Wind Shear Energy Extraction using Dynamic Soaring

WindShearEnergyExtractionusingDynamicSoaringTechniquesNaseemAkhtar,∗JamesFWhidborne†andAlastairKCooke†CranfieldUniversity,UK,MK450ALThepaperdescribesresultsofatrajectorygenerationtechniquesuitableforreal-timeimplementation.Thetechniqueisusedforenergyextractioninwindshear.ItisbasedonthedirectmethodofTaranenkoandisusedforgeneratingtrajectoriesforapoweredsailplane.Thetrajectoriesaregeneratedtominimizetheenergyusedperdistancetravelledinthelateraldirectioninthedynamicsoaringcycle.Thetrajectoriesarealsogeneratedtomaximisethespeed.Thetrajectoryfollowingissuesareaddressedandanarchitectureforthecontrolsystemisbrieflydescribed.Simulationisperformedusingafullmodelofapoweredsailplanetoverifythetrajectorygenerationmethod.Theresultsoffuelsavingbenefitquantificationusinglinearwindshearmodelsandalsononlinearwindshearmodelsaredescribed.NomenclatureβWindgradient.KInduceddragfactor.EmaxAerodynamicefficiency.CLLiftcoefficient.CDDragcoefficient.CD0Zeroliftdragcoefficient.TThrust.x,y,hPositionrelativetoearthaxis.V0Initialspeed.VSpeed.mMass.gAccelerationduetogravity.γFlightpathangle.φBankangle.ψHeadingangle.¯(·)Normalizedstates.tfFinaltime.τThevirtualarc.nLoadfactor.ρAirdensity.¯ρNormalizedwindconditioningparameter.I.IntroductionThedynamicsoaringprocessinvolvesextractionofenergyfromwindshear.UnmannedAerialVehicles(UAVs)andpoweredsailplanescanutilizewindgradientspresentatlowaltitudestoeithergainheightor∗PHDStudent,DepartmentofAerospaceSciences,CranfieldUniversity,BedfordshireMK450AL,UK,n.akhtar@cranfield.ac.ukandAIAAStudentMember.†SeniorLecturer,DepartmentofAerospaceSciences,CranfieldUniversity,BedfordshireMK450AL,UK.1of15AmericanInstituteofAeronauticsandAstronautics47thAIAAAerospaceSciencesMeetingIncludingTheNewHorizonsForumandAerospaceExposition5-8January2009,Orlando,FloridaAIAA2009-734Copyright©2009bytheAmericanInstituteofAeronauticsandAstronautics,Inc.Allrightsreserved.totravelinonedirectionsoreducefuelusage.Dependingonflightrequirementsthetimeofexecutionofcyclecouldbeminimizedorenergyusedduringflightcouldbeoptimized.Otherpossibleusagesincludemaximizationofheightgained.Inatypicalpatternofdynamicsoaringasailplanewoulddescendwiththeprevailingwindtogainairspeed.Ongettingclosetotheseasurface,itturnsintowindandbeginstoclimb.Althoughthegroundspeeddecreasesduetotheheightgainedthesailplanemaintainssufficientliftduetoincreasedairspeedprovidedbythewindgradient.Whenthepeakwindspeedisreachedthesailplanechangesdirectiontodescendandstartstheprocessagain.Itispossible,ifthewindgradientissteep,forthesailplanetoextractsufficientenergytomaintainflightwithoutusingfuel.ThedirectmethodofTaranenkoisusedtogeneraterealtimetrajectoriesasdescribedbyYakimenko.5Thetrajectoriescouldbegeneratedforloiteringortravelling.Theloiteringmodeinvolvesexecutingverticalloopswhereattheendoftheloopthesailplanereturnstoitsoriginalposition.Inthismodethesailplanecangainheightineachdynamicsoaringloop.Inthetravellingmodeasailplanecoversahorizontaldistanceattheendofdynamicsoaringloop.Thetrajectorieswhenfollowedinwindshearresultinminimizationofacostfunction.Inthispaperresultsoftrajectorygenerationarepresentedwheretwodifferentcostfunctionsareused.Thefunctioninvolvesminimizationoftheaveragepowerusedinadynamicsoaringcycle.AsixdegreesoffreedommodelofapoweredsailplaneisusedinSIMULINKtoverifythetrackingofthetrajectories.Acontroller,basedonaclassicalarchitecture,wasdesignedtotrackthetrajectoriesgeneratedbytheoptimizationroutine.Thefuelsavingbenefitsofthedynamcisoaringtechniquesarealsodescribedandsensitivitytochangeinthewindmodelisalsoexplored.Theworkpresentedinthepaperdemonstratestheabilityofthedirectmethodtechniquetoproducetrajectoriesrapidlyenoughtobesuitableforreal-time,on-lineimplementation.TheabilityofthetrajectoryfollowingcontrollerwastestedusingasixdegreesoffreedomSIMULINKbasedsimulation.Theabilityofthecontrollertoholditsspeed,altitude,bankandheadingangleinthepresenceofwindsheardisturbanceshasalsobeenconsidered.Linearwindshearmodelsaswellasnonlinearwindshearmodelsweretested.Variousvaluesofwindgradienthavebeenconsideredtotesttheresponseofthecontroller.Zhao6hasmadeavaluablecontributionbystudyingoptimaldynamicsoaringflightsofUAVsthatutiliselowaltitudewindgradientsforreducingfuelconsumption.ThreepointmassUAVequationsofmotionwereused.PoweredUAVsoaringflightsutilizingwindgradientswerestudiedbyformulatingitasanonlinearoptimalcontrolproblem.Variousperformanceindicesareusedtominimizetheaveragepowerrequiredpercycle.TheproblemswereformulatedbyconsideringUAVequationsofmotion,operationalconstraintsandboundaryconditionsthatenforceaperiodicflight.Howevertheirmethodsarenotintendedtoproducepracticalschemesthatcanbeusedforon-boardimplementation.Theyhavefocusedonthemainbenefitsofvariousflightstrategies.IntheirstudytheyhaveusedapoweredUAVthatcanutilizeboththeenginepowerandalsowindgradients.InZhao’s6publicationtheboundaryconditionsarebasedoninitialandfinalairspeed,headingangle,flightpathangle,altitudeandhorizontalposition.Thevaluesofinitialairspeedandheadingaredeterminedfromthesolutionprocess.Toaccommodatetheperformanceboundari