Integral Sliding Mode Fault Tolerant Control Schemes with Control Allocation

224 Pages·2013·2.73 MB·English

Integral Sliding Mode Fault Tolerant Control Schemes with
Control Allocation
Thesis submitted for the degree of
Doctor of Philosophy
at the University of Leicester
by
Mirza Tariq Hamayun
B.Sc, M.Sc Electrical and Electronic Engineering
Department of Engineering
Control and Instrumentation Research Group
University of Leicester
June21,2013
Abstract
Integral Sliding Mode Fault Tolerant Control Schemes with
Control Allocation
MirzaTariqHamayun
ThekeyattributeofaFaultTolerantControl(FTC)systemistomaintainoverallsystemstability
and acceptable performance in the face of faults and failures within the system. In this thesis
new integral sliding mode (ISM) control allocation schemes for FTC are proposed, which have
the potential to maintain the nominal fault free performance for the entire system response, in
the face of actuator faults and even complete failures of certain actuators. The incorporation of
ISM within a control allocation framework uses the measured or estimated values of the actua-
toreffectivenesslevelsto redistributethecontroleffort amongthehealthyactuatorsto maintain
closed-loop stability. This combination allows one controller to be used in both fault free as
well as in fault or failure situations. A fault tolerant control allocation scheme which relies on
an a posteriapproach, buildingon an existingstatefeedback controllerdesignedusingonly the
primaryactuators,isalsoproposed. Retro-fittingofanISMschemetoanexistingfeedbackcon-
trollerisadvantageousfroman industrialperspective,becausefaulttolerancecanbeintroduced
withoutchangingtheexistingcontrolloops. Todealwithawiderrangeofoperatingconditions,
thefault tolerantfeatures ofISM arealsoextendedto linearparametervaryingsystems. A FTC
scheme considering only the availability of measured system outputs is also proposed, where
now the feedback controller design is based on the estimated states. In each of the ISM fault
tolerant schemes proposed, a rigorous closed-loop analysis is carried out to ensure the stability
oftheslidingmotioninthefaceoffaultsorfailures.. Ahighfidelitybenchmarkmodelofalarge
transportaircraft is usedto demonstratetheefficacy ofthenewFTC schemes.
Acknowledgments
First of all I want to thank to almighty ALLAH, who is the most merciful, the compassionate,
whogavemeabilityand strengthfortheaccomplishmentofthisresearch work;
special thanks to my respected supervisor, Professor Christopher Edwards who always helped
mein allthephases ofmy learningand research;
specialgratitudeto myrespected parents fortheirsupportand love;
thankstoCOMSATSInstituteofinformationTechnologyPakistanforawardingmescholarship
formyPhD study;
thankstoDrHalimAlwiforhelpingmeinsomeresearch issues;
specialthankstomylovingwifeAttiyaTariqand mykidsMehreenTariqand AbdurRafe, who
alwayspushmeup morally;
Mirza Tariq Hamayun
June 21, 2013
i
Nomenclature and Abbreviations
Nomenclature
a ,b ,g angleofattack, sideslipandflight pathangle(rad)
B†,W weightedrightpseudoinverseofB
B‡ left pseudoinverseofB
C field ofcomplexnumbers
R field ofreal numbers
R(B) rangespaceofinputmatrixB
subset
⊂
G Slidingmodematrix
s linearswitchingfunction
S slidingsurface
. Euclideannormforvectors orinduced spectral normformatrices
k k
r nonlinearmodulationgain
n virtualcontrolinput
p,q,r rollrate, pitchrate andyaw rate(deg/sec)
s Laplacevariable
V trueairspeed (m/sec)
tas
W allowablesetoffault orfailure
W actuatoreffectivenessmatrix
f ,q ,y rollangle, pitchangleandyaw angle(rad)
h ,x ,y geometricearth positionwithrespect to thez (altitude),xand y axis(m)
e e e
l ,l (.) minimumand maximumeigenvalues
min(.) max
ii
Abbreviations
AFTC ActiveFault TolerantControl
air,aor,ail,aol aileroninner, outerrightand aileroninner, outerleft
BRL Bounded Real Lemma
CA ControlAllocation
CG Centreofgravity
DI DynamicInversion
DOF DegreeofFreedom
EPR EnginePressureRatio
FDI FaultDetectionand Isolation
FPA FlightPathAngle
FTC FaultTolerant Control
FTLAB FlightLab
GARTEUR GroupforAeronautical Research and TechnologyinEurope
GS GainScheduling
G(s) Transferfunction
ISM IntegralSlidingModes
ISMC IntegralSlidingModeControl
IMM InteractingMultipleModel
LMI LinearMatrixInequallity
LPV LinearParameterVarying
LQR LinearQuadraticRegulator
LTI LinearTimeInvariant
MMST MultipleModelSwitchingand Tuning
MPC ModelPredictiveControl
MRAC ModelReference AdaptiveControl
PFTC PassiveFaultTolerant Control
PIM Pseudo InverseMethod
SMC SlidingModeContol
s.p.d SymmetricPositiveDefinite
sp spoiler
STC SelfTuningControl
UIO UnknownInputObserver
VSC VariableStructureControl
VSCS VariableStructureControlSystems
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Contents
Acknowledgments i
NomenclatureandAbbreviations ii
1 Introduction 1
1.1 Motivationand Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Organizationand Contributionofthethesis . . . . . . . . . . . . . . . . . . . 4
2 FaultTolerantControl 8
2.1 Fault andFailureand theirClassification . . . . . . . . . . . . . . . . . . . . . 8
2.1.1 Modelingfaultsand failures . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 IntroductiontoFaultTolerant ControlSystems . . . . . . . . . . . . . . . . . 14
2.3 IntroductiontoFaultDetection andIsolation(FDI) . . . . . . . . . . . . . . . 16
2.4 Fault TolerantControlMethods . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.4.1 PassiveFault TolerantControl Systems . . . . . . . . . . . . . . . . . 20
2.4.1.1 RobustControl . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.4.2 ActiveFaultTolerantControl Systems . . . . . . . . . . . . . . . . . . 21
2.4.2.1 Adaptation . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4.2.2 ControlAllocation . . . . . . . . . . . . . . . . . . . . . . . 24
2.4.2.3 SlidingModeControl . . . . . . . . . . . . . . . . . . . . . 26
2.4.2.4 ControlSignal Redistribution . . . . . . . . . . . . . . . . . 27
2.4.2.5 MultipleModel . . . . . . . . . . . . . . . . . . . . . . . . 30
2.4.2.6 Scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.4.2.7 Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3 Integral Sliding Mode Control 35
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.2 Problem statementandequivalentcontrol . . . . . . . . . . . . . . . . . . . . 37
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3.2.1 SlidingModeControl Laws . . . . . . . . . . . . . . . . . . . . . . . 39
3.3 Reachability Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.4 A simplesimulationexample . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.4.1 Spring MassDamperSystem . . . . . . . . . . . . . . . . . . . . . . . 42
3.4.2 SimulationobjectiveandSMC design . . . . . . . . . . . . . . . . . . 44
3.4.3 SimulationResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.5 Practical SlidingModeControllaw . . . . . . . . . . . . . . . . . . . . . . . 47
3.6 Properties oftheSlidingMode . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.7 Integral SlidingModeControl(ISMC) . . . . . . . . . . . . . . . . . . . . . . 50
3.7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.7.2 Problem Statementand ISM Controllerdesign . . . . . . . . . . . . . 52
3.7.3 DesignPrinciples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.7.4 IntegralSwitchingSurface . . . . . . . . . . . . . . . . . . . . . . . . 55
3.7.5 IntegralSlidingModeControlLaws . . . . . . . . . . . . . . . . . . 57
3.7.6 TheReachabilityCondition . . . . . . . . . . . . . . . . . . . . . . . 57
3.7.7 Properties ofIntegralSlidingMode . . . . . . . . . . . . . . . . . . . 59
3.7.8 SimulationExample . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.8 OutputIntegralSlidingModeControl . . . . . . . . . . . . . . . . . . . . . . 62
3.9 SlidingModesas acandidateforFTC . . . . . . . . . . . . . . . . . . . . . . 66
3.10 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4 DesignandAnalysisofanIntegral Sliding Mode FaultTolerantControl Scheme 69
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.2 System descriptionand problemformulation . . . . . . . . . . . . . . . . . . . 71
4.3 Integral SlidingModeControllerDesign . . . . . . . . . . . . . . . . . . . . . 76
4.3.1 Integral-typeswitchingsurface design . . . . . . . . . . . . . . . . . . 77
4.3.2 Closed-loopStabilityAnalysis . . . . . . . . . . . . . . . . . . . . . . 80
4.3.3 IntegralSlidingModecontrollaws . . . . . . . . . . . . . . . . . . . . 82
4.3.4 DesignoftheControllerGains . . . . . . . . . . . . . . . . . . . . . . 84
4.4 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.4.1 Slidingmodefault reconstructionscheme . . . . . . . . . . . . . . . . 89
4.4.2 Manoeuvreand faultscenarios . . . . . . . . . . . . . . . . . . . . . . 90
4.4.2.1 Aileronfaultsand Lock inplacefailure . . . . . . . . . . . . 91
4.4.2.2 RudderLockin placefailure . . . . . . . . . . . . . . . . . 94
4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
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5 ApplicationofanIntegral Sliding ModeFTC fora LargeTransport Aircraft 97
5.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.2 Integral slidingmodeFTC Design . . . . . . . . . . . . . . . . . . . . . . . . 98
5.2.1 Designprocedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.2.2 FTLAB747 v6.5/v7.1Software and DesignObjectives . . . . . . . . . 102
5.2.3 LongitudinalControllerDesign . . . . . . . . . . . . . . . . . . . . . 102
5.2.4 Lateral ControllerDesign . . . . . . . . . . . . . . . . . . . . . . . . 104
5.3 Non-linearFTCSimulationsResults . . . . . . . . . . . . . . . . . . . . . . . 105
5.3.1 FaultFree Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.3.2 ElevatorLockin placefailure . . . . . . . . . . . . . . . . . . . . . . 105
5.3.3 HorizontalstabilizerHardover/runawayfailure . . . . . . . . . . . . . 106
5.3.4 AileronLock inplace failure . . . . . . . . . . . . . . . . . . . . . . . 106
5.3.5 RudderHardover/runawayfailure . . . . . . . . . . . . . . . . . . . . 106
5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6 AnAugmentation Scheme forFaultTolerant Control usingIntegral Sliding Modes114
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
6.2 System descriptionand problemformulation . . . . . . . . . . . . . . . . . . . 116
6.3 Integral SlidingModeControllerDesign . . . . . . . . . . . . . . . . . . . . . 120
6.3.1 StabilityAnalysisoftheClosed-loopSlidingmotion . . . . . . . . . . 122
6.3.2 IntegralSlidingModecontrollaws . . . . . . . . . . . . . . . . . . . . 125
6.4 Simulations: yawdampingofalargetransportaircraft . . . . . . . . . . . . . 127
6.4.1 FaultTolerant ControlLaw forYawDamping . . . . . . . . . . . . . . 128
6.5 Baselinecontrol lawforyawdamping . . . . . . . . . . . . . . . . . . . . . . 129
6.6 NonlinearSimulationResultsforYaw Damper . . . . . . . . . . . . . . . . . 130
6.6.1 Case 1: FaultFree Case WithPerfect EstimationofW(t) . . . . . . . . 130
6.6.2 Case 2: FaultFree Case WithImperfect EstimationofW(t) . . . . . . . 131
6.6.3 Case 3: Primary FailureWithImperfect EstimationofW(t) . . . . . . . 131
6.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
7 Linear ParameterVarying FTC Scheme using Integral Sliding Modes 136
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
7.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
7.3 Integral slidingmodecontrollerdesign . . . . . . . . . . . . . . . . . . . . . . 140
7.3.1 DesignofIntegralswitchingfunction: . . . . . . . . . . . . . . . . . . 140
7.3.2 Closed-loopstabilityanalysis: . . . . . . . . . . . . . . . . . . . . . . 143
7.3.3 ISM Control Laws: . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
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7.3.4 Designofthestatefeedback gain . . . . . . . . . . . . . . . . . . . . 145
7.4 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
7.4.1 LPV modelofatransportaircraft . . . . . . . . . . . . . . . . . . . . 147
7.4.2 Control designobjectives . . . . . . . . . . . . . . . . . . . . . . . . . 148
7.4.3 SimulationResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
7.4.3.1 Faultfree scenario . . . . . . . . . . . . . . . . . . . . . . . 151
7.4.3.2 ElevatorLock inplace/jamfailure . . . . . . . . . . . . . . 151
7.4.3.3 Elevatorfloat failure . . . . . . . . . . . . . . . . . . . . . . 152
7.4.3.4 HorizontalStabilizerLock inplace/jam failure . . . . . . . . 152
7.4.3.5 HorizontalStabilizerhardover/runawayfailure . . . . . . . . 152
7.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
8 AnOutput Integral Sliding Mode FTC Scheme Using Control Allocation 159
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
8.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
8.3 ISM ControllerDesign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
8.3.1 Closed-loopStabilityAnalysis . . . . . . . . . . . . . . . . . . . . . . 168
8.3.2 LMISynthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
8.3.3 ISM Control Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
8.4 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
8.4.1 SimulationResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
8.4.1.1 NominalVs perturbedsystemmatrix . . . . . . . . . . . . . 177
8.4.1.2 ElevatorLock inplace/jamfailure . . . . . . . . . . . . . . 177
8.4.1.3 HorizontalstabilizerHardover/runawayfailure . . . . . . . . 178
8.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
9 Conclusions andFuture work 183
9.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
9.2 FutureWork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
ListofPublications 185
A Benchmark model ofLarge TransportAircraft 188
A.1 Benchmark modelFTLAB747v6.5/v7.1Release2.2 . . . . . . . . . . . . . . 188
B Closedloopstabilityandsynthesis offeedback gain 193
B.1 L gainandsmallgaintheorem . . . . . . . . . . . . . . . . . . . . . . . . . 193
2
B.1.1 L gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
2
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B.1.2 Small gaintheorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
B.2 MatlabLMImulti-modelstatefeedback synthesis . . . . . . . . . . . . . . . . 194
B.3 LMIequivalenceofclosed-loopstabilityanalysis . . . . . . . . . . . . . . . . 195
B.3.1 LMIFormulationofLQR . . . . . . . . . . . . . . . . . . . . . . . . 196
B.3.2 LMIFormulationofBRL . . . . . . . . . . . . . . . . . . . . . . . . 197
Bibliography 210
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