Advanced control of aircraft, spacecraft and rockets

449 Pages·2011·4.777 MB·English

by  Ashish Tewari

ADVANCED CONTROL OF
AIRCRAFT, SPACECRAFT
AND ROCKETS
AerospaceSeriesList
BasicHelicopterAerodynamics:ThirdEdition SeddonandNewman July2011
CooperativePathPlanningofUnmanned
AerialVehicles Tsourdosetal November2010
PrinciplesofFlightforPilots Swatton October2010
AirTravelandHealth:ASystems Seabridgeetal September2010
Perspective
DesignandAnalysisofComposite Kassapoglou September2010
Structures:Withapplicationstoaerospace
Structures
UnmannedAircraftSystems:UAVS
Design,DevelopmentandDeployment Austin April2010
IntroductiontoAntennaPlacementand
Installations Macnamara April2010
PrinciplesofFlightSimulation Allerton October2009
AircraftFuelSystems Langtonetal May2009
TheGlobalAirlineIndustry Belobaba April2009
ComputationalModellingandSimulationof
AircraftandtheEnvironment:
Volume1-PlatformKinematicsand
SyntheticEnvironment Diston April2009
HandbookofSpaceTechnology Ley,Wittmann April2009
andHallmann
AircraftPerformanceTheoryand Swatton August2008
PracticeforPilots
SurrogateModellinginEngineering Forrester,Sobester August2008
Design:APracticalGuide andKeane
AircraftSystems,ThirdEdition MoirandSeabridge March2008
IntroductiontoAircraftAeroelasticity
AndLoads WrightandCooper December2007
StabilityandControlofAircraftSystems Langton September2006
MilitaryAvionicsSystems MoirandSeabridge February2006
DesignandDevelopmentofAircraft
Systems MoirandSeabridge June2004
AircraftLoadingandStructuralLayout Howe May2004
AircraftDisplaySystems Jukes December2003
CivilAvionicsSystems MoirandSeabridge December2002
ADVANCED CONTROL OF
AIRCRAFT, SPACECRAFT
AND ROCKETS
AshishTewari
DepartmentofAerospaceEngineering
IndianInstituteofTechnology,Kanpur,India
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LibraryofCongressCataloguing-in-PublicationData
Tewari,Ashish.
Advancedcontrolofaircraft,rockets,andspacecraft/AshishTewari.
p.cm.
Includesbibliographicalreferencesandindex.
ISBN978-0-470-74563-2(hardback)
1. Flightcontrol. 2. Airplanes–Controlsystems. 3. Spacevehicles–Controlsystems. 4. Rockets
(Aeronautics)–Controlsystems. I. Title.
TL589.4.T492011
629.1’1–dc22
2011009365
AcataloguerecordforthisbookisavailablefromtheBritishLibrary.
PrintISBN:9780470745632
ePDFISBN:9781119971207
oBookISBN:9781119971191
ePubISBN:9781119972747
MobiISBN:9781119972754
Setin9/11ptTimesbyThomsonDigital,Noida,India.
Theintellectualorlogicalman,ratherthantheunderstandingorobservant
man,sethimselftoimaginedesigns–todictatepurposestoGod.
–EdgarAllanPoe
Contents
SeriesPreface xiii
Preface xv
1 Introduction 1
1.1 NotationandBasicDefinitions 1
1.2 ControlSystems 3
1.2.1 LinearTrackingSystems 7
1.2.2 LinearTime-InvariantTrackingSystems 9
1.3 GuidanceandControlofFlightVehicles 10
1.4 SpecialTrackingLaws 13
1.4.1 ProportionalNavigationGuidance 13
1.4.2 Cross-ProductSteering 16
1.4.3 Proportional-Integral-DerivativeControl 19
1.5 DigitalTrackingSystem 24
1.6 Summary 25
Exercises 26
References 28
2 OptimalControlTechniques 29
2.1 Introduction 29
2.2 Multi-variableOptimization 31
2.3 ConstrainedMinimization 33
2.3.1 EqualityConstraints 34
2.3.2 InequalityConstraints 38
2.4 OptimalControlofDynamicSystems 41
2.4.1 OptimalityConditions 43
2.5 TheHamiltonianandtheMinimumPrinciple 44
2.5.1 Hamilton–Jacobi–BellmanEquation 45
2.5.2 LinearTime-VaryingSystemwithQuadraticPerformanceIndex 47
2.6 OptimalControlwithEnd-PointStateEqualityConstraints 48
2.6.1 Euler–LagrangeEquations 50
2.6.2 SpecialCases 50
2.7 NumericalSolutionofTwo-PointBoundaryValueProblems 52
2.7.1 ShootingMethod 54
2.7.2 CollocationMethod 57
2.8 OptimalTerminalControlwithInteriorTimeConstraints 61
2.8.1 OptimalSingularControl 62
2.9 TrackingControl 63
viii Contents
2.9.1 NeighboringExtremalMethodandLinearQuadraticControl 64
2.10 StochasticProcesses 69
2.10.1 StationaryRandomProcesses 75
2.10.2 FilteringofRandomNoise 77
2.11 KalmanFilter 77
2.12 RobustLinearTime-InvariantControl 81
2.12.1 LQG/LTRMethod 82
2.12.2 H2/H∞DesignMethods 89
2.13 Summary 96
Exercises 98
References 101
3 OptimalNavigationandControlofAircraft 103
3.1 AircraftNavigationPlant 104
3.1.1 WindSpeedandDirection 110
3.1.2 NavigationalSubsystems 112
3.2 OptimalAircraftNavigation 115
3.2.1 OptimalNavigationFormulation 116
3.2.2 ExtremalSolutionoftheBoundary-ValueProblem:Long-Range
FlightExample 119
3.2.3 GreatCircleNavigation 121
3.3 AircraftAttitudeDynamics 128
3.3.1 TranslationalandRotationalKinetics 132
3.3.2 AttitudeRelativetotheVelocityVector 135
3.4 AerodynamicForcesandMoments 136
3.5 LongitudinalDynamics 139
3.5.1 LongitudinalDynamicsPlant 142
3.6 OptimalMulti-variableLongitudinalControl 145
3.7 Multi-inputOptimalLongitudinalControl 147
3.8 OptimalAirspeedControl 148
3.8.1 LQG/LTRDesignExample 149
3.8.2 H∞DesignExample 160
3.8.3 AltitudeandMachControl 166
3.9 Lateral-DirectionalControlSystems 173
3.9.1 Lateral-DirectionalPlant 173
3.9.2 OptimalRollControl 177
3.9.3 Multi-variableLateral-DirectionalControl:Heading-HoldAutopilot 180
3.10 OptimalControlofInertia-CoupledAircraftRotation 183
3.11 Summary 189
Exercises 192
References 194
4 OptimalGuidanceofRockets 195
4.1 Introduction 195
4.2 OptimalTerminalGuidanceofInterceptors 195
4.3 Non-planarOptimalTrackingSystemforInterceptors:3DPN 199
4.4 FlightinaVerticalPlane 208
4.5 OptimalTerminalGuidance 211
Contents ix
4.6 VerticalLaunchofaRocket(Goddard’sProblem) 216
4.7 Gravity-TurnTrajectoryofLaunchVehicles 219
4.7.1 LaunchtoCircularOrbit:ModulatedAcceleration 220
4.7.2 LaunchtoCircularOrbit:ConstantAcceleration 227
4.8 LaunchofBallisticMissiles 228
4.8.1 Gravity-TurnwithModulatedForwardAcceleration 232
4.8.2 ModulatedForwardandNormalAcceleration 233
4.9 PlanarTrackingGuidanceSystem 237
4.9.1 Stability,Controllability,andObservability 241
4.9.2 NominalPlantforTrackingGravity-TurnTrajectory 243
4.10 RobustandAdaptiveGuidance 247
4.11 GuidancewithStateFeedback 250
4.11.1 GuidancewithNormalAccelerationInput 250
4.12 Observer-BasedGuidanceofGravity-TurnLaunchVehicle 254
4.12.1 Altitude-BasedObserverwithNormalAccelerationInput 255
4.12.2 Bi-outputObserverwithNormalAccelerationInput 260
4.13 MassandAtmosphericDragModeling 266
4.14 Summary 274
Exercises 275
References 275
5 AttitudeControlofRockets 277
5.1 Introduction 277
5.2 AttitudeControlPlant 277
5.3 Closed-LoopAttitudeControl 281
5.4 RollControlSystem 281
5.5 PitchControlofRockets 282
5.5.1 PitchProgram 282
5.5.2 PitchGuidanceandControlSystem 283
5.5.3 AdaptivePitchControlSystem 288
5.6 YawControlofRockets 294
5.7 Summary 295
Exercises 295
Reference 296
6 SpacecraftGuidanceSystems 297
6.1 Introduction 297
6.2 OrbitalMechanics 297
6.2.1 OrbitEquation 298
6.2.2 PerifocalandCelestialFrames 299
6.2.3 TimeEquation 301
6.2.4 Lagrange’sCoefficients 304
6.3 SpacecraftTerminalGuidance 305
6.3.1 MinimumEnergyOrbitalTransfer 307
6.3.2 Lambert’sTheorem 311
6.3.3 Lambert’sProblem 313
6.3.4 LambertGuidanceofRockets 322
6.3.5 OptimalTerminalGuidanceofRe-entryVehicles 327
x Contents
6.4 GeneralOrbitalPlantforTrackingGuidance 334
6.5 PlanarOrbitalRegulation 339
6.6 OptimalNon-planarOrbitalRegulation 345
6.7 Summary 352
Exercises 352
References 355
7 OptimalSpacecraftAttitudeControl 357
7.1 Introduction 357
7.2 TerminalControlofSpacecraftAttitude 357
7.2.1 OptimalSingle-AxisRotationofSpacecraft 358
7.3 Multi-axisRotationalManeuversofSpacecraft 364
7.4 SpacecraftControlTorques 375
7.4.1 RocketThrusters 375
7.4.2 ReactionWheels,MomentumWheelsandControlMomentGyros 377
7.4.3 MagneticFieldTorque 378
7.5 SatelliteDynamicsPlantforTrackingControl 379
7.6 EnvironmentalTorques 380
7.6.1 Gravity-GradientTorque 382
7.7 Multi-variableTrackingControlofSpacecraftAttitude 383
7.7.1 ActiveAttitudeControlofSpacecraftbyReactionWheels 385
7.8 Summary 389
Exercises 389
References 390
AppendixA:LinearSystems 391
A.1 Definition 391
A.2 Linearization 392
A.3 SolutiontoLinearStateEquations 392
A.3.1 HomogeneousSolution 393
A.3.2 GeneralSolution 393
A.4 LinearTime-InvariantSystem 394
A.5 LinearTime-InvariantStabilityCriteria 395
A.6 ControllabilityofLinearTime-InvariantSystems 395
A.7 ObservabilityofLinearTime-InvariantSystems 395
A.8 TransferMatrix 396
A.9 SingularValueDecomposition 396
A.10 LinearTime-InvariantControlDesign 397
A.10.1 RegulatorDesignbyEigenstructureAssignment 397
A.10.2 RegulatorDesignbyLinearOptimalControl 398
A.10.3 LinearObserversandOutputFeedbackCompensators 398
References 400
AppendixB:Stability 401
B.1 Preliminaries 401
B.2 StabilityintheSenseofLagrange 402
B.3 StabilityintheSenseofLyapunov 404
B.3.1 AsymptoticStability 406