Principles of Spacecraft Control: Concepts and Theory for Practical Applications

202 Pages·2022·3.68 MB·English

by  Walter Fichter, Ramin T. Geshnizjani

Principles of Spacecraft Control
Walter Fichter • Ramin T. Geshnizjani
Principles of Spacecraft
Control
Concepts and Theory for Practical
Applications
WalterFichter RaminT.Geshnizjani
InstitutfürFlugmechanikundFlugregelung InstitutfürFlugmechanikundFlugregelung
UniversityofStuttgart UniversityofStuttgart
Stuttgart,Germany Stuttgart,Germany
ISBN978-3-031-04779-4 ISBN978-3-031-04780-0 (eBook)
https://doi.org/10.1007/978-3-031-04780-0
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2023
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Preface
The design of spacecraft control systems is, first of all, a system engineering task. This
concernsnotonly the controlsystem itself (sensors,actuators,computers,and software)
but also the mission objectives and interfaces to other subsystems. With increasingly
demanding mission and system requirements, the interconnection between spacecraft
controlsystem,instrumentpayload,andplatformbecomesevenmoredistinct.Therefore,
a thorough understanding of the functional principles of a spacecraft control system as
wellasitslimitationsisrequiredforefficientsystemengineering.
Thisbookiswrittenasatextbook.Theobjectiveistoprovidethemathematicalmodels
andalgorithmsneededtodevelopathoroughunderstandingofallcontrolsystemfunctions
of a rigid-body spacecraft. Relatively simple but practically applicable algorithms are
presentedratherthanrecentadvances.Wetrytoavoiddetailedandspecializedissuesthat
are of less importance for the fundamentalunderstanding,such as detailed environment
models. Furthermore, control problems that can be cast in standard formulations and
solved with existing methods are not treated here. Instead, we intend to provide an
understanding of the principles, put them in an engineering context, and try to give all
explanationsasconciseaspossible.
Besides conventional three-axis attitude control systems, the following topics are
treatedinthisbook:
(cid:129) Controlofagilerotationmaneuversusingcontrolmomentgyros
(cid:129) Precisepointingcontrolwitherrorclassesforpointinginstruments
(cid:129) Controlsystemswithaccelerometersandfree-flyingtestmasses,whichprovidelow-
disturbanceordisturbance-freeenvironments
We believe that these topics are of considerable relevance for the design of future
spacecraft control systems, especially in the field of science and Earth observation
missions. On the other side, the topics of robotic spacecraft and formation flying are
excludedhere.
Forcontrolsystemdesign,asoundunderstandingoftheunderlyingspacecraftdynam-
ics is crucial. Therefore, motion models are described in detail, which includes control
momentgyrosandtestmasses.
vii
viii Preface
There are several excellent books in the field of attitude determination. Here, first
principlesonlyaredescribedinordertoprovideanoverallunderstanding.Actuationand
controlalgorithmsaretreatedinmoredetail,yetwithafocusonbasicprinciples.
Thisbookisintendedforgraduatestudentsandpracticingengineerswhoareinterested
inspacecraftcontrolsystems.Sincefunctionalprinciplesarebestdescribedwithanalytical
modelsandmathematicalnotation,someunderstandinginthefieldsofanalyticalmechan-
ics,signalsandsystems,andcontrolsisrequiredasitisusuallytaughtatmaster’slevel.
Theauthorstriedtoincludetheirpersonalexperienceinspaceflight,comprisingmany
spacecraftandmissionsinthefieldofcommunicationsandconstellations,observationand
science,andtechnologydemonstrators.
WewouldliketothankmanycolleaguesfromAirbusDefenceandSpaceforinsightful
discussions,inparticularNicoBrandt,AndreyKornienko(nowatESA-ESTEC),Thomas
Ott, AlexanderSchleicher,Stefan Winkler,and TobiasZiegler. Any correctionsare wel-
comeviaemailtowalter.fi[email protected]@mailbox.org.
Stuttgart,Germany WalterFichter
August2022 RaminGeshnizjani
Contents
1 SystemEngineeringBasics......................................................... 1
1.1 ObjectivesandInterfacesofControlSystems ............................... 1
1.2 FunctionalArchitectureandEnvironment ................................... 5
1.2.1 OverviewandTerminology .......................................... 5
1.2.2 ExternalDisturbances................................................ 6
1.2.3 Sensors................................................................ 10
1.2.4 Actuators.............................................................. 14
1.3 DesignProcess................................................................. 16
1.4 SystemDesignRules.......................................................... 17
1.4.1 Performance........................................................... 17
1.4.2 ActuatorSizing ....................................................... 19
1.4.3 ProcessingandSoftware ............................................. 21
1.4.4 Redundancy........................................................... 21
1.5 BudgetsandSpecifications.................................................... 22
1.5.1 KeyParameters ....................................................... 22
1.5.2 SpecificPerformanceParameters.................................... 23
References............................................................................ 27
2 SatelliteMotionModels ............................................................ 29
2.1 RotationalKinematics......................................................... 30
2.1.1 AttitudeParametrization ............................................. 30
2.1.2 Conversions........................................................... 32
2.1.3 DifferentialEquations................................................ 35
2.1.4 Two-AxisInertialPointing........................................... 37
2.2 Single-BodySpacecraftandGyrostat........................................ 38
2.2.1 DynamicsofRotationandTranslation .............................. 38
2.2.2 WheelDynamics...................................................... 42
2.2.3 GravitationalForceandTorque...................................... 43
2.2.4 MultipleWheelsandSummary...................................... 45
ix
x Contents
2.3 Single-BodySpacecraftwithControlMomentGyros....................... 46
2.3.1 RotationalDynamics ................................................. 47
2.3.2 FlywheelandGimbalDynamics..................................... 53
2.3.3 SummaryandCMGArrayDynamics............................... 55
2.3.4 Singularities........................................................... 56
2.4 Multi-BodySpacecraftwithTestMass....................................... 62
2.4.1 EquationsofMotion.................................................. 63
2.4.2 Discussion............................................................. 67
References............................................................................ 67
3 RotationalStateDetermination ................................................... 69
3.1 AttitudeDetermination........................................................ 69
3.1.1 ConceptsandtheTwoUnitVectorCase............................. 69
3.1.2 ThreeorMoreUnitVectorMeasurements.......................... 77
3.2 AngularRateEstimation...................................................... 78
3.3 AttitudeObservationandFiltering ........................................... 81
3.3.1 ConceptofaKinematicModel ...................................... 81
3.3.2 YawObservationDuringEarthPointing ............................ 82
3.3.3 Model-BasedFiltering................................................ 83
References............................................................................ 88
4 ActuatorCommanding............................................................. 89
4.1 ReactionWheelActuationandControl ...................................... 89
4.1.1 DistributiontoIndividualWheels.................................... 91
4.1.2 WheelMomentumControl........................................... 92
4.2 ControlMomentGyroActuation............................................. 93
4.2.1 CMGSteeringLaws.................................................. 94
4.2.2 GimbalControlLoop................................................. 98
4.3 ThrusterSelectionandActuation............................................. 101
4.3.1 TorquewithFourThrusters .......................................... 101
4.3.2 ForceandTorque ..................................................... 104
4.3.3 ModulationofSingleThrusters...................................... 109
4.4 MagneticTorquerActuation.................................................. 111
References............................................................................ 112
5 AttitudeandMomentumControl................................................. 115
5.1 ArchitecturesandConcepts................................................... 115
5.2 NonlinearAttitudeandRateControl......................................... 119
5.2.1 RateControl .......................................................... 120
5.2.2 Two-AxisAttitudeAcquisition ...................................... 126
5.2.3 Three-AxisAttitudeControl......................................... 128
Contents xi
5.3 AngularMomentumControl.................................................. 136
5.3.1 MotivationandSingleAxisExample................................ 136
5.3.2 WheelBodyMomentumandNullspaceMomentum............... 138
5.3.3 OptionsforMomentumDesaturation................................ 139
5.3.4 WheelBodyMomentumControl.................................... 140
5.3.5 NullspaceMomentumControl....................................... 142
5.4 LinearAttitudeControl ....................................................... 143
5.4.1 EarthPointingwithMomentumBias................................ 143
5.4.2 PrecisionPointingControl........................................... 148
References............................................................................ 153
6 AccelerometersandDrag-FreeControl.......................................... 155
6.1 Accelerometer................................................................. 155
6.2 DragCompensation ........................................................... 159
6.3 Drag-FreeControlofaCubicTestMass..................................... 160
6.3.1 ObjectiveandPrinciple............................................... 160
6.3.2 ControlLoopStructure............................................... 161
6.3.3 ClosedLoopandControllerDesign ................................. 166
6.4 NotesonSphericalTestMass................................................. 170
References............................................................................ 170
7 ClosingRemarks.................................................................... 173
A CoordinateSystems................................................................. 175
A.1 InertialCoordinateSystem.................................................... 175
A.2 OrbitCoordinateSystem...................................................... 175
A.3 ReferenceAttitudeCoordinateSystem....................................... 175
A.4 SpacecraftBodyCoordinateSystem ......................................... 176
B UsefulToolsofAppliedMathematics............................................. 179
B.1 VectorNotationandCrossProductEquations............................... 179
B.2 SingularValueDecomposition................................................ 180
B.3 ConceptsofLyapunovTheory................................................ 182
B.3.1 Time-InvariantSystems .............................................. 182
B.3.2 Time-VaryingSystems ............................................... 184
B.4 FloquetTheory ................................................................ 185
References............................................................................ 187
C Gravity-GradientForce............................................................ 189
Index...................................................................................... 191