AIAA-1997-3786-162

Copyright©1997,AmericanInstitutefAeronauticoAstronauticsdsan,Inc.A97-37218AIAA-97-3786DYNAMICINVERSIONAPPLIEF-117ETHAODTRichardColgren.D.Ph,LockheedMartinSkunkWorks1011LockheedWay,Bldg.608,Plant10Palmdale,CA93599-2525andDale.EnnsD.Ph,HoneywellTechnologyCenter3660TechnologyDrive,Minneapolis,MN55418ABSTRACTWhenusingclassicaldesignmethodoriginallss(ayusendidevelopinF—117egthAflightcontrolsystem)successiveobjectiveworThethfkeodocumentethindispapeswarsingleloopclosureperformedesar,wherebdesirableythetodevelopdesignproceduresforapplyingmultivariablecharacteristicsachievedinthefirstclosuremaybelostincontroltheorytofighteraircraftcontrollawdesign.thesecond.ThisadvantageisveryimportantwiththeSpecificallydynamieth,cinversionmultivariablecontroladvenfocontrol—configuretdvehicledstronansgdesignmethodwasappliedtotheF-117Atomeetcross-couplingbetweenvehicleaxes[Do84].stability,performance,anddisturbancerejectionrequirements.PrecompensationusespilotinputsandResultsindicatethatmethodsstudiedundertheMCTcreatescommandfeedbacethrsfokloop.Threecontrolsatisfactorileefforbncatyappliereaodtlaircraftcontrolvariableswereconstructedfromvarioussensedproblems.Dynamicinversioncontrollershaveprovedquantities.Thesewereshapegeneratodtdesireethedespeciallyportablebetweenaircrafttypes.valuesforthederivativesofthecontrolledvariables.F-117ADESCRIPTIONINTRODUCTIONTheF-117AshowninplanandsideviewinFigure1isaThispaperdocumentsdesignworkaccomplisheethrfodsingleseatfighter-bomberinthe36,000to52,000poundUSAirForce,WrightLaboratories-FlightDynamicsclassweaponrlAl.stoweysiinternandilbays,whichopenDirectorate,Dayton,Ohioundercontractnumberundeecentethrefuselagertharefoa.PrimarypilotF33615-92-C-3607"ApplicationofMultivariablecontrolcenteaesarrstick,pedalpowedsanrleverseTh.ControlTheorAircrafytotControlLaws".ThisworkwascombinatioshapfnoattainabldeaneC.G.locationresultsconductedbycompaniesoftheLockheedMartinaircrafninatwhicmucrunstablshifohwyapitcneidhanCorporationreportingtotheHoneywellTechnologyflighosfittenvelopeexhibittI.largsaedihedraleffecdantCenter.TheobjectiveofthiscontractwastodevelopnosapitchinpeugmomentwithsideslihigdpanhanglesdesignguidelinerapplicatiosfomultivariablfnoecontrolofattackbeyonsitIehuma.dthnpilot'scapabilitoyttheorytoaircraftcontrollaws.Thisstudywaspartofacompensateforthesecharacteristics.Theanalogthree-yearU.S.AirForcecontract[WL96].Itwasanfly-by-wireflightcontrolsystem(PCS)ontheF-117Aentirelyanalyticstudy.Flightcontrolsystemsweretrimeaircrafthsconstraindantsflighitstwithinsafaedevelopedforthreedifferentaircraft(F—117A,F-16,envelope.ThePCSprovidesstabilityasdefinedinandYF-22).InthisstudyfourdifferentmaneuversusingMIL-F-8785controllerCfodflight[Mi80].Theronseithreedifferentmultivariablecontroldesignmethodsmechanicalbackup.((^-synthesis,dynamicinversiondeigenstructuran,esynthesis)wereevaluated.FullnonlineardatabaseswereWheeF-117thnAprograsstartedmwaeonlth,yusedtosatisfynonlinearsimulationrequirements.fly—by-wiresysteminproductionwasontheF-16,SpecificallycoveredinthispaperarethedynamicwhicjusdhhatenteredoperationalservicereducoT.einversionmultivariablecontroldesignsdevelopedbythetechnicalriskfortheF-117AprogramandavoidthecostLockheedMartinSkunkWorksfortheF—117AaircraftPCwoSnefcomponentdevelopment,maximuswaemus(seeFigure1).ThisdesignworkincludedsystemmadmaturfeoeF—16technology.performancevalidationusinglinearandnonlinearmodelsandnon—realtimenonlinearsimulation.horizontaeThlcontrolsurfacefouethreelevensarnsoThebasicadvantageclaimedforMultivariableControlthesharplysweptwings.Theyarelabeledleftoutboard,Theory(MCT)methodsisthatmultiplecontrolloopsareleftinboard,rightinboardrighdan,toutboard.Therseiclosedsimultaneously,meetingperformancaecriterion.horizontaonltail.VerticalcontrolsurfacefullethyesarrotatingleftandrightfinsoftheV—tail.ThefinsconsistCopyright(c)199Richar6ybdColgreDal&neEnns.ofapproximatelV—taiethpivofdshafaoanln%otty70PublishedbytheAmericanInstituteofAeronauticsandextendingthroughthestubfins.SurfacerateandpositionAstronautics,Inc.withpermission.limitgiveesarTablnigride1eitheThn.soresidthfeo275Copyright©1997,AmericanInstituteofAeronauticsandAstronautics,Inc.Figure1:F-117APlaSiddnaneViewsF40EG4oenginestweethinletcanopthr.foesarycontroldesires.PurenzwasinitiallyusedtoemulatetheExhaustnozzlerectangulaethesarropeningsparalleotlgcommandnatureoftheclassicallydesignedF-117Athetrailingedgeofthefuselage.controllaws.LateraCMCVwasusedtoprovideanaturalchangeincontrolpriorityfromrotationtoTable1:SurfaceRatesandPositionLimitstranslatioairspeesnadincreases.NotethaopeetthnloopresponsecontrolleethfsodvariablesmusthavrighoentControlSurfaceRate(deg/sec)Position(deg)halfplanezeros.InboardElevon±150±45Step2:Theaircraftmodelisdefined.ThekeycomponentOutboard+200±45inthisstepisthedevelopmentofasimplifiedElevonaerodynamicmodelthatcanberuninrealtime.ThisleastsquaresCk(awritte=modeebki\.)CnM,Herscalnae±84±19FinsCkisthevectorofleastsquaresaerodynamiccoefficients,evectothfCsaerodynamiiokrccoefficientethniscompleteaerodynamicanonlineadatabassidanerDYNAMICINVERSIONfunctiofanglonMacdfattacaneoh)numbek(ar(M).TFinally,bp/2VP,[1,,cq/2V=TJ,br/2V,5a,5e,e5thr]siThedynamicinversionmethodusedinthisworkisvectoindependenfrotvariables.Thesevariableethesardocumente[Ho9ndiWL96]d2anvariableeTh.sLCV,sideslipanglescalee,thdroll,pitchyadw,eanratesthd,anrepresenVMCVNCvariabledethtan,controlleebostdrollcontrow,pitchyadlan,surfacedeflections.intheroll,pitch,andyawaxesrespectively.TheyareablenvarioufdossensedsignalsfivA.estepprocesthesinSte:Nexp3desireethtdcharacteristiccontrolleethfsodusedtoimplementadynamicinversioncontroller.variable(Vespecifiedar).Ideallyedynamith,cdesSte:Choosp1ablenefvariableodoconstructsethtinversionportiocontroethfnollaw,alongwithopenloopcontrolledvariablesamannenI.daircrafttheseareaircraftdynamics,produceintegrationnsaedesireTh.ddeschosentoprovideadequatehandlingqualities.FordynamicfjZ]+[fbecV,VVarcm=s-wherdeexamplemusVechoictthMC,reflecfoeepilot'thtsostandartweb(V=zdThcmcasede.—arsV)276Copyright©1997,AmericanInstituteofAeronauticsandAstronautics,Inc.proportionalfeedback(fc=l,f;=0)andproportionalplusforlevelflightengineTh.epowerleveadvancesriethodtintegralfeedback(fc=0.5,fj=0.25).maximumpowersetting(militarypowermaneuveeths)arStep4:Hereforcesandmomentscorrespondingtoisinitiated.Rollstickinitiatiovariensifin"worsodetdthtundesiredaerodynamic,gravitational,and/orinertialcase"coupling.Fullstickinputsaremadeintobothaxescontributionemodelearssfunctionademeasurethfosdwitintenehthcapturinfoteightngaydegreebankanglestatevariables.Opposingforcemomentdansethearsnwhileremainingontheangleofattacklimiter.Therollcommandedtonegatetheundesiredcontributions.Intheinpucombinatioasitnonlineaethfnorpilotainpudantsimpleelinearizethcasfoedaircraftrollaxismodeethlsubsequentlineareterminamodethrfollbankanglecapturetask.Operationally,thismaneuvermightbedynamicequationisp=Lpp+L6a8a.Invertingthisinitiateadefensivsadebreakoreductturronaedynamicequationforthecontrolinputyieldsopponent'smissilelaunchenvelope.Thismaneuverisdesigneprovidodtdifficuleatcontrolintegrationtasrkfo5j—[p=agenerae-Lthpnp]Il.casenonlineaeth,rL&atheF-117A.equationsofmotionarex=F(u,x)=f(x)+g(x)u.vectoeHerthsstatfiroexvectoeethvariablesfiroudsaneseconThdmanualmaneuverutilizeeabilitthsfoycontrolsurfacesetimThe.derivativvectoeeththffeoormoderncontrolmethodstohandletheintegrationofcontrolvariablesisV=^x=^f(x)+^g(x)umultiplesurfacesF-117eTh.Asuitcontrofeolsurfaces5x5xv5x&v'andtheircouplingcharacteristicesucarshthatSISOa(x=dynamieb(x)+)Thu.cinversioenthparfot(SingleInputSingleOutput)classicalmethodmoresarecontroswritteiwedesirentermlaithnlfosdcontrolthanadequatcontrorefolsynthesisordenI.providorteanoperationallyapplicablescenarioandincreasethevariableasucmd=|g(x)ydes-neetreaodttsurfaceintegratioMIMasnaO(MultipleOXInputMultipleOutput)taskeseconth,dmanual=b(x)-I[V-ta(x)]o.maneuvesperformeirvariounodsfailedestatethfossurfacesefailureThemodele.arsyartificiallbdyfinaethlStenIste:handlinep5pthgqualitietuneesardconstrainingcombinationsrudderfoelevendsanfixeostdusingprecompensation.Forexample,stickandrudderneutraldeflections.pedalgainshapedsandefinedesar.ThelandingtaskprovidesadesignchallengesincelowerNONLINEARSIMULATIONairspeedsrequirehigherfeedbackgaindlarganseamplitudecontroldeflectionsformaneuvering.OftentheThisphaseuseenonlineathdrF-117AFortrantakeoflandindanfgphasessizcontroeethlpoweethrrfosimulationincludingnonlinearpropulsiodannvehicle.MIL—F—8785CprovidesautomaticflightaerodynamicdatabaseotdirectlsycomparethecontrolmoderequirementswhichcanbeutilizedinacontrollersdevelopedusinemultivariablthgecontrolanalyticaldesigdvalidatioannnenonlineataskTh.rmethodswitheachothewitdclassicalleranhthydesignedsimulationincludespitchandrollattitudecontrol,F-117Acontrollaws.TheclassicalF-117Acontrollawsheadingcontrolaltitudd,anecontrol.aregainscheduledtoaccommodateparametervariationthroughouttheflightenvelope.DynamicinversioncontrotrequirllawnoosdegainschedulintinsteagbudThesecondautomaticmaneuverutilizesthePilotActivatedAutomaticRecoverySystem(PAARS)usetheleastsquaresaerodynamicdatabase.TheaerodynamipropulsiodcannmodelsvarnonlineaanyirdesignedfortheF-117A.Thisautomaticmaneuvermannerthroughoutthesimulatedmaneuver.exercisesthecontroldesigninhighpitchandrollattitudesituationsthroughlargerangefcoupleosdattitudeTwoautomatiomanuatwdanlcmaneuvereusearsodtchanges.validatethecontrolsystemdesign.Allofthemaneuverse"unconventionalaresenstheni"thattheyrequirePAARSprovideall-attitudnaserecoverycapabilitoytcontrofdynamiolccouplingbetweenaxesemanuaTh.lprotectagainstpilotdisorientatiosensor/displaotenduymaneuversconsistofarapidpullintotheangleofattackfailure,pilotvertigoinducelaceexternafthkoydblvisuallimiterfollowedbyabankanglecapturewhileremainingcuesatnight,and/orpilotdistractionduetohighelimitethnoracleafor)1n:configuratio)2dannworkload.PAARSgeneratescommandstotheFlightsimulatedcombinationsofrudderandelevonfailures.ManagementSystem(outerloop/autopilot)whichinturnTheautomaticmodesconsistof:1)acoupledglideslopegeneratescommandFlighethosttControlSystem(innerandheadingcaptureand2)aPilotActivatedAutomaticloop)erecoverTh.ycommandsthatPAARSgeneratesRecoverySystem(PAARS)maneuver.emulatethecommandsfromafullylucidpilotinthesameflightsituation.PAARSutilizesectosarschemewhichTherapidpull—upisinitiatedat300knotsequivalentdivideeattitudthseenvelopeintosevenoperatingairspeed,Ig,wingslevel,10,000ft,andatapowersettingregions.ThisschemeisshowninFigure2.277Copyright©1997,AmericanInstituteofAeronauticsandAstronautics,Inc.PITCHATTITUDE(DEG)NOSEUPSECTOR7:+NZ(PULL)ANDZEROROLLRATESECTOR1SECTOR1(PULLZ+N)+NZ(PULL)ANDANDROLLINVERTEDROLLINVERTEDSECTOR2SECTOR2-NZ(PUSH)(PUSHZ-N)ANDANDBANKSECTOR3ROLLUPRIGHTROLLUPRIGHTSECTOR3BANKANGLEROLLUPRIGHTROLLUPRIGHTANGLE(DEG)(DEG)LWD-180-135RWDSECTOR5SECTOR4SECTOR4SECTOR5-NZ(PUSH)+NZ(PULL)+NZ(PULL)-NZ(PUSH)ANDANDANDANDROLLUPRIGHTROLLUPRIGHTROLLUPRIGHTROLLUPRIGHTSECTOR6SECTOR6(PULLZZERD+N)ANOROLLRATE+NZ(PULL)ANDZEROROLLRATENOSEDOWNFigure2:PAARSRecoveryVersusAttitudesPILOTMODELcommandedopenloopacceleratioe(i.ethn.inportiofnothepullandrollmaneuver).F-117eThAsimulationcontainsimplsaenonlinearpilotSIMULATIONRESULTSpitcmodelethhnIaxi.s(seeFigur)there3rneozearangleofattack(a)commandmodelswhichusealead-lagThefirstmaneuversimulatedisaPLA(powerleverangle)followeProportionaaydbIntegratodanlr(PI)filteotrincreasewithapullandrollto80degreesbankangle.ThisgeneratezerosteadystateerrorrolelTh.axismodesilresponsshowseiFigurnni.eSom6eworrequireskiodtmorecomplex,withdifferentmodesdependingonmakethepitchresponseacceptabletoapilot.Thegwhethefularlstickcommanrequiresdid(seeFigur.e4)responseistoosluggishduringtheinitialpullup.RollingForsmallbankangleerrors(andlowerrollrates)abankathighangleofattackcausesatoincreasefurther.anglhelseidwithdampingproviderolydblratefeedback.ElevendeflectionlargoratdtoeanelimitearsdduringWhentheAcommandislargeitgoestoafullstickinput,rolethlmaneuver(deflectionsshould<2eb0degreeesducomputingthetimetoeasebackonthestickcommandtotohingemomentlimits).OntheF-117Atheinboardacquirethedesiredbankangle.Intheyawaxisduringeleveoloan0degrees/second12ratsiedwhiletheapproachtoalandingthepilotmodelachievesasideslipoutboardelevennoloadrateis160degrees/second.Finconstanarotlateral-directionalflightpath(i.epiloe.thtdeflectionssaturateandratelimitduringtheroll(finmodelcontroleaircrafthsostattyealignethnoddeflectionshouldbe<14degrees).TheactualmaximumcenterlinerunwaythfFigureose,.Thie5)smodesilnoloadrateis70degrees/secondwhileatthisconditionusedwitrolehthlaxispilotmodelepoweTh.rlevesiritisapproximately55degrees/second.gnzcmdCommand0.15"r_TZS+1pKs__tps+1Hola0d-0.15"«Cmd1->•1Kp=1.0T=1.0Z5SK,=0.2T0.7=D740.K=qFigurLongitudina:e3lPilotModel278Copyright©1997,AmericanInstitutefAeronauticoAstronauticsdsan,Inc.Partialstickmodeif=0orinfullstickmod1e°ph25dFullstickmode:onifphd>25,offifdelphi+i|)>phicmd(right)or25°fullstickgotoK,qsch-&-——>if<25°2.6"+-L*+.1+/O<25°Pb\r1——>•^psch*Rollstickcommandphdcmd°ph25d•^-0.15"fullstickrightbank—1L——ym————*•+\r1-^K->•yrnlSFigure5:ApproachtoLandingDirectionalPilotModelTheseproblemswereexperienceddurinethwhegnrunninegroundthedynamingoTh.cnonlineardevelopmentoftheclassicallydesignedF—117Acontrolinversioncontrollerexpectstheaircraft'sresponsetosystem.Theyresultfromthegreatereffectivenessofcorrespondtotheflightcontrolsystem'sinternalmodel.downversusupelevonandfromhingemomentMismatcheeeffectivelarsyerrorsignals,whichcauselimitations.Theyweresolvedbyusinghighpitchgainsforwardloopintegratorstoruninanefforttocorrecttheandstrong,multiplestagealimiters.Variablelimitsneederror.Wheeaircrafnthttouchesdown,thervereearytobeaddedtodynamicinversioncontrollaws.largeforcesinputtotheplantwhicharenotexpectedbytheinversionscheme.ThiscauseslargemismatchesandThesecondmaneuversimulatedisthesamePLAincreaserunawayintegrators.Thiscanresultinthelossofthewitdegree0pulh8roladotlanlsbankangleexceptwithaircrafsituatioethtfaddresseitnosnidproperly.surfacaefailure.ThisresponsshowseiFigureniTh.e7rollaxishasaveryrapidresponse.Whentrisbelow0.4similaArconditionresultelandinndigoscillationnossecondaircrafesthexperiencncaterollratchetinroldglananothertyp(WeighaircraftGfeoWOGearntoA.)switchPilotInducedOscillation(PIO).ThereforeTrneedebostwasusedtostoptheforwardloopintegrators.SwitchadjustedhigheeTh.rrollresponsalsnadjusteeocabydbmalfunctionscouldhaveseriousconsequencesethfI.implementingthelower,variablelimits.Thereisaneedaircraftexperiencedalighttouchdowntheaircraftcouldtoremixtheelevensduetopitchinputsresultingfromrollwitintegratoehthrstillrunning.Wheswitcenthshwalargerrightrudderdeflectionsaftelefartrudderfailure.finallysetthecontrollawswouldgenerateanoseupThethirdmaneuversimulatedwasadescenttolandingpitchingmoment,scrapinnozzlegthrunwayneoeTh.(seeFigure8).Elevondeflectionsweresmallforlargepilotwouldthencommannosdaedownsticblodekwanthstickdeflectionspriortolanding.Thecommandgainsnosewheeltire.Afaderwasaddedtoreducetheappearedtobetoosmall.APLAincreasewasneededjustcommandedpitchingmoments.Complexlogicwasalsobeforetouchdowntoslowthesinkrate.AtthisairspeedrequiredforwhentheaircraftlandedononemaingearandsinkrategroundeffectsshouldbesufficienttoslowfirsbouncerotlandingndoF—117AethnI.forwareth,dthesinkrate.Thiswasprobablyduetotheaerodynamicloopintegratocancellesrwadupongearextension,ratherswitchthaGusinynbWOadvantageg.athThidshafeomodel.usinmorgaereliableswitchingmechanismwitcontroohnlelevoeThnsaturatestrailingedg,theeupntrailingedgelawchangesattouchdown,whereflightismostpronetodownafterlandingintegratoeTh.zerottorseneedebostproblems.280Copyright©1997,AmericanInstituteAeronauticfoAstronauticsdsan,Inc.Pstick(inches)4.000-3.000-2.000-1.000-0.000-0.006.008.00TIMERstick(inches)0.002.004.006.008.0010.00TIMEPLA(%).60.00-40.00-20.00-0.002.004.006.008.0010.00TIMEAngleofAttack(deg)10.00-8.00-6.00-4.00-0.002.004.006.008.0010.00Sideslip(deg)0.002.004.096.008.0010.00TIMEBankAngle(deg)«>M20.00-Classicalo.oo-Dyn.Inv.0.002.0D4.006.008.0010.00TIMEisseesFigurF-117:e6ARolPuldanlManeuver281Copyright©1997,AmericanInstituteofAeronauticsandAstronautics,Inc.AngleofAttack(deg)Sideslip(deg)BankAngle(deg)LeftElevon(deg)20(RightEleven(deg)O.oo--10.00--20.00--30.00--40.00-II0.002.00TIMERudder(deg)ClassicalDyn.Inv.TIMEisseesFigure7:F-117ARollandPullManeuverwithFailure282Copyright©1997,AmericanInstituteofAeronauticsandAstronautics,Inc.Altitude(feet)300.0-200.0-100.0-o.o-0.00AltitudeRate(Ft/sec)Airspeed(knotsequivalent)FlightPathAngle(deg)o.ooo-•1.000--2.000-0.0020.0040.0060.0080.00TIMEAngleofAttack(deg)PitchAttitude(deg)e.ooUIo-66.00(0-4.000-2.000-o.ooo-ITIMseeEsisFigure8:F—117AApproachandLanding283Copyright©1997,AmericanInstituteofAeronauticsandAstronautics,Inc.CONCLUSIONSANDSUMMARYsimulationswereusedtocompareclosedloopdynamicresponseswiththosegeneratedusineexistinthggThelargestintegrationissuesinapplyingthedynamicF-117Acontrollaws.MultiplemaneuverswereinversionmethodologytotheF-117Awerenotrelatedtoexaminedemonstratodteperformanctmaneaypointnsithecontrollaws.Instead,theyweresoftwarerelatedflighethtenvelopewithougaiethtnschedulingrequiredissues(i.e.commonblockcaldansllists,singleversusexistinbeythgclassicallydevelopedF—117Acontrollaws.doubleprecision,trimminecontrothgllawsaftercompletingaerodynamictrim).AsmallleastsquaresREFERENCESaerodynamicdatabaseprovedsufficientforuseinthecontrollawsfortheinversionprocess.Anexcellentfitto[Do84]Doyle,J.C.,etal.,"LectureNotes,enonlineathrdatabassobtaineewadusinglineartrimONR/HoneywellWorkshoponAdvancesinMultivariablepoints.FewpointswererequiredtodefinetheControl,"HoneywellCorp,Minneapolis1984,,MN.aerodynamiccurvesforthisdatabase.[Ho92]"DynamicInversionBasedFlightControlLawscontroeThlsurfacepositioratdneanlimitdynamiethnsicfortheHARV,"HoneywellSystemsandResearchCenter,inversioncontrollawswertconstrainenoethnisadMinneapolis,MN,3March1992.existingF-117Acontrollawswert,buesimplifiefixeodtd[MiSO]"MilitarySpecification,FlyingQualitiefosvalues.GroundeffectsprovedtobemuchweakerthanPilotedAirplanes,"MIL-F-8785C,5November1980.expectedinthelatestF-117Aaerodynamicdatabase.scopethffthieoostefforoutThineedsebubtswaost[WL96]"ApplicatioMultivariablfnoeControlTheoroytexploredfurther.AircraftControlLaws—FinalReport:MultivariableControlDesignGuidelines,"WL-TR-96-3099,FlightThedynamicinversioncontroldesignmethodologywasDynamicsDirectorate,WrightLaboratory,OH,MaysuccessfullyappliedtotheF-117A.Fullnonlinear1996.284