Systems with hysteresis: analysis, identification and control using the Bouc-Wen model

223 Pages·2007·1.693 MB·English

by  Fayçal Ikhouane, José Rodellar

Systems with Hysteresis

Systems with Hysteresis
Analysis, Identification and Control using
the Bouc–Wen Model
Fayçal Ikhouane
Department of Applied Mathematics III
School of Technical Industrial Engineering
Technical University of Catalunya
Barcelona, Spain
José Rodellar
Department of Applied Mathematics III
School of Civil Engineering
Technical University of Catalunya
Barcelona, Spain
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Ikhouane,Fayçal.
Systemswithhysteresis:analysis,identificationandcontrolusingtheBouc-Wen
model/FayçalIkhouane,JoséRodellar.
p. cm.
Includesbibliographicalreferencesandindex.
ISBN978-0-470-03236-7(cloth)
1. Hysteresis—Mathematicalmodels. I. Rodellar,José. II. Title.
QC754.2.H9I342007
621—dc22
2007019894
BritishLibraryCataloguinginPublicationData
AcataloguerecordforthisbookisavailablefromtheBritishLibrary
ISBN-13978-0-470-03236-7
Typesetin11/13ptSabonbyIntegraSoftwareServicesPvt.Ltd,Pondicherry,India
PrintedandboundinGreatBritainbyTJInternational,Padstow,Cornwall
Thisbookisprintedonacid-freepaperresponsiblymanufacturedfromsustainableforestry
inwhichatleasttwotreesareplantedforeachoneusedforpaperproduction.
To my mother and brothers, Imad and Hicham F. Ikhouane
To Anna, Laura and Silvia J. Rodellar

Contents
Preface xi
List of Figures xv
List of Tables xix
1 Introduction 1
1.1 Objective and Contents of the Book 1
1.2 The Bouc–Wen Model: Origin and Literature Review 5
2 Physical Consistency of the Bouc–Wen Model 13
2.1 Introduction 13
2.2 BIBO Stability of the Bouc–Wen Model 16
2.2.1 The Model 16
2.2.2 Problem Statement 16
2.2.3 Classification of the BIBO-Stable Bouc–Wen
Models 17
2.2.4 Practical Remarks 23
2.3 Free Motion of a Hysteretic Structural System 24
2.3.1 Problem Statement 24
2.3.2 Asymptotic Trajectories 25
2.3.3 Practical Remarks 31
2.4 Passivity of the Bouc–Wen model 32
2.5 Limit Cases 33
2.5.1 The Limit Case n=1 33
2.5.2 The Limit Case (cid:2)=1 34
2.5.3 The Limit Case (cid:2)=0 34
2.5.4 The Limit Case (cid:3)+(cid:4)=0 34
2.6 Conclusion 34
viii CONTENTS
3 Forced Limit Cycle Characterization of the Bouc–Wen
Model 37
3.1 Introduction 37
3.2 Problem Statement 38
3.2.1 The Class of Inputs 38
3.2.2 Problem Statement 39
3.3 The Normalized Bouc–Wen Model 39
3.4 Instrumental Functions 42
3.5 Characterization of the Asymptotic Behaviour of the
Hysteretic Output 46
3.5.1 Technical Lemmas 49
3.5.2 Analytic Description of the Forced Limit
Cycles for the Bouc–Wen Model 56
3.6 Simulation Example 59
3.7 Conclusion 61
4 Variation of the Hysteresis Loop with the Bouc–Wen
Model Parameters 63
4.1 Introduction 63
4.2 Background Results and Methodology of the
Analysis 64
4.2.1 Background Results 64
4.2.2 Methodology of the Analysis 67
4.3 Maximal Value of the Hysteretic Output 69
4.3.1 Variation with Respect to (cid:5) 69
4.3.2 Variation with Respect to (cid:6) 71
4.3.3 Variation with Respect to n 74
4.3.4 Summary of the Obtained Results 77
4.4 Variation of the Zero of the Hysteretic Output 79
4.4.1 Variation with Respect to (cid:5) 79
4.4.2 Variation with Respect to (cid:6) 81
4.4.3 Variation with Respect to n 82
4.4.4 Summary of the Obtained Results 84
4.5 Variation of the Hysteretic Output with the
Bouc–Wen Model Parameters 85
4.5.1 Variation with Respect to (cid:5) 87
4.5.2 Variation with Respect to (cid:6) 89
4.5.3 Variation with Respect to n 94
4.5.4 Summary of the Obtained Results 94
4.6 The Four Regions of the Bouc–Wen Model 96
4.6.1 The Linear Region R 97
l
CONTENTS ix
4.6.2 The Plastic Region R 105
p
4.6.3 The Transition Regions R and R 107
t s
4.7 Interpretation of the Normalized Bouc–Wen
Model Parameters 107
4.7.1 The Parameters (cid:7) and (cid:5) 107
4.7.2 The Parameter (cid:6) 109
4.7.3 The Parameter n 110
4.8 Conclusion 110
5 Robust Identification of the Bouc–Wen Model Parameters 113
5.1 Introduction 113
5.2 Parameter Identification of the Bouc–Wen
Model 115
5.2.1 Class of Inputs 115
5.2.2 Identification Methodology 116
5.2.3 Robustness of the Identification Method 119
5.2.4 Numerical Simulation Example 137
5.3 Modelling and Identification of a
Magnetorheological Damper 142
5.3.1 Some Insights into the Viscous +
Bouc–Wen Model for Shear Mode MR
Dampers 142
5.3.2 Alternatives to the Viscous + Bouc–Wen
Model for Shear Mode MR Dampers 147
5.3.3 Identification Methodology for the
Viscous + Dahl Model 154
5.3.4 Numerical Simulations 156
5.4 Conclusion 164
6 Control of a System with a Bouc–Wen Hysteresis 165
6.1 Introduction and Problem Statement 165
6.2 Control Design and Stability Analysis 167
6.3 Numerical Simulation 175
6.4 Conclusion 177
Appendix Mathematical Background 179
A.1 Existence and Uniqueness of Solutions 179
A.2 Concepts of Stability 181
A.3 Passivity and Absolute Stability 182
A.3.1 Passivity in Mechanical Systems 182
A.3.2 Positive Realness 184