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Nonlinear Simulation of a Micro Air Vehicle

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NONLINEARSIMULATIONOFAMICROAIRVEHICLEByJASONJOSEPHJACKOWSKIATHESISPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFMASTEROFSCIENCEUNIVERSITYOFFLORIDA2004

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IdedicatethisworktomywonderfulandlovelyanceEllenBozarth.Withoutherloveandsupport,Icouldnothavedonethis.

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ACKNOWLEDGMENTSIthanktheAFRL-MNandEglinAirForceforfundingthisproject.IwanttothanktheentireightcontrolslabwhichincludeRyanCausey,KristinFitzpatrick,JoeKehoe,MujahidAbdulrahim,AnukulGoel,andRobertEick.IwouldliketothankJasonGrzywnaandJasonPlewfortheirhelpandexpertiseinsoldering.IwouldliketothankDr.RickLindforhisadvisementandguidanceduringthisproject.AbigthanksgoestomybrotherJeJackowskiwhohelpedmemakearesolution-enhancingcircuitboardforouraltimeterduringChristmasbreak. iii

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TABLEOFCONTENTS page ACKNOWLEDGMENTS ............................. iii LISTOFTABLES ................................. vi LISTOFFIGURES ................................ vii ABSTRACT .................................... ix CHAPTER 1INTRODUCTION .............................. 1 1.1Motivation ............................... 1 1.2Background .............................. 2 1.2.1MicroAirVehicles ....................... 2 1.2.2AVCAAFVehicle ....................... 4 1.2.3AVCAAFAutopilot ...................... 5 1.3Overview ................................ 9 2SIMULATIONARCHITECTURE ..................... 11 2.1SimulationOverview ......................... 11 2.2Non-LinearDynamicsPlant ..................... 11 3NONLINEAREQUATIONSOFMOTION ................. 14 3.1FramesofReference .......................... 14 3.2Rotations ............................... 14 3.3KinematicEquations ......................... 16 3.4ForceandMomentCalculations ................... 20 3.5CalculationofStates ......................... 21 4CHARACTERIZATIONMETHODS .................... 22 4.1PhysicalMeasurements ........................ 22 4.2FiniteElementMethods ....................... 22 4.3WindTunnel ............................. 22 4.4ComputationalFluidDynamics ................... 23 4.5FlightTesting ............................. 23 iv

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5AVCAAFCHARACTERIZATION ..................... 24 5.1Overview ................................ 24 5.2ExperimentalAerodynamics ..................... 24 5.2.1Testing ............................. 24 5.2.2Results ............................. 26 5.3AnalyticalInertias .......................... 27 5.4AnalyticalAerodynamics ....................... 29 5.5ModelIntegration ........................... 31 5.5.1WindTunnelDataAnalysis ................. 31 5.5.2Aerodynamics ......................... 33 5.6LinearizedDynamics ......................... 34 5.6.1Longitudinal .......................... 34 5.6.2Lateral-Directional ...................... 37 5.7ModelingResults ........................... 41 6AVCAAFSUBSYSTEMS .......................... 43 6.1SensorSubsystem ........................... 43 6.1.1CameraSubsystem ...................... 43 6.1.2GPSSubsystem ........................ 48 6.1.3AltitudeSubsystem ...................... 49 6.2ActuatorSubsystem ......................... 49 6.3ControllerSubsystem ......................... 50 7RESULTSANDCONCLUSIONS ...................... 51 7.1Results ................................. 51 7.2Conclusion ............................... 51 8RECCOMENDATIONS ........................... 53 8.1Overview ................................ 53 8.2WindTunnelCharacterization .................... 53 8.3ComputationalFluidDynamicsCharacterization .......... 54 8.4StreamliningMAVDesigntoCFDCharacterizationProcess ... 54 8.5MiscellaneousReccomendations ................... 54 REFERENCES ................................... 56 BIOGRAPHICALSKETCH ............................ 60 v

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LISTOFTABLES Table page 1{1AVCAAFvehiclegeneralproperties ................... 5 2{1Standardatmosphereairdensities .................... 12 5{1AVCAAFvehiclecomponentmasses ................... 28 5{2Analyticalinertiaproperties ....................... 29 5{3Estimateddynamicderivatives ...................... 30 5{4Analyticalandexperimentalstabilityderivatives ............ 34 5{5Longitudinalderivatives .......................... 36 5{6Longitudinaleigenvalues .......................... 36 5{7Longitudinaleigenvectors ......................... 37 5{8Lateraldirectionalderivatives ....................... 39 5{9Lateral-directionaleigenvalues ...................... 39 5{10Lateral-directionaleigenvectors ...................... 40 5{11Lateral-directionaleigenvector ...................... 40 vi

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LISTOFFIGURES Figure page 1{1Flexiblewing6inMAV ......................... 3 1{2MAV .................................... 4 1{3HorizonDetectionExample ....................... 6 1{4Lateralstabilityaugmentationsystem .................. 7 1{5Longitudinalstabilityaugmentationsystem ............... 7 1{6Directionalcontrolsystem ........................ 8 1{7Altitudecontrolsystem .......................... 8 1{8SuccessfulAVCAAFwaypointnavigation ................ 9 2{1MicroAirVehiclesimulationarchitecture ................ 11 2{2Nonlineardynamicsplant ........................ 12 3{1Earth-xedandbody-xedframesofreference ............. 15 3{2SetofrotationsthroughtheEulerangles ................ 16 5{1AVCAAFmodelintestsection ..................... 25 5{2CLversusangleofattack ......................... 26 5{3CLversusCD ............................... 27 5{4Analyticalmodel ............................. 27 5{5Explodedview ............................... 28 5{6Geometryofpanels ............................ 30 5{7WindtunneldataandttedcurveofCL ................ 31 5{8WindtunneldataandttedcurveofCD ................ 31 5{9WindtunneldataandttedcurveofCm ................ 32 5{10Measuredvaluesofsideforce ....................... 33 5{11Variationindutchrollfrequency ..................... 41 vii

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6{1AVCAAFsensorssubsystem ....................... 43 6{2Imageprojectionandpitchpercentage ................. 44 6{3Triangularandtrapezoidalgroundareas ................ 45 6{4NTSCcameraimage ........................... 46 6{5NTSCimageboxandgroundintersection ................ 47 6{6Simulatedhorizonfromcamerasubsystem ............... 49 viii

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AbstractofThesisPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofMasterofScienceNONLINEARSIMULATIONOFAMICROAIRVEHICLEByJasonJosephJackowskiDecember2004Chair:RichardC.Lind,Jr.MajorDepartment:MechanicalandAerospaceEngineeringSimulationsofmicroairvehiclesarerequiredfortasksrelatedtomissionplanningsuchascontroldesignandightpathoptimization.Theightdynamicsofthesevehiclesarediculttomodelbecauseoftheirsmallsizeandlowairspeeds.Thismodellingdicultymakestheprocessofdesigningcontrollersforsuchaircraftdicultandoftendonebytrialanderror.Thisthesispresentsaproceduretocreateasimulationofamicroairvehicle.Methodsforcharacterizingtheaircraftarepresentedanddiscussed.Theresultingmodelissimulatedwithasetofnonlinearequationsofmotion.Thesimulationwillbeusedforfutureautopilotdevelopment,missionplanning,andmorphingaircraftcontrollerdesign.Anexampleofcharacterizingamicroairvehicleispresentedinthisthesis.Characterizingthemicroairvehicleisperformedusingacombinationofphysicalmeasurements,niteelementmethods,windtunneldataandcomputationalmethods.ThischaracterizationincludesdesigningSimulinksubsystemstorepresentthesensors,hardware,andcontrollersusedonthemicroairvehicle.Accurate ix

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characterizationofthecomponentsoftheaircraft,harware,andsensorsshouldprovideasimulationsuitedforcontrollerdesignandanalysis. x

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CHAPTER1INTRODUCTION 1.1 MotivationMicroAirVehicles,typicallycalledMAVs,havebeengaininginterestintheresearchcommunity.MAVsareaclassofaircraftwhoselargestdimensionrangesfrom6-30inches[ 9 ]andoperateatspeedsupto30mph[ 1 ].ThesmalldimensionsandlightweightoftheMAVsmakethemveryportabletoremotelocations.MAVscanbedesignedforhighagilitytooperateinurbanenvironmentsorusedtodeployfrommunitionstoassessdamageinictedonatarget.TheseMAVscanbeequippedwithquietelectricmotors,cameras,GPS,andothersensors.ThewiderangeofpossiblepayloadsleadstoaplethoraofusesforMAVs.AutonomousMAVsarehighlyattractivetothemilitaryforbattleeldre-connaisancemissions.AMAVcouldbecomeastandardpieceofequipmentforspecialforcesteamsoradvancedscoutforces.ThesesoldierscouldquicklylaunchanautonomousMAVtoscoutapotentiallyhazardousareawithoutendangeringthemselves.CurrentlysattelitesorlargerUnmannedAirVehiclestaketimetodeployorre-positiontogivegroundtroopstheimagerytheyneed.MAVspresentacheapandquickalternativeforbattleeldreconnaisance.Hazardouschemicalspillsrequireexpensiveequipmentforhumanstoventureinto,map,andcleanuptheinfectedarea.AMAVcanbeequippedwithasensortodetectharmfulchemicalsandrelaythatinformationtoahazardousmaterialsteam.AutonomousMAVscanbeusedtomapouttheareaandlocatetrappedpeople.TheMAVcanassistinndinganescaperoutearoundthechemicalspill.Thisobjectivecanbedoneveryquicklyandwithoutrisktothehazardousmaterialteams. 1

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2 ThesescenarioshighlighthowfurtherresearchinautonomousMAVscouldbebenecial.Asimulationcapabilityaspresentedinthisthesis,willassistthedevelopmentandpathplanningoftheMAVs. 1.2 Background 1.2.1 MicroAirVehiclesTheUniversityofFloridahasbeenactivelypursuingMAVresearchforoversixyears.Overtheseyearsthesize,design,andpayloadcapacityhaveseensignicantimprovements.PracticalusesforMAVswouldnotbepossiblewithoutrecenttechnologicaldevelopments.ThesmalldimensionsofMAVshavedrivenaneedfortheminiatur-izationofmanyRadioControlledairplaneelectronics.ThecellularphoneindustryhasalsobeenbenecialtoMAVsbyprovidingminiaturizationofbatteries.Theseadvancesalongwithothercomputer,communications,andvideocameratech-nologieshaveallowedMAVstostarthavingon-boardcomputerprocessingandautonomy.Aerovironment'sBlackWidowwastherstmissioncapableMAV[ 16 ].TheBlackWidowhasawingspanof6in,iselectricallypowered,weighs80g,hasarangeof1.8km,andhasanenduranceof30min.TheBlackWidowisarigid-wingplatformwiththreeverticalstabilizers.On-boardsystemsincludeacustom-madevideocamera,controlsystem,videotransmitter,pitot-statictube,magnetometer,anddatalogger.Thecontrolsystemcanperformaltitudehold,airspeedhold,headinghold,andyawdamping.ThelatterisimportantasMAVstendtohavehighDutchrolloscillations.Theyawdamperreducestheseoscillationsandhelpsstabilizethevideocameraimage.ThevideocamerasystemallowsapilottocontroltheMAVbyvideoalone.TheBlackWidowdemonstratedthatMAVscanmakepracticalplatformsforvariousmissions.

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3 TheresearchattheUniversityofFloridastartedwithDr.PeterIfju'sworkonaexiblewingMAV[ 17 ].Thewingconsistedofalatexrubberstretchedoveracarbonberstructureofaleadingedgeandbattens.Theideawasbasedonsailpoweredvesselsusingsailtwisttoproduceamoreconstantthrustoverawiderrangeofwindconditions[ 40 ].Anexampleofa6inMAVispresentedinFigure 1{1 Figure1{1:Flexiblewing6inMAV Aninherentfeaturetothisexiblewingisadaptivewashout,allowingthewingtodeformwhenencounteringagust.ThisadaptivewashouthelpstostabilizetheMAVduringightbyadjustingtotheairow[ 17 34 39 ].AtlowReynolds'numbers,airowaroundthewingsurfacehasafasterseparationwhichincreasesdrag.Theexiblewingallowstheairowtoremainattachedlongerthanarigidwing.Dr.IfjuhasestablishedarapidprotypingfacilityforMAVsattheUniversityofFlorida.Thisfacilityallowscomputerbaseddesignofthewings.ThecomputersoftwarecanthenuseaCNCmachinetocreateahardfoamtooltomanufacturethewing[ 21 ].Thesetoolsareusedtoshapecarbonberpre-pregandwingmaterialforcuringinavaccumbaginanoven.ConstructionofMAVscantakefromtwototendaysbasedonthedesign[ 21 ].Processesinstreamliningthis

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4 constructionprocessarecontinuallyimplementedtoobtainstrictertolerancesbetweenthesametypeofMAVandtoreduceproductiontime.TherstcharacterizationofaMAVwasperformedona6inMAVfromtheUniveristyofFloridaintheBasicAerodynamicsResearchTunnelBARTatNASALangleyResearchCenter[ 39 ].SimulationsoftheMAVwerethencreatedusingthewindtunneldata[ 40 ].ThisworkresultedinasetoflinearizeddynamicmodelscharacterizingtheMAVatdierentightconditions.Thesimulationswerealsousedtodesigncontrollersbasedonadynamicnon-linearinversionapproach. 1.2.2 AVCAAFVehicleThemicroairvehicleusedforsimulationisshowninFigure 1{2 .ThevehicleisavariantofabaselinetypewhichhasbeendesignedattheUniversityofFlorida[ 17 ].Inthiscase,theMAVis21ininlengthand24ininwingspan.Thetotalweightofthevehicle,includingallinstrumentation,isapproximately540grams.ThebasicpropertiesaregiveninTable 1.2.2 .ThisMAVistheighttest-bedfortheActiveVisionControlofAgileAutonomousFlightAVCAAFprojectattheUniversityofFloridaandiscalledtheAVCAAFvehicle. Figure1{2:MAV Theairframeisconstructedalmostentirelyofcompositeandnylon.Thefuselageisconstructedfromlayersofwovencarbonberwhicharecuredtoform

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5 Table1{1:AVCAAFvehiclegeneralproperties PropertyValue MaximumTakeoMass540gramsWingSpan60:96cmWingArea5:67cm2MeanAerodynamicChord9:3cmStaticThrust3:2NPayloadCapacity200grams arigidstructure.Thethin,under-camberedwingconsistsofacarbonberspar-and-battenskeletonthatiscoveredwithanylonwingskin.TheAVCAAFwingwasderivedfromatail-lessMAVwingandhasarelexedairfoil[ 21 ].Theoriginalpurposeofthereexedairfoilwastoprovidestabilizationusuallygeneratedbythetail.Atailempannage,alsoconstructedofcompositeandnylon,isconnectedtothefuselagebyacarbon-berboomthatrunsconcentricallythroughthepusher-propdisc.Controlisaccomplishedusingasetofcontrolsurfacesonthetail.Specically,arudderalongwithapairofindependentelevatorscanbeactuatedbycommandstoseparateservos.Therudderobviouslyaectsthelateral-directionaldynamicsresponsewhiletheelevatorscanbemovedsymmetricallytoaectthelongitudinaldynamicsanddierentiallytoaectthelateral-directionaldynamics.Theon-boardsensorsconsistofaGPSunit,analtimeter,andavideocamera.TheGPSunitismountedhorizontallyonthetopofthenosehatch.Thealtimeter,whichactuallymeasurespressure,ismountedinsidethefuselageunderthenosehatch.Thevideocameraisxedtopointdirectlyoutthenoseoftheaircraft. 1.2.3 AVCAAFAutopilotTheautopilotoperatesonano-boardgroundstationattherateof50Hz.Thisgroundstationessentiallyconsistsofalaptopwithcommunicationlinks.Separatestreamsforvideoandinertialmeasurementsaresentusingtransceivers

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6 ontheaircraft.TheimageprocessorandcontrolleranalyzethesestreamsandtransmitcommandstotheRadioControlledRCtransmitter.TheRCtransmittermixesthesymmetricandanti-symmetricelevatorcommandsintoservocommands.TheAVCAAFautopilotperforms3-DwaypointnavigationusingtheGPSreceiver,altimeter,andvideocamera[ 22 ].Thevideosignalsenttothegroundstationisanalyzedforpitchpercentageandrollangle.Thepitchpercentageisthepercentofgroundseenintheimage.Thisiscalculatedbyrstdetectingthehorizonbystatisticalmodeling.Thehorizondetectionalgorithmdeterminesthehorizonthatbestdividestheimageinto"ground"and"sky"basedonpreviouscalibration.Thehorizonlineisalsousedtodeterminethecurrentrollangle.AnexampleofthehorizondetectionalgorithmisshowninFigure 1{3 Figure1{3:HorizonDetectionExample Theautopilotconsistsofalateralandlongitudinalstabilityaugmentationsystem,directionalcontroller,andanaltitudecontrolsystem.Thelateralstabilityaugmentationsystemstabilizesthevehicleandallowstrackingofrollcommands.ThearchitectureofthelateralstabilityaugmentationsystemisshowninFigure 1{4 .ThecontrollerconsistsofaintegralgainKI,porportionalgainK,alter,acameraC,andavisionprocessingelementV.

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7 K 6 KI ? MAV C V ? environment Figure1{4:Lateralstabilityaugmentationsystem ThelongitudinalstabilityaugmentationsystemstabilizestheAVCAAFvehicleandtrackspitchpercentagecommands.ThearchitectureofthelateralstabilityaugmentationsystemisshowninFigure 1{5 .ThecontrollerconsistsofaporportionalK,acameraC,andavisionprocessingelementV. K MAV C V ? environment Figure1{5:Longitudinalstabilityaugmentationsystem ThedirectionalcontrollerisanouterloopoflateralstabilityaugmentationsystemshowninFigure 1{6 .HereKistheporportionalgainandSistheGPSsensor.ThecurrentlongitudeandlattitudeisprovidedbytheGPSreceiverata1Hzrate.TheheadingiscalculatedfromthecurrentandpreviousGPSposition.Thiscreatesalaginthesystemtocalculatetheheadinganddoesnotprovidereal-timeGPScoordinates.Thisissueisaddressedbycalculatingpositionandheadingestimateswhichupdateatthe50Hzrateofthecontrolsystem.Thealtitudecontrollercommandsthealtitudetoreachthecorrectaltitudeofthecurrentwaypoint.Includedinthiscontrollerisaswitchingelementtousealtitudeerrororpitchpercentageerrortodeterminetheelevatordeection

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8 c K K 6 KI ? MAV C V ? environment S 6 Figure1{6:Directionalcontrolsystem showninFigure 1{7 .HereKIhisthealtitudeintegralgain,Khisthealtitudeporportionalgain,andKeisagaintocouplethelongitudinaldynamicswiththelateral-directionaldynamics.Thecontrollerlimitsthepitchpercentagetoensurethatthereisalwaysavisiblehorizonforpitchpercentageandrollanglecalculation. hc Kh 6 KIh ? switch MAV C V K lim ? environment S 6 6 Ke 6 Figure1{7:Altitudecontrolsystem TheAVCAAFautopilotunderwentaseriesofightteststoexperimentallytunethevariousgainsofthecontrolsystems.Theseighttestsresultedinanautopilotcapableof3-Dwaypointnavigation.Figure 1{8 showstheightpathoftheAVCAAFvehicleasittracksthreewaypoints,showninredboxes,multipletimes.

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9 Figure1{8:SuccessfulAVCAAFwaypointnavigation 1.3 OverviewThisthesispresentsaMATLAB/Simulinksimulationarchitectureformicroairvehicles.NonlinearequationsofmotionarederivedtosimulateMAVs.Theseequa-tionsdonotassumesymmetryandcanbeusedformorphingaircraft.Methodsofcharacterizingaircraftarethenpresentedanddiscussed.AnexampleofcharacterizingaMAVispresented.TheAVCAAFvehicleischaracterizedusingniteelementmethods,windtunnelanalysis,andcomputa-tionaluiddynamicsanalysis.Themodelislinearizedaboutatrimconditiontoanalyzetheaircraftdynamicstoquantifythelevelofcondenceinthemodel.Subsystemsinthesimulationarecreatedtoemulatethesensors,hardware,andcontrolsystemthatwasimplementedontheAVCAAFvehicle.Thesubsys-temsemulatethecamera,GPSreceiver,andaltimetersensors.Thecontrolsystemusedtoperform3-DwaypointnavigationontheAVCAAFvehicleisconvertedfromC++andimplementedinthesimulation.Thecontrolsurfaceactuatorsaresimulatedbyaddingrateandpositionlimitsonthecontrolsurfacecommands.

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10 Theprocessofcharacterizingmicroairvehiclesinthisthesiswillbeusedtomodelfuturemicroairvehicles.Thisthesisattemptstolaythegroundworktoallowcontrollerdesignonfuturemicroairvehicles.

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CHAPTER2SIMULATIONARCHITECTURE 2.1 SimulationOverviewTheMAVsimulatorisaMATLAB/Simulinkprogramthatnumericallyintegratesthenonlinearequationsofmotionofthesystem.Thesimulatorconsistsoffourmajorsubsystems:ControllerK,ActuatorsA,NonlinearDynamicsPlantP,andSensorsSasshowninFigure 2{1 Figure2{1:MicroAirVehiclesimulationarchitecture Thestructureofthesimulationisbuiltasatop-down"architecture.Eachsubsystemismodularandcontainsmoresubsystemswhichareeasilyrecongured.Thisarchitectureallowsaplug-and-play"capabilityallowingthesimulationtosimulatedierentaircraft,controllers,andsensorseasilybysimplyreplacingasubsystem. 2.2 Non-LinearDynamicsPlantThestructureoftheNonlinearDynamicsPlant,depictedinFigure 2{2 ,doesnotchangebetweenaircraftplatforms.TheothersubsystemsarespecicallydesignedfortheAVCAAFvehicleandaredescribedinChapter 6 11

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12 Figure2{2:Nonlineardynamicsplant TheAirDensityLook-Upblockndstheairdensitybasedoncurrentaltitude.Theairdensityiscalculatedusingrst-orderinterpolationbetweenpointsfromthestandardatmospheretable.Itinterpolatesbetween-200metersto1000meters;however,alargerrangecouldbecoveredifmorereferencepointswereadded.Table 2{1 showsthealtitudeandairdensityvaluesused. Table2{1:Standardatmosphereairdensities AltitudemAirDensitykg=m3 -2001.2487-1001.236801.22501001.21332001.20713001.19014001.17865001.16736001.15607001.14488001.13379001.122610001.1117

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13 TheNLDynamicssubsystemcalculatestheforcesandmomentsactingontheaircraftateachtime-step.Thesubsystem'sinputsarethecontrolsurfacedeections,aircraftmomentsofinertia,aircraftgeometry,airdensity,and12statesdeningtheaircraft'sposition,orientation,linearvelocityandangularvelocity.Thesubsystemcalculatesthenewlinearandangularaccelerationsduetotheforcesandmomentsactingontheaircraft.Thiscalculationusesthestandard12equationsofmotion[ 31 ]andpolynomialcoecientsthatcharacterizetheaircraft,describedinSection 3.4 .Theseaccelerationsalongwiththepreviousvelocitiesaretheoutputofthissubsystem.TheIntegratorsubsystemnumericallyintegratesthevelocitiesandacceler-ationseachtime-stepofthesimulation.Asetofinitialconditionscanbesetbytheusertodenetheinitialposition,orientation,andvelocityoftheaircraft.Theintegratorusestheseinitialvaluestosetthestateswhenthesimulationbegins.TheAngleLimitersubsystemconvertstheEuleranglestoarangebetween0and360o.TheBodyAxisStatestoEarthInertialFORsubsystemconvertsthecurrentaircraftposition,orientation,andvelocityintotheEarthinertialframeofreference.ThesestatesarethenpassedtotheSensormodulefromFigure 2{1 forsensoruse.

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CHAPTER3NONLINEAREQUATIONSOFMOTIONThischapterderivesthenonlinearequationsofmotionsusedbytheNonlinearDynamicsSubsystempresentedinSection 2.2 .Theequationsofmotiondescribetherigidbodydynamicsandneglectthestructuraldynamics.MAVsobeythesameequationsofmotionasanyairplane.Thefollowingderivationisforthegeneralairplaneasdetailedin[ 13 31 ]andexpandedtoincludeassymetries. 3.1 FramesofReferenceTheMAVmovesinanearth-xedinertialreferenceframeEdenedbythebasisvectors^e1;^e2;^e3.Thevector^e3pointsinthesamedirectionasgravity.Vectors^e1and^e2arepositionedtomakeEaright-handedcoordinatesystem.Theearth-xedreferenceframeEisshowninFigure 3{1 .SixDegreesOfFreedomDOFarenecessarytofullydescribetheMAV'spositionandorientationfromaspeciedpoint.TherstthreeDOFsdenethedistancefromtheMAVtothexed-referenceframe.TheotherthreeDOFsareEuleranglesanddenetherotationbetweenthexed-referenceframeandtheMAVbody-xedreferenceframe.Thebody-xedreferenceframeBhasitsoriginattheMAVcenterofgravityandisdenedbythebasisvectors^b1;^b2;^b3.Thevector^b1pointstowardthenoseoftheMAV,vector^b2pointstowardtheleftwing,andvector^b3makesBaright-handedcoordinatesystem.Thisorientationisthestandardaircraftbody-xedcoordinateframe. 3.2 RotationsAsequenceofthreerotationscantransformapositionfromonecoordinatesystemtoanother.Thissequenceofrotationsisdone,inorder,throughthethree 14

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15 Figure3{1:Earth-xedandbody-xedframesofreference Euleranglesyaw,pitch,androll.Thissequenceisastandard3-2-1rotation.Whentheserotationsareperformed,twointermediatereferenceframesarecreatedwithbasisvectors^x1;^y1;^z1and^x2;^y2;^z2.Therotationsareperformedinthefollowingorder: 1. RotatetheEearth-xedreferenceframeabout^e3throughyawangletoreachintermediateframe^x1;^y1;^z1. 2. Rotate^x1;^y1;^z1about^y1throughpitchangletoreachintermediateframe^x2;^y2;^z2. 3. Rotate^x2;^y2;^z2about^x2throughrollangletoobtainbody-xedframeB.Figure 3{2 showsthesequenceofrotationsgraphicly.TherotationsequencecanalsobeshownmathematicallyEquation 3.1

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16 Figure3{2:SetofrotationsthroughtheEulerangles 8>>>><>>>>:^b1^b2^b39>>>>=>>>>;=2666641000CS0)]TJ/F22 11.955 Tf 9.298 0 Td[(SC377775266664C0)]TJ/F22 11.955 Tf 9.298 0 Td[(S010S0C377775266664CS0)]TJ/F22 11.955 Tf 9.299 0 Td[(SC00013777758>>>><>>>>:^e1^e2^e39>>>>=>>>>;=266664CCCS)]TJ/F22 11.955 Tf 9.298 0 Td[(SCSS)]TJ/F22 11.955 Tf 11.955 0 Td[(CSSSS+CCSCCSC+SSCSS)]TJ/F22 11.955 Tf 11.955 0 Td[(CSCC3777758>>>><>>>>:^e1^e2^e39>>>>=>>>>;=E B8>>>><>>>>:^e1^e2^e39>>>>=>>>>;.1Convertingavectorfromthebody-xedframeBbacktotheearth-xedframeEisdonebyinvertingthematrixE Bandmultiplyingitbythevector. 3.3 KinematicEquationsTherigidbodyequationsofmotioncanbederivedfromNewton'ssecondlaw.XF=d dtmv.2XM=d dtH.3

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17 FistheforceappliedtotherigidbodyandHistheangularmomentumoftherigidbody.Thevectorcomponentsof 3.2 canbedecoupledintothreecomponentsshownin 3.4 .XF=d dtmvc+d dtmv^b2+d dtmv^b3=Fx^b1+Fy^b2+Fz^b3 .4 Fx;Fy;andFzaretheforcesalongthen^b1;^b2;^b3oaxesrespectively.ThevelocityofthecenterofgravityCGoftheMAVisVc.WiththedenitionofVcandtherigidbodyassumption,velocitiesatotherpointsontheMAVmaybefound.LetrbethepositionvectorfromtheCGtoadierentialmasselementm.Thevelocityofthismasselementisexpressedin 3.5 .V=Vc+dr dt=Vc+E!Br.5HereE!BistheangularvelocityofBinEdenedin 3.6 .E!B=p^b1+q^b2+r^b3.6Assumingthemassisconstant,thenthebody-xedaccelerationscanbefoundusing 3.7 3.8 ,and 3.9 Fx=m_u+qw)]TJ/F22 11.955 Tf 11.955 0 Td[(rv .7 Fy=m_v+ru)]TJ/F22 11.955 Tf 11.955 0 Td[(pw .8 Fz=m_w+pv)]TJ/F22 11.955 Tf 11.956 0 Td[(qu .9 Theangularmomentumofthemasselementisexpressedin 3.10

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18 Xrvcm+Xr)]TJ/F44 7.97 Tf 5.48 -4.748 Td[(E!Br.10Expandingrintoitscomponentsyields 3.11 .r=x^b1+y^b2+z^b3.11Hcannowbeexpressedas 3.12 .H=p^b1+q^b2+r^b3X)]TJ/F22 11.955 Tf 5.48 -9.683 Td[(x2+y2+z2m)]TJ/F28 11.955 Tf 11.955 11.358 Td[(Xx^b1+y^b2+z^b3px+qy+rzm.12ThescalarpartsofHareshownin 3.13 3.14 ,and 3.15 .Hx=pX)]TJ/F22 11.955 Tf 5.479 -9.684 Td[(y2+z2m)]TJ/F22 11.955 Tf 11.955 0 Td[(qXxym)]TJ/F22 11.955 Tf 11.955 0 Td[(rXxzm .13 Hy=)]TJ/F22 11.955 Tf 9.298 0 Td[(pXxym+qX)]TJ/F22 11.955 Tf 5.479 -9.683 Td[(x2+z2m)]TJ/F22 11.955 Tf 11.955 0 Td[(rXyzm .14 Hz=)]TJ/F22 11.955 Tf 9.298 0 Td[(pXxzm)]TJ/F22 11.955 Tf 11.955 0 Td[(qXyzm+rX)]TJ/F22 11.955 Tf 5.479 -9.684 Td[(x2+y2m .15 Thesummationsof 3.13 arethemomentsandproductsofinertiadenedin 3.16 3.17 3.18 3.19 3.20 ,and 3.21 .Thedomainofintegrationfortheseequationsistheentireaircraftbody.

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19 Ixx=ZZZ)]TJ/F22 11.955 Tf 5.479 -9.684 Td[(y2+z2m .16 Iyy=ZZZ)]TJ/F22 11.955 Tf 5.479 -9.684 Td[(x2+z2m .17 Izz=ZZZ)]TJ/F22 11.955 Tf 5.479 -9.684 Td[(x2+y2m .18 Ixy=ZZZxym .19 Ixz=ZZZxzm .20 Iyz=ZZZyzm .21 Usingtheequationsforthemomentsandproductsofinertia,thescalarpartsofHbecome 3.22 3.23 ,and 3.24 .Hx=pIxx)]TJ/F22 11.955 Tf 11.955 0 Td[(qIxy)]TJ/F22 11.955 Tf 11.955 0 Td[(rIxz .22 Hy=)]TJ/F22 11.955 Tf 9.298 0 Td[(pIxy+qIyy)]TJ/F22 11.955 Tf 11.955 0 Td[(rIyz .23 Hz=)]TJ/F22 11.955 Tf 9.298 0 Td[(pIxz)]TJ/F22 11.955 Tf 11.955 0 Td[(qIyz+rIzz .24 Using 3.3 3.22 3.23 ,and 3.24 themomentequationscanbeexpressed 3.25 3.26 ,and 3.27 .L=_Hx+qHz)]TJ/F22 11.955 Tf 11.955 0 Td[(rHy .25 M=_Hy+rHx)]TJ/F22 11.955 Tf 11.956 0 Td[(pHz .26 N=_Hz+pHy)]TJ/F22 11.955 Tf 11.955 0 Td[(qHx .27 WhereL,M,andNarethemomentsaboutn^b1;^b2;^b3oaxesrespectively.Makingtheassumptionthattherateofchangeofthemomentsandproductsof

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20 inertiaarenegligibleandassumingtheaircraftisnotsymmetric,theequationscanbeexpandedinto 3.28 3.29 ,and 3.30 .L=_pIxx)]TJ/F15 11.955 Tf 15.575 0 Td[(_qIxy)]TJ/F15 11.955 Tf 15.241 0 Td[(_rIxz)]TJ/F22 11.955 Tf 13.416 0 Td[(pqIxz+)]TJ/F22 11.955 Tf 5.48 -9.684 Td[(r2)]TJ/F22 11.955 Tf 11.955 0 Td[(q2Iyz+qrIzz+rpIxy)]TJ/F22 11.955 Tf 13.416 0 Td[(qrIyy.28M=)]TJ/F15 11.955 Tf 11.586 0 Td[(_pIxy+_qIyy)]TJ/F15 11.955 Tf 14.507 0 Td[(_rIyz+rpIxx)]TJ/F22 11.955 Tf 12.682 0 Td[(qrIxy+)]TJ/F22 11.955 Tf 5.48 -9.684 Td[(p2)]TJ/F22 11.955 Tf 11.955 0 Td[(r2Ixz+pqIyz)]TJ/F22 11.955 Tf 12.683 0 Td[(prIzz.29N=)]TJ/F15 11.955 Tf 11.585 0 Td[(_pIxz)]TJ/F15 11.955 Tf 14.938 0 Td[(_qIyz+_rIzz+)]TJ/F22 11.955 Tf 5.479 -9.684 Td[(q2)]TJ/F22 11.955 Tf 11.955 0 Td[(p2Ixy+pqIxy)]TJ/F22 11.955 Tf 12.778 0 Td[(prIyz)]TJ/F22 11.955 Tf 12.778 0 Td[(pqIxx+qrIxz.30Equations 3.7 3.8 3.9 3.28 3.29 ,and 3.30 aretheequationsofmotionusedinthesimulation. 3.4 ForceandMomentCalculationsTheforcesandmomentstheaircraftactingontheaircraftarerepresentedasfunctionsoftheightcondition.Theightconditionincludesangleofattack,slide-slipangle,aircraftvelocity,airdensity,andcontrolsurfacedeections.Theequationsforthecoecientsoftheforcesandmomentsaregivenin 3.31 3.32 3.33 3.34 3.35 ,and 3.36 .CL=CL22+CL+CL0+CLsymsym+CL__ .31 CD=CD22+CD+CD0+CDsymsym .32 CY=CYpp+CYrr+CYrr+CYasyasy+CY .33 Cm=Cm33+Cm22+Cm+Cm0+Cmsymsym+Cm__ .34 Cl=Clpp+Clrr+Clrr+Clasyasy+Cl .35 Cn=Cnpp+Cnrr+Cnrr+Cnasyasy+Cn .36

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21 TheseequationsusethemethodspresentedinChapter 4 tocharacterizetheaircraft.Duringeachtimestepofthesimulation,theforcesandmomentsactingontheaircraftarecalculatedatthatparticularinstant.Thiscalculationisdonebyevaluating 3.31 3.32 3.33 3.34 3.35 ,and 3.36 atthatparticularightcondition.Thecoecientsarethenmultipliedbythecurrentdynamicpressure,wingarea,andreferencelengthifapplicable. 3.5 CalculationofStatesThebodyaxislinearaccelerationsarecalculatedusing 3.7 3.8 ,and 3.9 .Theforceswerepreviouslycalculatedandthemass,currentangularratesandvelocityareknown.Thebodyaxisangularaccelerationsarecalculatedusing 3.28 3.29 ,and 3.30 .Theinertialproperties,currentangularrates,andmomentsareknown.Thesebodyaxislinearandangularaccelerationsarerotatedintotheearth-xedinertialreferenceframeandintegratedeachtimestep.

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CHAPTER4CHARACTERIZATIONMETHODSThischapterpresentsvedierentmethodsthatcanbeusedtohelpcharac-terizeaircraft.Somemethodsmaynotcompetelycharacterizetheaircraftsodatafrommultiplemethodscanbecombinedtogenerateamodel. 4.1 PhysicalMeasurementsPhysicalmeasurementscanbetakendirectlyfromtheaircraft.Geometricpropetriessuchaswingspan,wingarea,andthemeanaerodynamicchordcanbeapproximatedusingaruler.Themassiseasilyobtainedusingascaleandthecenterofgravitycanbeexperimentallylocated.Torsionalpendulumscanbeusedtodeterminethemomentsofinertiaandprincipleaxesoftheaircraft. 4.2 FiniteElementMethodsAhighdelityniteelementmodelcanproduceanalyticalvaluesformass,momentsofinertia,productsofinertia,wingarea,andothergeometricproperties.ProgramssuchasProEngineer[ 35 ]canbeutilizedtocreatecomputermodelsofeachairplanecomponent.Thesecanthenbeassembledinaightconguration.Subsequentanaylsiscanresultinvaluesfortheaforementionedproperties. 4.3 WindTunnelAwindtunnelcanbeusedtoaccuratelycharacterizeforcesandmomentsactingonamicroairvehicle.Microairvehiclescanbesmallenoughtomountafull-sizeMAVmodelintothewindtunneltestsectionwithoutrequiringscalinglaws.ThistestingallowsthewindtunneldatatoincludethestrongviscousforcesassociatedwiththelowReynoldsnumbersencounteredbyMAVs[ 3 ]. 22

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23 Accurateresultsfromwindtunnelsdependontheinstrumentationusedtomeasuretheforcesandmoments.A6inMAVcanhaveforcesontheorderof0.02newtons[ 3 ].Suchsmallforcescanbeeasilydistortedbynoiseorpoorcalibration.Resultsfromwindtunneltestingcanincludestaticderivativesandcurvesfortheforcesandmomentsbasedonangleofattack,side-slipangle,controlsurfacedeection,andthrust.Dynamicderivativescanbediculttomeasureinawindtunnelandisoftenapproximatedbyequations. 4.4 ComputationalFluidDynamicsTheuseofComputationalFluidDynamicsCFDcanassistinevaluatinghardtodetermineparameters,suchasthedynamicderivatives,aswellaseasiertodetermineparameters,suchasstaticderivatives.CFDmethodscanalsobeusedwhenawindtunnelcannotbeused.VorticeLatticeMethodsVLMcanbeused;however,thecompleteNavier-Stokesequationswillprovidemoreaccurateresults.SomeVLMprogramsdonotincludeviscidskinfrictionwhichbecomesasignicantforceinlowReynoldsnumberow. 4.5 FlightTestingAnaircraftequippedwithsensors,suchasaccelerometersandgyroscopes,canlogighttestdataforanalysis.Thisdatacanbeusedtoperformregressionanalysistorelategyromeasurementsofrollrate,pitchrate,andyawratetocontrolsurfacecommands.Theaircraftdynamicsaredeterminedbyaleast-squaresapproachtotheighttestdata[ 27 ].Thismethodcanobtaininaccurateresultsduetonoisysensormeasurements.

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CHAPTER5AVCAAFCHARACTERIZATION 5.1 OverviewThischapterpresentsanexampleofcharacterizingaMAV.ThisexampleconsistsofidentifyingthelongitudinalandlateraldynamicsoftheAVCAAFvehi-cleusingniteelementmethods,windtunnelandcomputationaldata.Thewindtunneldataisusedtondthestaticaerodynamicforceandmomentcoecients.Theaerodynamicsoftwarepackage,Tornado,approximatesthedynamicderivativesoftheAVCAAFvehicle[ 29 ].TheaerodynamiccharacteristicsareintegratedintothestandardlongitudinalandlaterallineardynamicstocharacterizetheAVCAAFatatrimcondition.Theselinearizeddynamicsareanalyzedformodalproperties.Theanalysisisperformedtocheckstabilityandtoquantifythecondenceofthemodelcreatedfromthewindtunnelandcomputationaldata.Theactualimplementationofthedynamicswillinvolveregressionanalysisofthewindtunneldata,supplementedbythecomputationaldata,resultinginfunctionsforforceandmomentcoecients.ThisimplementationallowssimulationoftheMAVatdierentightconditions. 5.2 ExperimentalAerodynamics 5.2.1 TestingTheaerodynamicsassociatedwiththeAVCAAFaircraftareexperimentallydeterminedusingawindtunnelattheUniversityofFlorida.Thiswindtunnelisahorizontal,open-circuitlow-speedfacility.Thewindtunnelhasabellmouthinletandseveralowstraighteners.Thetestsectionissquarewithdimensions914mmandalengthof2m.Thefanspeedisregulatedbyavariablefrequencycontroller 24

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25 andoperatedremotelybyacomputer.Themaximumvelocityfortestpurposesisapproximately15m/swhichcorrelatestoamaximumReynoldsnumberof100,000.Testingofthetunneliscontrolledbyacomputer.Thiscomputercontrolstheangleofattackofthemodelalongwithacquiringdataandperformingreal-timeanalysis. Figure5{1:AVCAAFmodelintestsection Thevehicleismountedontoastingbalanceandtheresultingstructurecon-nectstoanaluminumarmasinFigure 5{1 .Theinternalstingbalancemeasuresveforcesandonemoment.Theforcesareconvertedinrealtimetothecoe-cients,fCL;CD;Cm;Cn;CY;Clg,usingthedynamicpressureandreferencedataforwingareaandreferencelength.Themainpotentialsourcesofuncertaintyareerrorsassociatedwithsolvingthestingbalanceforcesandmoments,angleofattackmeasurements,andthedynamicpressuredetermination.Additionalminorfactorsincludeuncertaintiesinthedeterminationofgeometricquantitiessuchaswingareaorchordline.Inactuality,theMAVgeneratesloadsconsiderablysmallerthanusualcalibrationweightssothestingbalanceisareasonableexpectationasthemainsourceoferror[ 39 30 ].Apreliminaryestimateofthiserrorwasdonebyrunninganextensivesetofcalibrationchecks[ 19 ].

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26 5.2.2 ResultsTheaerodynamicsoftheAVCAAFvehiclearedeterminedusingafreestreamvelocityof13m/s.Thevehiclewasmountedwings-leveltoconsidersweepsacrossangleofattackandmountedatarollangleof90otoconsidersweepsacrossangleofsideslip.Acompletesetofstaticderivativesinpitch,rollandyawarecomputed[ 3 ].ArepresentativesetofthisaerodynamicdataisgiveninFigure 5{2 andFigure 5{3 .Thesedataconsidertheaerodynamicsatavarietyofsymmetricdeectionsfortheelevators.Unfortunately,thefacilitydidnotallowformeasuringthedynamicderiva-tives.Consequently,thedataobtainedfromthewindtunnelisnotsucienttocompletelycharacterizeamodeloftheightdynamics.TheAVCAAFvehiclewasalsonottestedwithitsmotorturnedon.TestingtheAVCAAFvehiclewiththemotoronwouldrequireanawkwardmouningsystemwhichdoesnotcurrentlyexist.Sincethedierentialelevatorsandrudderareintheprop-washduringactualight,thewindtunneldatamaynotaccuratelydepicttheelevatoreectiveness. Figure5{2:CLversusangleofattack

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27 Figure5{3:CLversusCD 5.3 AnalyticalInertiasTheinertiapropertiesoftheaircraftareestimatedfromniteelementmethods.ThisanalysisusesaCADmodel,showninFigure 5{4 ,andtheProEngineer[ 35 ]softwarepackage.ThemodelwascreatedbydimensioningeachcomponentoftheMAVandassemblingtheminaightconguration.AnexplodedviewoftheProEngineermodelisshowninFigure 5{5 andalistofcomponentsispresentedinTable 5.3 .TheestimatedinertiapropertiesaregiveninTable 5.3 Figure5{4:Analyticalmodel Themodelusedtocalculatethesevaluesaccountsforthedominantmasselements;however,somesmallerrorsremain.Themassofthemodelis6.5%less

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28 Figure5{5:Explodedview Table5{1:AVCAAFvehiclecomponentmasses ComponentMassgrams AltimeterBoard27:0Avionics61:0Battery131:7CameraMount5:0CameraTransmitter18:2Fuselage47:9Hatch6:7HorizontalStabilizer8:9Motor50:0Propeller9:0PropulsionGearing24:6RCReceiver8:0Servox329:7ServoMount7:0SpeedController12:2TailBoom6:5VideoCamera11:9VerticalStabilizer10:6Wing34:0 TotalMass509:9 thantheactualvehiclebecausesmallparts,suchaswiresandcontrolrods,areexcludedfromthemodel.Thecenterofgravityisalsoinerrorandlies0.125inaft

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29 Table5{2:Analyticalinertiaproperties Propertykgm2 Ixx1:127e)]TJ/F21 7.97 Tf 6.587 0 Td[(03Iyy6:604e)]TJ/F21 7.97 Tf 6.586 0 Td[(03Izz7:130e)]TJ/F21 7.97 Tf 6.586 0 Td[(03Ixy)]TJ/F15 11.955 Tf 9.298 0 Td[(3:920e)]TJ/F21 7.97 Tf 6.587 0 Td[(05Ixz)]TJ/F15 11.955 Tf 9.298 0 Td[(3:798e)]TJ/F21 7.97 Tf 6.587 0 Td[(04Iyz)]TJ/F15 11.955 Tf 9.298 0 Td[(9:670e)]TJ/F21 7.97 Tf 6.587 0 Td[(06 oftheactualposition.TheseerrorsarequitesmallsothepropertiesinTable 5.3 areacceptedwithreasonablecondence.ThesevalueswillalsobeusedbythesimulationfortheAVCAAFMAV. 5.4 AnalyticalAerodynamicsAcomputationalanalysisisalsousedtoestimatetheaerodynamicsofthevehicle.Inthiscase,theaerodynamicsareestimatedusingtheTornadosoftwarepackage[ 29 ].Thissoftwareusesavortexlatticemethodtosolveforowoverliftingsurfaces.TheanalysisassumesincompressibleowwhichiscertainlyappropriatefortheightregimeofaMAV.Theanalysisalsoassumesinviscidowwhichcreatessomeerrorsintheresultingsolution;however,theinviscidpressuresarestillrepresented.Theanalysisrepresentstheliftingsurfacesasasetofpanels.ThegeometryofthesepanelsusedfortheAVCAAFaircraftisshowninFigure 5{6 .Thesoftwareonlyconsiderswingsandtailssothefuselage,alongwithitsassociatedaerody-namiccontribution,isnotmodeled.ThereferencepointaboutwhichmomentsarecalculatedisalsoshowninFigure 5{6 .Asetofstaticanddynamicderivativesarecomputedfromacentraldierenceexpansionaboutagivenightcondition.Inthiscase,atrimstateassociatedwithstraightandlevelightisusedforthecondition.Theoutputcontainsalmostallofthestabilityderivativesneededtoformasetoffull-statelinearized

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30 Figure5{6:Geometryofpanels dynamics.Someparameters,suchasfCLu;Cmu;CDug,wereneglectedbecausetheaerodynamicswereassumedtohavenovariationwithMach.ThedynamicderivativesobtainedfromtheanalysisarelistedinTable 5{3 Table5{3:Estimateddynamicderivatives ParameterValue Cmq-6.0391CYp-0.2920CYr0.7587Cnp0.0190Cnr-0.3061Clp-0.3857Clr0.3178 ThederivativesinTable 5{3 areacceptedwithamoderatelevelofcondence;however,theyarerecognizedtohavesomeleveloferror.Anobvioussourceoferrorincludesthelackofaerodynamiccontributionassociatedwiththefuselage.Anothersourceoferroristheeectsofareexedairfoilwhichexistsonthephysicalvehiclebutisdiculttomodelwiththesoftware.Tornadoalsoassumestheliftingsurfacestoberigid.SincetheAVCAAFvehiclehasexiblewings,thedataobtainedfromTornadowillnotaccuratelyrepresenttheadaptivewashout

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31 phenomenon.Finally,thrustisnotmodeledsotheanalysisassumedthrustequaledthealigneddragcomponentforthetrimcondition. 5.5 ModelIntegration 5.5.1 WindTunnelDataAnalysisRegressionanalysisisusedtoobtainstaticderivativesoftheforceandmomentcoecientsfromthewindtunneldata.Thedatawasttoasetofpolynomialsrepresentingseparateparameterssuchasliftandpitchmoment.Figures 5{7 5{8 ,and 5{9 showtheactualwindtunneldataandthecurvesttedtothedata.Theresultingequationsareinradiansare 5.1 5.2 ,and 5.3 Figure5{7:WindtunneldataandttedcurveofCL Figure5{8:WindtunneldataandttedcurveofCD

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32 Figure5{9:WindtunneldataandttedcurveofCm CD=5:54752)]TJ/F15 11.955 Tf 11.955 0 Td[(1:0587+0:0814 .1 CL=10:53812+5:0342)]TJ/F15 11.955 Tf 11.955 0 Td[(0:1514 .2 Cm=)]TJ/F15 11.955 Tf 9.299 0 Td[(49:23293+10:74732)]TJ/F15 11.955 Tf 11.955 0 Td[(0:8158)]TJ/F15 11.955 Tf 11.955 0 Td[(0:0002 .3 Derivativesofthesepolynomialsweretakenwithrespectto.Otherderiva-tivesthatareindependentofweredeterminedbyndingalinearrelationshipwithrespecttotheassociatedparameter,r,sym,etc.Finally,thederivativeswereevaluatedattheightconditionusedtocomputetheanalyticalaerodynamicscorrespondingtoangleofattackof5o.Thisangleofattackisconsideredatrimconditionandisanalyzedonlytodetermineaircraftstabilityatthiscondition.Someanomaliesarenotedintheexperimentalaerodynamics.Inparticular,thesideforceshowninFigure 5{10 seemserroneous.Thesideforceduringasweepthroughangleofattackshouldbenearlyzerobutismeasuredwithasignicantmagnitude.Thesideforceduringthelongitudinaltestwasactuallythesameorderofmagnitudeasthatmeasuredduringlateral-directionaltestingthatvariedrudderandangleofsideslip.Thisanomalyisnotfullyexplainedbutmaybecausedfrom

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33 theasymmetryofthemodel,thealignmentofthemodelinthetunnel,orthecalibrationofthestingbalance. Figure5{10:Measuredvaluesofsideforce 5.5.2 AerodynamicsTheaerodynamicsusedforanalyzingtheightdynamicsoftheAVCAAFvehicleareextractedfromTable 5{4 .Thesevaluespresentbothexperimentalestimatesandanalyticalestimates.Thevaluesinboldfontaretheactualvaluesusedinformulatingthemodel.ThevaluesextractedfromTable 5{4 aredividedbetweentheexperimentalestimatesandanalyticalestimates.Theexperimentalestimateswouldnormallybepreferredbutsomeanomalies,suchasthesideforce,resultedinhighercondencebeingassociatedwithsomeanalyticalvalues.ThederivativeswithrespecttoweretakenfromTornadodataduetothewindtunneldatasetcontainingtwovaluesofatzeroandvedegrees.ThephysicalmountingoftheAVCAAFaircraftinthewindtunnelcurrentlylimitstherangeofside-slipthatcanbemeasured.Also,thevaluesofCm_andCL_werenotobtainedfromeitherexperimentalanalysisoranalyticalanalysis.Thevalueforthisparameterwasestimatedfromapublishedvalueforadierentvehicle[ 5 ].

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34 Table5{4:Analyticalandexperimentalstabilityderivatives StabilityDerivativeTornadoWindTunnel CL4.44868.7162Cm-0.3519-0.3347CD0.4639-0.2329CY00.4596CLo0.5204-0.2443CDo0.01660.0836Cmo0.11120.0144CLsym0.90090.7833Cmsym-1.6461-1.4177CDsym0.0274-0.1064CYr0.69290.1377Clr0.02840.0753Cnr-0.3239-0.3312CYasy0.68590.1556Clasy-0.0280-0.0675Cnasy-0.2883-0.2920CY-0.71210.4488Cl-0.07692.2056Cn0.312747.6871 ThesimulationusesthedataselectedinTable 5{4 aswellasthedynamicderivativesin 5{3 tosupplementthewindtunneldata. 5.6 LinearizedDynamicsThesemodesareinitialestimatesoftheightdynamicsandmustbeacceptedwithcaution.Theaerodynamicsusedtogeneratethemodelshoweddiscrepanciesbetweenexperimentalandanalyticalestimatessothemodelisinherentlyquestion-able.Theaircraftisundergoingighttestingbutthesensorpackagedoesnotyetmeasureparameterssucientforextensivemodeling[ 22 ]. 5.6.1 LongitudinalTheightdynamicsdescribinglongitudinalmaneuversaroundthetrimconditionarecomputedbycombiningdatafromTable 5.3 ,Table 5{3 ,andTable 5{4 .Theresultingmodelrepresentsthelinearizeddynamicsforwhichlongitudinal

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35 andlateral-directionalcomponentsaredecoupled.Thedynamicsarerealizedasastate-spaceexpression[ 31 ].266666664_u_w_q_377777775=Alon266666664uwq377777775+BlonsymWheretheAlonandBlonmatricesarecomprisedoflongitudinalderivatives.ThelongitudinalderivativesaredenedinTable 5{5 .Alon=266666664XuXw0)]TJ/F22 11.955 Tf 9.298 0 Td[(gZuZwu00Mu+M_wZuMw+M_wZwMq+M_wu000010377777775Blon=266666664XsymZsymMu+M_wZsym0377777775ThefollowingaretheAlonandBlonmatricesfortheAVCAAFvehicleat=5o.Alon=266666664)]TJ/F15 11.955 Tf 9.299 0 Td[(0:17990:46170)]TJ/F15 11.955 Tf 9.299 0 Td[(9:81)]TJ/F15 11.955 Tf 9.299 0 Td[(1:1198)]TJ/F15 11.955 Tf 9.298 0 Td[(9:46781300:0942)]TJ/F15 11.955 Tf 9.298 0 Td[(1:8271)]TJ/F15 11.955 Tf 9.298 0 Td[(3:294500010377777775

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36 Table5{5:Longitudinalderivatives ParameterValue Xu)]TJ/F15 14.346 Tf 7.749 -1.096 Td[(CDu+2CD0QS mu0Xw)]TJ/F15 14.346 Tf 7.749 -1.096 Td[(CD+2CL0QS mu0Zu)]TJ/F15 14.346 Tf 7.749 -1.096 Td[(CLu+2CL0QS mu0Zw)]TJ/F15 14.346 Tf 7.749 -1.096 Td[(CL+2CD0QS mu0MuCmuQSc u0IyM_wCm_c 2u0QSc uoIyMwCmQSc u0IyMqCmqc 2u0QSc IyXsym)]TJ/F22 11.955 Tf 9.299 0 Td[(CDsymQS mZsym)]TJ/F22 11.955 Tf 9.299 0 Td[(CLsymQS m Blon=266666664)]TJ/F15 11.955 Tf 9.299 0 Td[(0:382810:9559)]TJ/F15 11.955 Tf 9.299 0 Td[(144:54320377777775Theeigenvaluesofthismodelrelatethenaturalfrequenciesanddampingsoftheightmodes.ThesepropertiesarepresentedinTable 5{6 andindicateapairofoscillatorymodesarepresentinthedynamics. Table5{6:Longitudinaleigenvalues ModeFrequencyrad/sDamping phugoid0.71730.0664shortperiod7.48460.8582

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37 TheeigenvectorsassociatedwiththeseeigenvaluesaregiveninpolarforminTable 5{7 .Notetheseareintermsofnon-dimensionalstates. Table5{7:Longitudinaleigenvectors ShortPeriodModePhugoidModeMagnitudePhaseMagnitudePhase ^u0.1518)]TJ/F15 11.955 Tf 9.298 0 Td[(8:22o1.0264)]TJ/F15 11.955 Tf 9.298 0 Td[(102:05o^w1.559098:00o0.0478)]TJ/F15 11.955 Tf 9.299 0 Td[(69:12o^q0.0268149:12o0.0026)]TJ/F15 11.955 Tf 9.299 0 Td[(93:81o1.00000:00o1.00000:00o Amodeisdescribedasphugoidmodebecauseofitsrelationshipbetweenpitchangleandairspeed.Themodehasasmallnaturalfrequencyandislightlydamped.Assuch,themodehascharacteristicswhichareclassicallyassociatedwithaphugoidmode.Theremainingmodeisdescribedasashortperiodmode.Thismodehasacloserelationshipbetweenangleofattackandpitchrate.Also,thenaturalfrequencyofthismodeisanorderofmagnitudehigherthanthephugoidmode.Consequently,thismodeissimilarinnaturetotheclassicdenitionofashortperiodmode. 5.6.2 Lateral-DirectionalTheightdynamicsassociatedwithlateral-directionalmaneuversaroundtrimarealsocomputedusingdatafromTable 5.3 ,Table 5{3 ,andTable 5{4 .Thedynamicsareagainrealizedasastate-spaceexpression[ 31 ].266666664__p_r_377777775=Alat266666664pr377777775+Blat264asyrud375

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38 WheretheAlatandBlatmatriciesarecomprisedoflateraldirectionalderivatives,denedinTable 5{8 .Alat=266666664Y u0Yp u0)]TJ/F28 11.955 Tf 11.291 13.27 Td[(1)]TJ/F23 7.97 Tf 13.15 4.707 Td[(Yr u0gcos0 u0LLpLr0NNpNr00100377777775Blat=2666666640Yr u0LasyLrNasyNr00377777775ThefollowingaretheAlatandBlatmatricesfortheAVCAAFvehicleat=5o.Alat=266666664)]TJ/F15 11.955 Tf 9.299 0 Td[(0:7661)]TJ/F15 11.955 Tf 9.299 0 Td[(0:0074)]TJ/F15 11.955 Tf 9.298 0 Td[(0:05780:7546)]TJ/F15 11.955 Tf 9.299 0 Td[(111:8602)]TJ/F15 11.955 Tf 9.298 0 Td[(13:159110:84190157:66090:2247)]TJ/F15 11.955 Tf 9.298 0 Td[(3:618200100377777775Blat=26666666400:7455)]TJ/F15 11.955 Tf 9.299 0 Td[(34:0289109:5044)]TJ/F15 11.955 Tf 9.298 0 Td[(147:1914)]TJ/F15 11.955 Tf 9.298 0 Td[(166:943300377777775ThemodalparametersarecomputedfromtheeigenvaluesandeigenvectorsofAlat.ThenaturalfrequenciesanddampingsresultingfromtheeigenvaluesaregiveninTable 5{9 .Inthiscase,thelateral-directionaldynamicshaveadivergence,aconvergence,andanoscillatorymode.

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39 Table5{8:Lateraldirectionalderivatives ParameterValue YQSCy mYpQSbCyp 2mu0YrQSbCyr 2mu0LQSbCl IxxLpQSb2Clp 2Ixxu0LrQSb2Clr 2Ixxu0NQSbCn IzzNpQSb2Cnp 2Izzu0NrQSb2Cnr 2Izzu0YrQSCyr mLasyQSbClasy IxxLrQSbClr IxxNasyQSbCnasy IzzNrQSbCnr Izz Table5{9:Lateral-directionaleigenvalues ModeFrequencyrad/sDamping spiral2.0888-1.0000dutchroll5.70780.4526roll14.46491.0000 TheeigenvectorsassociatedwiththedivergenceandconvergencearegiveninTable 5{10 .Notetheseareintermsofnon-dimensionalstates.

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40 Table5{10:Lateral-directionaleigenvectors RollModeSpiralModeMagnitudePhaseMagnitudePhase ^v0.0045180o0.00570o^p0.3392180o0.02200o^r0.02680o0.04900o1.00000o0.45020o0.0791180o1.00000o Thestablemodehasobviouscharacteristicsassociatedwiththeclassicaldenitionofrollmode.Theresponseofthismodeispredominatelyarollmotionwithonlyminorvariationinangleofsidesliporyaw.Theunstablemodeischaracterizedasaspiraldivergencebutwithsomereservations.Theeigenvectorindicatestheresponseresemblesaclassicspiralmodeinthatexcitationofthismodeisessentiallyyawwithsomeroll.Conversely,themagnitudeoftheeigenvalueisquitelargetobeconsideredaspiralpole.TheremainingmoderelatestoadutchrolldynamicasevidencedbyitseigenvectorinTable 5{11 .Themotionassociatedwiththismodeisacomplexrelationshipbetweenyawandrollandangleofsideslip.Thephasesandmagnitudesslightlydierfromthemotionsoflargeaircraft;however,thedynamicsareclearlydutchroll. Table5{11:Lateral-directionaleigenvector DutchRollModeMagnitudePhase ^v0.0160)]TJ/F15 11.955 Tf 9.299 0 Td[(117:02o^p0.1338116:91o^r0.1446162:61o1.00000o1.080145:70o Also,thenaturalfrequencyassociatedwiththedutchrollagreeswithabasictrend.Namely,themagnitudeofthenaturalfrequencyshouldincreaseaswing

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41 spandecreases.Figure 5{11 indicatesthenaturalfrequencyestimatedfortheAVCAAFaircraftliesalongareasonablecurvewithvaluesfromotheraircraft. Figure5{11:Variationindutchrollfrequency 5.7 ModelingResultsThischapterhasshownthedevelopmentofthelinearizedlongitudinalandlateraldynamicsofamicroairvehicleusingwindtunnelandcomputationaldata.Thewindtunneldatadidnotincludethedynamicderivativesandincludedsomespuriousdata.ThesoftwarepackageTornadowasusedtosupplementthewindtunneldatatocompletethemodel.Thelinearizedmodelhasmodalpropertiesthataresimilartostandardaircraftmodes.Thespiralmodewasanalyzedasunstable.Thisinstabilityhasnotbeenconrmedbyighttestingduetothedicultyofrecognizingspiraldivergenceduringight.Itshouldbestatedagainthatthedynamicspresentedwereforoneightcondition.ThesimulationwillencompaseawiderrangeofightconditionsbyusingfunctionstosolvefortheforcesandmomentstheMAVexperienceseachtimestep.ThereisnotmuchcondenceinthismodelaccuratelycharacterizingtheactualAVCAAFvehicle.ThisisduetotheconictingresultsobtainedfromtheTornadoandwindtunneldata.Somesourcesofinaccuraciesincludecomputational

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42 databasedoninviscidow,inaccuratemodelingoftheexiblewings,dicultyinmodelingthereexedairfoil,andspuriousexperimentaldata.

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CHAPTER6AVCAAFSUBSYSTEMSThesubsystemsdesignedspecicallyfortheAVCAAFaircraftweretheSensorsblock,Controllerblock,andActuatorblockinFigure 2{1 .Thischapterdiscussesthedesignofthesesubsystems. 6.1 SensorSubsystemTheSensorsblockfromFigure 2{1 iscomprisedofthreesubsystemsfortheAVCAAFvehicle.ThesesubsystemsaretheCamera,GPS,andAltitudeblocksshowninFigure 6{1 Figure6{1:AVCAAFsensorssubsystem 6.1.1 CameraSubsystemThecamerasubsystememulatesthevisionoutputthecontrollerreceivesfromthegoundstationforhorizonanalysis.Thesubsystemcalculatesthepitch 43

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44 percentageseenbythecamerabasedonpitchangle,rollangle,andcameraviewangle.Pitchpercentageisthepercentofground"seenintheimage.Itisassumedthatwhenthepitchangleandrollanglearezerothepitchpercentageis50%.Thisequationcanbefurthermodiedtoaccountforaltitudeanddistancetothehorizon. 6{2 showsasideviewoftheMAVcapturinganimagewithitscamera.Thiscaseassumesthereisnorollangle.Hereisthecameraviewhalf-angle,isthepitchangle,A)]TJ/F22 11.955 Tf 12.186 0 Td[(Aistheimageplane,andDisthelengthfromthecameratotheimageplane.Listhelengthfromthecameratotheimageplanealongthecamerahalf-angle.hpisthepercentageofgroundseenintheimageplane.Thegeometricidentities 6.1 and 6.2 canbeobserved. Figure6{2:Imageprojectionandpitchpercentage L=D cos .1 hp=Lsin)]TJ/F22 11.955 Tf 11.955 0 Td[(Dtan .2 6.2 canbeexpandedinto 6.3 .hp=Dtan)]TJ/F22 11.955 Tf 11.955 0 Td[(tan6.3

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45 Thepitchpercentagecanbefoundbedividinghpbytheimageplanelength,shownin 6.4 .ThecontrollerfortheAVCAAFvehiclerequiresthisvaluetobebetween0and1,where1correlatestoapitchpercentageof100%ground"completelyllstheimage.pitch%=hp 2Dtan=Dtan)]TJ/F22 11.955 Tf 11.955 0 Td[(tan 2Dtan=1 2)]TJ/F22 11.955 Tf 18.499 8.088 Td[(tan 2tan.4 6.4 isonlyvalidforthecasewheretherollangleiszero.Theequationforpitchpercentageismorecomplexwhenrollisadded.Therearetwodierentgeneralcasestoconsiderwhencalculatingpitchpercentagewithrolladded.Thesecasesarewhenthegroundareaseenbythecameraiseitheratriangleortrapezoid,asshowninFigure 6{3 Figure6{3:Triangularandtrapezoidalgroundareas Figure 6{3 alsoshowstheimagetakenfromthecameraisnotcircular.ThecameraintheAVCAAFtransmitsastandardNTSCvideosignal.Thisvideoformatwillalsomakethepitchpercentagecalculationmorecomplex.ThestandardNTSCsignalhasaratioof3:4fortheheightandlengthoftheimagerespectively.Thepitchpercentagewillnowbecalculatedasthepercentofgroundintherectangularimageplane.

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46 Figure 6{4 showsamoredetailedviewoftherectangularimageplane.FromFigure 6{2 thedistancefromthecenteroftheimagetothehorizonisfoundtobeDtan.Itisknownthatthecircleencompasingthe3:4rectanglehasadiameterof2Dtan. Figure6{4:NTSCcameraimage Tondtheareaofthegroundintheimageplane,letBrepresentthein-tersectionofthehorizonwiththerightmostsideoftherectangularimage.Sinceanegativerollwillresultinthesamepitchpercentageasapositiverollofthesamemagnitude,allnegativerollswillbeanalyzedaspositiverollstosimplifythecalculation.LetCrepresenttheintersectionofthehorizonandtheleftmostsideoftherectangularimage.LetAbethepointonthehorizonclosesttothecenteroftheimage.ThesepointsaredepictedinFigure 6{5

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47 Figure6{5:NTSCimageboxandgroundintersection ThecoordinatesofA,B,andCaretakenfromthecenteroftheimage,givenin 6.5 6.6 ,and 6.7 .A=)]TJ/F22 11.955 Tf 9.298 0 Td[(Dtansin;)]TJ/F22 11.955 Tf 9.299 0 Td[(Dtancos .5 B=)]TJ/F22 11.955 Tf 9.298 0 Td[(Dtansin+Scos;)]TJ/F22 11.955 Tf 9.299 0 Td[(Dtancos)]TJ/F22 11.955 Tf 11.955 0 Td[(Ssin .6 C=)]TJ/F22 11.955 Tf 9.298 0 Td[(Dtansin)]TJ/F22 11.955 Tf 11.956 0 Td[(Pcos;)]TJ/F22 11.955 Tf 9.298 0 Td[(Dtancos+Psin .7 ThevalueofPandSwilldependontheorientationofthehorizon.TherearetwocasesforthelocationofpointB:pointBiseitherontherightmostimageboundaryoronthebottomimageboundary.ThecamerasubsystemassumesthattherollangleoftheAVCAAFvehiclewillnotexceed90omeaningtheMAVwillnotbeinverted.Thecamerasubsystemalsoconvertsanegativerollangleintoapositiveangleforthepitchpercentagecalculation;thesamemagnituderollanglewillresultinthesamepitchpercentageifitisnegativeorpositive.TosolveforthelengthSfromFigure 6{5 ,thetwocasesforthelocationofpointBareevaluated.Settingthex-coordinateofBto4 5DtansetsBatthe

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48 rightmostimageboundary.Settingthey-coordinateofBto)]TJ/F21 7.97 Tf 10.494 4.707 Td[(3 5DtansetsBatthebottomimageboundary.ThelengthofSforbothcasesare 6.8 and 6.9 .S=D cos4 5tan+tansinRightmostBoundary .8 S=D sin3 5tan)]TJ/F22 11.955 Tf 11.955 0 Td[(tancosBottomBoundary .9 ThecorrectvalueforSwillbetheminimumpositivevalueresultingfrom 6.8 and 6.9 .AsimilarmethodisusedtondthevalueofP.P=D cos4 5tan)]TJ/F22 11.955 Tf 11.956 0 Td[(tansinLeftmostBoundary .10 P=D costancos)]TJ/F15 11.955 Tf 13.15 8.088 Td[(3 5tanBottomBoundary .11 Theareaofgroundseenintheimageplaneisnowsimplyacombinationoftriangleandrectangleareas.Figure 6{6 showsasimulationofthehorizonlinebasedona10opitchangleanda25orollangle.Thecircleindicatesthecenteroftheimage.ThisimageissimilartoFigure 1{3 depictinganimageprocessedbytherealhorizondetectionalgorithm.Herethelowerleftcornerunderneaththelineisconsideredground." 6.1.2 GPSSubsystemTheGPSsubsystemgivesthecontrollerthecurrentlongitudeandlattitude.Usingtheequations 6.12 and 6.13 ,thesubsystemdeterminesthecurrentlattitudeandlongitudebasedonthestartingpositionandcurrentposition.TheactualGPSreceiverontheAVCAAFvehiclerefreshesata1Hzrate.ThisrefreshratehastobesimulatedinSimulinktoaccuratelymodeltheGPSreceiver.

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49 Figure6{6:Simulatedhorizonfromcamerasubsystem 1Longitudeminute=1582cosLattitudedegreesmeters .12 1Lattitudeminute=1582meters .13 6.1.3 AltitudeSubsystemThealtimeterontheactualAVCAAFaircraftmeasurespressureandoutputsasignalof0-5volts.TheavionicspackageoftheAVCAAFvehicletakesthissignalandusesa8-bitA-Dconverterchangingthesignalintoanintegerfrom0-255.Forthepurposesofsimulatingthissignal,itisassumedthealtimeterhasaonemeterperintegerresolution,basedonpilotobservation.Thus,asimplecalculationemulatesthealtimeter:altimeterreadingequalsinitialaltimeterreadingminustheearth-xedinertialframeZvalueanegativeZvaluecorrespondstoapositivealtitude. 6.2 ActuatorSubsystemTheActuatorsubsystemallowssaturationandratelimitstobeimposedonthecontrolservos.Thepositionlimitsare20oonthedierentialelevatorsand25oontherudder.Theratelimitsare260deg=sforalltheservos.Thisactuatormodelinghelpsmakethesimulationmorerealistic.

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50 6.3 ControllerSubsystemTheControllersubsystemcontrolsthedierentialelevatorsandrudderdeections.FuturesimulationsformorphingaircraftwillallowthecontrollertochangethegeometryoftheMAVbychangingthemomentsofinertia,productsofinertia,wingarea,wingspan,andmeanaerodynamicchord.ThecurrentcontollerimplementedinthissubsystemwastakenfromtheAVCAAFvehiclecontroller.TheoriginalcontrollerwascodedinC++andconvertedintoaMATLAB/Simulinkimplementationmanually.Thiscontrollerhastheabilitytoperformthreedimensionalwaypointnavigation.Thewaypointsarepre-denedbytheuser.ThecontrollergivescontrolsurfacecommandstotheMAVtoreachthewaypoints.Thiscontrollercanonlychangethedierentialelevatordeections.IntheactualAVCAAFcontrolsystemthegroundstationsendssymmetricandanti-symmetricelevatorcommandstotheRadioControlRCtransmitter.TheRCtransmittermixesthesesignalstocreateindividualcontrolsurfacedeections.TheRCtransmitterwasprogrammedtouse100%ofthesymmetricelevatordeectioncommandand75%oftheanti-symmetricdeectioncommandwhencomputingtheservocommands.Thissignalmixingwasimplementedinthecontrollersubsystem.

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CHAPTER7RESULTSANDCONCLUSIONS 7.1 ResultsTheexampleMAVcharacterizedinChapter 5 and 6 wasnotsuccessfullysimulated.TheattemptatsimulatingtheAVCAAFvehicleresultedinanunstableaircraftthatcouldnotbecontrolledbytheControllersubsystem.Thegainswereadjustedbyatrialanderrormethodbutfailedtocontroltheaircraft.ThisfailuretoaccuratelysimulatetheAVCAAFvehicleandcontrolsystemwasmainlyduetothemodeledAVCAAFvehiclenotaccuratelyrepresentingtheactualAVCAAFvehicle. 7.2 ConclusionThisthesishasdevelopedasimulationenvironmentforMicroAirVehiclesMAVs.Thissimulationwasdesignedtohaveaplug-and-play"capabilitywiththeaircraftsensors,aircraft,andcontrollerstomakeiteasyfortheusertosimulatevariousaircraftusingdierentcontrolsystems.Asetofnonlinearequationsofmotionwerederivedforasymmetricaircraft.TheseequationsrequirecharacterizationoftheforcesandmomentsencounteredbytheMAV.ThecontrollersubsystemcanutilizetheasymmetricequationsofmotiontocontrolmorphingaircraftbychangingtheaircraftgeometryAnexampleMAVcharacterizationispresentedinthisthesis.TheAVCAAFvehicle,a24inwingspanMAV,wasmodeledusingphysicalmeasurements,niteelementmethods,windtunneltesting,andcomputationaluiddynamicsanalysis.ThesubsystemsrepresentingtheAVCAAFvehicle'ssensorsandcontrolsystemweredevelopedtoemulatetheactualhardwareandsoftware.TheresultoftheAVCAAFvehiclemodelingdidnotresultinanaccuratesimulation.Thecontrol 51

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52 systemimplementedinthesimulationhadthesamearchitectureandgainsasusedontheactualAVCAAFvehicle.SincethedynamicsdierbetweentheactualandmodeledAVCAAFvehicle,itisnotsurprisingthatthecontrolsystemcouldnotcontrolthesimulatedvehicle.ThegroundworkforsimulatingMAVshasbeenestablished.MethodstocharacterizeMAVshavebeenattempted.FurtherresearchwillmoreaccuratelymodelMAVs.Accuratecharacterizationwillallowthesimulatedvehicletoaccuratelyrepresenttheactualvehiclemakingcontrollerdesignpossibleinthesimulatedenvironment.

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CHAPTER8RECCOMENDATIONS 8.1 OverviewThischapterisintendedtopresentreccomendationsfortheAVCAAFpro-gram. 8.2 WindTunnelCharacterizationUsingthewindtunneltocharacterizeMAVsisideal.ThewindtunnelallowsaccuratecharacterizationofactualightconditionsusingtheactualMAV.RenementincharacterizingtheMicroAirVehiclesneedstoberesearched.ProblemsassociatedwithtestingtheAVCAAFvehicleincluded: Limitedangleofattackrange Unreliablesideforcecomponent Limitedside-slipanglerange Testingdidnotincludepoweredthrust DynamicderivativescouldnotbeobtainedTestingthesecondgenerationAVCAAFvehicledenotedasAVCAAFvehicle2.0hasrecentlystarted.Thecongurationofthenewvehicleeliminatessomeoftheseproblems.TheAVCAAFvehicle2.0hasbeentestedthroughacompleterangeofangleofattackincludingstallangle.Thetestinghasalsoincludedpoweredthrustsincethewindtunnelmountingdoesnotinterferewiththepropeller.DespitetheAVCAAFvehicle2.0improvementsthesideforceanddynamicderivativesarestilllacking.Renementinthesideforcecomponentmustbeaccomplishedtoprovideaccurateresults.Thedynamicderivativesmayproveto 53

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54 beimpracticaltomeasureinthewindtunnelandshouldbetheonlyparametersapproximatedbycomputer. 8.3 ComputationalFluidDynamicsCharacterizationTherearetwomajorproblemswithusingcomputationaluiddynamicstocharacterizetheMAVs:poorMAVgeometryrepresentationandlackofviscousforces.ThecurrentCFDprogram,Tornado,didnotincludetheMAVfuselage,exibilityofthewings,anddidnotmodelthereexedwingcurvature.Fluent,anotherCFDprogram,isreccomendedtoreplaceTornado.FluenthasthecapabilityofimportingComputerAidedDraftingmodelsfromprogramssuchasNASTRANtoaccuratelymodeltheentireMAV.Thiswillallowtheex-ibilewingstoberepresentedandanalyzedaccuratelyastheydeformthroughight.FluentalsoincludesviscousforcesthatMAVswillencounterattheirlowReynold'snumberightregimes.ThesecapabilitiesofFluentshouldresultinaccurateapproximationsofthedynamicderivatives. 8.4 StreamliningMAVDesigntoCFDCharacterizationProcessCurrentlyMAVfuselagesarehandmadefromhardfoamtomakemolds.Thisprocessintroducesasymmetriesinthefuselageandmakesitdiculttocreateanaccuratecomputermodelofthefuselage.ItisreccommendedthatthedesignofthefuselagesshouldbecreatedinaCADprogramcompatiblewithFluent.ThiswillallowthedesignertoeliminatefueslageasymmetriesandwillstreamlinetheprocessfromdesigntoCFDcharacterization.TheCADmodelwillbeeasytoimportintoFluentandbeaccuratelyanalyzed. 8.5 MiscellaneousReccomendationsSincethetwograduatestudentsworkingonmodelingMAVsaregraduatinginDecemeber2004,thiswillresultalossofknowledgeunlesssomeoneistrainedinthisarea.Atleastonegraduatestudentshouldbecommisionedtobecomefamiliarwiththeworkpresentedinthisthesis.Thisshouldincludefamiliarization

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55 intestingproceeduresandsimulationarchitectureandcode.ThestudentshouldalsostartdialoguewiththepersoninchargeoftheHILSfacilitytodeterminehowtoimplementthesimulationinthefacility.

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REFERENCES [1] M.Abdulrahim,H.Garcia,R.Lind,FlightTestingaMicroAirVehicleUsingMorphingforAeroservoelasticControl,"AIAAStructures,StructuralDynamics,andMaterialsConference,PalmSprings,CA,AIAA-2004-1674,April2004. [2] AmericanInstituteofAeronauticsandAstronautics,CalibrationandUseofInternalStrainGageBalanceswithApplicationtoWindTunnelTesting,"RecommendedPracticeAIAAR-091-2003. [3] R.Albertani,P.Hubner,P.Ifju,R.Lind,J.Jackowski,ExperimentalAerodynamicsofMicroAirVehicles,"submittedtoSAEWorldAviationConference,Reno,Nevada,November2004. [4] M.AmprikidisandJ.E.Cooper,DevelopmentofSmartSparsforActiveAeroelasticStructures,"AIAA-2003-1799,2003. [5] J.H.Blakelock,AutomaticControlofAircraftandMissiles,JohnWiley&Sons,Inc.,NewYork,NY,1965. [6] J.Blondeau,J.RichesonandD.J.Pines,Design,DevelopmentandTestingofaMorphingAspectRatioWingusinganInatableTelescopicSpar,"AIAA-2003-1718. [7] J.Bowman,B.SandersandT.Weisshar,EvaluatingtheImpactofMorphingTechnologiesonAircraftPerformance,"AIAA-2002-1631,2002. [8] D.Cadogan,T.Smith,R.LeeandS.Scarborough,InatableandRigidizableWingComponentsforUnmannedAerialVehicles,"AIAA-2003-1801,2003. [9] R.CauseyALateralVision-BasedControlAutopilotForMicroAirVehcilesUsingaHorizonDetectionApproach,"MasterofScienceThesis2003. [10] C.E.S.CesnikandE.L.Brown,ActiveWarpingControlofaJoined-WingAirplaneConguration,"AIAA-2003-1716,2003. [11] J.B.Davidson,P.ChwalowskiandB.S.Lazos,FlightDynamicSimulationAssessmentofaMorphableHyper-EllipticCamberedSpanWingedCongura-tion,"AIAA-2003-5301,2002. [12] M.Drela,Higher-OrderBoundaryLayerFormulationandApplicationtoLowReynoldsNumberFlows,"inFixedandFlappingWingAerodynamicsfor 56

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57 MicroAirVehicleApplications,editedbyT.J.Mueller,AmericanInstituteofAeronauticsandAstronautics,RestonVA,2001. [13] B.EtkinandL.D.Reid,DynamicsofFlight,JohnWileyandSons,Inc.,NewYork,NY,1996. [14] S.M.Ettinger,M.C.Nechyba,P.G.IfjuandM.Waszak,Vision-GuidedFlightStabilityandControlforMicroAirVehicles,"IEEEInternationalConferenceonIntelligentRobotsandSystems,October2002,pp.2134-2140. [15] H.Garcia,M.AbdulrahimandR.Lind,RollControlforaMicroAirVehicleusingActiveWingMorphing,"AIAAGuidance,NavigationandControlConference,AIAA-2003-5347,2003. [16] J.M.GrasmeyerandM.T.Keennon,DevelopmentoftheBlackWidowMicroAirVehicle,"AIAA-2001-0127,2001. [17] P.G.Ifju,D.A.Jenkins,S.Ettinger,Y.Lian,W.ShyyandM.R.Waszak,Flexible-Wing-BasedMicroAirVehicles,"AIAA-2002-0705,2002. [18] J.S.JangyandC.J.Tomlinz,LongitudinalStabilityAugmentationSystemDesignfortheDragonFlyUAVUsingaSingleGPSReceiver,"AIAA-2003-5592,2003. [19] J.J.Jackowski,K.Boothe,R.Albertani,R.Lind,andP.G.Ifju,ModelingtheFlightDynamicsofaMicroAirVehicle,"submittedtoEuropeanMicroAirVehicleConf.,July2004. [20] C.O.Johnston,D.A.Neal,L.D.Wiggins,H.H.Robertshaw,W.H.MasonandD.J.Inman,AModeltoComparetheFlightControlEnergyRequirementsofMorphingandConventionallyActuatedWings,"AIAA-2003-1716,2003. [21] S.Jung,"DesignandDevelopmentofaMicroAirVehicleMAV:Test-BedforVision-BasedControl,"MasterofScienceThesis2004. [22] J.Kehoe,J.Grzywna,R.Causey,J.Plew,M.Abdulrahim,M.NechybaandR.Lind,WaypointNavigationforaMicroAirVehicleusingVision-BasedAttitudeEstimation,"EuropeanMicroAirVehicleConference,July2004. [23] P.J.KunzandI.Kroo,AnalysisandDesignofAirfoilsforUseatUltra-lowReynoldsNumbers,"inFixedandFlappingWingAerodynamicsforMicroAirVehicleApplications,editedbyT.J.Mueller,AmericanInstituteofAeronauticsandAstronautics,RestonVA,2001. [24] E.V.Laitone,WindTunnelTestsofWingsandRingsatLowReynoldsNumbers,"inFixedandFlappingWingAerodynamicsforMicroAirVehicleApplications,editedbyT.J.Mueller,AmericanInstituteofAeronauticsandAstronautics,RestonVA,2001.

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PAGE 70

BIOGRAPHICALSKETCHJasonJoesphJackowskiwasborninToledo,Ohio,onOctober12,1979.HegrewupinDeltona,Florida,afterhisfamilymovedwhenhewasthree.HisfamilytookanactiverollintheBoyScoutsofAmericaandbothhisbrotherJeandJasonearnedtheirEagleScoutawards.Jasonpersuedmanyextracurricularactivitiesinhighschoolincludingacting,KEYclub,AcademicTeam,EnvironthonTeam,andwrestling.AftercompletingseveraladvancedplacementcoursesinhighschoolJasonwaspreparedtoattendtheUniversityofFlorida.JasoncompletedhisBachelorofSciencedegreeinAerospaceEngineering.DuringhisundergraduatedegreeJasoninternedatGeneralElectricAircraftEnginesforonesummerandBoeingfortwosummers.JasonthendecidedtoattendgraduateschoolattheUniversityofFloridaworkingintheFlightControlsLaboratoryunderDr.RickLind. 60


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NONLINEAR SIMULATION OF A MICRO AIR VEHICLE


By

JASON JOSEPH JACKOWSKI

















A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA


2004















I dedicate this work to my wonderful and lovely fiance Ellen Bozarth. Without

her love and support, I could not have done this.















ACKNOWLEDGMENTS

I thank the AFRL-MN and Eglin Air Force for funding this project. I want to

thank the entire flight controls lab which include Ryan Causey, Kristin Fitzpatrick,

Joe Kehoe, Muli ,!id Abdulrahim, Anukul Goel, and Robert Eick. I would like to

thank Jason Grzywna and Jason Plew for their help and expertise in soldering.

I would like to thank Dr. Rick Lind for his advisement and guidance during this

project. A big thanks goes to my brother Jeff Jackowski who helped me make a

resolution-enhancing circuit board for our altimeter during C'1! -1I i,-, break.















TABLE OF CONTENTS
page

ACKNOWLEDGMENTS ................... ...... iii

LIST OF TABLES ...................... ......... vi

LIST OF FIGURES ..................... ......... vii

ABSTRACT ...................... ............. ix

CHAPTER

1 INTRODUCTION .................... ....... 1

1.1 M otivation . . . . . . . 1
1.2 Background .. .. ... .. .. .. .. ... .. .. .. .. ... 2
1.2.1 M icro Air Vehicles ................... .... 2
1.2.2 AVCAAF Vehicle .......... ............ 4
1.2.3 AVCAAF Autopilot ........... .......... 5
1.3 Overview .................. ....... ..... 9

2 SIMULATION ARCHITECTURE ........ ......... .... 11

2.1 Simulation Overview ......................... 11
2.2 Non-Linear Dynamics Plant ........ ......... .... 11

3 NONLINEAR EQUATIONS OF MOTION ....... ......... 14

3.1 Frames of Reference ................... .... 14
3.2 Rotations ................... ....... 14
3.3 Kinematic Equations ......................... 16
3.4 Force and Moment Calculations .................. .. 20
3.5 Calculation of States .................. ..... .. 21

4 CHARACTERIZATION METHODS .............. ... .. .. 22

4.1 Physical Measurements .................. ... .. 22
4.2 Finite Element Methods .................. .. 22
4.3 W ind Tunnel .................. .......... .. 22
4.4 Computational Fluid Dynamics ................. 23
4.5 Flight Testing .. ... .. .. .. .. ... .. .. .. 23









5 AVCAAF CHARACTERIZATION ................. .... 24

5.1 Overview ............................ 24
5.2 Experimental Aerodynamics ........ ............. 24
5.2.1 Testing ............... ........ .. 24
5.2.2 Results ...... ................... .. 26
5.3 Analytical Inertias ............... ...... .. 27
5.4 Analytical Aerodynamics ...... ......... .... 29
5.5 Model Integration ............... ........ .. 31
5.5.1 Wind Tunnel Data Analysis .............. .. 31
5.5.2 Aerodynamics ................ ... .... .. 33
5.6 Linearized Dynamics ................ ... .... .. 34
5.6.1 Longitudinal ............... ....... .. 34
5.6.2 Lateral-Directional ..... ........ ... . 37
5.7 Modeling Results ............... ........ .. 41

6 AVCAAF SUBSYSTEMS .................. .... 43

6.1 Sensor Subsystem .................. .. 43
6.1.1 Camera Subsystem .................. 43
6.1.2 G PS S-1.-i-1 ..i . . . .... . 48
6.1.3 Altitude S- l -i v-1. i ................ .. .... 49
6.2 Actuator Subsystem .................. ..... .. 49
6.3 Controller Subsystem .................. ..... .. 50

7 RESULTS AND CONCLUSIONS .................. ..... 51

7.1 Results ................... ..... ....... 51
7.2 Conclusion .................. ............ .. 51

8 RECCOMENDATIONS .................. .. 53

8.1 Overview. .................. ............ 53
8.2 Wind Tunnel (C i iterization ... . . .... 53
8.3 Computational Fluid Dynamics (C!i '.terization . ... 54
8.4 Streamlining MAV Design to CFD (C! i '.terization Process 54
8.5 Miscellaneous Reccomendations .................. .. 54

REFERENCES ................... ... ... ........ .. 56

BIOGRAPHICAL SKETCH .................. ......... .. 60















LIST OF TABLES


AVCAAF vehicle general properties .. .....

Standard atmosphere air densities .. ......

AVCAAF vehicle component masses .......

Analytical inertia properties .....

Estimated dynamic derivatives .. ........

Analytical and experimental stability derivatives

Longitudinal derivatives .. ............

Longitudinal eigenvalues .. ............

Longitudinal eigenvectors .. ...........

Lateral directional derivatives .. .........

Lateral-directional eigenvalues .. ........

Lateral-directional eigenvectors .. ........

Lateral-directional eigenvector .. ........


Table


page















LIST OF FIGURES
Figure

1-1 Flexible wing 6 in MAV . ........

1-2 M AV . . . . . .

1-3 Horizon Detection Example . ......

1-4 Lateral stability augmentation system . .

1-5 Longitudinal stability augmentation system .

1-6 Directional control system . .......

1-7 Altitude control system . ........

1-8 Successful AVCAAF waypoint navigation .

2-1 Micro Air Vehicle simulation architecture .

2-2 Nonlinear dynamics plant . .

3-1 Earth-fixed and body-fixed frames of reference .

3-2 Set of rotations through the Euler angles .


AVCAAF model in test section .

CL versus angle of attack . .

CL versus CD ...........

Analytical model . ....

Exploded view . .....

Geometry of panels . ...

Wind tunnel data and fitted curve

Wind tunnel data and fitted curve

Wind tunnel data and fitted curve

Measured values of side force .

Variation in dutch roll frequency .


of CL .

ofCD ..

ofC, ....


page

3

4

6

7

7

8

8

9

11

12

15

16

25

26

27

27

28

30

31

31

32

33

41









6-1 AVCAAF sensors subsystem.... ........... ..... 43

6-2 Image projection and pitch percentage ................ 44

6-3 Triangular and trapezoidal ground areas ............... ..45

6-4 NTSC camera image .................. ........ .. 46

6-5 NTSC image box and ground intersection ............... ..47

6-6 Simulated horizon from camera ii- v-, in . . 49















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

NONLINEAR SIMULATION OF A MICRO AIR VEHICLE

By

Jason Joseph Jackowski

December 2004

C('!h I: Richard C. Lind, Jr.
Major Department: Mechanical and Aerospace Engineering

Simulations of micro air vehicles are required for tasks related to mission

planning such as control design and flight path optimization. The flight dynamics

of these vehicles are difficult to model because of their small size and low airspeeds.

This modelling difficulty makes the process of designing controllers for such aircraft

difficult and often done by trial and error.

This thesis presents a procedure to create a simulation of a micro air vehicle.

Methods for characterizing the aircraft are presented and discussed. The resulting

model is simulated with a set of nonlinear equations of motion. The simulation will

be used for future autopilot development, mission 1p'1 ,ilir I. and morphing aircraft

controller design.

An example of characterizing a micro air vehicle is presented in this thesis.

C(i o ,iterizing the micro air vehicle is performed using a combination of physical

measurements, finite element methods, wind tunnel data and computational

methods. This characterization includes designing Simulink subsystems to represent

the sensors, hardware, and controllers used on the micro air vehicle. Accurate









characterization of the components of the aircraft, harware, and sensors should

provide a simulation suited for controller design and analysis.















CHAPTER 1
INTRODUCTION

1.1 Motivation

Micro Air Vehicles, typically called MAVs, have been gaining interest in the

research community. MAVs are a class of aircraft whose largest dimension ranges

from 6-30 inches [9] and operate at speeds up to 30 mph [1]. The small dimensions

and light weight of the MAVs make them very portable to remote locations. MAVs

can be designed for high agility to operate in urban environments or used to

deploy from munitions to assess damage inflicted on a target. These MAVs can be

equipped with quiet electric motors, cameras, GPS, and other sensors. The wide

range of possible 1p i"loads leads to a plethora of uses for MAVs.

Autonomous MAVs are highly attractive to the military for battlefield re-

connaisance missions. A MAV could become a standard piece of equipment for

special forces teams or advanced scout forces. These soldiers could quickly launch

an autonomous MAV to scout a potentially hazardous area without endangering

themselves. Currently sattelites or larger Unmanned Air Vehicles take time to

deploy or re-position to give ground troops the imagery they need. MAVs present a

cheap and quick alternative for battlefield reconnaissance.

Hazardous chemical spills require expensive equipment for humans to venture

into, map, and clean up the infected area. A MAV can be equipped with a sensor

to detect harmful chemicals and relay that information to a hazardous materials

team. Autonomous MAVs can be used to map out the area and locate trapped

people. The MAV can assist in finding an escape route around the chemical spill.

This objective can be done very quickly and without risk to the hazardous material

teams.









These scenarios highlight how further research in autonomous MAVs could

be beneficial. A simulation capability as presented in this thesis, will assist the

development and path planning of the MAVs.

1.2 Background

1.2.1 Micro Air Vehicles

The University of Florida has been actively pursuing MAV research for over six

years. Over these years the size, design, and p load capacity have seen significant

improvements.

Practical uses for MAVs would not be possible without recent technological

developments. The small dimensions of MAVs have driven a need for the miniatur-

ization of many Radio Controlled airplane electronics. The cellular phone industry

has also been beneficial to MAVs by providing miniaturization of batteries. These

advances along with other computer, communications, and video camera tech-

nologies have allowed MAVs to start having on-board computer processing and

autonomy.

Aerovironment's Black Widow was the first mission capable MAV [16]. The

Black Widow has a wing span of 6 in, is electrically powered, weighs 80 g, has a

range of 1.8 km, and has an endurance of 30 min. The Black Widow is a rigid-wing

platform with three vertical stabilizers. On-board systems include a custom-made

video camera, control system, video transmitter, pitot-static tube, magnetometer,

and data logger. The control system can perform altitude hold, airspeed hold,

heading hold, and yaw damping. The latter is important as MAVs tend to have

high Dutch roll oscillations. The yaw damper reduces these oscillations and helps

stabilize the video camera image. The video camera system allows a pilot to control

the MAV by video alone. The Black Widow demonstrated that MAVs can make

practical platforms for various missions.









The research at the University of Florida started with Dr. Peter Ifju's work

on a flexible wing MAV [17]. The wing consisted of a latex rubber stretched over

a carbon fiber structure of a leading edge and battens. The idea was based on sail

powered vessels using sail twist to produce a more constant thrust over a wider

range of wind conditions [40]. An example of a 6 in MAV is presented in Figure

1-1.














Figure 1-1: Flexible wing 6 in MAV


An inherent feature to this flexible wing is adaptive washout, allowing the

wing to deform when encountering a gust. This adaptive washout helps to stabilize

the MAV during flight by adjusting to the airflow [17, 34, 39]. At low Reynolds'

numbers, airflow around the wing surface has a faster separation which increases

drag. The flexible wing allows the airflow to remain attached longer than a rigid

wing.

Dr. Ifju has established a rapid protyping facility for MAVs at the University

of Florida. This facility allows computer based design of the wings. The computer

software can then use a CNC machine to create a hard foam tool to manufacture

the wing [21]. These tools are used to shape carbon fiber pre-preg and wing

material for curing in a vaccum bag in an oven. Construction of MAVs can take

from two to ten dv based on the design [21]. Processes in streamlining this









construction process are continually implemented to obtain stricter tolerances

between the same type of MAV and to reduce production time.

The first characterization of a MAV was performed on a 6 in MAV from the

Univeristy of Florida in the Basic Aerodynamics Research Tunnel (BART) at

NASA Langley Research Center [39]. Simulations of the MAV were then created

using the wind tunnel data [40]. This work resulted in a set of linearized dynamic

models characterizing the MAV at different flight conditions. The simulations were

also used to design controllers based on a dynamic non-linear inversion approach.

1.2.2 AVCAAF Vehicle

The micro air vehicle used for simulation is shown in Figure 1-2. The vehicle

is a variant of a baseline type which has been designed at the University of

Florida [17]. In this case, the MAV is 21 in in length and 24 in in wingspan.

The total weight of the vehicle, including all instrumentation, is approximately

540 ,'ar,,,- The basic properties are given in Table 1.2.2. This MAV is the flight

test-bed for the Active Vision Control of Agile Autonomous Flight (AVCAAF)

project at the University of Florida and is called the AVCAAF vehicle.













Figure 1-2: MAV


The airframe is constructed almost entirely of composite and nylon. The

fuselage is constructed from lI- rs of woven carbon fiber which are cured to form









Table 1-1: AVCAAF vehicle general properties

Property Value
Maximum Takeoff Mass 540 ,.an-
Wing Span 60.96 cm
Wing Area 5.67 cm2
Mean Aerodynamic Chord 9.3 cm
Static Thrust 3.2 N
Payload Capacity 200 grams



a rigid structure. The thin, under-cambered wing consists of a carbon fiber spar-

and-batten skeleton that is covered with a nylon wing skin. The AVCAAF wing

was derived from a tail-less MAV wing and has a relflexed airfoil [21]. The original

purpose of the reflexed airfoil was to provide stabilization usually generated by the

tail. A tail empannage, also constructed of composite and nylon, is connected to

the fuselage by a carbon-fiber boom that runs concentrically through the pusher-

prop disc.

Control is accomplished using a set of control surfaces on the tail. Specifically,

a rudder along with a pair of independent elevators can be actuated by commands

to separate servos. The rudder obviously affects the lateral-directional dynamics

response while the elevators can be moved symmetrically to affect the longitudinal

dynamics and differentially to affect the lateral-directional dynamics.

The on-board sensors consist of a GPS unit, an altimeter, and a video camera.

The GPS unit is mounted horizontally on the top of the nose hatch. The altimeter,

which actually measures pressure, is mounted inside the fuselage under the nose

hatch. The video camera is fixed to point directly out the nose of the aircraft.

1.2.3 AVCAAF Autopilot

The autopilot operates on an off-board ground station at the rate of 50 Hz.

This ground station essentially consists of a laptop with communication links.

Separate streams for video and inertial measurements are sent using transceivers









on the aircraft. The image processor and controller analyze these streams and

transmit commands to the Radio Controlled (RC) transmitter. The RC transmitter

mixes the symmetric and anti-symmetric elevator commands into servo commands.

The AVCAAF autopilot performs 3-D waypoint navigation using the GPS receiver,

altimeter, and video camera [22].

The video signal sent to the ground station is analyzed for pitch percentage

and roll angle. The pitch percentage is the percent of ground seen in the image.

This is calculated by first detecting the horizon by statistical modeling. The

horizon detection algorithm determines the horizon that best divides the image into

"ground" and "-Ly: based on previous calibration. The horizon line is also used to

determine the current roll angle. An example of the horizon detection algorithm is

shown in Figure 1-3.














Figure 1-3: Horizon Detection Example


The autopilot consists of a lateral and longitudinal stability augmentation

system, directional controller, and an altitude control system. The lateral stability

augmentation system stabilizes the vehicle and allows tracking of roll commands.

The architecture of the lateral stability augmentation system is shown in Figure

1-4. The controller consists of a integral gain KI., porportional gain KO, a filter A,

a camera C, and a vision processing element V.









environment






KO


Figure 1-4: Lateral stability augmentation system


The longitudinal stability augmentation system stabilizes the AVCAAF

vehicle and tracks pitch percentage commands. The architecture of the lateral

stability augmentation system is shown in Figure 1-5. The controller consists of a

porportional K, a camera C, and a vision processing element V.

environment



----- -K^_~--- \!A -




Figure 1-5: Longitudinal stability augmentation system


The directional controller is an outer loop of lateral stability augmentation

system shown in Figure 1-6. Here K, is the porportional gain and S is the GPS

sensor. The current longitude and attitude is provided by the GPS receiver at a

1 Hz rate. The heading is calculated from the current and previous GPS position.

This creates a lag in the system to calculate the heading and does not provide

real-time GPS coordinates. This issue is addressed by calculating position and

heading estimates which update at the 50 Hz rate of the control system.

The altitude controller commands the altitude to reach the correct altitude

of the current waypoint. Included in this controller is a switching element to

use altitude error or pitch percentage error to determine the elevator deflection









environment


Figure 1-6: Directional control system


shown in Figure 1-7. Here KI, is the altitude integral gain, Kh is the altitude

porportional gain, and KO~ is a gain to couple the longitudinal dynamics with the

lateral-directional dynamics. The controller limits the pitch percentage to ensure

that there is ahv--, a visible horizon for pitch percentage and roll angle calculation.

lim
environment
K, V C









Figure 1-7: Altitude control system


The AVCAAF autopilot underwent a series of flight tests to experimentally

tune the various gains of the control systems. These flight tests resulted in an

autopilot capable of 3-D waypoint navigation. Figure 1-8 shows the flight path of

the AVCAAF vehicle as it tracks three waypoints, shown in red boxes, multiple

times.










31.25


31.2




31.1



31.05


4 33.4 33.35 33.3 33.25 33.2 33.15
Longitude from 82 W (min)

Figure 1-8: Successful AVCAAF waypoint navigation


1.3 Overview

This thesis presents a MATLAB/Simulink simulation architecture for micro air

vehicles. Nonlinear equations of motion are derived to simulate MAVs. These equa-

tions do not assume symmetry and can be used for morphing aircraft. Methods of

characterizing aircraft are then presented and discussed.

An example of characterizing a MAV is presented. The AVCAAF vehicle is

characterized using finite element methods, wind tunnel analysis, and computa-

tional fluid dynamics analysis. The model is linearized about a trim condition to

analyze the aircraft dynamics to quantify the level of confidence in the model.

Subsystems in the simulation are created to emulate the sensors, hardware,

and control system that was implemented on the AVCAAF vehicle. The subsys-

tems emulate the camera, GPS receiver, and altimeter sensors. The control system

used to perform 3-D waypoint navigation on the AVCAAF vehicle is converted

from C++ and implemented in the simulation. The control surface actuators are

simulated by adding rate and position limits on the control surface commands.







10

The process of characterizing micro air vehicles in this thesis will be used to

model future micro air vehicles. This thesis attempts to lay the ground work to

allow controller design on future micro air vehicles.















CHAPTER 2
SIMULATION ARCHITECTURE

2.1 Simulation Overview

The MAV simulator is a MATLAB/Simulink program that numerically

integrates the nonlinear equations of motion of the system. The simulator consists

of four 1i i ri subsystems: Controller K, Actuators A, Nonlinear Dynamics Plant

P, and Sensors S as shown in Figure 2-1.



S





K A P



Figure 2-1: Micro Air Vehicle simulation architecture


The structure of the simulation is built as a "top-d- *.,- architecture. Each

subsystem is modular and contains more subsystems which are easily reconfigured.

This architecture allows a IlLg-and-]l li- capability allowing the simulation to

simulate different aircraft, controllers, and sensors easily by simply replacing a

subsystem.

2.2 Non-Linear Dynamics Plant

The structure of the Nonlinear Dynamics Plant, depicted in Figure 2-2, does

not change between aircraft platforms. The other subsystems are specifically

designed for the AVCAAF vehicle and are described in C(i lpter 6.


























Figure 2-2: Nonlinear dynamics plant


The Air Density Look-Up block finds the air density based on current altitude.

The air density is calculated using first-order interpolation between points from the

standard atmosphere table. It interpolates between -200 meters to 1000 meters;

however, a larger range could be covered if more reference points were added. Table

2-1 shows the altitude and air density values used.

Table 2-1: Standard atmosphere air densities

Altitude (m) Air Density (kg/m3)
-200 1.2487
-100 1.2 ;-:
0 1.2250
100 1.2133
200 1.2071
300 1.1901
400 1.1786
500 1.1673
600 1.1560
700 1.1448
800 1.1337
900 1.1226
1000 1.1117









The NL Dynamics subsystem calculates the forces and moments acting on

the aircraft at each time-step. The subsystem's inputs are the control surface

deflections, aircraft moments of inertia, aircraft geometry, air density, and 12 states

defining the aircraft's position, orientation, linear velocity and angular velocity.

The subsystem calculates the new linear and angular accelerations due to the

forces and moments acting on the aircraft. This calculation uses the standard 12

equations of motion [31] and polynomial coefficients that characterize the aircraft,

described in Section 3.4. These accelerations along with the previous velocities are

the output of this -, 11.-- -. 11,

The Integrator subsystem numerically integrates the velocities and acceler-

ations each time-step of the simulation. A set of initial conditions can be set by

the user to define the initial position, orientation, and velocity of the aircraft. The

integrator uses these initial values to set the states when the simulation begins.

The Angle Limiter -, 1ii,--,. in converts the Euler angles to a range between 0

and 360.

The Body Axis States to Earth Inertial FOR subsystem converts the current

aircraft position, orientation, and velocity into the Earth inertial frame of reference.

These states are then passed to the Sensor module from Figure 2-1 for sensor use.















CHAPTER 3
NONLINEAR EQUATIONS OF MOTION

This chapter derives the nonlinear equations of motions used by the Nonlinear

Dynamics Subsystem presented in Section 2.2. The equations of motion describe

the rigid body dynamics and neglect the structural dynamics. MAVs obey the same

equations of motion as any airplane. The following derivation is for the general

airplane as detailed in [13, 31] and expanded to include .'ii. 1 i. -.

3.1 Frames of Reference

The MAV moves in an earth-fixed inertial reference frame E defined by the

basis vectors (1, &2, e3). The vector 63 points in the same direction as gravity.

Vectors &1 and &2 are positioned to make E a right-handed coordinate system. The

earth-fixed reference frame E is shown in Figure 3-1.

Six Degrees Of Freedom (DOF) are necessary to fully describe the MAV's

position and orientation from a specified point. The first three DOFs define the

distance from the MAV to the fixed-reference frame. The other three DOFs are

Euler angles and define the rotation between the fixed-reference frame and the

MAV body-fixed reference frame.

The body-fixed reference frame B has its origin at the MAV center of gravity

and is defined by the basis vectors (6i, 62; 3 ). The vector 61 points toward the

nose of the MAV, vector b2 points toward the left wing, and vector 63 makes

B a right-handed coordinate system. This orientation is the standard aircraft

body-fixed coordinate frame.

3.2 Rotations

A sequence of three rotations can transform a position from one coordinate

system to another. This sequence of rotations is done, in order, through the three









Body Fixed
Frame










Inertial Frame





e21e




Figure 3-1: Earth-fixed and body-fixed frames of reference

Euler angles yaw ('), pitch (0), and roll (4). This sequence is a standard 3-2-1

rotation. When these rotations are performed, two intermediate reference frames

are created with basis vectors (1,1i, i ) and (2, 2,i2). The rotations are

performed in the following order:

1. Rotate the E earth-fixed reference frame about &3 through yaw angle P to

reach intermediate frame (i1, 1, 41).

2. Rotate (,1, ,i1) about il through pitch angle 0 to reach intermediate

frame (22, 2, i2).

3. Rotate (2, Y2, z2) about t2 through roll angle K to obtain body-fixed frame

B.

Figure 3-2 shows the sequence of rotations graphicly. The rotation sequence

can also be shown mathematically Equation 3.1.


















e,,z,


Figure 3-2: Set of rotations through the Euler angles


b, 1 0 0 ce 0 -So CT ST 0

b2 0 C) S) 0 1 0 -SP CT 0 2

63 0 -S C( SO 0 CH 0 0 1 i3

C(Ci( C(OS -S( i

C/S'S8 C('S SeSOST + C'C' SCe 62 (3.1)

CASec + S@s$ CAses CTSc COCs ;3



=E_B e2

e3

Converting a vector from the body-fixed frame B back to the earth-fixed frame

E is done by inverting the matrix EB and multiplying it by the vector.


3.3 Kinematic Equations

The rigid body equations of motion can be derived from Newton's second law.


SF

YM


d
t(mv)

-H
dt


(3.2)

(3.3)


tl t:


t' t'









F is the force applied to the rigid body and H is the angular momentum

of the rigid body. The vector components of 3.2 can be decoupled into three

components shown in 3.4.


d d d
F = (mv) c + (mv) 62 + (m) 63
cdt dt dt (3.4)
= Fbl + Fyb2 + FAb3

F, Fy, and Fz are the forces along the {b, b 62 3 axes respectively.

The velocity of the center of gravity (CG) of the MAV is V,. With the

definition of Vc and the rigid body assumption, velocities at other points on the

MAV may be found.

Let r be the position vector from the CG to a differential mass element 6m.

The velocity of this mass element is expressed in 3.5.


dr
V = + = V + EWB x r (3.5)
dt
Here E B is the angular velocity of B in E defined in 3.6.


E B = pbl + q2 + r63 (3.6)

Assuming the mass is constant, then the body-fixed accelerations can be found

using 3.7, 3.8, and 3.9


F, = m (+ qw- rv) (3.7)

F, = m (i + ru pw) (3.8)

F, = m ( + pv qu) (3.9)


The angular momentum of the mass element is expressed in 3.10.










(3.10)


S r x vc6m + Y, [r x (EWB x r)]


Expanding r into its components yields 3.11.


r = xb6 + Yb2 + zb3


(3.11)


H can now be expressed as 3.12.



H =(pb + 1qb + + rb) (x2 +y2Z + 2) 6m

(xbi + yb2 + zb3) (px + qy + rz) 6m (3.12)

The scalar parts of H are shown in 3.13, 3.14, and 3.15.


P (2 + 2) Zm q xy 6m r :xz 6m
-p xy 6mq (x2 6m r yz 6m

-p xz 6m q yz 6m + r Yr (x2 + y2) 6m


(3.13)

(3.14)

(3.15)


The summations of 3.13 are the moments and products of inertia defined in
3.16, 3.17, 3.18, 3.19, 3.20, and 3.21. The domain of integration for these equations
is the entire aircraft body.












I = I-J (y2+ ) 6m (3.16)




S JJ (x2 + y2) 6M (3.18)

J = xy 6m (3.19)

I,, = xz 6m (3.20)

Iy= yz 6m (3.21)

Using the equations for the moments and products of inertia, the scalar parts
of H become 3.22, 3.23, and 3.24.



Hx = pIxx q Ixy rIzz (3.22)

H, = -pIxy + qlyy rIy (3.23)

Hz = -pIzz qlyz + rIz (3.24)

Using 3.3, 3.22, 3.23, and 3.24 the moment equations can be expressed 3.25,

3.26, and 3.27.



L = + qH rH (3.25)

M = H, + rHx pH, (3.26)

N = H + pHy qH, (3.27)

Where L, M, and N are the moments about {b i, b2, b3 axes respectively.

Making the assumption that the rate of change of the moments and products of









inertia are negligible and assuming the aircraft is not symmetric, the equations can

be expanded into 3.28, 3.29, and 3.30.



L = plx qly, plz. pql,, + (r2 _- 2) ly + qrlzz + rp y qrlyy (3.28)



M =-ply + qvyy ly, + rpIm qr ,y + (p2 r2) z + /,./ pr (3.29)



N = -plz ql + Hl + (q2 p2) Ixy + pqly prFly pql, + qrl, (3.30)

Equations 3.7, 3.8, 3.9, 3.28, 3.29, and 3.30 are the equations of motion used in
the simulation.

3.4 Force and Moment Calculations

The forces and moments the aircraft acting on the aircraft are represented

as functions of the flight condition. The flight condition includes angle of attack,

slide-slip angle, aircraft velocity, air density, and control surface deflections. The

equations for the coefficients of the forces and moments are given in 3.31, 3.32,

3.33, 3.34, 3.35, and 3.36.



CL = C +2 +CL a +CLo +CL, 6sym + CL (3.31)

CD CDa2 + CDa + CDo +CD,, sym (3.32)

Cy = CYp+C r +CY6&+CY6 ,sy+Cy3_ (3.33)

Cm r C= M a3 ma2CO + Ca mo m6 sym + Cm>Oi (3.34)

C1 C= ,p + Cr+ + C116J + C1, 6asy + C3" (3.35)

C, = C,,p + Cr + Cn, r + C Jasy + Cn/3 (3.36)









These equations use the methods presented in C'!h pter 4 to characterize the

aircraft. During each timestep of the simulation, the forces and moments acting on

the aircraft are calculated at that particular instant. This calculation is done by

evaluating 3.31, 3.32, 3.33, 3.34, 3.35, and 3.36 at that particular flight condition.

The coefficients are then multiplied by the current dynamic pressure, wing area,

and reference length if applicable.

3.5 Calculation of States

The body axis linear accelerations are calculated using 3.7, 3.8, and 3.9. The

forces were previously calculated and the mass, current angular rates and velocity

are known.

The body axis angular accelerations are calculated using 3.28, 3.29, and 3.30.

The inertial properties, current angular rates, and moments are known.

These body axis linear and angular accelerations are rotated into the earth-

fixed inertial reference frame and integrated each time step.















CHAPTER 4
CHARACTERIZATION METHODS

This chapter presents five different methods that can be used to help charac-

terize aircraft. Some methods may not completely characterize the aircraft so data

from multiple methods can be combined to generate a model.

4.1 Physical Measurements

Physical measurements can be taken directly from the aircraft. Geometric

propetries such as wing span, wing area, and the mean aerodynamic chord can

be approximated using a ruler. The mass is easily obtained using a scale and the

center of gravity can be experimentally located. Torsional pendulums can be used

to determine the moments of inertia and principle axes of the aircraft.

4.2 Finite Element Methods

A high fidelity finite element model can produce analytical values for mass,

moments of inertia, products of inertia, wing area, and other geometric properties.

Programs such as ProEngineer [35] can be utilized to create computer models of

each airplane component. These can then be assembled in a flight configuration.

Subsequent in 1v-i-; can result in values for the aforementioned properties.

4.3 Wind Tunnel

A wind tunnel can be used to accurately characterize forces and moments

acting on a micro air vehicle. Micro air vehicles can be small enough to mount a

full-size MAV model into the wind tunnel test section without requiring scaling

laws. This testing allows the wind tunnel data to include the strong viscous forces

associated with the low Reynolds numbers encountered by MAVs [3].









Accurate results from wind tunnels depend on the instrumentation used to

measure the forces and moments. A 6 in MAV can have forces on the order of 0.02

newtons [3]. Such small forces can be easily distorted by noise or poor calibration.

Results from wind tunnel testing can include static derivatives and curves for

the forces and moments based on angle of attack, side-slip angle, control surface

deflection, and thrust. Dynamic derivatives can be difficult to measure in a wind

tunnel and is often approximated by equations.

4.4 Computational Fluid Dynamics

The use of Computational Fluid Dynamics (CFD) can assist in evaluating

hard to determine parameters, such as the dynamic derivatives, as well as easier to

determine parameters, such as static derivatives. CFD methods can also be used

when a wind tunnel cannot be used. Vortice Lattice Methods (VLM) can be used;

however, the complete Navier-Stokes equations will provide more accurate results.

Some VLM programs do not include viscid skin friction which becomes a significant

force in low Reynolds number flow.

4.5 Flight Testing

An aircraft equipped with sensors, such as accelerometers and gyroscopes,

can log flight test data for analysis. This data can be used to perform regression

analysis to relate gyro measurements of roll rate, pitch rate, and yaw rate to

control surface commands. The aircraft dynamics are determined by a least-squares

approach to the flight test data [27]. This method can obtain inaccurate results

due to noisy sensor measurements.















CHAPTER 5
AVCAAF CHARACTERIZATION

5.1 Overview

This chapter presents an example of characterizing a MAV. This example

consists of identifying the longitudinal and lateral dynamics of the AVCAAF vehi-

cle using finite element methods, wind tunnel and computational data. The wind

tunnel data is used to find the static aerodynamic force and moment coefficients.

The aerodynamic software package, Tornado, approximates the dynamic derivatives

of the AVCAAF vehicle [29]. The aerodynamic characteristics are integrated into

the standard longitudinal and lateral linear dynamics to characterize the AVCAAF

at a trim condition. These linearized dynamics are analyzed for modal properties.

The analysis is performed to check stability and to quantify the confidence of the

model created from the wind tunnel and computational data.

The actual implementation of the dynamics will involve regression analysis

of the wind tunnel data, supplemented by the computational data, resulting in

functions for force and moment coefficients. This implementation allows simulation

of the MAV at different flight conditions.

5.2 Experimental Aerodynamics

5.2.1 Testing

The aerodynamics associated with the AVCAAF aircraft are experimentally

determined using a wind tunnel at the University of Florida. This wind tunnel is a

horizontal, open-circuit low-speed facility. The wind tunnel has a bell mouth inlet

and several flow straighteners. The test section is square with dimensions 914 mm

and a length of 2 m. The fan speed is regulated by a variable frequency controller









and operated remotely by a computer. The maximum velocity for test purposes is

approximately 15 m/s which correlates to a maximum Reynolds number of 100,000.

Testing of the tunnel is controlled by a computer. This computer controls the

angle of attack of the model along with acquiring data and performing real-time

analysis.














Figure 5-1: AVCAAF model in test section


The vehicle is mounted onto a sting balance and the resulting structure con-

nects to an aluminum arm as in Figure 5-1. The internal sting balance measures

five forces and one moment. The forces are converted in real time to the coeffi-

cients, {CL, CD, Cm, C Cy, C 1}, using the dynamic pressure and reference data for

wing area and reference length.

The main potential sources of uncertainty are errors associated with solving

the sting balance forces and moments, angle of attack measurements, and the

dynamic pressure determination. Additional minor factors include uncertainties

in the determination of geometric quantities such as wing area or chord line. In

actuality, the MAV generates loads considerably smaller than usual calibration

weights so the sting balance is a reasonable expectation as the main source

of error [39, 30]. A preliminary estimate of this error was done by running an

extensive set of calibration checks [19].










5.2.2 Results

The aerodynamics of the AVCAAF vehicle are determined using a freestream

velocity of 13 m/s The vehicle was mounted wings-level to consider sweeps across

angle of attack and mounted at a roll angle of 90 to consider sweeps across angle

of sideslip.

A complete set of static derivatives in pitch, roll and yaw are computed [3]. A

representative set of this aerodynamic data is given in Figure 5-2 and Figure 5-3.

These data consider the aerodynamics at a variety of symmetric deflections for the

elevators.

Unfortunately, the facility did not allow for measuring the dynamic deriva-

tives. Consequently, the data obtained from the wind tunnel is not sufficient to

completely characterize a model of the flight dynamics.

The AVCAAF vehicle was also not tested with its motor turned on. Testing

the AVCAAF vehicle with the motor on would require an awkward mouning

system which does not currently exist. Since the differential elevators and rudder

are in the prop-wash during actual flight, the wind tunnel data may not accurately

depict the elevator effectiveness.

0 =0
S 8e=10
15- > 8=30







-05

-5 0 5 10 15 20
AOA (deg)
Figure 5 2: CL versus angle of attack












8 =30

1 5




-0 5
0

-05-

0 005 01 015 02 025 03 035
CD
Figure 5-3: CL versus CD


5.3 Analytical Inertias

The inertia properties of the aircraft are estimated from finite element

methods. This analysis uses a CAD model, shown in Figure 5-4, and the

ProEngineer [35] software package. The model was created by dimensioning

each component of the MAV and assembling them in a flight configuration. An

exploded view of the ProEngineer model is shown in Figure 5-5 and a list of

components is presented in Table 5.3. The estimated inertia properties are given in

Table 5.3.













i" 1t '-




Figure 5-4: Analytical model



The model used to calculate these values accounts for the dominant mass

elements; however, some small errors remain. The mass of the model is 6.5'. less











..... .... ..

......... ........
~ ,. ....................


r dlk 0


Figure 5-5: Exploded view

Table 5-1: AVCAAF vehicle component masses


Component
Altimeter Board
Avionics
Battery
Camera Mount
Camera Transmitter
Fuselage
Hatch
Horizontal Stabilizer
Motor
Propeller
Propulsion Gearing
RC Receiver
Servo x3
Servo Mount
Speed Controller
Tail Boom
Video Camera
Vertical Stabilizer
Wing
Total Mass


M ass (,,i,,-')
27.0
61.0
131.7
5.0
18.2
47.9
6.7
8.9
50.0
9.0
24.6
8.0
29.7
7.0
12.2
6.5
11.9
10.6
34.0
509.9


than the actual vehicle because small parts, such as wires and control rods, are

excluded from the model. The center of gravity is also in error and lies 0.125 in aft









Table 5-2: Analytical inertia properties

Property kg m2
Imm 1.127 e-03
Iy 6.604 e-03
I, 7.130 e-03
Iy -3.920 e-05
1, -3.798 e-04
7y, -9.670 e-06



of the actual position. These errors are quite small so the properties in Table 5.3

are accepted with reasonable confidence. These values will also be used by the

simulation for the AVCAAF MAV.

5.4 Analytical Aerodynamics

A computational analysis is also used to estimate the aerodynamics of the

vehicle. In this case, the aerodynamics are estimated using the Tornado software

package [29]. This software uses a vortex lattice method to solve for flow over

lifting surfaces. The analysis assumes incompressible flow which is certainly

appropriate for the flight regime of a MAV. The analysis also assumes inviscid flow

which creates some errors in the resulting solution; however, the inviscid pressures

are still represented.

The analysis represents the lifting surfaces as a set of panels. The geometry of

these panels used for the AVCAAF aircraft is shown in Figure 5-6. The software

only considers wings and tails so the fuselage, along with its associated aerody-

namic contribution, is not modeled. The reference point about which moments are

calculated is also shown in Figure 5-6.

A set of static and dynamic derivatives are computed from a central difference

expansion about a given flight condition. In this case, a trim state associated

with straight and level flight is used for the condition. The output contains

almost all of the stability derivatives needed to form a set of full-state linearized










3-D Wing configuration




V 05o

025
02
0 15
o ",,
0 C 03
02
-0 15-02 0 1
Wing y-coordinate -025 0
Wing x-coordinate

Figure 5-6: Geometry of panels


dynamics. Some parameters, such as {CL,, Cm,, CD, }, were neglected because

the aerodynamics were assumed to have no variation with Mach. The dynamic

derivatives obtained from the analysis are listed in Table 5-3.

Table 5-3: Estimated dynamic derivatives

Parameter Value
Cmq -6.0391
Cyp -0.2920
Cy 0.7587
0.0190
C,, -0.3061
CQ, -0.3857
C, 0.3178




The derivatives in Table 5-3 are accepted with a moderate level of confidence;

however, they are recognized to have some level of error. An obvious source of

error includes the lack of aerodynamic contribution associated with the fuselage.

Another source of error is the effects of a reflexed airfoil which exists on the

physical vehicle but is difficult to model with the software. Tornado also assumes

the lifting surfaces to be rigid. Since the AVCAAF vehicle has flexible wings, the

data obtained from Tornado will not accurately represent the adaptive washout













phenomenon. Finally, thrust is not modeled so the analysis assumed thrust equaled


the aligned drag component for the trim condition.


5.5 Model Integration


5.5.1 Wind Tunnel Data Analysis


Regression analysis is used to obtain static derivatives of the force and moment


coefficients from the wind tunnel data. The data was fit to a set of polynomials


representing separate parameters such as lift and pitch moment. Figures 5-7, 5-8,


and 5-9 show the actual wind tunnel data and the curves fitted to the data. The


resulting equations are in radians are 5.1, 5.2, and 5.3.


14

1 2 -Wind Tunnel Data
Regression curve


08
06
d 04
02
0
-02
-04


-2 0 2 4 6
Angle of Attack (deg)


8 10 12


Figure 5-7: Wind tunnel data and fitted curve of CL


0 18'

0 16

0 14

0 12-
0
01

0 08

006-

004-

002
-4


SWind Tunnel Data
Regression curve















2 0 2 4 6 8 10 12
Angle of Attack (deg)


Figure 5-8: Wind tunnel data and fitted curve of CD










015
Wind Tunnel Data
1- Regression curve

0 05

0-
E






-02
-\\
-0 05



-015

-4 -2 0 2 4 6 8 10 12
Angle of Attack (deg)

Figure 5-9: Wind tunnel data and fitted curve of Cm






CD = 5.5475a2 1.0587a + 0.0814 (5.1)

CL = 10.5381c2 + 5.0342 0.1514 (5.2)

Cm = -49.2329a3 + 10.7473a2 0.8158a 0.0002 (5.3)


Derivatives of these polynomials were taken with respect to a. Other deriva-

tives that are independent of a were determined by finding a linear relationship

with respect to the associated parameter (3, 6,, 6sym, etc). Finally, the derivatives

were evaluated at the flight condition used to compute the analytical aerodynamics

corresponding to angle of attack of 5. This angle of attack is considered a trim

condition and is analyzed only to determine aircraft stability at this condition.

Some anomalies are noted in the experimental aerodynamics. In particular,

the side force shown in Figure 5-10 seems erroneous. The side force during a sweep

through angle of attack should be nearly zero but is measured with a significant

magnitude. The side force during the longitudinal test was actually the same order

of magnitude as that measured during lateral-directional testing that varied rudder

and angle of sideslip. This anomaly is not fully explained but may be caused from










the .mi-mmetry of the model, the alignment of the model in the tunnel, or the

calibration of the sting balance.

006

0 04

0 02

0> 0

-0 02

-004

-0 06
-4 -2 0 2 4 6 8 10 12
a (deg)

Figure 5-10: Measured values of side force


5.5.2 Aerodynamics

The aerodynamics used for analyzing the flight dynamics of the AVCAAF

vehicle are extracted from Table 5-4. These values present both experimental

estimates and analytical estimates. The values in bold font are the actual values

used in formulating the model.

The values extracted from Table 5-4 are divided between the experimental

estimates and analytical estimates. The experimental estimates would normally be

preferred but some anomalies, such as the side force, resulted in higher confidence

being associated with some analytical values. The derivatives with respect to 3

were taken from Tornado data due to the wind tunnel data set containing two

values of 3 at zero and five degrees. The physical mounting of the AVCAAF

aircraft in the wind tunnel currently limits the range of side-slip that can be

measured.

Also, the values of Ca, and CL, were not obtained from either experimental

analysis or analytical analysis. The value for this parameter was estimated from a

published value for a different vehicle [5].









Table 5-4: Analytical and

Stability Derivative
CL
Cm
CD,
CY.
CLo
CDo
Cm0
CL6,m
Lmsym
Cm
CDsym





c
CY6
C16,



C
Cy
CI,
C."2


experimental stability derivatives

Tornado Wind Tunnel
4.4486 8.7162
-0.3519 -0.3347
0.4639 -0.2329
0 0.4596
0.5204 -0.2443
0.0166 0.0836
0.1112 0.0144
0.9009 0.7833
-1.6461 -1.4177
0.0274 -0.1064
0.6929 0.1377
0.0284 0.0753
-0.3239 -0.3312
0.6859 0.1556
-0.0280 -0.0675
-0.21-; -0.2920
-0.7121 0.4488
-0.0769 2.2056
0.31274 7.6871


The simulation uses the data selected in Table 5-4 as well as the dynamic

derivatives in 5-3 to supplement the wind tunnel data.

5.6 Linearized Dynamics

These modes are initial estimates of the flight dynamics and must be accepted

with caution. The aerodynamics used to generate the model showed discrepancies

between experimental and analytical estimates so the model is inherently question-

able. The aircraft is undergoing flight testing but the sensor package does not yet

measure parameters sufficient for extensive modeling [22].

5.6.1 Longitudinal

The flight dynamics describing longitudinal maneuvers around the trim

condition are computed by combining data from Table 5.3, Table 5-3, and Table 5

4. The resulting model represents the linearized dynamics for which longitudinal









and lateral-directional components are decoupled. The dynamics are realized as a

state-space expression [31].


Au Au

Aw Aw

Ag Aq

AO AO

Where the Alo and BlI, matrices are comprised of longitudinal derivatives.

The longitudinal derivatives are defined in Table 5-5.


X, X, 0 -g

AZ, Z, Uo 0

II + M Z. M + MZ, M1, + Muo 0





Bsym
Bl, ym
+I +1, 7Z.

0

The following are the Alon and Blo matrices for the AVCAAF vehicle at

a = 5.


-0.1799 0.4617 0 -9.81

-1.1198 -9.4678 13 0
Aln
0.0942 -1.8271 -3.2945 0

0 0 1 0










Table 5-5: Longitudinal derivatives

Parameter Value

-(cDv+2CDo)QS

-(CD,+2CLo)QS
X,
muo

-(cL,+2CLo)QS
muo
-(CLa+2CDo)QS
Z muo

C (QSc)




M. C (Q
c QSc


m' m 2uo 1y
C QSD Q
6sy, -D6sym m

Z -CL6 Q
"sym m




-0.3828

10.9559
B1.
-144.5432

0

The eigenvalues of this model relate the natural frequencies and dampings of

the flight modes. These properties are presented in Table 5-6 and indicate a pair of

oscillatory modes are present in the dynamics.

Table 5-6: Longitudinal eigenvalues

Mode Frequency (rad/s) Damping
phugoid 0.7173 0.0664
short period 7.4846 0.8582









The eigenvectors associated with these eigenvalues are given in polar form in

Table 5-7. Note these are in terms of non-dimensional states.

Table 5-7: Longitudinal eigenvectors

Short Period Mode Phugoid Mode
Magnitude Phase Magnitude Phase
Aui 0.1518 -8.220 1.0264 -102.050
Aw 1.5590 98.000 0.0478 -69.12
Aq 0.0268 149.12 0.0026 -93.81
AO 1.0000 0.000 1.0000 0.000



A mode is described as phugoid mode because of its relationship between

pitch angle and airspeed. The mode has a small natural frequency and is lightly

damped. As such, the mode has characteristics which are classically associated with

a phugoid mode.

The remaining mode is described as a short period mode. This mode has

a close relationship between angle of attack and pitch rate. Also, the natural

frequency of this mode is an order of magnitude higher than the phugoid mode.

Consequently, this mode is similar in nature to the classic definition of a short

period mode.

5.6.2 Lateral-Directional

The flight dynamics associated with lateral-directional maneuvers around

trim are also computed using data from Table 5.3, Table 5-3, and Table 5-4. The

dynamics are again realized as a state-space expression [31].


A AO

Af Ap [Aasy
SAlat + BIoat
At Ar A6Srd

a AO










Where the Aiat and Biat matricies are comprised of lateral directional derivatives,

defined in Table 5-8.


Y- 1_ Yv, ( cos Oo
Uo 0o uo Uo

ALt L p Lp L 0
Alat =
Np Np NT, 0

0 1 0 0

0 Y6,


Blat =
N6a^y NVr

0 0

The following are the Aiat and Biat matrices for the AVCAAF vehicle at

a 50.


-0.7661 -0.0074 -0.0578 0.7546

-111.8602 -13.1591 10.8419 0
Alat
157.6609 0.2247 -3.6182 0

0 1 0 0

0 0.7455

-34.0289 109.5044
Blat
-147.1914 -166.9433

0 0

The modal parameters are computed from the eigenvalues and eigenvectors

of Aiat. The natural frequencies and dampings resulting from the eigenvalues are

given in Table 5-9. In this case, the lateral-directional dynamics have a divergence,

a convergence, and an oscillatory mode.










Table 5-8: Lateral directional derivatives

Parameter Value

QSCy
Yp m
QSbCy,
y 2muo
QSbCyr
2muo
QSbC1
I..
Q1,, ClP
p 2Ixxuo

L Qp,- Cl,
2r Ixuo
3 QSbC,


NP 2Izuo

N, Q" fl-,Cn
2r 2Izuo
QSCY6
Ys6 m
QSbCl,
L6.y I..
QSbC1,

QSbC.


QSbC,,
N 6,. I~



Table 5-9: Lateral-directional eigenvalues

Mode Frequency (rad/s) Damping
spiral 2.0888 -1.0000
dutch roll 5.7078 0.4526
roll 14.4649 1.0000



The eigenvectors associated with the divergence and convergence are given in

Table 5-10. Note these are in terms of non-dimensional states.









Table 5-10: Lateral-directional eigenvectors

Roll Mode Spiral Mode
Magnitude Phase Magnitude Phase
Au 0.0045 180 0.0057 0
Ap 0.3392 180" 0.0220 0
Ar 0.0268 0" 0.0490 0
AO 1.0000 0" 0.4502 0
AQ 0.0791 180 1.0000 0



The stable mode has obvious characteristics associated with the classical

definition of roll mode. The response of this mode is predominately a roll motion

with only minor variation in angle of sideslip or yaw.

The unstable mode is characterized as a spiral divergence but with some

reservations. The eigenvector indicates the response resembles a classic spiral mode

in that excitation of this mode is essentially yaw with some roll. Conversely, the

magnitude of the eigenvalue is quite large to be considered a spiral pole.

The remaining mode relates to a dutch roll dynamic as evidenced by its

eigenvector in Table 5-11. The motion associated with this mode is a complex

relationship between yaw and roll and angle of sideslip. The phases and magnitudes

slightly differ from the motions of large aircraft; however, the dynamics are clearly

dutch roll.
Table 5-11: Lateral-directional eigenvector

Dutch Roll Mode
Magnitude Phase
A O 0.0160 -117.02"
Ap 0.1338 116.91
Ar 0.1446 162.61
AO 1.0000 0"
AQ 1.0801 45.70



Also, the natural frequency associated with the dutch roll agrees with a basic

trend. Namely, the magnitude of the natural frequency should increase as wing











span decreases. Figure 5-11 indicates the natural frequency estimated for the

AVCAAF aircraft lies along a reasonable curve with values from other aircraft.

25
S15 cm Micro Air Vehicle

20-
S Black Widow
S15
>,
3 10
LC
AVCAAF
5 DragonFly UAV
OF-16 Boeing 747
o
10 100 101 102
Wingspan (m)

Figure 5-11: Variation in dutch roll frequency


5.7 Modeling Results

This chapter has shown the development of the linearized longitudinal and

lateral dynamics of a micro air vehicle using wind tunnel and computational data.

The wind tunnel data did not include the dynamic derivatives and included some

spurious data. The software package Tornado was used to supplement the wind

tunnel data to complete the model. The linearized model has modal properties that

are similar to standard aircraft modes. The spiral mode was analyzed as unstable.

This instability has not been confirmed by flight testing due to the difficulty of

recognizing spiral divergence during flight. It should be stated again that the

dynamics presented were for one flight condition. The simulation will encompase

a wider range of flight conditions by using functions to solve for the forces and

moments the MAV experiences each time step.

There is not much confidence in this model accurately characterizing the

actual AVCAAF vehicle. This is due to the conflicting results obtained from the

Tornado and wind tunnel data. Some sources of inaccuracies include computational







42

data based on inviscid flow, inaccurate modeling of the flexible wings, difficulty in

modeling the reflexed airfoil, and spurious experimental data.















CHAPTER 6
AVCAAF SUBSYSTE\ IS

The subsystems designed specifically for the AVCAAF aircraft were the

Sensors block, Controller block, and Actuator block in Figure 2-1. This chapter

discusses the design of these subsystems.

6.1 Sensor Subsystem

The Sensors block from Figure 2-1 is comprised of three subsystems for the

AVCAAF vehicle. These subsystems are the Camera, GPS, and Altitude blocks

shown in Figure 6-1.




SCamera >
Pitch Angle Pitch
Roll Angle Percentage




S GPS '
X Latitude
Y Longitude




Altimeter
Z Pressure
Integer




Figure 6-1: AVCAAF sensors subsystem


6.1.1 Camera S- il-,-I in

The camera subsystem emulates the vision output the controller receives

from the goundstation for horizon analysis. The subsystem calculates the pitch









percentage seen by the camera based on pitch angle, roll angle, and camera view

angle. Pitch percentage is the percent of "ground" seen in the image. It is assumed

that when the pitch angle and roll angle are zero the pitch percentage is 50'.

This equation can be further modified to account for altitude and distance to the

horizon.

6-2 shows a side view of the MAV capturing an image with its camera. This

case assumes there is no roll angle. Here 7 is the camera view half-angle, 0 is the

pitch angle, A A is the image plane, and D is the length from the camera to the

image plane. L is the length from the camera to the image plane along the camera

half-angle 7. hp is the percentage of ground seen in the image plane. The geometric

identities 6.1 and 6.2 can be observed.

A





Horizon
SLine
C.G. hp
L A
A

Figure 6-2: Image projection and pitch percentage




D
L = (6.1)
cos (7)
hp =L sin (7) D tan (0) (6.2)


6.2 can be expanded into 6.3.


hp = D (tan (7) tan (0))


(6.3)









The pitch percentage can be found be dividing hp by the image plane length,

shown in 6.4. The controller for the AVCAAF vehicle requires this value to be

between 0 and 1, where 1 correlates to a pitch percentage of 101 ("ground"

completely fills the image).



pitch hp
2D tan (7)
D (tan (7)- tan (0))
(6.4)
2D tan (7)
1 tan (0)
2 2 tan (y)

6.4 is only valid for the case where the roll angle is zero. The equation for

pitch percentage is more complex when roll is added. There are two different

general cases to consider when calculating pitch percentage with roll added. These

cases are when the ground area seen by the camera is either a triangle or trapezoid,

as shown in Figure 6-3.









Figure 6-3: Triangular and trapezoidal ground areas


Figure 6-3 also shows the image taken from the camera is not circular. The

camera in the AVCAAF transmits a standard NTSC video signal. This video

format will also make the pitch percentage calculation more complex. The standard

NTSC signal has a ratio of 3:4 for the height and length of the image respectively.

The pitch percentage will now be calculated as the percent of ground in the

rectangular image plane.









Figure 6-4 shows a more detailed view of the rectangular image plane. From

Figure 6-2 the distance from the center of the image to the horizon is found to be

D tan (0). It is known that the circle encompassing the 3:4 rectangle has a diameter

of 2D tan (7).






\ Dtanildl 6
S6Dtan(/) 2Dtan(y)
\





-Dtan(y)
5


Figure 6-4: NTSC camera image


To find the area of the ground in the image plane, let B represent the in-

tersection of the horizon with the rightmost side of the rectangular image. Since

a negative roll will result in the same pitch percentage as a positive roll of the

same magnitude, all negative rolls will be analyzed as positive rolls to simplify the

calculation.

Let C represent the intersection of the horizon and the leftmost side of the

rectangular image. Let A be the point on the horizon closest to the center of the

image. These points are depicted in Figure 6-5.

















-Dtan(y)
5 A S


SB
SDtan ()
5

Figure 6-5: NTSC image box and ground intersection

The coordinates of A, B, and C are taken from the center of the image, given

in 6.5, 6.6, and 6.7.

A (-D tan () sin () ,-D tan () cos ()) (6.5)

B = (-D tan (0) sin () + S cos (Q) ,-D tan (0) cos ()- S sin (Q)) (6.6)

C = (-D tan (O) sin ()-P cos () ,-D tan (O) cos ()+ P sin ()) (6.7)


The value of P and S will depend on the orientation of the horizon. There

are two cases for the location of point B: point B is either on the rightmost image

boundary or on the bottom image boundary. The camera I ,-v-lI i !i assumes that

the roll angle of the AVCAAF vehicle will not exceed 90 meaning the MAV will

not be inverted. The camera subsystem also converts a negative roll angle into a

positive angle for the pitch percentage calculation; the same magnitude roll angle

will result in the same pitch percentage if it is negative or positive.

To solve for the length S from Figure 6-5, the two cases for the location of

point B are evaluated. Setting the x-coordinate of B to TD tan (7) sets B at the









rightmost image boundary. Setting the y-coordinate of B to D tan (7) sets B at

the bottom image boundary. The length of S for both cases are 6.8 and 6.9.



S c ( tan (7) + tan (0) sin ()) Rightmost Boundary (6.8)
cos (0) 5

S ( tan (7) tan (0) cos () Bottom Boundary (6.9)
sin (0) (5

The correct value for S will be the minimum positive value resulting from 6.8

and 6.9. A similar method is used to find the value of P.



P = (4 tan (7) tan (0) sin () Leftmost Boundary (6.10)
cos (0) \5

P = tan (0) cos ()- -tan (7) Bottom Boundary (6.11)
cos (0) ( 5

The area of ground seen in the image plane is now simply a combination of

triangle and rectangle areas. Figure 6-6 shows a simulation of the horizon line

based on a 100 pitch angle and a 25 roll angle. The circle indicates the center of

the image. This image is similar to Figure 1-3 depicting an image processed by the

real horizon detection algorithm. Here the lower left corner underneath the line is

considered "ground."

6.1.2 GPS Subsystem

The GPS -,1 -i--I, ii gives the controller the current longitude and attitude.

Using the equations 6.12 and 6.13, the subsystem determines the current attitude

and longitude based on the starting position and current position. The actual GPS

receiver on the AVCAAF vehicle refreshes at a 1 Hz rate. This refresh rate has to

be simulated in Simulink to accurately model the GPS receiver.
























Figure 6-6: Simulated horizon from camera subsystem




1 Longitude minute = 1582 cos (Lattitude degrees) meters (6.12)

1 Lattitude minute = 1582 meters (6.13)


6.1.3 Altitude S- JI--i. iii

The altimeter on the actual AVCAAF aircraft measures pressure and outputs a

signal of 0 5 volts. The avionics package of the AVCAAF vehicle takes this signal

and uses a 8-bit A-D converter changing the signal into an integer from 0-255.

For the purposes of simulating this signal, it is assumed the altimeter has a one

meter per integer resolution, based on pilot observation. Thus, a simple calculation

emulates the altimeter: altimeter reading equals initial altimeter reading minus

the earth-fixed inertial frame Z value (a negative Z value corresponds to a positive

altitude).

6.2 Actuator Subsystem

The Actuator subsystem allows saturation and rate limits to be imposed on

the control servos. The position limits are 200 on the differential elevators and

250 on the rudder. The rate limits are 260 deg/s for all the servos. This actuator

modeling helps make the simulation more realistic.









6.3 Controller S- Ji-,- 1 i -

The Controller i'- i--1, i controls the differential elevators and rudder

deflections. Future simulations for morphing aircraft will allow the controller to

change the geometry of the MAV by changing the moments of inertia, products of

inertia, wing area, wing span, and mean aerodynamic chord.

The current contoller implemented in this subsystem was taken from the

AVCAAF vehicle controller. The original controller was coded in C++ and converted

into a MATLAB/Simulink implementation manually. This controller has the ability

to perform three dimensional waypoint navigation. The waypoints are pre-defined

by the user. The controller gives control surface commands to the MAV to reach

the waypoints. This controller can only change the differential elevator deflections.

In the actual AVCAAF control system the ground station sends symmetric and

anti-symmetric elevator commands to the Radio Control (RC) transmitter. The RC

transmitter mixes these signals to create individual control surface deflections. The

RC transmitter was programmed to use 1(I11' of the symmetric elevator deflection

command and 7' of the anti-symmetric deflection command when computing the

servo commands. This signal mixing was implemented in the controller subsystem.















CHAPTER 7
RESULTS AND CONCLUSIONS

7.1 Results

The example MAV characterized in C'! lpter 5 and 6 was not successfully

simulated. The attempt at simulating the AVCAAF vehicle resulted in an unstable

aircraft that could not be controlled by the Controller -, i ,-i--. in The gains were

adjusted by a trial and error method but failed to control the aircraft. This failure

to accurately simulate the AVCAAF vehicle and control system was mainly due

to the modeled AVCAAF vehicle not accurately representing the actual AVCAAF

vehicle.

7.2 Conclusion

This thesis has developed a simulation environment for Micro Air Vehicles

(! AVs). This simulation was designed to have a "plug-and-]l li- capability with

the aircraft sensors, aircraft, and controllers to make it easy for the user to simulate

various aircraft using different control systems.

A set of nonlinear equations of motion were derived for .,-vmmetric aircraft.

These equations require characterization of the forces and moments encountered by

the MAV. The controller -,t1i-i--1 i- can utilize the .-i-iiiii, lic equations of motion

to control morphing aircraft by changing the aircraft geometry

An example MAV characterization is presented in this thesis. The AVCAAF

vehicle, a 24 in wingspan MAV, was modeled using physical measurements, finite

element methods, wind tunnel testing, and computational fluid dynamics analysis.

The subsystems representing the AVCAAF vehicle's sensors and control system

were developed to emulate the actual hardware and software. The result of the

AVCAAF vehicle modeling did not result in an accurate simulation. The control







52

system implemented in the simulation had the same architecture and gains as used

on the actual AVCAAF vehicle. Since the dynamics differ between the actual and

modeled AVCAAF vehicle, it is not surprising that the control system could not

control the simulated vehicle.

The ground work for simulating MAVs has been established. Methods to

characterize MAVs have been attempted. Further research will more accurately

model MAVs. Accurate characterization will allow the simulated vehicle to

accurately represent the actual vehicle making controller design possible in the

simulated environment.















CHAPTER 8
RECCOMENDATIONS

8.1 Overview

This chapter is intended to present reccomendations for the AVCAAF pro-

gram.

8.2 Wind Tunnel Characterization

Using the wind tunnel to characterize MAVs is ideal. The wind tunnel

allows accurate characterization of actual flight conditions using the actual MAV.

Refinement in characterizing the Micro Air Vehicles needs to be researched.

Problems associated with testing the AVCAAF vehicle included:

Limited angle of attack range

Unreliable side force component

Limited side-slip angle range

Testing did not include powered thrust

Dynamic derivatives could not be obtained

Testing the second generation AVCAAF vehicle (denoted as AVCAAF

vehicle 2.0) has recently started. The configuration of the new vehicle eliminates

some of these problems. The AVCAAF vehicle 2.0 has been tested through a

complete range of angle of attack including stall angle. The testing has also

included powered thrust since the wind tunnel mounting does not interfere with the

propeller.

Despite the AVCAAF vehicle 2.0 improvements the side force and dynamic

derivatives are still lacking. Refinement in the side force component must be

accomplished to provide accurate results. The dynamic derivatives may prove to









be impractical to measure in the wind tunnel and should be the only parameters

approximated by computer.

8.3 Computational Fluid Dynamics ('C i i:'terization

There are two 1i i i" problems with using computational fluid dynamics to

characterize the MAVs: poor MAV geometry representation and lack of viscous

forces. The current CFD program, Tornado, did not include the MAV fuselage,

flexibility of the wings, and did not model the reflexed wing curvature.

Fluent, another CFD program, is reccomended to replace Tornado. Fluent

has the capability of importing Computer Aided Drafting models from programs

such as NASTRAN to accurately model the entire MAV. This will allow the flex-

ibile wings to be represented and analyzed accurately as they deform through

flight. Fluent also includes viscous forces that MAVs will encounter at their low

Reynold's number flight regimes. These capabilities of Fluent should result in

accurate approximations of the dynamic derivatives.

8.4 Streamlining MAV Design to CFD ('!i '.terization Process

Currently MAV fuselages are hand made from hard foam to make molds. This

process introduces .,-vmmetries in the fuselage and makes it difficult to create an

accurate computer model of the fuselage. It is recommended that the design of the

fuselages should be created in a CAD program compatible with Fluent. This will

allow the designer to eliminate fueslage .,i-,ii,. I l. and will streamline the process

from design to CFD characterization. The CAD model will be easy to import into

Fluent and be accurately analyzed.

8.5 Miscellaneous Reccomendations

Since the two graduate students working on modeling MAVs are graduating

in December 2004, this will result a loss of knowledge unless someone is trained

in this area. At least one graduate student should be commissioned to become

familiar with the work presented in this thesis. This should include familiarization







55

in testing procedures and simulation architecture and code. The student should

also start dialogue with the person in charge of the HILS facility to determine how

to implement the simulation in the facility.














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BIOGRAPHICAL SKETCH

Jason Joesph Jackowski was born in Toledo, Ohio, on October 12, 1979.

He grew up in Deltona, Florida, after his family moved when he was three. His

family took an active roll in the Boy Scouts of America and both his brother Jeff

and Jason earned their Eagle Scout awards. Jason persued many extracurricular

activities in high school including ..11 li i KEY club, Academic Team, Environthon

Team, and wrestling. After completing several advanced placement courses in high

school Jason was prepared to attend the University of Florida. Jason completed

his Bachelor of Science degree in Aerospace Engineering. During his undergraduate

degree Jason interned at General Electric Aircraft Engines for one summer and

Boeing for two summers. Jason then decided to attend graduate school at the

University of Florida working in the Flight Controls Laboratory under Dr. Rick

Lind.