Robust Switching Recovery Control of a Quadcopter Aerial Vehicle Model

181 Pages·2017·6.57 MB·English

Robust Switching Recovery Control of a
Quadcopter Aerial Vehicle Model
Thesis submitted for the degree of
Doctor of Philosophy
at the University of Leicester
by
Hasan Bas¸ak MSc (Manchester)
Control Research Group
Department of Engineering
University of Leicester
2018
Abstract
Robust Switching Recovery Control of a Quadcopter
Aerial Vehicle Model
HasanBas¸ak
This thesis presents recovery control schemes that enable a quadcopter unmanned
aerialvehicle(UAV)modeltocopewithafaultyactuationsystem.
First, the computational aspects of the design of fixed-order H controllers are in-
1
vestigatedalongwiththeperformancetheyprovideforthequadcopterUAV.Double-loop
control structures are developed to control the translational velocities of the UAV subject
totwodifferentintermittentactuationproblems. Fixed-orderH controllersaredesigned
1
forthenominalandthefaultymodesofoperation. Theseclosed-loopmodesaremodelled
as a switched system for which stability is analysed using minimum dwell time theory.
Average dwell times are also computed by exploiting multiple Lyapunov-like functions
thataccountforthedelaysinthedetectionofafault.
The other key contribution of this thesis is the design of a switched recovery control
scheme that does not require the explicit detection of the faults. Sufficient conditions
are given in terms of linear matrix inequalities (LMIs) coupled with a scalar, and depend
on modified Lyapunov-Metzler inequalities. The switched recovery scheme developed
consists of jointly designed state feedback gains switched according to a min-switching
strategy that preserves closed-loop stability and satisfy a prescribed H or H perfor-
1 2
mance.
Finally,theinherentfastswitchingissueofthemin-switchingstrategyistreatedatthe
expenseofconservativereformulatedLMIsconditions. Furthermore,thestate-dependent
switched control scheme is extended to output feedback case. Simulation results demon-
strate the potential of the developed switching recovery control schemes to overcome
variousactuationfaults.
i
ACKNOWLEDGEMENT
Firstly, I would like to express my sincere gratitude to my supervisor, Dr. Emmanuel
Prempain,forhiscontinuousmoralandtechnicalsupport,aswellashisenthusiasm. Iam
indebted to him for providing the initial motivation for the research topic of this thesis,
for answering all of my questions, constructive suggestions and stimulating discussions.
IamgratefultoProf. MattTurnerforprovidingguidanceduringmyAPGtransfer. Ialso
wish to acknowledge financial support from Republic of Turkey, Ministry of National
Education.
I would also like to thank my friends and their families in Leicester for their friend-
shipsandsupport: Dr. AngelikiLekka,Dr. EmreKemer,Dr. AliYavuzPolat,Dr. Ioannis
Kyriakopoulos, Dr. Caner Gerek, Dog˘an Gu¨ner, Go¨kmen Durmus¸, Hu¨samettin Ates¸, Er-
bilC¸elik,EdipDemirel. ThankstofriendscurrentlyandformerlyoftheControlResearch
Group: Dr. Hessam Mahdianfar, Dr. Bharani Chandra, Dr. Peter Norton, Xiaoxing Fu,
TengD.Chollom,Dr. NkemdilimOfodile,TomasPuller,JahazAlotaibi,HaoYang.
Special thanks to Yılmaz Aydemir, Zuhal Aydemir and their families for their contin-
uessupport.
Finally, I am greatly indebted to my wife for her patience and understanding while I
wasworkingeveningsandweekendsandtomyparentswhohavesupportedmethrough-
outmystudieswiththeirencouragementandlove.
HasanBAS¸AK
25July,2017
ii
CONTENTS
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 ThesisOutline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 LiteratureReview 7
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 ReviewonControlApporachestoQuadcopterUAVs . . . . . . . . . . . 7
2.2.1 FlightControlApproaches . . . . . . . . . . . . . . . . . . . . . 7
2.2.2 Fault-TolerantControlApproaches . . . . . . . . . . . . . . . . 9
2.3 ReviewonFaultTolerantControl . . . . . . . . . . . . . . . . . . . . . 13
2.3.1 ModellingMultiplicativeActuatorFaults/Failures . . . . . . . . 14
2.3.2 CurrentFTCApproaches . . . . . . . . . . . . . . . . . . . . . . 14
2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3 BackgroundonStabilityofSwitchedSystems 27
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2 LinearisationandLocalStability . . . . . . . . . . . . . . . . . . . . . . 27
3.2.1 Linearisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2.2 ClassicalStabilityConcepts . . . . . . . . . . . . . . . . . . . . 29
3.3 StabilityofSwitchedSystems . . . . . . . . . . . . . . . . . . . . . . . 30
3.3.1 CommonQuadraticLyapunovFunctions . . . . . . . . . . . . . 31
iii
iv CONTENTS
3.3.2 MultipleLyapunovFunctions . . . . . . . . . . . . . . . . . . . 32
3.3.3 DwellTimeSwitching . . . . . . . . . . . . . . . . . . . . . . . 33
3.3.4 MinimumLyapunovfunctionSwitchingStrategy . . . . . . . . . 34
3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4 SystemDescription 38
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.2 QuadcopterKinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.3 Newton-EulerEquations . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.4 Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5 InvestigationofLow-orderH ControlOptimisationTools 50
1
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.2 GeneralControlConfiguration . . . . . . . . . . . . . . . . . . . . . . . 51
5.2.1 H MixedSensitivitySetup . . . . . . . . . . . . . . . . . . . . 52
1
5.3 H controlApproaches . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
1
5.3.1 Fixed-orderH Optimisation . . . . . . . . . . . . . . . . . . . 54
1
5.3.2 StucturedH Synthesis . . . . . . . . . . . . . . . . . . . . . . 55
1
5.3.3 LinearMatrixInequality(LMI)Approach . . . . . . . . . . . . . 57
5.3.4 MixedSensitivityH OptimisationApproach . . . . . . . . . . 59
1
5.4 ControlLawsDesigns . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.5 TimeDomainSimulationResultsandDiscussion . . . . . . . . . . . . . 70
5.5.1 TimeDomainSimulationResults . . . . . . . . . . . . . . . . . 70
5.5.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
6 SwitchingRecoveryControlSchemesintheCaseofIntermittentFaults 77
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
6.2 ProblemDescription . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
6.2.1 Case A: Problem of an Intermittent Loss of Control (ILOC) Ef-
fectiveness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
6.2.2 CaseB:ProblemofanIntermittentLossofMotor(ILOM) . . . . 80
6.2.3 LinearModelofTranslationalDynamics . . . . . . . . . . . . . 82
CONTENTS v
6.3 ControlStructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
6.3.1 SwitchedInner-loopControllerDesigns . . . . . . . . . . . . . . 85
6.3.2 DesiredAnglesCalculation . . . . . . . . . . . . . . . . . . . . 89
6.3.3 TranslationalVelocityController . . . . . . . . . . . . . . . . . . 90
6.4 StabilityAnalysisofSwitchedSystems . . . . . . . . . . . . . . . . . . 90
6.4.1 Dwell-time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.4.2 MultipleLyapunov-likeFunctionswithaTimeDelayinFaultDe-
tection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6.5 TransientImprovementoftheSwitchedControllers . . . . . . . . . . . . 98
6.6 TimeSimulationResults . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.6.1 CaseA:IntermittentLossofControlEffectiveness . . . . . . . . 100
6.6.2 CaseB:IntermittentLossofMotor . . . . . . . . . . . . . . . . 104
6.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
7 State-dependent Switched Control Schemes in the Presence of Undetected
Faults 109
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
7.2 ProblemStatement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
7.3 SwitchedH Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
1
7.3.1 StabilityAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . 114
7.3.2 SwitchedH StateFeedbackControl . . . . . . . . . . . . . . . 116
1
7.3.3 SwitchedH DynamicOutputFeedbackControl . . . . . . . . 120
1
7.4 SwitchedH Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
2
7.4.1 StabilityAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . 127
7.4.2 SwitchedH StateFeedbackControl . . . . . . . . . . . . . . . 128
2
7.5 SwitchedFaultTolerantControlDesigns . . . . . . . . . . . . . . . . . . 131
7.5.1 SwitchedH StateFeedbackControl . . . . . . . . . . . . . . . 133
1
7.5.2 SwitchedH StateFeedbackControl . . . . . . . . . . . . . . . 134
2
7.5.3 ConstantH StateFeedbackControl . . . . . . . . . . . . . . . . 135
2
7.5.4 SwitchedH DynamicOutputFeedbackControl . . . . . . . . 135
1
7.6 SimulationResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
7.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
vi CONTENTS
8 ConclusionsandFutureResearch 145
8.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
8.2 FutureResearch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
LIST OF TABLES
2.1 SummaryoftheadvantagesanddisadvantagesofFTCapproaches. . . . . 25
4.1 Quadcopterparameters[139]. . . . . . . . . . . . . . . . . . . . . . . . 47
5.1 Controlobjectives. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.2 Weightfunctionparameters. . . . . . . . . . . . . . . . . . . . . . . . . 64
5.3 Comparisonofcontrollawdesigns. . . . . . . . . . . . . . . . . . . . . 64
vii
LIST OF FIGURES
1.1 Robustswitchingrecoverycontrolstructure. . . . . . . . . . . . . . . . . 3
2.1 Faultswithrespecttotime(a)abrupt;(b)incipient;(c)intermittent(adopted
from[68]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Astructureofanactivefaulttolerantcontrolsystem(adoptedfrom[160]). 15
2.3 Classificationoffaulttolerantcontrol(adoptedfrom[5]). . . . . . . . . 16
2.4 Closed-loopsystem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.5 Adaptivecontrolsystems(a)MRAC,(b)STC(adoptedfrom[9]). . . . . 20
3.1 Illustrations of (a) a stable equilibrium in the sense of Lyapunov, and (b)
anasymptoticallystableequilibrium. . . . . . . . . . . . . . . . . . . . 29
3.2 Multiple Lyapunov function values versus time (N = 2). Solid/dotted
denotescorrespondingsystemactivity/inactivity(adoptedfrom[21]). . . 32
3.3 Lyapunov function values versus time (N = 2) with the min-switching
strategy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.1 Body-fixedandinertial-fixedframesforaquadcopterUAVmodel. . . . . 40
4.2 ThemotionsofquadcopterUAVs. . . . . . . . . . . . . . . . . . . . . . 41
5.1 Standardfeedbacksystem. . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.2 Frequenciesatcurrentiterationtobuildatangentmodel[44]. . . . . . . . 56
5.3 Closed-loopcontrolstructure. . . . . . . . . . . . . . . . . . . . . . . . 61
viii
ListofFigures ix
5.4 Singular value plots of the sensitivity function and inverse of the perfor-
manceweightwiththecontrollerdesignedusingthehifoo. . . . . . . . . 66
5.5 Singularvalueplotsofthecomplementarysensitivityfunctionandinverse
ofthestabilityweightwiththehifoo. . . . . . . . . . . . . . . . . . . . . 66
5.6 Singular value plots of the sensitivity function and inverse of the perfor-
manceweightwiththehinfstruct. . . . . . . . . . . . . . . . . . . . . . . 67
5.7 Singularvalueplotsofthecomplementarysensitivityfunctionandinverse
ofthestabilityweightwiththehinfstruct. . . . . . . . . . . . . . . . . . 67
5.8 Singular value plots of the sensitivity function and inverse of the perfor-
manceweightwiththeLMI. . . . . . . . . . . . . . . . . . . . . . . . . 68
5.9 Singularvalueplotsofthecomplementarysensitivityfunctionandinverse
ofthestabilityweightwiththeLMI. . . . . . . . . . . . . . . . . . . . . 68
5.10 Singular value plots of the sensitivity function and inverse of the perfor-
manceweightwiththeGlover-Doyle. . . . . . . . . . . . . . . . . . . . 69
5.11 Singularvalueplotsofthecomplementarysensitivityfunctionandinverse
ofthestabilityweightwiththeGlover-Doyle. . . . . . . . . . . . . . . . 69
5.12 Closed-loop step responses obtained with the hifoo controller and rotor
forceswiththenon-linearmodel. . . . . . . . . . . . . . . . . . . . . . . 72
5.13 Closed-loop step responses obtained with the hinfstruct controller and
rotorforceswiththenon-linearmodel. . . . . . . . . . . . . . . . . . . . 73
5.14 Closed-loop step responses obtained with the LMI controller and rotor
forceswiththenon-linearmodel. . . . . . . . . . . . . . . . . . . . . . . 74
5.15 Closed-loopstepresponsesobtainedwiththeGlover-Doylecontrollerand
rotorforceswiththenon-linearmodel. . . . . . . . . . . . . . . . . . . 75
6.1 Thedouble-loopcontrolstructurefortranslationaltracking(a)inthecase
ofILOC,(b)inthecaseofILOM. . . . . . . . . . . . . . . . . . . . . . 83
6.2 FlowdiagramofthedevelopedcontrolstructureofFig. 6.1(a). . . . . . . 84
6.3 FlowdiagramofthedevelopedcontrolstructureofFig. 6.1(b). . . . . . 85
6.4 Inner-loopcontrolstructureinthecaseofILOC,whereK 2 fK ;K g. . 86
i 1 2
6.5 Singular value plots of the S(j!) and inverse of the performance weight
in the case of ILOC (a) for the healthy mode, and (b) for the faulty mode
ofoperation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86