Dynamic modeling, simulation and control design of a parafoil-payload system for ship launched

192 Pages·2017·15.31 MB·English

by  Anand S. Puranik

MMiicchhiiggaann TTeecchhnnoollooggiiccaall UUnniivveerrssiittyy
DDiiggiittaall CCoommmmoonnss @@ MMiicchhiiggaann TTeecchh
Dissertations, Master's Theses and Master's Dissertations, Master's Theses and Master's
Reports - Open Reports
2011
DDyynnaammiicc mmooddeelliinngg,, ssiimmuullaattiioonn aanndd ccoonnttrrooll ddeessiiggnn ooff aa ppaarraaffooiill--
ppaayyllooaadd ssyysstteemm ffoorr sshhiipp llaauunncchheedd aaeerriiaall ddeelliivveerryy ssyysstteemm ((SSLLAADDSS))
Anand S. Puranik
Michigan Technological University
Follow this and additional works at: https://digitalcommons.mtu.edu/etds
Part of the Mechanical Engineering Commons
Copyright 2011 Anand S. Puranik
RReeccoommmmeennddeedd CCiittaattiioonn
Puranik, Anand S., "Dynamic modeling, simulation and control design of a parafoil-payload system for
ship launched aerial delivery system (SLADS)", Dissertation, Michigan Technological University, 2011.
https://doi.org/10.37099/mtu.dc.etds/401
Follow this and additional works at: https://digitalcommons.mtu.edu/etds
Part of the Mechanical Engineering Commons
DYNAMICMODELING,SIMULATIONANDCONTROLDESIGNOFA
PARAFOIL-PAYLOADSYSTEMFORSHIPLAUNCHEDAERIAL
DELIVERYSYSTEM(SLADS)
By
AnandSPuranik
ADISSERTATION
Submittedinpartialfulfillmentoftherequirementsforthedegreeof
DOCTOROFPHILOSOPHY
(MechanicalEngineering–EngineeringMechanics)
MICHIGANTECHNOLOGICALUNIVERSITY
2011
Copyright©2011AnandSPuranik
This dissertation, “Dynamic Modeling, Simulation And Control Design Of A Parafoil-
PayloadSystemForShipLaunchedAerialDeliverySystem(SLADS),”isherebyapproved
in partial fulfillment for the requirements for the Degree of DOCTOR OF PHILOSOPHY
INMechanicalEngineering–EngineeringMechanics.
DepartmentofMechanicalEngineering–EngineeringMechanics
Advisor:
Dr.GordonParker
CommitteeMember:
Dr.ChrisPaserrello
CommitteeMember:
Dr.JasonBlough
CommitteeMember:
Dr.AllanStruthers
DepartmentChair:
ProfessorWilliamW.Predebon
Date:
Contents
ListofFigures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
ListofTables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 AerodynamicDecelerators . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.1 Parachute . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.2 Parasail . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.3 Paraglider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.3.1 ParafoilCanopy . . . . . . . . . . . . . . . . . . . . . . 7
1.2.3.2 LeadingEdge . . . . . . . . . . . . . . . . . . . . . . . 7
1.2.3.3 TrailingEdge . . . . . . . . . . . . . . . . . . . . . . . 7
1.2.3.4 SuspensionLines . . . . . . . . . . . . . . . . . . . . . 7
iv
1.2.3.5 ControlLines . . . . . . . . . . . . . . . . . . . . . . . 7
1.2.3.6 Risers . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3 ShipLaunchedAerialDeliverySystem(SLADS) . . . . . . . . . . . . . . 8
1.4 ResearchContributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.5 DissertationOutline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2. LiteratureReview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1 ParafoilEvolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 HangglidersandParagliders . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 DynamicModels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4 AerodynamicTheory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.4.1 AngleOfAttack(α) . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.4.2 SideSlipAngle(β) . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.4.3 AerodynamicForces . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.4.3.1 Drag . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.4.3.2 Lift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4.3.3 SideForce . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4.4 AerodynamicMoments . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4.4.1 PitchingMoment . . . . . . . . . . . . . . . . . . . . . 22
2.4.4.2 RollingMoment . . . . . . . . . . . . . . . . . . . . . . 22
2.4.4.3 YawingMoment . . . . . . . . . . . . . . . . . . . . . . 23
2.5 StabilityAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.6 ControlInput . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.7 ApparentMassEffects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
v
3. ModelingOfTowedParafoil-PayloadSystem . . . . . . . . . . . . . . . . . . 32
3.1 ModelDescriptionAndModelingAssumptions . . . . . . . . . . . . . . . 32
3.2 EquationsOfMotion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2.1 RotationMatrices . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.2.2 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.2.3 LagrangeEquations . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2.4 GeneralizedForces . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2.5 DynamicEquations . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3 AerodynamicModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3.1 ControlInputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.4 GeometricandInertialProperties . . . . . . . . . . . . . . . . . . . . . . . 50
3.4.1 InertiaCalculations . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.5 2DSimulationResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.6 Operator-In-The-LoopSimulation . . . . . . . . . . . . . . . . . . . . . . 60
4. StabilityAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.2 LinearModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.2.1 Lyapunov’sLinearizationMethod . . . . . . . . . . . . . . . . . . 64
4.2.2 LinearizationofDynamicSystem . . . . . . . . . . . . . . . . . . 65
4.3 SteadyStateFlight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.4 LinearandNonlinearModelComparison . . . . . . . . . . . . . . . . . . 71
4.5 StabilityBoundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.5.1 ElevationAngleη . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.5.2 SymmetricBrakeDeflectionδ . . . . . . . . . . . . . . . . . . . 81
s
vi
4.5.3 EffectofTowPointLocation . . . . . . . . . . . . . . . . . . . . . 82
4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5. ControlSystemDesign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.1 ControlObjectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.2 ControllabilityAndObservability . . . . . . . . . . . . . . . . . . . . . . 87
5.2.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.2.2 CaseI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.2.3 CaseII: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.2.4 CaseIII: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.3 TowUpControlStrategy . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.3.1 ControllerforAscentRate . . . . . . . . . . . . . . . . . . . . . . 99
5.4 LateralStabilityControl . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.4.1 LateralStateFeedbackController . . . . . . . . . . . . . . . . . . 104
5.4.2 FullStateFeedbackController . . . . . . . . . . . . . . . . . . . . 108
5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6. ConclusionsAndFutureWork . . . . . . . . . . . . . . . . . . . . . . . . . . 115
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
A. NonlinearDynamicEquationCoefficients . . . . . . . . . . . . . . . . . . . . 122
B. DerivationofEquationsofMotion: MapleScript . . . . . . . . . . . . . . . . 149
C. SteadyStateValues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
D. Copyrights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
List of Figures
1.1 An American paratrooper using a MC1-1C series parachute (1). (See Ap-
pendixDforthedocumentationthatthismaterialisinpublicdomain.) . . . 5
1.2 Parasail is a towed parachute (2). (See Appendix D for the documentation
thatthismaterialisinpublicdomain.) . . . . . . . . . . . . . . . . . . . . 5
1.3 Significantpartsofaparagliderorram-airparachute(3). (SeeAppendixD
forthedocumentationofthepermissiontorepublishthisimage). . . . . . . 6
1.4 StagesofoperationofSLADS. . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1 FrancisRogallowithhisparawinginthewindtunnel. (Photocredit: NASA/courtesy
of nasaimages.org. See Appendix D for the documentation that this image
isinthepublicdomain.) . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 NASAX-38re-entryvehicle(4). Photocredit: NASA/courtesyofnasaim-
ages.org. (See Appendix D for the documentation that this image is in the
publicdomain.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 NineDOFdynamicmodelofparafoil-payloadsystemusedbySlegersand
Costello (5). (See Appendix D for the documentation of permssion to re-
publishthisfigurefrom(5).) . . . . . . . . . . . . . . . . . . . . . . . . . 17
viii
2.4 PaneldiscretizationusedbySlegersandCostello(5). (SeeAppendixDfor
thedocumentationofpermssiontorepublishthisfigurefrom(5).) . . . . . 18
2.5 Angleofattackα . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.6 Sideslipangleβ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.7 Longitudinalstaticanalysis(6). (SeeAppendixDforthedocumentationof
permssiontoreprintthisfigurefrom(6).) . . . . . . . . . . . . . . . . . . 25
3.1 Significantpointsofthemodel. . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2 Schematicdiagramofthestatesandreferenceframesofthemodel. . . . . . 35
3.3 Aerodynamicforces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.4 Modelingcontrolinputorparafoilbrakedeflection . . . . . . . . . . . . . 48
3.5 Steadystaterollangleϕ forvariouscontrolinputs . . . . . . . . . . . . . 48
20
3.6 Steadystateyawangleψ forvariouscontrolinputs . . . . . . . . . . . . 49
20
3.7 Steadystateoffplanetowangleψ forvariouscontrolinputs . . . . . . . 49
10
3.8 Parafoil used for testing. (courtesy: Flight Concepts Int’l, Inc. See Ap-
pendixDforthedocumentationofthepermissiontorepublishthisimage) . 50
3.9 Payloaddimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.10 SideviewofaparafoilpayloadsystemfornetCGcalculation . . . . . . . 54
3.11 Steadystatevaluesofin-planetowangleθ andpitchangleθ . . . . . . . 56
1 2
3.12 Steady state values of in-plane tow angle θ for various symmetric brake
1
inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.13 Steadystatevaluesofpitchangleθ forvarioussymmetricbrakeinputs . . 58
2
3.14 Inertial X component of the relative vector between point of attachment at
shipandtheparafoil-payloadsystem . . . . . . . . . . . . . . . . . . . . . 59
ix
3.15 Inertial Z component of the relative vector between point of attachment at
shipandtheparafoil-payloadsystem . . . . . . . . . . . . . . . . . . . . . 59
3.16 Operator-In-Loopsimulationsetup . . . . . . . . . . . . . . . . . . . . . . 60
4.1 Steadystateflightconditionforsymmetricbrakeinputδ = 0.2andasym-
s0
metricbrakeinputδ = 0.1 . . . . . . . . . . . . . . . . . . . . . . . . . 70
a0
4.2 Brakeinputperturbationof∆δ = 0.1 . . . . . . . . . . . . . . . . . . . . 71
4.3 Linearandnonlinearmodelcomparisonoflongitudinalstatestoasymmet-
ricbrakeperturbation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.4 Linearandnonlinearmodelcomparisonoflateralstates . . . . . . . . . . . 73
4.5 WindInputmodeledusingthreeparameters: v ,µandη . . . . . . . . . . 74
w
4.6 Stability boundaries for various η. Regions interior to each contour are
stable,andunstableexteriortoacontour. . . . . . . . . . . . . . . . . . . . 76
4.7 Stabilityboundariesforvariousδ . . . . . . . . . . . . . . . . . . . . . . 83
s
4.8 Stabilityboundaryshowingtheeffectoftowpointlocation . . . . . . . . . 84
5.1 TopviewofthesteadystateconfigurationincaseI . . . . . . . . . . . . . 91
5.2 TopviewofthesteadystateconfigurationincaseII . . . . . . . . . . . . . 93
5.3 TopviewofthesteadystateconfigurationincaseIII . . . . . . . . . . . . 95
5.4 OpenLoopPlantSchematic . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.5 Effect of symmetric brake deflection on ascent rate. Cable payout rate is
0.3meters/secstartingat10sec,negativep isanupwardmotion.. . . . 98
2/1,z
5.6 Schematicoftowupascentratecontrollerforparafoil-payloadsystem . . . 100
5.7 Ascentratecomparisonobtainedwithtwotypesofcontrollers . . . . . . . 101
5.8 Relativealtitudebetweenparafoil-payloadsystemandship:comparisonob-
tainedwithtwotypesofcontrollers . . . . . . . . . . . . . . . . . . . . . . 102