Toward Co-Design of Autonomous Aerospace Cyber-Physical Systems

148 Pages·2014·3.6 MB·English

Toward Co-Design of Autonomous Aerospace
Cyber-Physical Systems
by
JustinM.Bradley
Adissertationsubmittedinpartialfulfillment
oftherequirementsforthedegreeof
DoctorofPhilosophy
(AerospaceEngineering)
intheUniversityofMichigan
2014
DoctoralCommittee:
AssociateProfessorEllaM.Atkins,Chair
ProfessorDennisS.Bernstein
AssistantProfessorJamesW.Cutler
ProfessorIlyaV.Kolmanovsky
ProfessorKangG.Shin
ForHalwasthenervoussystemoftheship;withouthissupervision,Discoverywouldbe
amechanicalcorpse.
-ArthurC.Clarke“2001: ASpaceOdyssey”
©JustinM.Bradley
2014
Dedication
This work is dedicated to the many people the world over who find
they don’t really fit into the boxes their community has constructed for
them.
ii
A C K N O W L E D G M E N T S
Noworkofthismagnitudeisaccomplishedwithoutthesupportofmany
people. In my case this is particularly true thanks to the exceedingly
difficult circumstances which the last four years has brought me. The
University of Michigan, the Aerospace Dept., and its faculty and staff
have been gracious, kind, helpful, accommodating, and fair. The mem-
bers of my committee have provided useful feedback along the way that
hashelpedshapedthiswork.
The support I’ve received from individuals seems to never end. Ali
Nasir, Cat McGhan, Allen Hicken, Ryan Eubank, and others have spent
hours talking with me and helping in many ways. Derrick Yeo filled a
gap in my life that few have filled before. Thank you Derrick, I truly
could not have done this PhD without you. C.J. Sorenson has been a
source of great strength and encouragement since the 1st grade and his
supportduringthisPhDwasendless.
Perhaps the constant support through all of my time here has been
myadviser,EllaAtkins. Ellahasbeenmorethanjustanadviser,shehas
beenafriend,aresource,andanencouragment.
My mom, Sally, my dad, Phil, have both been my cheerleaders as
well as sources of emotional, and physical strength. My brother, Josh,
has become a friend and support in ways I never expected. Carrie en-
tered my life in an unusual way and we rapidly became friends which
blossomed into romance. Carrie continues to be a bedrock of love and
encouragmenttome.
Finally, I’d like to thank my children, Emily, Madison, and Caleb.
YouaremyprideandjoyandIloveyoudearlyandfiercely.
iii
TABLE OF CONTENTS
Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
ListofFigures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
ListofTables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
ListofAppendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
ListofAbbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii
Chapter
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 ResearchObjectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 CPSCo-Regulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 CPSCo-Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5 Innovations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.6 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 BackgroundandRelatedWork . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1 BriefHistoryofCPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.1 “Cyber” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.2 Communication . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.3 Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.1.4 Computing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 Real-TimeComputingMeetsControl . . . . . . . . . . . . . . . . . . . . 13
2.3 Computer-BasedControlResearch . . . . . . . . . . . . . . . . . . . . . 16
2.3.1 Time-DelaySystems . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.2 DigitalControl . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3.3 Real-TimeSystems . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3.4 RecentCPSResearch . . . . . . . . . . . . . . . . . . . . . . . 19
2.4 CPSTopicsinAerospace . . . . . . . . . . . . . . . . . . . . . . . . . . 22
iv
2.5 ConcludingRemarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3 Toward Continuous State-Space Regulation of Coupled Cyber-Physical Sys-
tems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.1 AMotivatingExample . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.1.1 Spring-Mass-DamperSystem . . . . . . . . . . . . . . . . . . . 26
3.1.2 Closed-loopController . . . . . . . . . . . . . . . . . . . . . . . 26
3.2 DevelopmentofaCyberModel . . . . . . . . . . . . . . . . . . . . . . . 28
3.3 CPSModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3.1 AugmentedSystem . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3.2 HybridAutomatonFormulation . . . . . . . . . . . . . . . . . . 31
3.3.3 ImplementationDetails . . . . . . . . . . . . . . . . . . . . . . . 31
3.4 Closed-LoopCo-RegulationofCyberandPhysical
States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.4.1 2nd-orderDampedOscillator . . . . . . . . . . . . . . . . . . . . 32
3.4.2 UnstableSystemResults . . . . . . . . . . . . . . . . . . . . . . 36
3.5 TowardaCoupledModel . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.5.1 EarlyCouplingResults . . . . . . . . . . . . . . . . . . . . . . . 42
3.5.2 FutureCouplingObjectives . . . . . . . . . . . . . . . . . . . . 46
3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4 Cyber-PhysicalSystemModelingandCo-RegulationofaCubeSat . . . . . . . 48
4.1 CubeSatEquationsofMotion . . . . . . . . . . . . . . . . . . . . . . . . 49
4.1.1 EquationsofMotion . . . . . . . . . . . . . . . . . . . . . . . . 50
4.2 DiscreteCubeSatModel . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.2.1 DiscreteCubeSatModel . . . . . . . . . . . . . . . . . . . . . . 52
4.2.2 PhysicalSystemControlLaws . . . . . . . . . . . . . . . . . . . 52
4.3 Cyber-PhysicalSystemModel . . . . . . . . . . . . . . . . . . . . . . . 56
4.3.1 State-VariableCyberModel . . . . . . . . . . . . . . . . . . . . 56
4.3.2 Open-LoopCyber-PhysicalSystemModel . . . . . . . . . . . . 57
4.3.3 CyberSystemControlLaw . . . . . . . . . . . . . . . . . . . . 58
4.3.4 Closed-LoopCPSModel . . . . . . . . . . . . . . . . . . . . . . 59
4.4 CPSMetrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.4.1 PerformanceMetrics . . . . . . . . . . . . . . . . . . . . . . . . 59
4.5 CubeSatCaseStudy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.5.1 PhysicalCharacteristicsandSetup . . . . . . . . . . . . . . . . . 62
4.5.2 CyberCharacteristicsandSetup . . . . . . . . . . . . . . . . . . 63
4.6 CubeSatCPSSimulationResults . . . . . . . . . . . . . . . . . . . . . . 64
4.6.1 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.6.2 GSDLQRCPSDesigns . . . . . . . . . . . . . . . . . . . . . . 65
4.6.3 FPRBCPSDesigns . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.6.4 DesignComparisons . . . . . . . . . . . . . . . . . . . . . . . . 67
4.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5 Cyber-PhysicalOptimizationforUnmannedAircraftSystems . . . . . . . . . 71
v
5.1 CostFunctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.1.1 PhysicalSystemTerms . . . . . . . . . . . . . . . . . . . . . . . 73
5.1.2 CyberSystemTerms . . . . . . . . . . . . . . . . . . . . . . . . 75
5.1.3 CPSCostFunction . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.2 SetupandSolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.2.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.2.2 SimplifiedCostFunction . . . . . . . . . . . . . . . . . . . . . . 80
5.2.3 AnalyticalSolutionandFeasibility . . . . . . . . . . . . . . . . 82
5.2.4 ExperimentalModelsandSetup . . . . . . . . . . . . . . . . . . 83
5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.3.1 ParetoFronts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
(cid:0) (cid:1)
5.3.2 OptimizationoverTotalCostFunction J v,r . . . . . . . . . . 88
τ
2
5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
6.1 Co-RegulationofCPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
6.1.1 CPSCo-RegulationFutureWork . . . . . . . . . . . . . . . . . 92
6.2 Co-OptimizationofCPS . . . . . . . . . . . . . . . . . . . . . . . . . . 93
Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
vi
LIST OF FIGURES
1.1 AbstractDualityofCyberandPhysicalSystems . . . . . . . . . . . . . . . . 4
1.2 CPSCo-RegulationBlockDiagram . . . . . . . . . . . . . . . . . . . . . . . 5
2.1 CPSHistory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 CyclicExecutiveScheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 PreemptiveSchedulingonaSingleProcessor . . . . . . . . . . . . . . . . . . 15
3.1 OpenLoopResponse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2 Closed-loopResponse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3 FractionofCompletedControlTask,y ,asaFunctionofTime . . . . . . . . . 29
c
3.4 FractionofCompletedControlTask,y ,asaFunctionofTimewithVarying f 29
c
3.5 HybridSystemModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.6 SimulationforCase1. x =200Hz, x =80Hz . . . . . . . . . . . . . . . 34
c2,0 c2,r
3.7 SimulationforCase2. x =3.4Hz, x =6Hz . . . . . . . . . . . . . . . . 35
c2,0 c2,r
3.8 SimulationforCase3. x =20Hz, x =5Hz . . . . . . . . . . . . . . . . 36
c2,0 c2,r
3.9 SimulationforCase1. x =200Hz, x =80Hz . . . . . . . . . . . . . . . 38
c2,0 c2,r
3.10 SimulationforCase2. x =6.66Hz, x =13Hz . . . . . . . . . . . . . . 39
c2,0 c2,r
3.11 SimulationforCase3. x =20Hz, x =7Hz . . . . . . . . . . . . . . . . 40
c2,0 c2,r
3.12 µ andµ asaFunctionofFrequency . . . . . . . . . . . . . . . . . . . . . 42
p1 p2
3.13 HybridSystemforCoupledCPSModel . . . . . . . . . . . . . . . . . . . . . 43
3.14 Simulationfor2nd-orderOscillatorwithCouplingTerms. x =20Hz, x =
c2,0 c2,r
5Hz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.15 SimulationForInvertedPendulumwithCouplingTerms. x =20Hz, x =
c2,0 c2,r
7Hz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.1 H PerformanceCostwithChangingSamplingRate . . . . . . . . . . . . . . 54
2
4.2 GainSchedulingOverr (k)(SamplingRate) . . . . . . . . . . . . . . . . . . 55
τ
1
4.3 GainScheduledDLQRCPSComparisons . . . . . . . . . . . . . . . . . . . . 67
4.4 FPRBCPSComparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.1 PowerCurveforSolarDronesUAS . . . . . . . . . . . . . . . . . . . . . . . 74
5.2 ProcessorUtilizationTimelineforTaskτ . . . . . . . . . . . . . . . . . . . . 76
5.3 EntropyCost H . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.4 J(v,r ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
τ
5.5 SolarSightSolar-poweredUAS . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.6 ParetoFrontfor J and J . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
p c
5.7 ParetoFrontsfor J . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
vii
A.1 TableSat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
A.2 LinearCurveFitUsing MATLAB’scftool . . . . . . . . . . . . . . . . . . 99
A.3 PowerandEnergyCurvesforTableSatPhysicalSystem . . . . . . . . . . . . 100
A.4 −I(ω,r ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
τ
A.5 InformationMetric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
B.1 CubeSatAttitudeDisturbanceResponseUsingFixed10HzDLQRControl . . 113
B.2 CubeSatAttitudeDisturbanceResponseUsingFixed1HzDLQRControl . . . 113
B.3 CubeSatAttitudeDisturbanceResponseUsingFixed0.1HzDLQRControl . . 114
B.4 CubeSatAttitudeDisturbanceResponseUsingGSDLQRControlUsingu . 114
c,1
B.5 CubeSatAttitudeDisturbanceResponseUsingGSDLQRControlUsingu . 115
c,2
B.6 CubeSatAttitudeDisturbanceResponseUsingFPRBControlUsingu . . . 115
c,1
B.7 CubeSatAttitudeDisturbanceResponseUsingFPRBControlUsingu . . . 116
c,2
viii