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Multi-objective H_1tn∞-GH_1tn2 preview control of active vehicle suspensions [Elektronische Ressource] / Ahmad Akbari Alvanagh

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¨ ¨TECHNISCHE UNIVERSITAT MUNCHENLehrstuhl fur¨ RegelungstechnikMulti-objective H /GH preview control of∞ 2active vehicle suspensionsAhmad Akbari AlvanaghVollst¨ andiger Abdruck der von der Fakult¨ at fur¨ Maschinenwesender Technischen Universit¨ at Munc¨ hen zur Erlangung des akademischen Grades einesDoktor-Ingenieursgenehmigten Dissertation.Vorsitzender: Univ.-Prof. Dr.-Ing. Bernd HeißingPrufer¨ der Dissertation:1. Univ.-Prof. Dr.-Ing. habil. Boris Lohmann2. Univ.-Prof. Dr.-Ing. habil. Ansgar Trac¨ htler,Universit¨ at PaderbornDie Dissertation wurde am 18.11.2008 bei der Technischen Universit¨ at Munc¨ heneingereicht und durch die Fakult¨ at fur¨ Maschinenwesen am 16.02.2009 angenommen.Multi-objective H /GH preview control of∞ 2active vehicle suspensionsAhmad Akbari AlvanaghThis work concerns with multi-objective H /GH control of preview-based active∞ 2vehicle suspensions. This control scheme has two main features:1. It allows the constrained outputs of the system, namely, suspension workingspace, to vary freely as long as they remain within their given bounds, in orderthat the best possible performance could be delivered.2. The optimization as well as constraint fulfillment is done for the worst case roaddisturbances in order that the designed system perform satisfactorily for a widerange of road irregularities. The H norm of (sub)system is minimized wherever∞minimization is required.

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Published 01 January 2009
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¨ ¨TECHNISCHE UNIVERSITAT MUNCHEN
Lehrstuhl fur¨ Regelungstechnik
Multi-objective H /GH preview control of∞ 2
active vehicle suspensions
Ahmad Akbari Alvanagh
Vollst¨ andiger Abdruck der von der Fakult¨ at fur¨ Maschinenwesen
der Technischen Universit¨ at Munc¨ hen zur Erlangung des akademischen Grades eines
Doktor-Ingenieurs
genehmigten Dissertation.
Vorsitzender: Univ.-Prof. Dr.-Ing. Bernd Heißing
Prufer¨ der Dissertation:
1. Univ.-Prof. Dr.-Ing. habil. Boris Lohmann
2. Univ.-Prof. Dr.-Ing. habil. Ansgar Trac¨ htler,
Universit¨ at Paderborn
Die Dissertation wurde am 18.11.2008 bei der Technischen Universit¨ at Munc¨ hen
eingereicht und durch die Fakult¨ at fur¨ Maschinenwesen am 16.02.2009 angenommen.Multi-objective H /GH preview control of∞ 2
active vehicle suspensions
Ahmad Akbari Alvanagh
This work concerns with multi-objective H /GH control of preview-based active∞ 2
vehicle suspensions. This control scheme has two main features:
1. It allows the constrained outputs of the system, namely, suspension working
space, to vary freely as long as they remain within their given bounds, in order
that the best possible performance could be delivered.
2. The optimization as well as constraint fulfillment is done for the worst case road
disturbances in order that the designed system perform satisfactorily for a wide
range of road irregularities. The H norm of (sub)system is minimized wherever∞
minimization is required. Also, for the constrained outputs, the GH -norm2
measure is used to fulfill system constraints for the worst case disturbances.
Moreover, it allows for considering pole location constraints to guarantee sufficient
stability margins for the system.
Output feedback nature of the design here makes it more convenient for practical
implementation.
The proposed approach is first evaluated numerically on a quarter car model and
compared to the state-of-the-art preview control algorithm in the literature, namely,
LQG-preview, and finally it is verified experimentally.ACKNOWLEDGMENTS
Firstly I wish to thank gratefully and sincerely my supervisor, Prof. Boris Lohmann
for his guidance, understanding, patience, and most importantly, his friendship during
my graduate studies. I have been amazingly fortunate to have a supervisor who gave
me the freedom to develop on my own, and at the same time the guidance to recover
when my steps faltered and helped me enrich my ideas.
I am grateful to all members of the institute of automatic control who accepted me
with open arms and provided support in many different ways. They provided me with
one of the most comfortable working places and friendly working atmosphere I have
ever had.
Particularly, I wish to extend my warmest thanks to Guido Koch, Sebastian Spirk
and Enrico Pellegrini, who built up and prepared the test-rig for the experimental
verification of this work.
Also, I owe my gratitude to all other friends in a wider community in Munich who
have made my life there both fruitful and enjoyable.
Most importantly, this wouldn’t have been possible without the love and patience of
my family. My family to whom this dissertation is dedicated, has been a constant
source of love, concern, support and strength all these years. I would like to express
my heart-felt gratitude to my family.
Ahmad Akbari Munich, October 2008TABLE OF CONTENTS
List of Figures vi
List of Tables x
I Preliminaries 1
Chapter 1: Introduction and Motivation 2
1.1 Suspensionstrategies ...... ........... .......... 3
1.1.1 Passivesuspensions ... 4
1.1.2 Semi-activesuspensions ........... .......... 5
1.1.3 Activesuspensions ... 9
1.2 Previewbasedactivesuspensions .......... .......... 12
1.3 Synopsis . . ........... ........... 15
Chapter 2: Design requirements 18
2.1 Systemdescription ....... ........... .......... 18
i2.1.1 Quartercarmodel ... ........... .......... 19
2.1.2 Halfcarmodel ..... 22
2.2 Designrequirementsandproblemformulation ... .......... 25
2.2.1 Performanceevaluationcriteria ....... 26
2.2.2 Suitabledesignframework .......... .......... 28
2.2.3 Systemnorms ...... ........... 29
2.2.4 Problemformulation . . .......... 31
2.2.5 Extensiontomoreprecisemodels ...... 32
2.3 Roaddisturbances ....... ........... .......... 33
2.3.1 Shock(singlebump) .. 33
2.3.2 Vibration ........ ........... .......... 34
II Potential Assessment 36
Chapter 3: Design scheme & look-ahead preview design 37
3.1 Whypreviewcontrol ...... ........... .......... 37
3.2 AbriefhistoryonPreviewcontrol.......... 39
3.3 Objective . ........... ........... .......... 41
ii3.4 Theunifieddesignframework . ........... .......... 42
3.4.1 Whydiscretetimeapproach? ........ 45
3.4.2 Augmentedplantdescription......... .......... 46
3.5 LQ-baseddesign ........ ........... 49
3.5.1 Discretization of performance index and covariance matrices . 50
3.5.2 LQRpreviewdesignscheme ......... .......... 52
3.5.3 KalmanFilteringwithpreview ....... 55
3.5.4 Applicationtotheproblem.......... .......... 56
3.6 Multi-objectivepreviewcontrol ........... 60
3.6.1 applicationtotheproblem.......... .......... 65
3.7 ComparisontoLQ-baseddesign ........... 70
3.7.1 Forvariousroaddisturbances ........ .......... 70
3.7.2 Robustness against parameter changes . . . 71
3.7.3 Concludingremarks... ........... .......... 72
3.8 Amulti-objectivedesignwithimprovedridesafety. 73
3.8.1 Systemperformanceatotherspeeds..... .......... 75
3.9 Inclusionofactuatordynamics. ........... 76
iiiChapter 4: A perspective on wheelbase preview design 78
4.1 Wheelbasepreview ....... ........... .......... 78
4.2 Controllerdesignscheme .... 80
4.3 Detectionoffrontwheeldisturbance ........ .......... 81
4.3.1 Estimatordesignscheme ........... 82
4.3.2 Applicationtotheproblem.......... .......... 87
4.3.3 SimulationResults ... ........... 88
4.3.4 Summary ........ .......... 90
III Experimental verification 92
Chapter 5: Experimental setup description and preview suspension
design 93
5.1 Descriptionofthetestrig ... ........... .......... 93
5.1.1 Linearmodel ...... 93
5.1.2 Nonlinearmodel .... ........... .......... 94
5.1.3 Actuatordynamics ... 95
5.2 Previewsuspensiondesign ... ........... .......... 97
5.3 Simulationresults........ 101
iv5.3.1 Comparisontopurefeedback ........ .......... 101
5.3.2 ComparisontoLQ-basedpreviewsuspension 103
Chapter 6: Implementation and related challenges 106
6.1 AnintroductiontodSPACEreal-timeenvironment .......... 106
6.2 Previewsignal.......... ........... 107
6.3 Handlingthedynamicsofbottomactuator ..... .......... 108
6.4 Handling the influence of top actuator on imitated road irregularities 111
6.5 Previewcontrolapplicationandresults ....... .......... 113
Chapter 7: Conclusion and Outlook 115
Glossary 118
Bibliography 121
vLIST OF FIGURES
1.1 Two most common front suspension types. Left: Control arm type,
Right: (McPherson) strut type. Figure from www.midas.com .... 3
1.2 Ride comfort vs. safety for different values of the suspension elements 5
1.3 Damper characteristics, left:passive suspension, right:semi-active sus-
pension; σ := z − z ...... ........... .......... 6s u
1.4 workingprincipleofMRdamper,figurefrom[36] . 8
1.5 Bosesuspensionsystem..... ........... .......... 11
1.6 ActiveBodyControl ...... 12
1.7 DisturbancedetectionschemeofABC-Prescan[49]. .......... 16
2.1 Aquarter-caractivesuspensionsystem ....... 19
2.2 Atypicalhalfcarmodelwithactivesuspension . . .......... 23
2.3 A real road profile; left: time history (ground vertical displacement),
right: power spectral density corresponding to ground vertical velocity 35
3.1 Feedforwardcontroldesignscheme ......... .......... 38
vi3.2 left: preview suspension concept, right: corresponding design framework 43
3.3 Picture of a laser sensor from SICK corporation, employed by ABC-
Prescan[49]............ ........... .......... 44
3.4 P-Kformulationofthediscretizedsystem ..... 48
3.5 Coefficientsofpreviewsignalsofdifferenttimesaheadofwheel.... 54
3.6 Frequency Response of the LQ-based design: Preview (–), Pure feed-
back(-.),Passive(..) ...... ........... .......... 58
3.7 Frequency Response of the Multi-objective design: Preview (–), Pure
feedback(-.),Passive(..) .... ........... .......... 67
3.8 Real road response of the Multi-objective design: Preview (–), Pure
feedback(-.),Passive(..) .... ........... .......... 68
3.9 relative RMS weighted acceleration: multi-objective preview(–), LQ-
basedpreview(-.) ........ ........... .......... 72
3.10 Frequency Response of the Multi-objective design with improved safety:
Preview(–),Purefeedback(-.),Passive(..)..... .......... 74
3.11 Componentsofperformanceindexforvaryingvehiclespeeds ..... 75
4.1 Wheelbasepreviewdesignframework ........ .......... 80
4.2 Estimatordesignframework . . ........... 82
4.3 Desiredpolelocation ...... .......... 85
vii