Johansen yvind N Smogeli Department of Engineering Cybernetics Norwegian University of Science and Technology Trondheim Norway Marine Cybernetics Vestre Rosten 77 NO7075 Tiller Norway Abstract Transient regimes arise when the propeller of a sh ip is ID: 22237
Download Pdf The PPT/PDF document "INTEGRATOR RESET ANTISPIN FOR MARINE THR..." is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
INTEGRATORRESETANTI-SPINFORMARINETHRUSTERSOPERATINGINFOUR-QUADRANTSANDEXTREMESEACONDITIONSJosteinBakkeheimLucaPivanoTorA.JohansenØyvindN.SmogeliDepartmentofEngineeringCybernetics,NorwegianUniversityofScienceandTechnology,Trondheim,NorwayMarineCybernetics,VestreRosten77,NO-7075Tiller,NorwayAbstract:Transientregimesarisewhenthepropellerofashipisoperatinginextremeseas,whereventilationandin-and-outofwatereffectsresultsinlossofpropellerthrust.ByintroducingLyapunovbasedcontrollerstatereset,theperformanceintransientregimesmaybeincreasedwithoutinuencingtheperformanceincalmseas.Improvementshavebeenpresentedpreviouslyfordynamicallypositioned(DP)vessels.Transitoperations,however,introducesadditionallossesduetovariationsinthepropelleradvancevelocity.ThecontrollerinthispapercombinesanexistingshaftspeedreferencegeneratorthatusesanestimateofthepropellertorquelosseswithaPIshaftspeedcontrollawwithintegratorreset.Moreover,ananti-spinstrategyisincludedtobeabletooperatealsoinextremeseas.Themethodisexperimentallyvalidatedinatowingtank.Keywords:Switchingalgorithms,Lyapunovfunction,Marinesystems,Anti-spinregulation,PIcontrollers,Propulsioncontrol1.INTRODUCTIONThecontrolhierarchyofmarinevesselswithelec-tricallydriventhrustersconsistsofahigh-levelcon-trollergivingcommandstoathrustallocationscheme.Thethrustallocationschemegivesinturncommandedset-pointstothedifferentlocalthrustercontrollers(LTC),seeSørensen(2005).Dynamicpositioning(DP)systems,joysticks,andautopilotsareexamplesofhigh-levelcontrollers,widelycoveredinthelitera-ture.InthelastyearsalsoLTChasgainedgrowingin-terestintheliteratureseeSmogeli(2006),WhitcombandYoerger(1999),Pivanoetal.(2007),Bakkeheimetal.(2006)andthereferencestherein.Today'sindustrialstandardforxedpitchpropellersisproportionalandintegral(PI)controllersonthepropellershaftspeed.Thesecontrollersareusuallytunedinsuchawaythattheperformanceismaximizedwhenoperatingincalmormoderateseas.Inextremeseaswhereventilationandin-and-outofwatereffectsmayoccur,thecontrollermaygivepoorperformanceduetoshaftloadvariations.This,inturn,mayleadtowearandtearofthemechanicalpartsofthepropulsionsystem,andundesiredtransientsonthepowernetworkthatmayincreasetheriskofblackoutsduetoover-loadingofthegeneratorsets,seeRadanetal.(2006).Differentanti-spinstrategieshavebeenintroducedinordertohandlethesephenomena,seeSmogelietal.(2004),Bakkeheimetal.(2006)andSmogeli(2006).Thesecontrollersutilizeanestimateofthetorquelosstodetectventilationincidents.Theanti-spincontrollerinSmogelietal.(2004)isbasedonacombinedpower/torquecontrollerwhichinordertakescontrolofthepropellershaftspeed.AsimilarapproachisconsideredinBakkeheimetal.(2006),butinsteadtheanti-spincontrollerisbasedonastandardshaftspeedPI-controller,wheretheintegratorvalueisresetifappropriate.ALyapunovfunctionisusedtodecidewhensucharesetissuitable.Thisstrategywillonlyaffecttheperformanceinthetransientregimes,byspeedingupthethecontrollerresponseonlywhenlargecontrolerrorsaremeasured,seeBakkeheimandJohansen(2006)andKalkkuhletal.(2001)forotherapplicationsusingthisstrategy.InbothSmogelietal.(2004)andBakkeheimetal.(2006)onlyDPvesseloperationsareconsidered.Ex-tensionsoftheapproachinSmogelietal.(2004)totransitaregiveninSmogeli(2006).InthispaperasimilarapproachasinBakkeheimetal.(2006)isuti-lized,alsocoveringtransitoperation,wherethevesselspeedislargerthaninDP.Intransitoperations,lossesduetononzeroadvancespeed(thespeedoftheinletwatertothepropellerdisc)introducescontrolerrorsintheactualpropellerthrustwhenusingastaticmappingfromthedesiredthrusttothedesiredshaftspeedasinBakkeheimetal.(2006).InPivanoetal.(2007)ady-namicmappingfromthedesiredthrusttothedesiredshaftspeedispresented,compensatingforlossesdue Fig.1.Localthrustercontrolsystem.tononzeroadvancespeed.BycombiningthedynamicmappinginPivanoetal.(2007)withtheintegratorre-settingstrategyinBakkeheimetal.(2006),wegetananti-spincontrollersuitablealsofortransitoperations.Experimentaltestresultsareincludedinordertodemonstratetheperformanceofthisstrategy.2.LOCALTHRUSTERCONTROLLERAnillustrationofalocalthrustershaftspeedcontrolsystemisgiveninFigure1.Fromthehigh-levelcon-trolmodule,thedesiredpropellerthrustTpdisgivenasaninputtothecontroller.Further,areferencegen-erator,accountingforlossesduetononzeroadvancespeed,mapsthedesiredthrustintothedesiredshaftspeedd.Thisisinturnfedintoaset-pointmapping,limitingthevalueofthedesiredshaftspeedtosomeoptimalvalueoptwhenventilationisdetected.API-controllerwithfeed-forwardfromthedesiredshaftspeedgivesthecommandedtorqueQctothemotordrivingthepropellershaft.ThemainideainthispaperisthattheintegratorstateinthePI-controllermaybeinstantaneouslyresettoadifferentvalue,ifappropri-ate.Consequently,thepropellershaftspeedmaytrackthedesiredonegivenbythereferencegeneratormoreaccurately.2.1PropellerModelThepropellermodeltobeconsideredisgivenbyarst-orderdynamicsystemJm_Qc ()kf2q(1)_q=0(2)whereispropellershaftspeed,JmisshaftmomentofinertiaandQciscommandedtorquetothemotordrive.Thismodelassumesthedynamicsoftheelec-tricalparttobenegligiblewhencomparedtotheshaftdynamics.Allthenonlinearitiesareincludedinthefunction ()=GQjjkf1arctankf3arctan(kf4)(3)wherethersttermisthenominalpropellertorqueatzeroadvancespeedinnormalconditions,whereGQGQ+;!0GQ ;!0:(4)TheconstantsGQ+andGQ arepositiveandingeneraldifferentsincethepropellerusuallyisnotsymmetricwithrespecttotheshaftspeed.Further,kfiandareconstantandpositive,includedinordertomodelthesystemfrictiontorque,seePivanoetal.(2007)formoredetails.Thepurposeofqistomodelunknowntorquelossesduetovariationsinthevesselspeed,propellersubmer-gence,crossowsetc.Remark1.Itisassumedthatqisconstant.Thisisasimplication.Inrealityqvariesslowlyduetothechangesinadvancespeed,andquickly,almostdiscrete,duetolossescausedbyventilationandin-and-out-ofwatereffects.Thecontrollerstateresetprocedureproposedinthispapermakesuseofanestimateofq.Thisestimate^qtriggerstheresetprocedureonlybysuddenchangesin^q.Duringtransientscausedbysuchanincident,wemayassumeqbeingconstantduetoslowlyvaryingadvancespeeddynamics.2.2DynamicControllerAssumedisasmoothandboundedreference,thecontrollerisgivenasQcJm_d (d)+kf2dzkP(d)(5)_zkI(d)includingafeedforwardpartfromdandaregularPI-controllerpartontheerrord,wherekP0andkI0aretheproportionalandintegralgains,respectively.Theintegratorstatezcanbeinterpretedasanestimateforq,usedinthefeedforwardcompensationin(5),hencesimilartotheadaptivecase.Thetwostateszandarestackedintothevectorx=[x1;x2]T,wherex1zandx2.Theclosed-looperrorstatesaredenedas~x1zqand~x2d,hencefrom(1)and(5)theerrorsystembecomes_~x1kI~x2(6a)_~x21Jm((kf2kP)~x2(~x2;!d)~x1)(6b)wherethenonlinearfunction(~x2;!d)= (~x2d) (d)isnondecreasingandinsidethesector[0;]inthevariable~x2,foranyxedd.2.3LyapunovfunctionALyapunovfunctionisusedbothinordertoprovetheclosed-loopsystemtobestableandasameasureoftheremainingtransientenergy,usedintheresetprocedure. Lemma1.ThefollowingLyapunovfunctionprovestheoriginoftheerrorsystem(6)tobeuniformlygloballystable(UGS)andconvergent:V12p11~x2112p22~x22(7)wherep11andp22aretwopositiveconstants,selectedsuchthatp11p22kIJm:(8)Proof:Thetimederivativeof(7)alongthetrajectoriesof(6)becomes_Vp11kI~x1~x2p22Jm~x2[(kf2kP)~x2~x1(~x2;!d)]:(9)Usingthefactthat(~x2;!d)~x20d;~x2,andselectingp11asin(8),(9)becomes_V p22Jm(kf2kP)~x22(10)hencetheoriginof(6)isUGS.SinceV0isboundedandnon-increasingintimewehavethatlimt!1V(~x(t))=V1existsand10K~x22( )d K10~x22( )d 10_V( )d V0V1(11)whereKp22Jm(kf2kP)andV0V(~x(0)).Theexpressionin(11)impliesthat~x22L2.Sinced2L1and~x1,~x22L1,duetoUGSoftheorigin(6),from(6b)also_~x22L1.Theseconditionsimplythatlimt!1~x2(t)=0fromBarbalat'slemma,seeKhalil(2001).Further,usingthefactthat(;)isdifferentiableand_d2L1,from(6b)Jm~x2(kf2kP)_~x2@g@~2(~x2;!d)_~x2@g@!d(~x2;!d)_dkI~x2leadingto~x22L1,hence_~x2beingUniformlyContinuous(UC).Next,weknowthatR10_~x2( )d ~x2()~x2(0)existsandisnite,andincombinationwith_~x2beingUC,_~x2(t)0ast!1usingBarbalat'slemma.From(6b)weconcludethatalsolimt!1~x1(t)=0,hencetheoriginoftheerrorsystem(6)isconvergent.Remark2.Ifdisconstant,theoriginof(6)willbegloballyasymptoticallystable(GAS).2.4PropellerTorqueLossObserverTheneedforanobserverestimatingthetorquelossesqistwofold;oneforapplyingthecontrollerstateresettingproceduredescribedinBakkeheimetal.(2006),andanothertoincludeqinthereferencegeneratordevelopedinPivanoetal.(2007).Anonlinearobserverwithgainl1andl2isdesignedinordertoestimatethetorqueloss^qandtheshaftspeed^=^y:Jm_^Qc (^)kf2^^ql1(y^y)_^ql2(y^y)(12)yDeningtheobservererrorvariablesas~^and~q=q^q,theobservererrordynamicsbecomesJm_~( () (^))l1~kf2~~q(13)_~ql2~!:(14)Lemma2.Ifthegainsl1andl2arechosensuchthatA1l1kf2A2l20(15)thentheoriginof(13)-(14)isUGSandconvergent.Proof:ConsiderthefollowingLyapunovfunctionfortheobservererrordynamics(13)-(14)Vo12a11~212~2q(16)wherea11Jml2apositiveconstant.Thetimederivativeof(16)alongthetrajectoriesof(13)-(14)is_Vol2( () (^))~l2(kf2l1)~2:(17)Furthermore,thefunction ()belongstothesector[0;]andisnon-decreasing,hence!;^[ () (^)](^)0,hence_Vol2(kf2l1)~2be-ingnegativesemi-denite.UsingthesameargumentasintheproofofLemma1,(16)willprovetheoriginoftheerrorsystem(13)-(14)UGSandconvergent.Theestimates^and^qcanbeusedtocomputeanestimateofthepropellertorquefrom^QpGQj^j^^q:(18)2.5ReferencegeneratorSincethereferenceisusuallygivenasdesiredpro-pellerthrustTpd,areferencegeneratormappingTpdtothedesiredpropellerspeeddisneeded.InPivanoetal.(2007)suchareferencegeneratorisproposed.Thereferencegeneratorisbasedonthepropellerchar-acteristics,usuallyintheformofthenon-dimensionalthrustandtorquecoefcientsKTandKQ,givenasafunctionoftheadvancenumberJ2ua!D(19)whereDispropellerdiameteranduaistheadvancespeed.ThecoefcientsKTandKQarecomputedasKT42Tpjj!D4(20)KQ42Qpjj!D5:(21)Theproposedreferencegeneratorisdividedintothreemainparts.TherstpartmapsTpdintothedesiredpropellertorqueQpd1^GQT(^J)Tpd(22)where^GQT(^J)KTj^JDKQj^J(23)isanestimateoftheactualthrust-torqueratio.Anestimateoftheadvancenumber^JisusedinsteadoftherealvalueJ,becausetheadvancespeeduaisnot availableinpractise,seePivanoetal.(2007)formoredetails.ThesecondpartmapsQpdintod:dvuutQpd^qGQsign(Qpd^q):(24)Thenalpartisasecondorderlowpasslterthatgeneratessmoothreferencesignalsdand_d:d+2c_d2cd2cd(25)wherecisthecutofffrequencyandisrelativedampingfactor.2.6ResetprocedureResettingoftheintegratorstateztoaproperlychosendifferentvaluezimayimprovethetransientperfor-manceoftheproposedcontrollerin(5),seeBakke-heimetal.(2006).Lemma3.Aresetoftheintegratorvaluez(t+)tozi,wheret+denotesaninnitelysmalltimeincrementoft,ofthesystemin(6)leadstoajumpintheLyapunovfunction(7)asfollows:Vi(t)=p112 z2i+2q(ziz(t))z2(t):(26)Proof:Let~x1izi+q.ThejumpintheLyapunovfunctionbecomsVi(t)=V(~x1i;~x2(t+))V(~x1(t);~x2(t))p112(zi+q)2(z(t)+q)2p112 z2i+2q(ziz(t))z2(t)(27)wherethefactthat~x2(t+)=~x2(t),duetothecon-tinuityofsolutionsofordinarydifferentialequations,hasbeenused.Weassumeanitesetofintegratorresetcandidates,Hfz1;:::;zng.Thefollowingresultstatesstabil-itywhentheintegratorisreset.Proposition1.Givenaclosed-loopsystemwithaPI-controllerasin(1)and(5).AssumethatV(~x)in(7)isaLyapunovfunctionthatprovestheequilibriumpointofthenonlinearsystemin(6)tobeUGSandconvergent.FurtherassumethatVi(t)denotesthejumpintheLyapunovfunctionvalueiftheintegratorofthePI-controllerin(5)isresettoadifferentvaluezi2H.Thenifz(t)isresettothevaluezionlyifVi(t)0,theequilibriumpointofthenonlinearsystemin(6)isUGSandconvergent.Proof:SeeBakkeheimetal.(2006).Notethatqin(26)isunknown.Insteadtheestimate^qin(12)isusedintheimplementationoftheresetalgorithm.Analyzingtheeffectofnoiseincalculationof(26)isneglected.However,inordertoreduceerroneousresetsandscatteringeffectsduetothisissue,apositivethresholdisaddedintheresettingprocedure.ThecriterionforperformingresetthenbecomesVi(t)+0.2.7VentilationdetectionAnestimateofthetorquelossfactor Qiscalculatedbasedontheestimatedpropellerloadtorque^Qpfrom(18)andthenominalloadtorqueQn:^ Q b()+(1 b())^QpQn:(28)where b()isaweightingfunctionofthetype b(y)=e kjpyjr:(29)k,pandrarepositivetuninggains,neededbecausetheestimateotherwisewouldbesingularforzeroshaftspeed.Thenominaltorque,i.e.incaseofnoventi-lation,iscomputedfromtheKQcoefcientthrough(21)asQnKQjj!D542:(30)ThenominalvalueofKQin(30)isderivedfromtheKQcharacteristicwherethenominalvalueofJiscomputedfrom(19)usingthesteady-staterelationua=(1wf)u(31)where0wf1isthewakefractionnumber,oftenidentiedfromexperimentaltests,anduisthevesselspeed.Thewakefractionnumberaccountsforthereductionofwatervelocitytothepropellercausedbythevesselhull.Theestimatedlossfactor^ Qmaybesubjecttosomeuctuationsduringtheperiodofventilation.Insteadofusingthisestimatedirectlyasameasureofwhetherthepropellerisventilatingornot,atranslationofthisvalueintoadiscretevaluemaybeappropriate,asinSmogelietal.(2004).Forasingleventilationincident,willhavethefollowingevolution:^ Q v;on=0(noventilation)^ Q v;on=1(ventilation)^ Q v;off=0(noventilation):(32)Notethattheventilationdetectionincludeshystere-sis,hencerobustnessduetomeasurementnoiseinthelossvalueestimate^ Qisachieved.2.8Set-pointmappingThereferencegenerator(24),designedtocounteractthelossesduetononzeroadvancespeed,failswhenventilationoccurs.Thisissobecauselossesduetoventilationarenotaccountedfor.Anti-spinset-pointmappingisusedinordertoreducetheshaftspeedreferenceincaseofventilationopt;if=1anddoptd;otherwise(33)whereoptissomeoptimalpropellershaftspeedduringventilation,seeSmogeli(2006)formodelsusedtocomputeopt.3.EXPERIMENTALTESTRESULTSAthrusterset-upwithpropellerdiscdiameterD0:25mandshaftmomentofinertiaJm=0:006kgms2wasusedtoexperimentallytesttheproposedstrategyintheMarineCyberneticsLaboratory(MCLab)atNTNU.Thetuningoftheoverallcontrollerwasperformedinseveralsteps.Thefrictionparameterskfiandwere identiedbyrunningthepropellerinfreeairatdif-ferentspeeds.TheparametersforthePI-controllerwerefoundbyfocusingonthecontrolperformanceincalmandmoderateseas.Theresultingparametersledtoarelativelyslowcontrollerresponse,wherethecommandedtorqueQcavoidswearandtearonthemechanicalcomponents.Next,thelossobserverandreferencegeneratorweretunedinordertooperateincalmseaconditions.Further,theventilationdetectionwithset-pointmappingwastunedinordertohandleextremeseasituations.Finally,theparametersoftheresetprocedurewastunedinextremeseaconditions.TheresultingparametersforthePI-controllerwaskP=0:07andkI=0:8.Theobserverparame-terswereselectedtobel1=3:2,satisfyingA1inLemma2,andl2160,satisfyingA2inLemma2.Theoptimalcontrollerspeedduringventilationwasselectedtobeopt+=45andopt =54forpositiveandnegativeshaftspeed,respectively.TheLyapunovfunctioncoefcientswereselectedtobep11=21andp22=0:1,hencesatisfying(8).Thetuningoftheresettingprocedurewasthenrestrictedtoselectasuitableinordertoyieldacceptableperformance.=100turnedouttoworkne.TheresetcandidatesHfz1;:::;zngbothneedtospantheworkingareaoftheintegratorstatezandtoad-dressrobustnesspropertiesfortheresetprocedurebyappropriatelyselectionofcandidatesparseness.Hf 6:6;4:4;2:2;0;2:2;4:4;6:6ggavesat-isfactoryperformance.Athrustermountedonamovingtowingcarriagewasemployedinordertodemonstratethestrategy.Ex-tremeseasconditionsweresimulatedbyraisingandloweringthethrusterintothewaterwithaperiodof6:6sandamplitudeof15cm.Thiswayofemulatingwavesgivestotalcontroloftheenvironmentalinterac-tionwiththethrustersetup.Thisleadstoamoreaccu-ratewayofcomparingdifferentcontrolleralgorithms.Figures2and3showdatafromthetestwithoutandwithresettingtheintegratorstate,respectively.Thethrusterverticalpositionwasmovedinordertotriggerventilationandin-and-outofwatereffects,presentedasrelativesubmergenceh=R,whereRD=2isthepropellerradiusandhisthesubmergenceofthepropellershaft.Thetimeseriesofshowsintegratorresetincidents.Whenisnonzero,sayi,aresettocandidatezi2Hisperformed.MotorpowerPmisincludedinordertoshowpoweructuationsgeneratingpowerpeaksonthepowernetwork.Thetestscenariowasthesameforbothcases.ThecommandedthrustTpdhadthepatternseeninFig-ure2(b),withamplitude120N.Theemulatedresult-ingspeedofthetowingcarriageuhadanamplitude0:7m=s,dephasedfromthecommandedthrust.ThecombinationofthebehaviorofTpdanduyieldsoper-ationin4quadrants.Inthiscase,uau.InFigure2thecontrolleristunedforoperatingincalmsea.AsseeninFigure2(b),thepropellerspeedincreaseswhenthepropellerrotatesclosetothewatersurface.Thesepeaksinrotationalspeedarereducedwhentheintegratorresetismadeactive,seeFigure3(b).Alsonotethereductioninpowerpeaks,hencereducingtheriskofblackoutsduetouctuationsontheelectricpowernetwork.Despitethisreductionsinpowerpeaks,theaveragethrustproductioniskeptmoreorlessconstant.4.CONCLUSIONSAnintegratorresetstrategyforaPIshaftspeedthrustercontrollerhasbeenpresented.ALyapunovfunctionisusedtodecidewhentoresetandtoproveasymptoticstabilityoftheoverallsystem.Adynamicreferencegeneratorisincludedinordertoincreasetheperformancewhenashipisintransitoperation.Inordertoemulateoperationin4quadrantsandextremeseasconditions,thepropellerwastowedthroughthewaterandatthesametimemovedalongitsverticalaxis.Testsshowedreducedpeaksinpro-pellerspeed,hencereductionofstructuralloadsonpropellerblades,whilenotchangingthemeanpro-pellerthrustsignicantly.Reductionofpowerpeakswasalsoachieved,hencereducedriskofblackoutsduetouctuationsontheelectricpowernetwork.5.ACKNOWLEDGEMENTSThisworkwasinpartsponsoredbytheResearchCouncilofNorway,projectnumber157805/V30.REFERENCESJ.BakkeheimandT.A.Johansen.TransientPerfor-mance,EstimatorResettingandFilteringinNon-linearMultipleModelAdaptiveBacksteppingCon-trol.IEEProc.-ControlTheoryAppl.,153:536545,2006.J.Bakkeheim,Ø.N.Smogeli,T.A.Johansen,andA.J.Sørensen.ImprovedTransientPerformancebyLyapunov-basedIntegratorResetofPIThrusterControlinExtremeSeas.InIEEEConferenceonDecisionandControl,SanDiego,USA,2006.J.Kalkkuhl,T.A.Johansen,J.L¨udemann,andA.Queda.NonlinearAdaptiveBacksteppingwithEstimatorResettingUsingMultipleObservers.InProc.WorkshoponHybridSystems,ComputationandControl,Rome,2001.H.K.Khalil.NonlinearSystems(3rdEd.).Prentice-Hall,NewYork,2001.L.Pivano,T.A.Johansen,Ø.N.Smogeli,andT.I.Fossen.NonlinearThrustControllerforMarinePropellersinFour-QuadrantOperations.toappearatthe26thAmericanControlConference(ACC07),NewYork,USA,July2007.D.Radan,Ø.N.Smogeli,A.J.Sørensen,andA.K. Adnanes.OperatingCriteriaforDesignofPowerManagementSystemsonShips.InProc.ofthe7thIFACConferenceonManoeuvringandControlofMarineCraft(MCMC'06),Lisbon,Portugal,2006.Ø.N.Smogeli.ControlofMarinePropellers:fromNormaltoExtremeConditions.PhDthesis,Depart-mentofMarineTechnology,NorwegianUniversityofScienceandTechnology(NTNU),2006.Ø.N.Smogeli,J.Hansen,A.J.Sørensen,andT.A.Johansen.Anti-spinControlforMarinePropulsionSystems.InIEEEConferenceonDecisionandControl,Bahamas,December2004.A.J.Sørensen.StructuralIssuesintheDesignandOperationofMarineControlSystems.IFACJour-nalofAnnualReviewsinControl,(29:1):125149,2005.L.L.WhitcombandD.Yoerger.Developement,Com-parison,andPreliminaryExperimentalValidationofNonlinearDynamicThrusterModels.IEEEJournalofOceanicEngineering,24(4):481494,Oct.1999.