advance in experiment test design for high perform

8-1ADVANCESINEXPERIMENTDESIGNFORHIGHPERFORMANCEAIRCRAFTEugeneA.MorelliDynamicsandControlBranchMS132,NASALangleyResearchCenterHampton,Virginia23681-2199USASUMMARYAgeneraloverviewandsummaryofrecentadvancesinexperimentdesignforhighperformanceaircraftispresented,alongwithresultsfromflighttests.Generaltheoreticalbackgroundisincluded,withsomediscussionofvariousapproachestomaneuverdesign.FlighttestexamplesfromtheF-18HighAlphaResearchVehicle(HARV)areusedtoillustrateapplicationsofthetheory.InputformsarecomparedusingCramér-Raoboundsforthestandarderrorsofestimatedmodelparameters.Directionsforfutureresearchinexperimentdesignforhighperformanceaircraftareidentified.LISTOFSYMBOLSaayz,linearaccelerations,g'sE{}expectationoperatorJcostfunctionL,M,NbodyaxisaerodynamicmomentsMinformationmatrixNtotalnumberofsampletimesp,q,rbodyaxisangularvelocities,rad/secRdiscretenoisecovariancematrixSi()outputsensitivitymatrixattimeitΔTmaneuverduration,secuni-dimensionalcontrolvectorVairspeed,ft/secxns-dimensionalstatevectoryno-dimensionaloutputvectoryi()outputvectorattimeitΔzi()measuredoutputvectorattimeitΔY,Zbodyaxisaerodynamicforcesaangleofattack,radbsideslipangle,radδijKroneckerdeltaΔtsamplinginterval,secδaailerondeflection,radδrrudderdeflection,radδsstabilatordeflection,radϕ,θ,ψEulerangles,radηelongitudinalstickdeflectionηalateralstickdeflectionηrrudderpedaldeflectionμjjthinputamplitudeconstraintνi()ithdiscretemeasurementnoisevectorθnp-dimensionalparametervectorθjjthmodelparameterσjCramér-Raoboundforthejthparameterτalateralstickequivalenttimedelay,secτrrudderpedalequivalenttimedelay,secξkkthoutputamplitudeconstraint∀forall,foreveryTrtraceSuperscriptsTtranspose-1matrixinverseSubscriptsoaverageortrimvaluesstabilityaxis1.INTRODUCTIONAircraftflighttestsdesignedtocollectdataformodelingpurposesaregenerallymotivatedbyoneormoreofthefollowingobjectives:1.Thedesiretocorrelateaircraftaerodynamiccharacteristicsobtainedfromwindtunnelexperimentsandaerodynamiccalculationswithflighttestdata.2.Refinementoftheaircraftmodelforcontrolsystemanalysisanddesign.3.Accuratepredictionoftheaircraftresponseusingthemathematicalmodel,includingflightsimulationandflightenvelopeexpansion.4.Aircraftacceptancetesting.Thedesignofanexperimenttoachieveanyoftheaboveobjectivesinvolvesspecificationoftheinstrumentation,thesignalconditioning,theflighttestoperationalprocedure,theinputsfortheflighttestmaneuver,themodelstructure,andthedataanalysismethods.Inthiswork,themaneuverdesign–specifically,designofflighttestinputsignals–willbestudiedindependentlyoftheotheraspectswhichimpactthesuccessoftheflighttest.8-2Theflighttestmaneuver(equivalently,theflighttestinput)hasamajorimpactonthequalityofthedataformodelingpurposes.Designinganinputforaccuratemodelparameterestimationrequiresrichexcitationofthesystem,whichisfrequentlyatoddswithvariouspracticalconstraints.Onesuchpracticalconstraintistherequirementthatoutputamplitudeexcursions(e.g.,inangleofattackorsideslipangle)abouttheflighttestconditionbelimitedinordertoassurethevalidityofanassumedmodelstructure.Inputamplitudesmustbeconstrainedforthesamereasons,andtoavoidnonlinearitiessuchasmechanicalstopsandratelimitingwhenthemodelislinear.Thesepracticalconstraintstranslatetoamplitudeconstraintsontheinputsandoutputsduringtheflighttest.Testsforhighperformanceaircraftofteninvolveflightathighanglesofattack,sometimesusingdropmodels.Inthesecases,flighttesttimeisextremelylimitedduetorapidaltitudeloss,anditisimperativethatinformationcontentinthedataperunitofflighttimebemaximizedforeffectiveuseofexpensiveflighttesttime.Suchconsiderationshighlighttheimportanceofoptimizingtheflighttestinputs.Ingeneral,anaircraftmodelcontainsmultipleresponsevariables,multipleaircraftmodelparameters,andoneormoreinputs.Theoverallgoalistodesignamaneuverthatproducesdatafromwhichmodelparameterscanbeestimatedaccurately.Thistranslatesintoexcitingthesystemmodessothatthesensitivitiesofthemodeloutputstotheparametersarehighandcorrelationsamongthesesensitivitiesarelow.Frequencysweepinputs1canbeusedtodothis,requiringlittlemorethanknowledgeofthefrequencyrangeofinterestforthemodeling.Thistechniqueisrestrictedtomovingasingleinputatatime,sothatoff-axisresponsesorcoupledmotionsaregenerallynotwellmodeledfromfrequencysweepdata.Frequencysweepsalsorequirerelativelylongmaneuvertimes(i.e.,1-2minutes)torunthroughthefrequencyrangeofinterest.Lowfrequencycomponentsofthefrequencysweepcontributetolongmaneuvertimes,andalsoincreasethetendencyfortheaircrafttodepartfromthedesiredflighttestcondition.Forhighperformanceaircraft,limitedflighttesttime,multiplecontroleffectors,andflightconditionssuchashighangleofattackmakethefrequencysweepapproachdifficulttouseandexpensive.Analternateapproachistotakeadvantageofaprioriknowledgeaboutthedynamicsoftheaircrafttofocustheinputenergyatfrequenciesnearthesystemmodes.Anapriorimodelcanbeassembledusingwindtunnelaerodynamicdataandknowledgeofrigidbodydynamicsandthecontrolsystem.Withtheapriorimodel,ashortflighttestmaneuvercanbedesignedtoproducedatawithhighinformationcontent.Resulti