Attitude Control Subsystem Design of the Stable and Highly Accurate Pointing Earth-imager David Ju

144 Pages·2017·5.02 MB·English

Attitude Control Subsystem Design of the
Stable and Highly Accurate Pointing
Earth-imager
A MSc Thesis
David Ju
By
in partial fulfillment of the requirements for the degree of
Master of Science
in Aerospace Engineering
at the Delft University of Technology
Department of Space Engineering
5th October 2017
Supervisor Dr.ir. J.M.Kuiper
CommitteeMembers Dr. A.Cervone
ir. B.C.Root
Abbreviations
ACS AttitudeControlSubsystem
ADCS AttitudeDeterminationandControlSubsystem
ARE AlgebraicRicattiEquation
ATS AttitudeThrusterSubsystem
CMG ControlMomentGyro
ConOps ConceptofOperations
COTS Commercialofftheshelf
EO EarthObservation
FMS1 FullMajorSpinup
FMS2 FullMinorSpinup
FOV FieldofView
IAGA InternationalAssociationofGeomagnetismandAeronomy
IFOV InstantaneousFieldofView
IGRF12 InternationalGeomagneticReferenceField12thgeneration
LEO LowEarthOrbit
LQR LinearQuadraticRegulator
MEMS microelectromechanicalsystem
MSAFE MarshallSolarActivityFutureEstimates(Model)
MSFC MarshallSpaceFlightCenter
MT Magnetorquer
MTF ModulationTransferFunction
MW MomentumWheel
MWTS MomentumWheelTorquingSubsystem
NASA NationalAeronauticsandSpaceAdministration
NRLMSISE00 NavalResearchLaboratoryMassSpectrometerandIncoherentScatterradarExosphere(2001Model)
PPL PrecessionPhaseLock
PS PartialSpinup
RW ReactionWheel
SHAPE StableandHighlyAccuratePointingEarth-imager
SMC SlidingModeControl
SMCS SlidingModeControlSpinup
SSO SunSynchronousOrbit
2
TBD ToBeDetermined
UTC CoordinatedUniversalTime
VLEO VeryLowEarthOrbit
Nomenclature
η NutationAngle[deg]
λ Longitude[deg]
µ PointingError[rad]
µ0 VacuumMagneticPermeability[4π·10−7TmA-1]
µ GravitationalParameterofEarth[398600km3s-2]
E
ω AngularBodyRateColumnVector[rads-1]
Ω PrecessionFrequency[rad/s]
p
ω RelativeRotorAngularVelocityAroundtheSpinAxis[rads-1]
s
φ Latitude[deg]
ρ TotalAirMassDensity[kgm-3]
ρ MaterialDensity[kgm-3]
m
τ ExternalTorque[Nm]
ξ DamperDisplacement[m]
A WettedSurfaceArea[m2]
a Semi-majorAxis[km]
B MagneticFluxDensity[T]
b InitialDamperMassLocationtoCenterofMassColumnVector[m]
c DampingCoefficient[kgsm-1]
d
C DragCoefficient[-]
D
F Thrust[N]
T
g SpinupTorque[Nm]
a
h Altitude[km]
H AngularMomentumColumnVector[Nms]
H RotorAngularMomentum[Nms]
s
I MassMomentofInertiaMatrix[kgm2]
I RotorMomentofInertiaAroundtheSpinAxis[kgm2]
s
k SpringStiffness[kgm-1]
d
3
m Mass[kg]
M DipoleMomentVectoroftheMagnetorquers[Am2]
A
M Earth’sMagneticMomentVector[8·1022Am2]
E
M SpacecraftMagneticMomentVector[Am2]
M
m DamperMass[kg]
d
n MeanMotion[rads-1]
n SpinAxisColumnVector[-]
p LinearMomentumVector[kgms-1]
p LinearMomentumofDamperMass[kgms-1]
n
T RotationalKineticEnergy[J]
t MaintenanceOperationTime[s]
m
t NominalOperationTime[s]
n
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Abstract
Astechnologyimproves,increasinglyhigherresolutionpayloadcanbeachievedusingCubesatsforEarthobservation.
The diffraction limit prevents the resolution to up to a few meters for these missions and are confined to Very Low
EarthOrbits(VLEO).Atthesealtitudes, strongdisturbancesactonthesystem, limitingitslifetimeandthepointing
capabilitiesofCubeSats. Asasolution,theDepartmentofSpaceEngineeringattheDelftUniversityofTechnology
hasproposeda6unitCubeSatnamedtheStableandHighlyAccuratePointingEarth-imager(SHAPE)orbitingataSun
synchronousVLEOwhichusesamomentumwheeltopassivelystabilizethesystemagainsttheexternalenvironment
withinacompetitivecostoflessthan500000e. Byutilizingthedual-spinstabilizationconcept,composedofastable
platformandaspinningrotor,itisexpectedtoperformpointingmissionsoflessthan1degree.
In this thesis, the SHAPE concept has been revisited and further developed based on the work of Kuiper and
DolkenstoconductwhetherthesetypesofmissionsarefeasiblewithintheaspectoftheAttitudeDeterminationand
ControlSubsystem(ADCS).Thisthesiscoversthebaseofthissubsystemapproachedfromatop-downmethodology;
designedfromthefinalnominalmissionmodetothedetumblingmodeonasystemlevel.
TheADCSdesignwillconsistofamomentumwheelwhichhasbeendeterminedtohaveanangularmomentumof
1Nms. Thisvalueisbasedonapredictionoftheworst-caseatmosphericdensityofthenextsolarcycle. Thedesign
point,atwhichthemomentumwheelhasbeensized,hasbeentakenat90%ofSHAPE’slifetimeafterseveraldesign
iterations. Hereby, the last 10% of the mission has been partially forfeited with degraded performances due to the
exponentialincreaseindisturbancesactingonthespacecraftatloweraltitudes. Astherefore,themassandsizeofthe
momentumwheelhasbeenreducedwith41%and20%,respectively. Tore-aligntheangularmomentumvectorwithin
the1degreepointingrequirement,asetofmagnetorquerswithadipolemomentof0.5Am2 hasbeenchosendueto
their low power consumption, mass, cost, and high reliability while capable of producing sufficient torque. Also, a
damperistobeintegratedasitprovidesthesystemasymptoticreductionofthetransversemomenta,thusincreasing
theimagequalitywithoutexpenditureofadditionalpower.
Toreachthenominalmissionobservationstate,severalmomentumwheelspinupstrategieshavebeeninvestigated.
Basedonatrade-offbetweenthreespinupconcepts,itwasconcludedthatthemajoraxisspinupismostsuited. This
type is initiated after the spacecraft as a whole has attained an angular momentum equivalent to that of the desired
endvalueofthemomentumwheel. Then,aconstantrotortorqueisapplied,providingamomentumtransferfromthe
platformtotherotor. Thedisadvantageofthisspinupprocedureisthatthesystem’ssolarpanelsarealignedparallelto
theorbitalplane,meaningthatpowercannotbegeneratedandbatteriesarerequiredduringthespinup. Despitethis,
it was found that after completing the spinup, the transverse angular momenta was minimized to marginal values in
contrasttotheotherspins. Theinclusionofthepassivedamperduringthemajoraxisspinfurtherimprovestheability
ofreducingthetransversemomentumasthedamper’sdissipativeenergypropertyaddsanasymptoticattractionatthe
pointoflowestenergy,locatedatthespinaxisneartheendofthespinup.
Theall-spunstateisachievedusingasetofthrusters. Thischoicewastakenasthemagnetorquerswasfoundnot
todeliversufficienttorque. Fromthedetumblinganalysis,itwasconcludedthatthemagnetorquersareabletoreduce
thetumblingrateswithmagnitudesofupto35deg/stomeanmotionvaluesinlessthananorbitusingastaticgain
B-dotcontroller.
Imperfectionsinthemomentumwheelcancausestaticanddynamicimbalance,impartinginternaldisturbancesto
thesystemwhichaffectstheimagequalitydetrimentally. Therefore,isolatorsaretobeintegratedwithinthemomentum
wheelsuspensionsubsystem. Ifthesedisturbancescanbenegatedusingisolators,itcanbeexpectedthatthepointing
error will stay within one degree and attitude stability can be achieved at least until the design altitude of 280 km.
However, the analysis and design of the isolators have yet to be done and thus the attainability of the pointing and
imagequalityrequirementsarestillinconclusive.
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6
" "
Life is the sum of all your choices.
- Albert Camus
7
8
Preface
Frommyyouth,Iwasalwaysfascinatedinrockets,planetsandtheuniverse(andalsoinsectsforwhichmycuriosity
to it has vanished). Pursuing science was very obvious. The interest of space and pursue to it were not during my
lifetime. Atmyfinalyearsofhighschool, mycarrierdecisionhadtobemadeandwasdividedintoeithermedicine
oraerospaceengineering; tohelppeopleorgointothedirectionofmyowninterest. Thisdecisionwastough, butI
decidedtopursueinaerospaceengineeringatDelftUniversityofTechnologymainlyasachallenge. Halfwaythough
my bachelor studies, aerospace engineering had not been motivating for me and pursuing this seemed to have been
disappointing. Doubtwasinmymind. Thischangedatthedesignsynthesisexercise. Focusingmoreonthespaceand
especiallyontheattitudecontrolsystemofthespacecrafthasawokenmyfascinationinspaceandhasenlightenedme
tofurtherpursuetodomymaster’sdegreeinspaceengineering.
TokeepthinkingaboutwhattodoandwhatwouldhavebeenifIhavechosenadifferentpathisathoughtoffutility
aslifeiscontinuousandflowinginasingledirection. OrasAlbertCamus,aphilosopheroftheAbsurd,hassaid;"You
willneverbehappyifyoucontinuetosearchforwhathappinessconsistsof. Youwillneverliveifyouarelookingfor
themeaningoflife."
IwouldliketothankmysupervisorHansKuiperforthesubjectofSHAPEandhispragmaticapproachtowards
engineering. Thissubjecthasgreatlyintroducedmetospinningspacecraft(whichIthoughttobeobsoleteforsatellites)
and its intriguing complex rotational motions. Furthermore, I am especially grateful for my parents and brother for
supportingmethroughoutmyacademiclifewiththeirloveforwhichIdedicatethisthesisto.
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Contents
1 Introduction 17
2 SystemObjective 19
2.1 CaseStudy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 SystemRequirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3 ControlModes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3.1 ControlModeRequirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.2 ModulationTransferFunctionRequirement . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.4 DesignMethodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.5 ConceptofOperations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3 BackgroundTheory 28
3.1 MathematicalNotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2 ReferenceFrames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.3 RotationalKinematics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3.1 DirectionCosineMatrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3.2 EulerAngles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3.3 Quaternions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3.4 KinematicDifferentialEquation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3.5 ConversionofAngularRepresentations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.4 RotationalDynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.4.1 DerivationofEuler’sRotationalEquationsofMotion . . . . . . . . . . . . . . . . . . . . . . 33
3.4.2 GyroscopicProperties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.5 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.5.1 StabilityintheSenseofLyapunov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.5.2 Lyapunov’sDirectMethod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.5.3 SpinStability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.5.4 EnergyDissipation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.6 MomentumSphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.7 Dual-SpinSpacecraft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.7.1 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.7.2 MomentumSphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.7.3 EnergyDissipation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4 NominalandMaintenanceModes 44
4.1 NominalOrientationandMomentofInertia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.2 EnvironmentalDisturbances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.2.1 GravityGradientDisturbance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.2.2 AerodynamicDisturbance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.2.3 MagneticFieldDisturbance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2.4 Eddy-CurrentDisturbance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.3 AtmosphericDensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
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