Aeroservoelasticity: Modeling and Control

323 Pages·2015·2.043 MB·English

by  Ashish Tewari

Control Engineering
SeriesEditor
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UniversityofMaryland
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MassachusettsInstituteofTechnology UniversityofTexasatDallas
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GrahamGoodwin MaartenSteinbuch
UniversityofNewcastle TechnischeUniversiteitEindhoven
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Forfurthervolumes:
http://www.springer.com/series/4988
Ashish Tewari
Aeroservoelasticity
Modeling and Control
AshishTewari
DepartmentofAerospaceEngineering
IndianInstituteofTechnology,Kanpur
Kanpur
UttarPradesh
India
ISSN2373-7719 ISSN2373-7727(electronic)
ControlEngineering
ISBN978-1-4939-2367-0 ISBN978-1-4939-2368-7(eBook)
DOI10.1007/978-1-4939-2368-7
MathematicsSubjectClassification(2010): 70Q05, 74H10, 74H15, 74F10, 74S05, 74S25,
76G25, 76H05, 76J20, 76M22, 76M23, 76M25, 76M40, 93B15, 93B30, 93B36, 93B52,
93B55,93C05,93C10,93C15,93C35,93C40,93C80,93D05,93D20,32D99
LibraryofCongressControlNumber:2015933384
SpringerNewYorkHeidelbergDordrechtLondon
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Totheorderandbeautyofnature,
anditsfinelycraftedcontrollaws.
Preface
This book presents aeroservoelasticity (ASE) as a well-formed discipline with a
systematic framework. While many research articles have appeared on the special
applications of ASE–such as active flutter suppression and gust load alleviation–
therearenotextbooksandmonographsonthegeneralandsystematicprocedureto
befollowedinthemodelingandanalysisofaeroservoelasticsystems.Thisbookis
afirststepintryingtofillthisimportantgapintheaerospaceengineeringliterature.
This book introduces the basic math modeling concepts and highlights important
developments involved in structural dynamics, unsteady aerodynamics, and con-
trol systems. It also attempts to evolve a generic procedure to be applied forASE
systemsynthesis.Thetreatmentincludesfinite-elementstructuralmodelingandde-
tailedunsteadyaerodynamicmodelingatvariousspeedsforderivingthenecessary
aeroelasticplants,withsamplecontrolapplicationstoactivefluttersuppression,load
alleviation,andadverseASEcoupling.
A general aeroelastic plant is derived via the finite-element structural dynamic
model,unsteadyaerodynamicmodelsforvariousregimesinthefrequencydomain,
andtheassociatedstate-spacemodelbyrationalfunctionapproximations.Formore
advancedmodels,thefull-potential,Euler,andNavier–Stokesmethodsfortreating
transonic and separated flows are also briefly addressed. EssentialASE controller
designandanalysistechniquesareintroducedtothereader. Introductiontorobust
control-law design methods of LQG/LTR and H2/H∞ synthesis is followed by a
briefcoverageofnonlinearcontroltechniquesofdescribingfunctionsandLyapunov
functions.
The fundamental concepts are presented in such a way that the most important
featurescanbeeasilydeduced.Thebreadthofcoverageissufficientforathorough
understandingofASE.
The focus of this book is on aeroservoelastic modeling, including a brief pre-
sentation on robust and optimal control methods that can be applied to important
aeroservoelastic design problems. It is not possible to give a more comprehensive
ASEtreatmentinasinglebook,anditisenvisagedthatafuturebookcanbedevoted
tomoreadvancedtopicssuchasadaptiveandnonlinearcontroldesigntechniques.
Thisbookisaimedatgraduatestudentsandadvancedresearchersinaerospaceen-
gineering,aswellasprofessionalengineers,technicians,andtestpilotsintheaircraft
vii
viii Preface
industryandlaboratories.Thereaderisassumedtohavetakenbasicundergraduate
coursesinmathematicsandphysics—particularlycalculus,complexvariables,lin-
earalgebra,andfundamentaldynamics—andisencouragedtoreviewtheseconcepts
atseveralplacesinthetext.
AbookonASEisdifficulttowriteduetothebreadthoftopicsitmustnecessarily
address.WhilethisbookcoverstheessentialsofmodelingaspectsofASEwithsome
controlapplications,itgivessufficientmotivationtoareaderwithspecificresearch
intereststofurtherexploretherelevanttopics.Furthermore,thetreatmentoftopicsis
suchthatanovicecanquicklybuilduphis/herunderstandingofASEwithoutmuch
difficulty.Referencesareselectedkeepingboththetypesofreadersinmind.
This book has been long in writing, with the intention first having occurred to
theauthorabout15yearsago. Nothavingaccesstotheindustrialcodesforfinite-
elementandunsteadyaerodynamicsnecessaryforbuildingsuchanexposition,and
notfindingthetimetowriteone’sowncodes, theprojectcontinuedtobedelayed
untilabout2yearsago,whencouragewasfinallygatheredforthispurpose.Testing
andvalidatingthecodesforthemanyexamplesinthebookwasitselfaformidable
task,whichrequiredmanyhoursofpatientprogramming.
I would like to thank Walt Eversman for his course on aeroelasticity, and for
advisingmeinmygraduatestudies.TheeditorialandproductionstaffofBirkhäuser
haveofferedmanyconstructiveinputsduringthepreparationofthemanuscript,for
whichIamindebtedtothem.IamalsogratefultoTheMathWorks,Inc.forproviding
thelatestMATLAB/Simulinkversionutilizedfortheexamplesthroughoutthebook.
November2014 AshishTewari
Contents
1 Aeroservoelasticity ............................................. 1
1.1 Introduction ............................................... 1
1.2 AnIllustrativeExample ..................................... 7
2 StructuralModeling............................................ 13
2.1 Introduction ............................................... 13
2.2 StaticLoadDeflectionModel ................................ 14
2.3 Beam-ShaftIdealization ..................................... 18
2.4 Dynamics ................................................. 22
2.5 LumpedParametersMethod ................................. 27
2.6 Rayleigh-RitzMethod....................................... 31
2.7 Finite-ElementMethod...................................... 33
2.7.1 WeakFormulationandGalerkin’sApproximation ......... 33
2.7.2 Euler-BernoulliBeamandShaftElements ............... 38
2.7.3 IllustrativeExample .................................. 47
2.7.4 PlateBendingElements............................... 51
3 UnsteadyAerodynamicModeling ................................ 59
3.1 Introduction ............................................... 59
3.2 GoverningEquations........................................ 61
3.2.1 ViscousFlow........................................ 61
3.2.2 InviscidFlow........................................ 64
3.2.3 PotentialFlow....................................... 65
3.2.4 TransonicSmall-DisturbanceFlow...................... 69
3.3 LinearizedSubsonicandSupersonicFlow...................... 71
3.4 IncompressibleFlowSolution ................................ 74
3.4.1 UnsteadyVortex-LatticeMethod........................ 80
3.4.2 ClassicalAnalyticalSolution........................... 91
3.5 IntegralEquationforLinearCompressibleFlow................. 102
3.5.1 VelocityPotentialFormulationbyGreen’sTheorem ....... 102
3.5.2 AccelerationPotentialFormulation ..................... 112
ix
x Contents
3.6 SubsonicKernelFunctionandtheDoublet-LatticeMethod........ 116
3.6.1 NumericalResults.................................... 128
3.7 SupersonicLiftingSurfaceMethods........................... 136
3.7.1 Mach-BoxMethod ................................... 139
3.7.2 Doublet-PointMethod ................................ 141
3.8 TransonicSmall-DisturbanceSolutionbyGreen’sFunctionMethod 144
3.8.1 TransonicGreen’sIntegralEquation .................... 144
3.8.2 TransonicDoublet-LatticeMethod...................... 149
4 Finite-StateAeroelasticModeling ................................ 155
4.1 Finite-StateUnsteadyAerodynamicsModel .................... 155
4.1.1 TraditionalFlutterAnalysis ............................ 156
4.1.2 UnsteadyAerodynamicsinTimeDomain ................ 157
4.2 TransientAerodynamicsinTwo-Dimensions.................... 160
4.2.1 RationalFunctionApproximation....................... 161
4.2.2 IndicialAdmittancebyDuhamel’sIntegral ............... 166
4.2.3 TransientAerodynamicsinThree-Dimensions ............ 167
4.2.4 AlternativeMethodsfor3DTransientAerodynamics....... 179
4.2.5 DirectIntegrationofGoverningEquations ............... 182
4.3 State-SpaceRepresentation .................................. 183
4.3.1 TypicalSectionModel ................................ 185
4.3.2 Three-DimensionalWingModel........................ 190
4.3.3 IllustrativeExample .................................. 195
5 LinearAeroelasticControl ...................................... 207
5.1 Introduction ............................................... 207
5.2 LinearFeedbackStabilization ................................ 208
5.2.1 Servo-Actuators ..................................... 210
5.3 OptimalControl............................................ 214
5.3.1 Hamilton-Jacobi-BellmanEquation ..................... 215
5.3.2 LinearSystemswithQuadraticPerformanceIndex ........ 216
5.4 KalmanFilter.............................................. 219
5.5 Infinite-HorizonLinearOptimalControl ....................... 223
5.6 AdverseAereoservoelasticInteraction ......................... 225
5.6.1 Closed-LoopStabilizationoftheASESystem ............ 233
5.6.2 ActiveManeuverLoadAlleviation ...................... 235
5.7 RobustControlofLinearTime-InvariantSystems................ 239
5.7.1 LQG/LTRMethod ................................... 243
5.7.2 H2/H∞Control ..................................... 246
5.8 ActiveFlutterSuppression ................................... 250
6 NonlinearAeroservoelasticApplications .......................... 257
6.1 NonlinearAeroservoelasticity ................................ 257
6.2 DescribingFunctionsforNonlinearASE ....................... 257
6.3 Flapping-WingFlight ....................................... 260
6.3.1 LiftandThrustforFlappingFlight...................... 263
Contents xi
6.4 Shock-InducedBuffet....................................... 271
6.5 TransonicFlutter ........................................... 272
6.5.1 AdaptiveSuppressionofTransonicLCO:IllustrativeExample 273
AppendixA....................................................... 279
Appendix-B....................................................... 285
Appendix-C....................................................... 289
Appendix-D....................................................... 301
References........................................................ 303
Index ............................................................ 311