Optimal Attitude Control of Agile Spacecraft Using Combined Reaction Wheel and Control Moment

168 Pages·2015·2.42 MB·English

by  Cole C. Doupe

OPTIMALATTITUDECONTROLOFAGILESPACECRAFTUSING
COMBINEDREACTIONWHEELANDCONTROLMOMENTGYROSCOPE
ARRAYS
DISSERTATION
ColeC.Doupe,Major,USAF
AFIT-ENY-DS-15-D-042
DEPARTMENT OF THE AIR FORCE
AIR UNIVERSITY
AIR FORCE INSTITUTE OF TECHNOLOGY
Wright-Patterson Air Force Base, Ohio
DistributionStatementA:
ApprovedforPublicRelease;DistributionUnlimited
Theviewsexpressedinthisdissertationarethoseoftheauthoranddonotreflecttheofficial
policyorpositionoftheUnitedStatesAirForce,theDepartmentofDefense,ortheUnited
StatesGovernment.
This material is declared a work of the U.S. Government and is not subject to copyright
protectionintheUnitedStates.
AFIT-ENY-DS-15-D-042
OPTIMALATTITUDECONTROLOFAGILESPACECRAFTUSINGCOMBINED
REACTIONWHEELANDCONTROLMOMENTGYROSCOPEARRAYS
DISSERTATION
PresentedtotheFaculty
GraduateSchoolofEngineeringandManagement
AirForceInstituteofTechnology
AirUniversity
AirEducationandTrainingCommand
inPartialFulfillmentoftheRequirementsforthe
DegreeofDoctorofPhilosphyinSpaceSystems
ColeC.Doupe,B.S.,M.S.
Major,USAF
December2015
DistributionStatementA:
ApprovedforPublicRelease;DistributionUnlimited
AFIT-ENY-DS-15-D-042
OPTIMALATTITUDECONTROLOFAGILESPACECRAFTUSINGCOMBINED
REACTIONWHEELANDCONTROLMOMENTGYROSCOPEARRAYS
ColeC.Doupe,B.S.,M.S.
Major,USAF
CommitteeMembership:
Dr. EricD.Swenson
Chair
Dr. RichardG.Cobb
Member
MajorScottJ.Pierce
Member
ADEDEJIB.BADIRU,Ph.D.
Dean,GraduateSchoolofEngineering
andManagement
AFIT-ENY-DS-15-D-042
Abstract
Thisdissertationexploresthebenefitsofcombinedcontrolmomentgyroscope(CMG)
andreactionwheelarray(RWA)actuationforagilespacecraft. Agilespacecraftarecapable
ofslewingtomultipletargetsinminimumtime. CMGsprovidethelargesttorquecapability
of current momentum exchange actuation devices but also introduce singularity events
in operation. RWAs produce less torque capability than CMGs but can achieve greater
pointing accuracy. In this research, a combined RWA and CMG (RWCMG) system is
evaluated using analytical simulations and hardware experiments. A closed-loop control
scheme is developed which takes advantage of the strengths of each actuator set. The
CMGsperformslewsforarepresentativetargetfield. Borrowingfromvariable-speedCMG
theory,asystemofswitchingbetweenCMGandRWAactuationallowstheRWAtoassume
control of the spacecraft when desired pointing tolerance is met for a given target. During
collection, the CMG gimbals may travel along null motion trajectories toward preferred
angles to prepare for the next slew. Preferred gimbal angles are pre-computed off-line
usingoptimizationtechniquesorsetbasedonlook-uptables. Logicisdevelopedtoensure
CMG gimbal angles travel the shortest path to the preferred values. The proportional-
integral-derivative, quaternion feedback, and nonlinear Lyapunov-based controllers are
assessed for the RWCMG system. Extended and unscented Kalman filter techniques are
explored for improved accuracy in analytical simulation. Results of RWCMG hardware
experiments show improvements in slew capability, pointing accuracy, and singularity
avoidancecomparedtotraditionalCMG-onlysystems.
iv
Acknowledgements
Mywifeandkidshaveenduredtheextratimeawayfromhome. MyadvisorDr.
Swenson has been steadfast in his leadership and devotion to this project. Dr. Cobb and
Dr. Pierce have provided expert knowledge and guidance in the subject area. Dr. Jonathan
Wrightlentassistancewithsimulatoroperation. Thankyoutoall.
ColeC.Doupe
v
TableofContents
Page
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
TableofContents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
ListofFigures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
ListofTables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii
ListofAbbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Motivation: SatelliteTrackingMission . . . . . . . . . . . . . . . . . . . . 2
1.2 ControlMomentGyroscopeActuation . . . . . . . . . . . . . . . . . . . . 3
1.3 RelevantResearchAreas . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4 ResearchObjectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.5 DissertationOverview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
II. Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.1 EquationsofMotion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2 MultipleTargetCollection . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3 VariableSpeedControlMomentGyroscopeArrays . . . . . . . . . . . . . 27
2.4 ApplicableControllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.5 SingularityAvoidance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.6 NullMotion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.7 StochasticEstimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.8 PreferredGimbalAngles . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.9 AppliedOptimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.10 SimSatSpacecraftExperimentPlatform . . . . . . . . . . . . . . . . . . . 44
III. Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.1 TheAgileSpacecraftMissionDefined . . . . . . . . . . . . . . . . . . . . 48
3.1.1 SimulatedSpacecraftParameters . . . . . . . . . . . . . . . . . . . 48
3.1.2 RepresentativeMissionDefinition . . . . . . . . . . . . . . . . . . 49
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Page
3.1.3 TheOptimalSolution-ABenchmark . . . . . . . . . . . . . . . . 51
3.2 AnalyticalModelClosed-LoopControlScheme . . . . . . . . . . . . . . . 53
3.2.1 CalculateParameters . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.2.2 ControllerImplementation . . . . . . . . . . . . . . . . . . . . . . 56
3.2.3 SingularityAvoidanceandWeighting . . . . . . . . . . . . . . . . 59
3.2.4 LimitEnforcement . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.2.5 SteeringLaw/NullMotion . . . . . . . . . . . . . . . . . . . . . . 64
3.2.6 Filter/Propagate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.2.7 MissionProgress . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.2.8 CalculationofPreferredGimbalAngles . . . . . . . . . . . . . . . 73
3.3 HardwareModelClosed-LoopControlScheme . . . . . . . . . . . . . . . 76
3.3.1 ConversionofAnalyticalCodetoSimSatPlatform . . . . . . . . . 77
3.3.2 Shortest-PathCMGGimbalNullMotion . . . . . . . . . . . . . . 78
3.4 MeansofAssessingSimulationPerformance . . . . . . . . . . . . . . . . 81
3.5 EvaluationMetricsDefined . . . . . . . . . . . . . . . . . . . . . . . . . . 83
IV. ResultsandDiscussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.1 ControllerEvaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.1.1 AnalyticalResults . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.1.2 ExperimentalResults . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.2 LimitEnforcementAccuracy . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.3 PreferredGimbalAngleandNullMotionPerformanceEvaluation . . . . . 117
4.3.1 NullMotionGainTuning . . . . . . . . . . . . . . . . . . . . . . 117
4.3.2 ControllerPerformanceforNullMotion . . . . . . . . . . . . . . . 123
4.3.3 PreferredGimalAngleImpactonNullMotion . . . . . . . . . . . 125
4.3.4 InitialGimbalAngleImpactonNullMotion . . . . . . . . . . . . 126
4.3.5 RWCMGActuationComparedtoTraditionalCSCMG . . . . . . . 128
4.4 StochasticEstimationPerformanceEvaluation-AnalyticalOnly . . . . . . 131
V. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
5.1 ResearchConclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
5.1.1 RWCMGResearchAreas . . . . . . . . . . . . . . . . . . . . . . 136
5.1.2 RWCMGClosed-LoopControlScheme . . . . . . . . . . . . . . . 137
5.1.3 ControllerandLimitEnforcementPerformance . . . . . . . . . . . 138
5.1.4 NullMotionandPreferredGimbalAnglePerformance . . . . . . . 139
5.1.5 RWCMGSystemPerformance . . . . . . . . . . . . . . . . . . . . 142
5.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
5.3 FutureWork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
5.3.1 FutureResearchAspect: Closed-LoopControlSchemeSetup . . . 144
5.3.2 FutureResearchAspect: Optimization . . . . . . . . . . . . . . . . 145
vii
Page
5.3.3 FutureResearchAspect: NullMotion . . . . . . . . . . . . . . . . 146
5.3.4 FutureResearchAspect: HardwareExperiments . . . . . . . . . . 147
viii
ListofFigures
Figure Page
1.1 Representative2DMultipleTargetObservationField . . . . . . . . . . . . . . 4
1.2 Single-GimbalControlMomentGyroscopeGeometry . . . . . . . . . . . . . . 4
1.3 Four Control Moment Gyroscope Pyramid Geometry, Showing a Singularity
withall(cid:126)h LyinginaPlane . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
i
1.4 Maps of Standard Four-CMG Pyramid Unit Angular Momentum Space,
External(left),Internal(right)(oneoffourshown)[1] . . . . . . . . . . . . . . 6
1.5 BoundsofCurrentResearchforAgileCMGSystems . . . . . . . . . . . . . . 14
2.1 SGCMGNumber4GeometryinPyramidArray . . . . . . . . . . . . . . . . . 21
2.2 StandardKalmanFilterAlgorithm . . . . . . . . . . . . . . . . . . . . . . . . 37
2.3 PreferredGimbalAnglesforVariousSecularTorqueDemands(Vadali[2]) . . 42
2.4 Open-loopImplementationofOptimizedGimbalAngles . . . . . . . . . . . . 43
2.5 UseofOptimalGimbalAnglesinClosedLoopControl[3] . . . . . . . . . . . 44
2.6 AFITSimSatHardwarewithActuatorsLabeled . . . . . . . . . . . . . . . . . 45
3.1 SimulatedAgileSpacecraftProperties . . . . . . . . . . . . . . . . . . . . . . 48
3.2 SimulatedCMGPyramidGeometrywithRWALayout,Top-View(left),Side-
View(right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.3 AnalyticalModelClosed-LoopControlScheme . . . . . . . . . . . . . . . . . 53
3.4 HardwareModelClosed-LoopControlScheme . . . . . . . . . . . . . . . . . 79
3.5 GimbalAngleShortestPathIllustration . . . . . . . . . . . . . . . . . . . . . 86
3.6 CMGGimbalShortestPathLogic . . . . . . . . . . . . . . . . . . . . . . . . 87
3.7 SampleEulerAnglevs.TimePlotforRWCMGMissionUsingPIDController 88
3.8 Sample Pointing Accuracy vs.Time Plot for RWCMG Mission Using PID
Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
ix