Analysis and Design of Reset Control Systems

201 Pages·2015·4.344 MB·English

by  Yuqian Guo, Lihua Xie, Youyi Wang

IETCONTROLENGINEERINGSERIES94
Analysis and Design
of Reset Control
Systems
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Volume94 AnalysisandDesignofResetControlSystemsY.Guo,L.XieandY.Wang
Analysis and Design
of Reset Control
Systems
Yuqian Guo, Lihua Xie
and Youyi Wang
TheInstitutionofEngineeringandTechnology
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Contents
Listoffigures viii
Listoftable xi
Preface xii
Acknowledgments xiv
1 Introduction 1
1.1 Motivationofresetcontrol 1
1.2 BasicconceptsofRCSs 10
1.2.1 Preliminariesandproblemsetup 10
1.2.2 SolutionstoRCSs 13
1.2.3 RCSswithdiscrete-timeresetconditions 15
1.3 Fundamentaltheoryoftraditionalresetdesign 17
1.3.1 Horowitz’sdesign 17
1.3.2 PI+CIresetdesign 22
Notes 24
References 24
2 Describingfunctionanalysisofresetsystems 27
2.1 Sinusoidinputresponse 27
2.2 Describingfunction 32
2.2.1 Generalcase 32
2.2.2 Gain-balancedFORE 38
2.3 ApplicationtoHDDsystems 41
2.3.1 Resetnarrowbandcompensator(RNBC) 41
2.3.2 Mid-frequencydisturbancecompensation 43
2.3.3 Simulationresults 46
Notes 48
References 48
3 Stabilityofresetcontrolsystems 51
3.1 Preliminaries 51
3.1.1 Annihilatorofmatrices 51
3.1.2 Passivesystems 52
3.2 Quadraticstability 57
3.3 StabilityofRCSswithtime-delay 63
vi Analysisanddesignofresetcontrolsystems
3.4 Resettimes-dependentstability 67
3.5 PassivityofRCSs 77
Notes 81
References 82
4 Robuststabilityofresetcontrolsystems 83
4.1 Definitionsandassumptions 83
4.2 Quadraticstability 86
4.2.1 RCSswithlow-dimensionalplants(n ≤2) 87
p
4.2.2 High-dimensionalcases 89
4.3 Affinequadraticstability 93
4.4 RobuststabilityofRCSwithtime-delay 96
4.5 Examples 106
Notes 112
References 112
5 RCSswithdiscrete-timeresetconditions 115
5.1 Preliminariesandproblemsetting 116
5.2 Stabilityanalysis 118
5.3 Aheuristicdesignmethod 122
5.4 Applicationtotrack-seekingcontrolofHDDsystems 125
5.4.1 Systemdescription 125
5.4.2 Baselinecontrollerdesign 126
5.4.3 Resetmode 127
5.4.4 Stabilityanalysis 127
5.4.5 Simulationresults 128
Notes 130
References 130
6 Resetcontrolsystemswithfixedresetinstants 133
6.1 Stabilityanalysis 133
6.1.1 Stabilityanalysisthroughinduceddiscretesystems 133
6.1.2 Lie-algebraiccondition 135
6.2 Movinghorizonoptimization 137
6.2.1 Trade-offbetweenstabilityandotherperformances 140
6.2.2 Observer-basedresetcontrol 141
6.3 Optimalresetlawdesign 142
6.3.1 EquivalencebetweenORLandLQR 144
6.3.2 SolutionstoORLproblems 147
6.4 ApplicationtoHDDsystems 149
6.4.1 DynamicsmodelofHDDsystems 149
6.4.2 Movinghorizonoptimalresetcontrol 150
6.4.3 Optimalresetcontrol 153
6.5 ApplicationtoPZT-positioningstage 160
6.5.1 ModelingofthePZT-positioningstage 160
Contents vii
6.5.2 Resetcontroldesign 161
6.5.3 Experimentalresults 162
Notes 166
References 167
7 Resetcontrolsystemswithconicjumpsets 169
7.1 Basicidea 169
7.2 L -gainanalysis 172
2
7.2.1 Passificationviareset 174
7.2.2 FiniteL gainstability 178
2
Notes 180
References 180
Index 183
List of figures
1.1 Linearfeedbackcontrolsystem 1
1.2 Thecurveoftheweightingfunctionlncoth(|v|/2) 2
1.3 Frequencydomainspecifications 3
1.4 OutputresponsesofLIandCItosinusoidalinpute=sint 4
1.5 BodeplotsofFOREandfirst-orderlinearelement 6
1.6 Theresetcontrolsystem(RCS)withaCI 7
1.7 CIequivalence 7
1.8 ReplacementoftheCIwithitsequivalence 7
1.9 Reducingovershootthroughreset 8
1.10 ResponsesoftheRCStounitrampandstepinputs,respectively 10
1.11 Twodifferenttriggeringconditions(a)zero-crossingtype;(b)sector
type 13
1.12 Deadlock 14
1.13 AnRCSwithtime-regularization 16
1.14 Discrete-time reset law defined by the triggering function given in
(1.44) 17
1.15 AFORERCS 18
1.16 AFOREequivalence 18
1.17 OvershootwithM=ω /basparameter 20
c
1.18 AFORERCSequivalence 21
1.19 PI+CIresetcontroller 22
2.1 GeneralRCS 28
2.2 OutputresponsesforExample2.1 31
2.3 Thespectrumofthepowerpercentageσ (R,ω) 38
k
2.4 ThephaseleadofGFOREinlargefrequencyrange:ϕ=ϕ(R,∞) 40
2.5 BodeplotofGFOREwithf =0.1(basedonDF) 41
r
2.6 BodeplotofGFOREwithR=−0.5(basedonDF) 42
2.7 BodediagramoftheNBCswithf =1×104anddifferentξ /ξ 42
1 1
Listoffigures ix
2.8 Resetnarrowbandcompensator 43
2.9 StructureofatypicalHDD 44
2.10 TheBodeplotsoftheplantandtheopenloopwiththePIcontroller 45
2.11 Mid-frequencydisturbancerejection 45
2.12 Responsestosinusoiddisturbanceat800Hz 46
2.13 Responsestosinusoiddisturbanceat800Hz(withinputdisturbance,
outputdisturbanceandwhitenoisesinserted) 47
3.1 NegativefeedbackinterconnectionofH andH 54
1 2
3.2 Resetcontrolsystem 57
3.3 PhasetrajectoryofanRCSwithanunstablebaselinesystem.(Left:
baselinesystem;right:resetsystem.) 59
3.4 TheNyquistplotsofH (s−ε)fordifferentβ 63
β
3.5 RCSwithtime-delay 64
3.6 Resetintervalfordifferentinitialstatefromthesetofafter-resetstates 75
3.7 MaxeigenvalueofeATtRPReAt−Pfordifferentr 76
3.8 Stateresponseforx(0)=[2 −1 6]T andr=−0.5 76
3.9 Aresetcontrolsystem 77
4.1 Responsesfortheuncertainty-freecase 108
4.2 Responsesforuncertaintyγ(t)=0.2sin(20t) 108
4.3 Responsesforconstantuncertaintyγ (r=−0.5) 109
4.4 Thecurvesofγ andγ overτ.(Foranygivenτ ∈[0,1.095],
l r
theRCSisrobustlystablerespecttotime-varyinguncertainty
γ(t)∈[γ(τ),γ (τ)]) 110
l r
4.5 Initialconditionresponsetox(0)=[−2 2]T 111
4.6 Inputu 111
p
5.1 AnRCSwithdiscrete-timetriggeringcondition 123
5.2 Stepresponsesforthebaselinesystem,resetmode,andtheRCSwith
R =0 124
r
5.3 StepresponsesoftheresetmodefordifferentR ∈[−1,1] 124
r
5.4 StepresponsesoftheRCSfordifferentR ∈[−1,0] 124
r
5.5 StepresponsesfordifferentR ((cid:9)=4.5T ) 128
r s
5.6 StepresponsesoftheresetmodefordifferentR 128
r
5.7 Stepresponsesfordifferent(cid:9)(R =0) 128
r
5.8 Comparisonbetweentraditionalandproposedresetcontrol 129
5.9 Controlinput 129