1、基于能耗最優化的動力定位推力分配邏輯算法研究_英文_ 第15卷第3期 2011年3月 ArticleID：1007-7294（2011） 03-0217-10船舶力學JournalofShipMechanicsVol.15No.3Mar.2011 OptimalThrustAllocationBasedonFuel-efficiency forDynamicPositioningSystem YANGShi-zhi1,2,WANGLei2,ZHANGShen2 (1ChinaClassificationSocietyNanjingBranch,Nanjing210011,China;2TheS

2、tateKeyLaboratoryof OceanEngineering,ShanghaiJiaoTongUniversity,Shanghai200240,China) Abstract:ThetwoseveralmethodsofthrustdistributioninapropulsionsystemofDynamicPosition-ingSystem(DPS)arepresentedinthispaper.Withdetailsimulationandanalysis,thispapercon-centratesonfindingoutanoptimalthrustallocatio

3、n(TA),whichcouldgaindesiredforcesandmo-mentsactingonthevehiclesoastokeepposition.Specialattentionispaidtosolvethenon-linearconstrainedthrustallocationproblems.AndtheproposedmethodsaretosetupaconfigurationmatrixwhichexactlydescribethelayoutofthrustersoftheDPpropulsionsystem.Anillustrativeexamplebased

4、onGeneticAlgorithm(GA)andSequentialQuadraticProgramming(SQP)isprovidedtodemon-stratetheeffectivenessandcorrectnessoftheproposedmethods.Fivealgorithmssuitedfordifferentcontrolconditionsarepresented. Keywords:ThrustAllocation(TA);DynamicPositioningSystem(DPS); GeneticAlgorithm(GA);SequentialQuadraticP

5、rogramming(SQP) CLCnumber:U664.3Documentcode:A 1Introduction Asthelastpotentialsupplierofnaturalresourcesandenergiesaswellasprovisionsontheearth,theoceanisrequestedmoreandmoretorevealitssubstancestohumanbeings.Dynam-icPositioningSystemisthemostpromisingmeansofposition-keepingfordeep-seaexplo-ration,

6、whichisnotconfinedbydepthofwaterandhasmuchgreatadvantagescomparedwithmooringsystem.BesidesDPcouldserveasanauxiliaryofmooringsysteminshallowwatercondition,whichcouldenhancethecapabilityofmooringsystem.BasicsofDPareshowninFig.1. Thisworkismotivatedbythefuel-efficiencyoptimalcontrolallocationproblemint

7、heDPpropulsionsystem,whichisessentialforDP.ThemaincontributionofthisworkistoanalyzetheobjectivefunctionandboundaryconditionbasedonGeneticAlgorithm(GA)andSequentialQuadraticProgramming(SQP).Inthispaper,wewilltrytosolvetheover-actuatedoptimalnonlinearconstraintcontrolallocationproblemusingthemethodpro

8、posedbyJohansen&Fos-sen(2004)1. Receiveddate：2010-04-09Reviseddate：2010-09-13 Foundationitem:SupportedbyNationalHi-techResearchandDevelopmentProgram(2008AA09Z315) Biography：YANGShi-zhi(1984-),male,master. 218船舶力學第15卷第3期 Fig.1Basicsof DP Itisallrighttointroducethetwooptimalmethodsandtheirappl

9、icationinDP.Anditwillbedescribedsimplyhowtheobjectivefunctionandboundaryconditionarebuiltbysomeoth-erauthors,suchasFossen(2004)andLiang&Cheng(2004)2.Somequestionsneededtobesolvedorcompleted,forexample,Garus(2004)3onlyconsideredonesituationthattheazimuthanglesofthrusterswerefixedanddidnotpres

10、enthowthethrusterconfigurationmatrixwasgivenout,andonlygaveoutaverysimplenumericalexampletosolvethestaticissues. Ingenerally,itisnotveryeasytosolvenonlinearconstrainedoptimalproblemswithPenal-tyFunctionMethod.ActuallybasedonGeneticAlgorithmorSQPthesedificienciescouldbeproperlyovercome.Asamatteroffac

11、t,generalizedmultipliermethodhasgreatadvantagesinsolvingnonlinearoptimalproblemswithhybridconstrainedboundaries.Johansen(2003)in-troducedaslackvariableformulationwhichcouldguaranteethattheoptimizationproblemal-wayshadafeasiblesolution,andhadsolvedthesingularityissueofthrusterconfigurationma-trixbase

12、donSQP. FocusingontheessentialrequirementsforaDPvesselthatcanrapidlyandexactlydis-tributethrustandrotatetheangleofthruster,thispaperpresentsaneffectiveoptimumcontrolofthrustersystem,usingtheSQPandGAwithconstraintsontheazimuththrustersofapropul-sionsystem.Comparingthesetwothrustallocationmethods,andt

13、woimportantusefulmethodsaregivenhowtoimprovetheminordertocarrythesetheoriesintopractice.Finallybasedonatypicalpropulsionsystemofonesemi-submergedplatform,onenumericalexamplewillbeelaboratedinthiswork. 2Statementof3-DOFthrustallocation InDP,only3surfacemotionsaretakenintoconsideration,whicharesurge,s

14、wayandyaw.Herethegeneralizedforcevectorproducedjointlybytheactuatorsisgivenby B!u(1)" x,y,n",anditscomponentsarethesurgeforcex,swayforceyandyawmo-where,!T 第3期YANGShi-zhietal:OptimalThrustAllocationBasedon219mentn.Thevectorucontainsthemagnitudeoftheforceproducedbyeachindividualactua-tor,uni

15、quelyrelatedviainvertibleactuatorcharacteristicstolow-levelcontrolsignalssuchaspropellerspeedorpitch,orintermediate-levelcontrolsignalssuchasshafttorqueorpower(Han,1977)4. 3PropulsionsystemofDP Amarinevesselisusuallyequippedwithanumberofpropulsiondevices,suchasmainpropellers,rudders,tunnelthrusters,

16、azimuththrustersandpoddedthrusters(Fossen,2002)5.Inthrustallocationlogicsometypicalcharacteristicsofpropulsionsystemrequiretobetakenintoconsideration,suchasthemaneuverabilityandhydrodynamicinteractionwithcurrentorhullofvessels.Actuallythrustlossduetothruster-thrusterinteractionisprovedtobeveryter-ri

17、ble,whentwoadjacentthrustersareparallelalignedinextremeseaconditions.Consequentlyoneboundaryofoptimalthrustallocationlogicnamedforbiddenvectorisaddedandprovedtobefeasible.Inthispaper,wewillgiveamathmodeltodepicttheforbiddenvector,asFig.2showingasketchofforbiddenvector.Itcanbeseenthattheforbiddenangl

18、eis15°. 3.1Mathmodelofthrustloss Atfirstwecouldgettheopenwatercharacteristicsofthethrustersthroughmodeltestornumericalcalculation,andboththrustcoefficientandmomentcoefficientcouldbeobtainedasacorrespondingcontinuousfunctionthroughcurvefittingmethod,justasfollows: nK=Ti=0nKQ= i=0iiDJPi,jJCCj=0nj

19、 j=0njTi,jiji(2)jQ AndthenthroughaseriesofthehydrodynamicinteractionmodeltestswecouldimprovetheEq.(2),andgive, 1,2,n1,n2,vcKT=f(3),n,n,vK=f1212cQ where,1isvectorofthethrusterand2isoneoftheotherthruster,n1andn2aretherota-tionalvelocitiesofthetwoadjacentthrustersrespectively,vciscurrentvelocity.Actual

20、lyitisdifficultforustogiveanexactmathmodeltodepictthethrustlossatdifferentconditions,forhydrodynamicinteractionproblemdependsonalotoffactors.Soweonlychooseseveraltypi-calconditionsinourlogics,forinstance,theExtremeSeaStatewhenallthrustersworkatmaxi-mumvelocity.Infactitisefficientandeffectivetochoose

21、asimplecaseatthethresholdofonecomplexproblem.Asforexactmathmodelofthrustloss,thereisstillalongwaytogo,whichshouldinvolvemanylayersintheoptimalthrustallocationlogicinordertosuitfordifferentconditions. 220船舶力學第15卷第3期 3.2Definitionofforbiddenvector TakeNo.5thrusterasanexample,supposingtheforbiddenangle

22、is15°.WhenboththeazimuthanglesofNo.5&No.1thrustersare-21°,thetwothrustersarealignedinaline,sotheazimuthangledomainof-41°to-11°isforbidden.Allazimuthanglesarefrom0°to360°,asaresult,theazimuthangleofNo.5thrusterhastosatisfyasfollows: uandl(4)Consequentlyweattained

23、oneinequalityinsteadof(3), +-gx=x2i-lu-ul0InFig.2,uequals349°andl equals319°.22(5) Fig.2Sketchofforbiddenvector 4Simplificationofthemathmodelandverification Generally,theobjectivesofthrustallocationlogicarethefuel-efficiencyandmaneuver-abilityoftheDPS,oranyoneoftheboth.Nowforsimplification

24、aspectsweonlytakethefu-el-efficiencyintoconsideration,actuallythemaneuverabilityofthesystemdependsonmanyfactors,suchasthesealoadscondition,thrusterorientationanditsresponsespeed.Andthemaneuverabilitywillbeverydifferentbetweenincalmwaterandincurrentflowconditions.However,inthispaperwemainlycomparethe

25、twooptimizationmethodsandgiveoutsomead-vicesfortheirengineeringapplication.Sowetakeaverysimplecaseasanexample,justonlyconsiderthefuel-efficiencyobjective. Forthesakeofsafety,weshouldsetsometermstoavoidsingularityinordertoimprovemaneuverabilityofDPinengineeringapplication,suchasthesingularityofthesys

26、tem.Anac-tuatorconfigurationissaidtobesingularifitcannotproduceforces/momentsineverydirec-tioninthe3-dimensionalspaceofsurgeforce,swayforceandyawmoment(Fossen,1994)6, 第3期YANGShi-zhietal:OptimalThrustAllocationBasedon 221whichcouldbeavoidedthroughimprovingtheconfigurationmatrix. 4.1SequentialQuadrati

27、cProgramming SQPapproachcanbeusedbothinlinesearchandtrust-regionframeworksanditisappro-priateforsmallorlargeproblems.Unlikesequentiallinearlyconstrainedmethods,whichareef-fectivewhenmostoftheconstraintsarelinear,SQPmethodsshowtheirstrengthwhensolv-ingproblemswithsignificantnonlinearities(Johansen&am

28、p;amp;Fossen,2004). SQPmethodsrepresentthestateoftheartinnonlinearprogrammingmethods.Schittkows-ki(1985)7,forexample,hasimplementedandtestedaversionthatoutperformseveryothertestedmethodintermsofefficiency,accuracy,andpercentageofsuccessfulsolutions,overalargenumberoftestproblems. BasedontheworkofBig

29、gs(1975)8,Han(1977),andPowell(1978)9-12,themethodal-lowsyoutocloselymimicNewtonsmethodforconstrainedoptimizationjustasisdoneforunconstrainedoptimization.Ateachmajoriteration,anapproximationismadeoftheHessianoftheLagrangianfunctionusingaquasi-Newtonupdatingmethod.Thisisthenusedtogener-ateaQPsubproble

30、mwhosesolutionisusedtoformasearchdirectionforalinesearchpro-cedure. 4.2GeneticAlgorithm GeneticAlgorithms(GA)areadaptiveheuristicsearchalgorithmpremisedontheevolution-aryideasofnaturalselectionandgenetic.ThebasicconceptofGAsisdesignedtosimulatepro-cessesinnaturalsystemnecessaryforevolution,specifica

31、llythosethatfollowtheprinciplesfirstlaiddownbyCharlesDarwinofsurvivalofthefittest.Assuchtheyrepresentanintelligentexploitationofarandomsearchwithinadefinedsearchspacetosolveaproblem. TheadvantageoftheGAapproachistheeasewithwhichitcanhandlearbitrarykindsofconstraintsandobjectives;allsuchthingscanbeha

32、ndledasweightedcomponentsofthefitnessfunction,makingiteasytoadapttheGAschedulertotheparticularrequirementsofaverywiderangeofpossibleoverallobjectives. 5Numericalmodel ThelocationofthrustersisshowninFig.3. Thelocationsof8azimuthingthrustersare illustratedbyamatrix(ai,bi) (-43.2,-25),(-17.6,-35); (-43

33、.2,25),(17.6,-35); (43.2,25),(-17.6,35); (43.2,-25),(17.6,35). Objectivefunction： f?x=x2i-1i=183/2(6) Fig.3Locationofthrusterss.t.: 222船舶力學 8x2i?g1?x2i-1cos?=0x=Fx- i=18?x2i?g2x=Fy-x2i-1sin?=0i=188x2i?x2i?g3?x2i-1cos?bi+x2i-1sin?ai=0x=M-i=1i=1 22l+uu-l?g=x-0x2i4220x2i180°,0x2i-1800kN第15卷第3期(7)?

34、 whereFxistherequiredtransverseforce;Fyistherequiredlongitudinalforce,Mistherequiredturningmoment. InEq.(7)g1,g2andg3couldbegreaterthanorequaltozero,whichcouldbemodifiedaccordingtorequirement.Inthispaper,therearefourcasesincludingwithorwithoutg4,andg1,g2andg3couldbegreaterthanorequaltozero,whichared

35、isplayedinTab.1. Inputsealoadvaluescomposedofrequiredtransverseforce,longitudinalforceandturningmoment,whichareincludingsomefewtypicalconditionsofsealoads,areasfollowingstaircasefunctions.TheinputvaluesofalllogicsinthispaperarethesamejustasshowninFig.4. Fig.4 Input valuesofthe requiredthrustand mome

36、ntSQMresultsareshowninthefollowingFig.5,whichiswithoutconstraintsonforbiddenvec-torofthrusters.Itcanbeseenthatthedeliveredthrustsandvectorofthe8azimuthingthrustersarenotverydifferent.Thatistosay,inconditionofnoforbiddenvectorofthrusters,thedirec-tionsofallthrustersarealmostthesame,whichis,justasouri

37、magination,theoptimalsolution. Fig.5ResultsoftheSQPwithoutforbiddenvector 第3期YANGShi-zhietal:OptimalThrustAllocationBasedon223 GeneticAlgorithmresultswithconstraintsontheforbiddenvectorofthrustersinordertoreducethruster-thrusterinteractionareshownasfollows.Forbiddenangleissetas10°,andtheinputva

38、luesarethesameasSQP. Tab.1Fourconditionsofthealgorithm ResultsbasedonGA inequalityconstraint forbiddenvectornoequalityconstraintforbiddenvectorno Thereisnotsomuchspaceinthispapertoshowallsimulationresults,sowetakeNo.4thrusterandNo.6thrusterasexamplestoillustratetheproblem,theresultsindifferentcon-di

39、tions areasfollows, shownasFigs.6-9. Fig.6Resultsof inequalitycontraintwith forbiddenvectorFig.7 Resultsofinequalitycontraintwithoutforbiddenvector Fig.8Resultsofequalitycontraintwithforbiddenvector 224船舶力學第15卷第3 期 Fig.9Resultsofequalitycontraintwithoutforbiddenvector 5.1Analysisofthesimulationresul

40、ts Fromthesimulationresults,itcanbeseenthattheoptimumsolutionisnotonlyone,butthereexistsasetofsolutions,whichareallsuitableforthecontrolsystemandsatisfytheobjec-tivefunctionandconstrainedboundaries.Oftheresults,itisapparentthatthemagnitudesoffu-el-consumptionbasedonSQParelessthantheonesbasedonGAatth

41、esameseaconditions.Thereasonisthatthelatteronetakesthruster-thrusterinteractionintoconsiderationandsetsforbiddenvector,butresultsofformerisnotandsupposesthatthethrustlosswassmall.Actual-lyinmostconditionsincludingoperationalseacondition,itistruethatthethrustlossisnotverybig,sointhethrustallocationlo

42、gicitdoesnotneedtobetakenintoconsideration.Abal-anceshouldbebuiltbetweenthrustlossduetothruster-thrusterinteractionandhowmuchef-fectcouldbedeliveredduetoaddedforbiddenvector.Thereisanotherquestionneededtobeverified,thatishowmanythrustersworktogetherinrelativelycalmsealoadenvironmentwhenitisnotnecess

43、aryforallthrustersworkatthesametimebutonlyseveralonesareneededtokeepstation.Bothofthesetwoquestionsarenotincludedinthepaper,nowwearehereaim-ingforafeasiblemethodtosolveoptimalthrustallocationproblem.Asforperfectionandim-provementoftheobjectiveandboundaries,itdependsonthespecialapplicationandrequest.

44、Andwecompaprethefuel-consumptionatfourdifferentboundariescondition,thatareinequa-tionconstrainedwithforbiddenvector,inequationconstrainedwithoutforbiddenvector,equa-tionconstrainedwithforbiddenvectorandequationconstrainedwithoutforbiddenvector.Lon-gitudinalcoordinatesinFig.10isthetotalenergyconsumpt

45、ion(P/kW)andhorizontalordinateshowsthetimedomainfrom0to600s.FromFig.10itcouldbeseenthatfourcasesarealmostaccordantwitheachother,butenergyconsumptionofthe3thcase(equationandforbidden)isthebiggestamongthefourcases.Thatistosay,forbiddenvectorboundaryonlymakessenseatsomespecialareawhichdependsontheseaco

46、nditions.However,inmosttime-domain,fu-el-consumptionofthecasewithforbiddenvectorisrelativelymorethanoneswithoutnofor-biddenvector,andthefuelconsumptionofequationconstrainedboundariesislittlemorethaninequationones,whichareallmatchwiththefact. 第3期YANGShi-zhietal:OptimalThrustAllocationBasedon 225 Fig.

47、10Comparisonof4differentboundaries 6Conclusions ThispaperpresentsseverallogicdesignmeansforTAlayerofDPS.ItconcentratesonfindingoutanoptimalTAlogicinordertogainidealvaluesofforcesandmomentsactingonthevehicle,aimingfortotallyauto-controlmodeofDPS.Specialattentionispaidtohowtobuildandsimplifytheconstra

48、inedboundaries.Oneproposedmeansbuildsaconfigurationmatrixtodescribethelayoutofthrustersinpropulsionsystem.AndthispaperanalysisseveralalgorithmsofTAfordifferentconstrainedcontrolconditions.OnedisadvantageofSQPisthatitishardtoattainaglobaloptimalsolution,whichterriblydependsontheinitialvalue.Soitisnec

49、essarytoimproveconstrainedboundariesusingsomespecialmethodssuchassettingaweighttermtopenalizetheerrorbetweenthecommandedandachievedgeneralizedforce,whichisaimingforguaranteeingthattheoptimizationproblemalwayshasafeasiblesolution(Johansen&Fos-sen).AsforGA,ithasagoodfeatureinglobalconvergencea

50、nddoesnotverydependontheinitialvalue,whichcouldbefitfortheoptimalthrustallocationalgorithmifproperlyimprovedinsomedetails.Ourresearchshowsthatitconvergesveryslowly. References 1JohansenTA,FossenTI,BergeSP.ConstrainednonlinearcontrolallocationwithsingularityavoidanceusingSe- quentialQuadraticProgrammingJ.IEEETrans.onCont.Syst.Technology,TCST-2004,12(1):211-216. 2LiangCC,ChengWH.TheoptimalcontrolofthrustersystemfordynamicallypositionedvesselsJ.OceanEngineering