Robust Control and Linear Parameter Varying Approaches : Application to Vehicle Dynamics

399 Pages·2013·6.018 MB·English

by  Olivier Sename (eds.)

Lecture Notes
in Control and Information Sciences 437
Editors
ProfessorDr.-Ing.ManfredThoma
InstitutfuerRegelungstechnik,UniversitätHannover,Appelstr.11,30167Hannover,
Germany
E-mail:[email protected]
ProfessorDr.FrankAllgöwer
InstituteforSystemsTheoryandAutomaticControl,UniversityofStuttgart,
Pfaffenwaldring9,70550Stuttgart,Germany
E-mail:[email protected]
ProfessorDr.ManfredMorari
ETH/ETLI29,Physikstr.3,8092Zürich,Switzerland
E-mail:[email protected]
SeriesAdvisoryBoard
P.Fleming
UniversityofSheffield,UK
P.Kokotovic
UniversityofCalifornia,SantaBarbara,CA,USA
A.B.Kurzhanski
MoscowStateUniversity,Russia
H.Kwakernaak
UniversityofTwente,Enschede,TheNetherlands
A.Rantzer
LundInstituteofTechnology,Sweden
J.N.Tsitsiklis
MIT,Cambridge,MA,USA
Forfurthervolumes:
http://www.springer.com/series/642
Olivier Sename, Péter Gáspár,
and József Bokor (Eds.)
Robust Control and
Linear Parameter
Varying Approaches
Application to Vehicle Dynamics
ABC
Editors
Prof.OlivierSename Prof.JózsefBokor
GIPSA-lab ComputerandAutomation
UMRCNRS5216 ResearchInstitute
DepartmentofControlSystems HungarianAcademyofSciences
(DptAutomatique) Budapest
GrenobleINP/ENSE3 Hungary
SaintMartind’Hères
Cedex
Grenoble
Prof.PéterGáspár
ComputerandAutomation
ResearchInstitute
HungarianAcademyofSciences
Budapest
Hungary
ISSN0170-8643 e-ISSN1610-7411
ISBN978-3-642-36109-8 e-ISBN978-3-642-36110-4
DOI10.1007/978-3-642-36110-4
SpringerHeidelbergNewYorkDordrechtLondon
LibraryofCongressControlNumber:2012955946
(cid:2)c Springer-VerlagBerlinHeidelberg2013
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Preface
This book results from the 32th International Summer School in Automatic that
heldinGrenoble,France,September,12-16,2011.15speakershavemergedtogive
presentations, aboutLinear Parameter Varying methodsand vehicle control, to an
audience of more than 50 people (researchers and PhD students), from different
europeancontries(Italy,Hungary,Austria,CzechRepublicandFrance).Theobjec-
tiveofthisschoolwastoproviderecentmethods(basedonrobustcontrolandLPV
technics)tothecontrolofvehicledynamics(mainlyroadvehicles).
Indeed,duetotherapidlychangingtechniquesandtechnologiesforinformation
and communication,the last decade hasseen increasingimprovementsof the per-
formanceofactivesystemsforroadvehicles.Thenembeddedcontrolisbecoming
more prevalentin vehicles (intelligentelectric actuators, sensors, etc..). Neverthe-
less,thepossibilitiesofferedbynewapproachestoimprovethesafetyofpassengers
andpedestrians,arestilllargelyunderused.Furthermorethevehiclesystems(non-
linear,multi-variable)becomenowmorecomplexsystemswheretheabundanceof
onboardfunctionsshouldensurebettersecurity.
OntheotherhandLPVmethodswhosetheoreticaldevelopmentsinthecontext
ofrobustcontrolareveryrecent(lessthanadecade),andarestillthetopicofanin-
tensiveresearch,haveshowntheiradvantageinvariousapplications[1].Theyallow
theapplicationoflinearmethodstoperformrobustcontrolofnonlinearsystemsand
/ or time-varyingparameters. These methodsneed to understandsome theoretical
conceptsrelated to modeling,analysis, observationand control. It is then particu-
larly interesting to evaluate the potentialof methodssuch as LPV oneswithin the
frameworkofvehicledynamics.IndeedsuchatypeofLPVmethodscanhelpto:
• proposed control-orientedmodel, complex enough to handle some system non
linearitiesbutstillsimpleforcontrolorobserverdesign,
• takeintoaccounttheadaptabilityofthevehicle’sresponsetosituationsencoun-
tered(normal,critical,dangerous...)andundertheconditionsofoperations,
• incorporateamodelofactuatorswhoseparametersareadjustable,
• manageinteractionsbetweenvariousactuatorstooptimizethedynamicbehavior
ofvehicles.
VI Preface
Themainobjectiveofthebookistodemonstratethevalueofthisapproachforcon-
trolling the dynamic behavior of vehicles. After some theoreticalbackgroundand
aviewonsomerecentworksonLPVapproaches(formodelling,analysis,control,
observationanddiagnosis),themainemphasisisputonroadvehiclesbutsomeillus-
trationsareconcernedwithrailway,aerospaceandunderwatervehicles.Itpresents,
inafirmway,backgroundandnewresultsonLPVmethodsandtheirapplicationto
vehicledynamics.
Thecontentofthebookisasfollows,anditisdividedin3parts.
InthefirstpartsomebackgroundsonLPVsystemsarepresented.MarcoLovera
introducesfirsttheconceptofLPVsystemsinChapter1.JózsefBokorandZoltán
SzabóthenpresentsinChapter2someimportantfeaturesofthegeometricapproach
forLPVsystemsanalysis,andinChapter3,theyintroduceaspecificclassofLPV
systems,namelythebimodalswitchingsystems,wheretheswitchfromonemode
to the other one depends on the state (closed-loop switching). In Chapter 4, Di-
dierHenrionpresentssomerecentresultsonLPVsystemswithpositivepolynomial
matrices. Chapter 5, from Meriem Halimi, Gilles Millerioux and Jamal Daafouz,
isdedicatedtopolytopicobserversforLPVdiscrete-timesystems.Chapter6tack-
les the fault diagnosis issue, and David Henry introduces the Fault Detection and
IsolationLPVfilterswithsomeaerospaceapplication.
ThesecondpartconcernstheapplicationofLPVmethodstoroadvehicles.First
Anh-Lam Do, Charles Poussot-Vassal, Olivier Sename and Luc Dugard present
someLPVcontrolapproachesinviewofcomfortimprovementofautomotivesus-
pensionsequippedwithMRdampers.InChapter8PéterGáspárproposessomede-
sign methodsof integratedcontrol(of suspension,brakingand steering actuators)
forroadvehicles.InChapter9,acoordinatedcontrolofbraking/steeringactuators
throughLPVtechnicsisproposedbyCharlesPoussot-Vassal,OlivierSename,So-
heibFergani,MoustaphaDoumiatiandLucDugard.InChapter10,JohnJ.Martinez
andSébastienVarrierpresentsomenewresultsonMultisensorFault-TolerantAuto-
motiveControlintheLPVframework.InChapter11,sometheoryandapplication
tobrakingcontroloftheVirtualReferenceFeedbackTuningapproachforLPVsys-
tems,arepresentedbySimoneFormentin,GiulioPanzaniandSergioM.Savaresi.
This part is concludedby Péter Gáspár and Zoltán Szabó in Chapter 12, with the
designofahierarchicalLPVcontrollerofanactivesuspensionsystemforafull-car
vehicle.
Thethirdandfinalpartisanopeningtoothervehiclessuchasrailway,aerospace
andunderwaterapplications,forwhichtheLPVapproachescanbeveryattractive.
FirstPéterGáspárandZoltánSzabópresentinChapter13anobserver-basedbrake
controlforrailways.ThenJean-MarcBiannicgives,inChapter14,alargeoverview
of LPV control strategies for aerospace applications. Finally Chapter 15 by Em-
ilie Roche, Olivier Sename and Daniel Simon, concludes the book with the de-
sign of LPV controllerswith varyingsampling forthe altitudecontrolof an AUV
(AutonomousUnderwaterVehicle),wheredepthmeasurementsareasynchronously
suppliedbyacousticsensors.
Preface VII
Wealsowouldliketomentionthatthisbookisalsopartoftheresultsofthe3-
yearsbilateralcollaborationprojectbetweentheCNRSandtheHungarianAcademy
ofSciences:RobustandfaulttolerantmultivariablecontrolforAutomotiveVehicle.
Wewouldliketothankallthecontributorsforprovidingveryniceandhighlevel
chaptersinthisbook.
Wehopethatthisbookwillinterestvariousresearchersandgraduatestudentsin
controlofvehicledynamicsaswallasinrobustcontrolandLPVsystems.
Reference
1. Mohammadpour, C.S. (ed.): Control of Linear Parameter Varying Systems with
Applications.Springer,Heidelberg(2012)
Grenoble(France), OlivierSename
August2012 PéterGáspár
JózsefBokor
Acknowledgements
TheEditorswouldliketothankthelocalorganizationoftheSummerSchool,which
have allowed the school to be a success in particular to Dr. Alexandre Seuret (on
leavefromCNRS,GIPSA-Lab,Grenoble,France).
Contents
PartI SomeBackgroundonLPVSystems(Modeling,IdentificationControl,
Observation)
1 LPVModellingandIdentification:AnOverview ................. 3
MarcoLovera,MarcoBergamasco,FrancescoCasella
1.1 Introduction.............................................. 3
1.2 Continuous-andDiscrete-TimeLPVModels .................. 5
1.3 AnalyticalLPVModelling.................................. 7
1.3.1 JacobianLinearisation ............................. 7
1.3.2 StateTransformation............................... 7
1.3.3 FunctionSubstitution .............................. 8
1.4 ExperimentalLPVModelling............................... 8
1.4.1 LocalMethods.................................... 9
1.4.2 GlobalMethods................................... 12
1.4.3 GlocalMethods................................... 14
1.5 ACaseStudy............................................. 15
1.5.1 ProcessDescriptionandSimulation .................. 15
1.5.2 NonlinearMathematicalModel...................... 16
1.5.3 AnalyticalLPVModelling.......................... 17
1.5.4 ExperimentalLPVModelling ....................... 18
1.5.5 ComparisonofResults ............................. 19
1.6 Conclusions.............................................. 20
References..................................................... 20
2 SystemAnalysis:AGeometricApproach........................ 25
JózsefBokor,ZoltánSzabó
2.1 Introduction.............................................. 25
2.2 Parameter-VaryingInvariantSubspaces....................... 31
2.2.1 ControlledInvariance .............................. 33
2.2.2 ConditionedInvariance............................. 35
XII Contents
2.2.3 Parameter-VaryingInvariantSubspaceAlgorithms...... 36
2.3 Applications ............................................. 38
2.3.1 InversionofLPVSystems .......................... 38
2.3.2 Fundamental Problem of Residual
Generation(FPRG)................................ 48
2.4 Conclusions.............................................. 52
References..................................................... 52
3 BimodalandLinearSwitchedSystems.......................... 55
JózsefBokor,ZoltánSzabó
3.1 Introduction.............................................. 55
3.2 LinearSwitchedSystems................................... 57
3.2.1 FiniteNumberofSwitchings,Sampling............... 61
3.3 LinearSwitchedSystemswithSignConstrainedInputs ......... 67
3.3.1 ControllabilityAnalysis ............................ 68
3.4 StabilizabilityofCompletelyControllableLinearSwitched
Systems ................................................. 69
3.4.1 Stabilizability by Generalized Piecewise Linear
Feedback ........................................ 70
3.5 BimodalSystems ......................................... 75
3.5.1 TheControllabilityResult .......................... 78
3.5.2 StabilizabilityofBimodalSystems................... 81
3.6 Conclusions.............................................. 81
References..................................................... 82
4 PositivePolynomialMatricesforLPVControllerSynthesis ........ 87
DidierHenrion
4.1 Introduction.............................................. 87
4.2 StabilityofPolynomialMatrices............................. 88
4.3 Fixed-OrderRobustControllerDesign........................ 91
4.3.1 H∞Performance .................................. 91
4.3.2 H Performance................................... 92
2
4.3.3 Robustness....................................... 92
4.4 LPVControllerDesign .................................... 93
4.4.1 AHierarchyofLMIProblems....................... 93
4.4.2 Parameter-DependentLyapunovFunctions ............ 94
4.5 Conclusion............................................... 95
References..................................................... 95
5 PolytopicObserversforLPVDiscrete-TimeSystems.............. 97
MeriemHalimi,GillesMillerioux,JamalDaafouz
5.1 Introduction.............................................. 97
5.2 Preliminaries............................................. 99
5.3 LPVModels ............................................. 99
5.3.1 MinimalPolytope .................................101
5.3.2 OnLinePolytopicDecomposition ...................102