,
AhmadTaherAzar,andSundarapandianVaidyanathan
11.1 Introduction 235
11.2 Windsensor-lessrotorspeedreferenceoptimization 237
11.3 Modeling‘AC/DC/ACconverter-DFIG’association 238
11.3.1 DFIG-AC/DCmodeling 239
11.3.2 AC/DCrectifiermodeling 242
11.4 Controllerdesign 244
11.4.1 Controlobjectives 244
11.4.2 Speedandstatorfluxnormregulatordesign 244
11.4.3 PFCandDCvoltagecontroller 250
11.5 Simulationresultsanddiscussions 252
11.6 Conclusion 256
References 258
12. Dynamicmodeling,identification,andacomparative
experimentalstudyonpositioncontrolofapneumatic
actuatorbasedonSoftSwitchingand
Backstepping–SlidingModecontrollers
AmirSalimiLafmejani,MehdiTaleMasouleh,andAhmadKalhor
12.1 Introduction 261
12.2 Relatedworks 264
12.3 ExperimentalsetupofthePneuSys 266