Modeling, Analysis, and Control of a Hypersonic Vehicle With Significant Aero-Thermo-Elastic ...

207 Pages·2010·6.06 MB·English

Modeling,Analysis,andControl ofaHypersonicVehicleWith
Significant Aero-Thermo-Elastic-PropulsionInteractions,
and PropulsiveUncertainty
by
AkshayShashikumarKorad
AThesisPresented inPartial Fulfillment
oftheRequirements fortheDegree
MasterofScience
ARIZONA STATEUNIVERSITY
May2010
Modeling,Analysis,andControl ofaHypersonicVehicleWith
Significant Aero-Thermo-Elastic-PropulsionInteractions,
and PropulsiveUncertainty
by
AkshayShashikumarKorad
hasbeen approved
April2010
GraduateSupervisoryCommittee:
Armando A.Rodriguez, Chair
KonstantinosS. Tsakalis
ValanaL. Wells
ACCEPTED BY THE GRADUATE COLLEGE
ABSTRACT
Thisthesisexaminesthemodeling,analysis,andcontrolsystemdesignissuesforscram-
jetpowered hypersonicvehicles. Anonlinearthreedegreesoffreedom longitudinalmodel
which includes aero-propulsion-elasticity effects was used for all analysis. This model is
based upon classical compressible flow and Euler-Bernouli structural concepts. Higher fi-
delitycomputationalfluiddynamicsandfiniteelementmethodsareneededformoreprecise
intermediate and final evaluations. The methods presented within this thesis were shown
to be useful for guiding initial control relevant design. The model was used to examine
the vehicles static and dynamic characteristics over the vehicles trimmable region. The
vehiclehas significant longitudinalcouplingbetween thefuel equivalencyratio (FER) and
the flight path angle (FPA). For control system design, a two-input two-output plant (FER
- elevator to speed-FPA) with 11 states (including 3 flexible modes) was used. Velocity,
FPA, and pitchwere assumedtobeavailableforfeedback.
Propulsion system design issues were given special consideration. The impact of en-
gine characteristics (design) and plume model on control system design were addressed.
Various engine designs were considered for comparison purpose. With accurate plume
modeling, effective coupling from the FER to the FPA was increased, which made the
peak frequency-dependent (singular value) conditioning of the two-input two-output plant
(FER-elevator to speed-FPA) worse. This forced the control designer to trade off desir-
able (performance/robustness) properties between the plant input and output. For the ve-
hicle under consideration (with a very aggressive engine and significant coupling), it has
been observed that a large FPA settling time is needed in order to obtain reasonable (per-
formance/robustness) properties at the plant input. Ideas for alleviating this fundamental
tradeoff were presented. Plume modeling was also found to be particularly significant.
Controllers based on plants with insufficient plume fidelity did not work well with the
higherfidelityplants. Giventheabove,thethesismakessignificantcontributionstocontrol-
relevanthypersonicvehiclemodeling,analysis,anddesign.
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To myFamily,Friends and Teachers
iv
ACKNOWLEDGEMENTS
IamverygratefulforthecooperationandsupportofmyadvisorDr. A.A.Rodriguez,who
has shownagreat deal ofpatienceand confidencein mywork.
Besides my advisor, I would like to thank the rest of my thesis committee: Drs. K.
Tsakalis,and V. Wells.
There are several other faculty members who have widened my horizons considerably
through their courses and guidance. In particular, I would like to thank Dr. Montgomery
and Dr. Mittelmann.
I would like to acknowledge the tremendous support and computing resources offered
by theIra A.Fulton SchoolofEngineeringHighPerformance ComputingInitiative.
I would also like to acknowledge the help and guidance of Jeffrey J. Dickeson and
Srikanth Sridharan.
Thiswork hasbeen supportedby NASAgrant NNX07AC42A. .
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TABLE OFCONTENTS
Page
LIST OFTABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
LIST OFFIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
CHAPTER
1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Related Workand LiteratureSurvey . . . . . . . . . . . . . . . . . 1
1.2.1 OverviewofHypersonicsResearch . . . . . . . . . . . . . 1
1.2.2 Controls-RelevantHypersonicVehicleModeling . . . . . . 8
1.2.3 Modelingand Control Issues/Challenges . . . . . . . . . . 10
1.3 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.4 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.5 TableofDefinitions . . . . . . . . . . . . . . . . . . . . . . . . . 19
2 OVERVIEWOF HYPERSONIC VEHICLE MODEL . . . . . . . . . . 22
2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2 VehicleLayout . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.3 EquationsofMotion . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.4 AerodynamicModeling . . . . . . . . . . . . . . . . . . . . . . . 32
2.4.1 U.S. Standard Atmosphere(1976) . . . . . . . . . . . . . . 32
2.4.2 ViscousEffects . . . . . . . . . . . . . . . . . . . . . . . . 35
2.4.3 UnsteadyEffects . . . . . . . . . . . . . . . . . . . . . . . 37
2.5 Properties Across aShock . . . . . . . . . . . . . . . . . . . . . . 38
2.6 Force andMomentSummations . . . . . . . . . . . . . . . . . . . 40
2.7 PropulsionModeling . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.7.1 Shock Conditions. . . . . . . . . . . . . . . . . . . . . . . 47
2.7.2 TranslatingCowl Door. . . . . . . . . . . . . . . . . . . . 47
2.7.3 Inlet Properties. . . . . . . . . . . . . . . . . . . . . . . . 47
2.7.4 DiffuserExit-CombustorEntranceProperties. . . . . . . . . 48
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CHAPTER Page
2.7.5 CombustorExitProperties. . . . . . . . . . . . . . . . . . 48
2.7.6 Internal Nozzle. . . . . . . . . . . . . . . . . . . . . . . . 56
2.7.7 External Nozzle. . . . . . . . . . . . . . . . . . . . . . . . 57
2.8 Structure Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.9 Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . . 61
3 StaticProperties ofVehicle . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.2 Trimming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.2.1 Trim-Steps andIssues . . . . . . . . . . . . . . . . . . . . 64
3.3 StaticAnalysis: TrimmableRegion . . . . . . . . . . . . . . . . . 65
3.4 StaticAnalysis: NominalProperties . . . . . . . . . . . . . . . . . 67
3.4.1 StaticAnalysis: TrimFER . . . . . . . . . . . . . . . . . . 67
3.4.2 StaticAnalysis: TrimElevator . . . . . . . . . . . . . . . . 68
3.4.3 StaticAnalysis: TrimAngle-of-Attack . . . . . . . . . . . 69
3.4.4 StaticAnalysis: TrimForebodyDeflection . . . . . . . . . 70
3.4.5 StaticAnalysis: TrimAftbodyDeflection . . . . . . . . . . 71
3.4.6 StaticAnalysis: TrimDrag . . . . . . . . . . . . . . . . . . 72
3.4.7 StaticAnalysis: TrimDrag (Inviscid) . . . . . . . . . . . . 73
3.4.8 StaticAnalysis: TrimDrag (Viscous) . . . . . . . . . . . . 74
3.4.9 StaticAnalysis: TrimDrag Ratio (Viscous/Total) . . . . . . 75
3.4.10 StaticAnalysis: TrimL/DRatio . . . . . . . . . . . . . . . 76
3.4.11 StaticAnalysis: TrimElevatorForce . . . . . . . . . . . . 77
3.4.12 StaticAnalysis: TrimCombustorMach . . . . . . . . . . . 78
3.4.13 StaticAnalysis: TrimCombustorTemp. . . . . . . . . . . . 79
3.4.14 StaticAnalysis: TrimFuel MassFlow . . . . . . . . . . . . 80
3.4.15 StaticAnalysis: TrimInternal NozzleMach . . . . . . . . . 81
3.4.16 StaticAnalysis: TrimInternal NozzleTemp. . . . . . . . . 82
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CHAPTER Page
3.4.17 StaticAnalysis: TrimReynoldsNumber . . . . . . . . . . 83
3.4.18 StaticAnalysis: TrimAbsoluteViscosity . . . . . . . . . . 84
3.4.19 StaticAnalysis: TrimKinematicViscosity . . . . . . . . . 85
3.5 Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . . 86
4 DynamicProperties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.2 Linearization -Stepsand Issues . . . . . . . . . . . . . . . . . . . 89
4.3 DynamicAnalysis: NominalProperties -Mach 8, 85kft . . . . . . 92
4.3.1 NominalPole-Zero Plot . . . . . . . . . . . . . . . . . . . 92
4.3.2 ModalAnalysis. . . . . . . . . . . . . . . . . . . . . . . . 93
4.4 DynamicAnalysis-RHP Pole, Zero variations . . . . . . . . . . . 95
4.4.1 DynamicAnalysis: RHPPole . . . . . . . . . . . . . . . . 95
4.4.2 DynamicAnalysis: RHPZero . . . . . . . . . . . . . . . . 96
4.4.3 DynamicAnalysis: RHPZero-Poleratio . . . . . . . . . . 97
4.5 DynamicAnalysis-Frequency Responses . . . . . . . . . . . . . 99
4.5.1 DynamicAnalysis-BodeMagnitudeResponse . . . . . . . 99
4.5.2 DynamicAnalysis-BodePhaseResponse . . . . . . . . . 99
4.6 DynamicAnalysis-SingularValues . . . . . . . . . . . . . . . . . 100
4.7 FPA ControlViaFER . . . . . . . . . . . . . . . . . . . . . . . . 101
4.8 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . 101
5 PlumeModelingand EngineDesignConsiderations . . . . . . . . . . . 103
5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.2 EngineParameterStudies . . . . . . . . . . . . . . . . . . . . . . 104
5.3 PlumeCalculationBased onP . . . . . . . . . . . . . . . . . . . 109
∞
5.3.1 Exact PlumeCalculation Based on P -(P -Exact) . . . . 113
∞ ∞
5.4 Exact PlumeCalculationBased on P - (P -Exact) . . . . . . 119
shock shock
5.5 New PlumeApproximationBased onP -(P -Approx) . . . 123
shock shock
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CHAPTER Page
5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
6 Control SystemDesign . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
6.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
6.2 Control Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . 130
6.3 ControllerDesign . . . . . . . . . . . . . . . . . . . . . . . . . . 136
6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
7.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
7.2 Ideas forFutureResearch . . . . . . . . . . . . . . . . . . . . . . 151
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
A CODE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
viii
LIST OF TABLES
Table Page
2.1 MassDistributionforHSV Model . . . . . . . . . . . . . . . . . . . . 30
2.2 States forHypersonicVehicleModel . . . . . . . . . . . . . . . . . . . 31
2.3 ControlsforHypersonicVehicleModel . . . . . . . . . . . . . . . . . 31
2.4 VehicleNominalParameterValues . . . . . . . . . . . . . . . . . . . . 32
2.5 ViscousInteractionSurfaces . . . . . . . . . . . . . . . . . . . . . . . 37
2.6 HSV -Forces and Moments . . . . . . . . . . . . . . . . . . . . . . . . 42
4.1 Polesat Mach 8, 85kft: LevelFlight,FlexibleVehicle . . . . . . . . . . 93
4.2 Zerosat Mach 8, 85kft: LevelFlight,FlexibleVehicle . . . . . . . . . . 93
4.3 EigenvectorMatrixatMach 8, 85kft: LevelFlight,FlexibleVehicle . . 94
5.1 Comparisonof3EngineDesigns(Mach 8, 85kft, LevelFlight) . . . . . 108
5.2 Momentsactingon vehicleat Mach 8,85 kft . . . . . . . . . . . . . . . 116
5.3 Momentsactingon vehicleat Mach 8,85 kft . . . . . . . . . . . . . . . 121
5.4 Momentsactingon vehicleat Mach 8,85 kft . . . . . . . . . . . . . . . 125
6.1 Gap betweenplants(Mach 8, 85kft) . . . . . . . . . . . . . . . . . . . 134
6.2 Closedloopproperties fordifferentsettlingtime . . . . . . . . . . . . . 148
6.3 Closedloopproperties(P -ApproxcontrollerwithP -ExactPlant) 148
shock shock
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