三相逆變器輸出LC濾波器有效的隱式模型預(yù)測控制外文文獻翻譯、中英文翻譯、外文翻譯

1、EfficientImplicitModel-PredictiveControlofaThree-PhaseInverterWithanOutputLCFilterThree-phaseinvertersarecommonlyusedtotransferenergyfromadcsourcetoacload.Inapplicationssuchasuninterruptiblepowersuppliesandvariablefrequencydrives,thethree-phaseinvertersarecommonlyusedwithanoutputLCfiltertosinusoidal

2、voltageswithlowharmonicdistortion.Severalcontrollershavebeenproposedintheliteraturetocontrolthree-phaseinverters.Hysteresisandproportionalintegral(PI)controllersarecommonlyusedforvoltageregulationofthree-phaseinverters.ConventionalstationaryframePIcontrollerdoesnotachievezerosteadystateerrorforasinu

3、soidalreference,andtheerrorincreaseswithanincreaseinref-erencesignalfrequency.SynchronousdqreferenceframePIcontrollerandproportionalresonantregulatorattainzerosteadystateerrorbutcannothandleconstraints.Adrawbackofhysteresiscontrollerisvariableswitchingfrequency,whichcanreducetheefficiencyofaconverte

4、rduetoanincreaseinswitchinglosses.Someothercontrolschemesincludedeadbeatcontrolandlinearquadraticregulator(LQR)control.Deadbeatcontrollerhasbeenextensivelyusedtocontrolinverters,andrectifiers.LQRprovidesagooddynamicperformance.However,noneoftheabove-mentionedcontrollerscansystematicallyhandleconstra

5、intonpeakfiltercurrentthatisrequiredtoensureprotectionofcomponentsoftheinverter.Model-predictivecontrol(MPC)hasbeenextensivelyusedinpowerelectronicsbecauseofitsflexibilitytoincludeconstraintsinthecontrolscheme.However,amajordrawbackofMPCisthatitrequiresalargenumberofonlinecompu-tations.Toreducetheco

6、mputationalrequirements,avariantcalledexplicitMPChasbeenproposed.InexplicitMPC,theoptimizationproblemissolvedofflineusingmultiparametricprogramming.Multiparametricprogrammingyieldsalookuptable,whichgivesoptimalcontrolactionasanexplicitfunc-tionofthestate.Thisapproachreducesthenumberofonlinecomputati

7、ons.However,explicitMPCcannotdirectlyaccountforreal-timechangesinthemodel,anditscomputationalcom-plexityincreasesexponentiallywiththenumberofstatesandconstraints.Inthispaper,weproposeanimplicitMPCthatsolvestheoptimizationproblemonlinewhilehavinglowercomputationalrequirementsthanexplicitMPC.Wehavebee

8、nabletoachievelowercomputationalrequirementsthanexplicitMPCbyusingimplicitMPCwithacustomizedactivesetapproachforasingle-steppredictionhorizon.Inactivesetmethods,aworkingset,whichisasetofpotentialactiveconstraints,ismaintainedandupdatedineachiterationofthealgorithm.Thecomputationalcomplexityofactives

9、etmethodsgrowsexponentiallywiththetotalnumberofconstraints.Intheproposedscheme,wehavebeenabletore-ducethecomputationalrequirementsbycombiningsomeoftheconstraints,therebyreducingthetotalnumberofconstraints.Wealsouseasingle-steppredictionhorizon.Althoughitreducesnumberofcomputationsforboththeimplicita

10、ndexplicitMPC,inourcase,itfurtheraidsusinreducingthenumberofconstraintsleadingtoanefficientoptimizationalgorithm.Whileasingle-stephorizonisnotcommoninMPCingeneral,thereasonthatitworksforthethree-phaseinverterwithanLCfilteristhatitisastableminimumphasesystemthatdoesnotrequirealongpredictionhorizon.Fo

11、rthisreason,thesingle-steppredictionhorizoncanalsobeseeninotherapplicationsinpowerconverters.Reducingthecomputationalrequirementsisofinterestsinceitallowsthecontrollertooperateathigherfrequenciesoralternatelyitallowsforimplementationonacheaperhardware.Thispaperisorganizedasfollows.SectionIIdealswith

12、theconvertermodeling.SectionIIIdescribesourproblemformu-lation.TheproposedschemeisdiscussedinSectionIV.Sim-ulationsresultsforaninductiveloadarepresentedinSectionVI.SectionVcomparesthecomputationalrequirementsoftheproposedcontrolschemeandexplicitMPC.Athree-phaseinverterwithanoutputLCfilterforproducin

13、gsinusoidalvoltages.Loadisassumedtobeunknownandbalanced.Eachlegofinverterhastwoswitchesthatoperateincomplementarymode.Theinverterhaseightdifferentswitchingstatesthatcanberepresentedbythreebinaryswitchingsignals,oneforeachlegoftheinverter,statedbelowinsteadoftheswitchingsignals.Usingstate-spaceaverag

14、inganddiscretization,weobtainthefollowingdiscrete-timestate-spacemodelforsamplingtimeTsBasedontheaboveswitchingsignals,wecanfindthefollowingcontinuous-timestate-spacemodeloftheinverter:wherecisthesamplingtimeindex,andda,k,db,k,anddc,karedutycyclesofthePWMsignalofrespectiveinverterlegs.Inobtainingthe

15、abovediscrete-timemodel,wehavealsousedthefactthatatanyinstant,da,k+db,k+dc,k=1.5forabalancedload.Aquadraticcostfunctiontoregulatetheoutputvoltagesforasingle-steppredictionhorizonisisnotusualinMPCforgeneralapplications.However,itisUsing,costfunctioncanberepresentedintermsofthewherea,02,03,and04arecon

16、stantcoefficientsdependingonandvaluesofLandC.Toavoidlargecurrents,whichcancausespikesinoutputvoltagesanddamagethecomponents,theinductorcurrentshavetobebounded.Theconstraintoninductorcurrentscanbestatedaswherethecurrentsandvoltagesaredefined.Outputcurrentistreatedasadisturbancebecauseofitsdependenceo

17、nanunknownload.Detailsofthemodelingcanbefoundin.ThemodelisnonlinearbecauseofthediscretenatureofswitchingsignalSa,Sb,andSc.Thestate-spaceaveragingtechniqueisusuallyemployedtoapproximateitwithalin-earmodelbyutilizingthedutycyclesofeachlegoftheinverter.Ineachiterationofactivesetmethods,theLagrangemul-t

18、ipliersarecomputedandtheworkingsetisupdated.nourcase,weonlyhavetwoconstraints,i.e.,anupperandlowerboundonthedutycycle.Moreover,thesetwoconstraintsarealsocomplementary,i.e.,boththeupperboundconstraintandlowerboundconstraintcannotbeactivesimultaneously.Therefore,toavoidcalculationsinvolvedinupdatingth

19、ework-ingset,weproposetocomputethecostforallpossibleworkingsetsandchoosethedutycycleforthelowestcostthatisfeasible.Therearethreepossibleworkingsets:noconstraintisactive,theupperboundinisactive,orthelowerboundinisactive.Whennoconstraintisactive,theoptimaldutycyclecanbecomputedbyusingthederivativeofth

20、ecostfunctionwithrespecttoda,kandequatingittozero,whichturnsouttobeThenumberofcomputationsinvolvedintheproposedcon-troller,i.e.,Algorithm1,areshowninTableI.Thetotalcom-putationsrequiredbytheproposedalgorithmforasingle-steppredictionhorizonandasinglephaseare27multiplicationsand22additions.Tocalculate

21、thecomputationsoftheexplicitMPCcontroller,itwasimplementedfortheoptimizationproblemusingtheMPCtoolbox.Themultiparametricprogrammingofex-plicitMPCgenerates274regions,leadingtoabinarysearchtreeofdepthequalto9.ComputationsofexplicitMPCcontrollerforasingle-steppredictionhorizonandsinglephaseturnouttobe1

22、20multiplicationsand120additions.Comparingthecomputationalrequirements,itcanbeob-servedthattheproposedalgorithmisapproximatelyfivetimesfasterthanexplicitMPC.phaseinverterwithanoutputLCfilter.TheproposedschemeiscomputationallyefficientascomparedtotheexplicitMPC.Theproposedschemereducesthecomputationa

23、lloadbyex-ploitingthestructureoftheinvertermodelandtheconstraints.Simulationshavebeenperformedtoshowthattheproposedal-gorithmregulatestheoutputvoltagesoftheinvertersubjecttoconstraintsonfiltercurrentanddutycycle.Thereducedcom-putationalrequirementscouldhelpoperationofthecontrollerathigherfrequencies

24、,implementationonacheaperhardware,oratradeoffbetweenthem.TheproposedschemewassimulatedusingSimulinkwiththeparametersgiveninTableII.Theoutputcurrentwasestimatedusingtheobserverin.Theperformanceoftheproposedimplicitcontrollerforaseriesinductive-resistiveloadof10mHand20Qisshown.Theloadisappliedat0.02s.

25、Itcanbeseenthatthecontrollerprovidesthedesiredoutputvoltagewhilerespectingtheconstraintsonboththedutycycleandtheinductorcurrent.Initially,thefiltercapacitortriestodrawalargeamountofcurrent;however,itisconstrainedbythecontroller.Itmaybenotedthatsincestate-spaceaveragingisused,whichneglectstheswitchin

26、gbehavior,thefiltercurrentisexpectedtoviolatetheconstraintsslightly.三相逆變器輸出LC濾波器有效的隱式模型預(yù)測控制三相逆變器通常用于能量從一個直流源轉(zhuǎn)移到一個交流負載。應(yīng)用在不間斷電源和變頻驅(qū)動器，三相逆變器常用的LC濾波器輸出為正弦電壓提供低諧波失真。在本文中提出了幾個控制器來控制三相逆變器。磁滯和比例積分（PI）S制器常用的三相逆變器的電壓調(diào)節(jié)。傳統(tǒng)靜止幀PI控制器不實現(xiàn)零穩(wěn)態(tài)誤差一個正弦參考，和增加的錯誤與參考信號頻率的增加。同步dq坐標系PI控制器和比例諧振調(diào)節(jié)器實現(xiàn)零穩(wěn)態(tài)誤差，但不能處理約束條件。滯環(huán)控制器方法的一個

27、缺點是可變開關(guān)頻率，可減少由于提高變換器的效率轉(zhuǎn)換損失。其他控制方案包括賴賬的控制和線性二次調(diào)節(jié)器（等）控制。賴賬的控制器已經(jīng)廣泛用于控制逆變器，和整流器。等方面提供了良好的動態(tài)性能。然而，沒有上述控制器可以系統(tǒng)地處理限制峰值濾波器電流所需保證逆變器的保護組件。模型預(yù)測控制（MPC）已廣泛應(yīng)用于電力電子由于其靈活性，包括約束的控制方案。然而，模型預(yù)測控制的一個主要缺點是，它需要大量的在線計算。減少計算需求，稱為明確提出了模型預(yù)測控制的變體。在明確的模型預(yù)測控制，使用多參數(shù)優(yōu)化問題是解決離線編程。多參數(shù)編程產(chǎn)生一個查找表，提供最優(yōu)控制行動的顯函數(shù)。這種方法減少了在線計算的數(shù)量。然而，顯式模型預(yù)測

28、控制不能直接占實時變化模型，及其計算復(fù)雜度成倍增加的狀態(tài)數(shù)和約束。在本文中，我們提出一個隱式的MPC解決了在線優(yōu)化問題，計算需求低于明確模型預(yù)測控制。我們已經(jīng)能夠?qū)崿F(xiàn)計算需求低于顯式MPC通過使用隱式MPC與一個定制的有效集方法單步預(yù)測地平線。在有效集方法，一個工作集，這是一組潛在積極約束，維護和更新的每個迭代算法。有效集方法的計算復(fù)雜性呈指數(shù)級增長的總數(shù)量限制。在該方案中，我們已經(jīng)能夠這種計算需求相結(jié)合的一些約束，從而減少的總數(shù)限制。我們也使用一個單步預(yù)測地平線。雖然減少數(shù)量的計算隱式和顯式MPC,在我們的例子中，它進一步幫助我們減少數(shù)量的限制導(dǎo)致了一種有效的優(yōu)化算法。而單步地平線在MPC一

29、般并不常見，三相逆變器的原因，它的工作原理與LC濾波器是一個穩(wěn)定的最小相位系統(tǒng)，不需要很長的預(yù)測地平線。出于這個原因，單步預(yù)測地平線功率變換器在其他應(yīng)用程序中也可以看到。減少了計算需求是感興趣的因為它允許控制器工作在更高的頻率或交替它允許在更便宜的硬件上實現(xiàn)。本文組織如下。第二部分處理變換器建模。第三部分描述我們的問題公式化。該方案將在第四部分討論。模擬結(jié)果歸納負荷提出了部分VI。第五部分比較了計算需求所提出的控制方案和明確的政策委員會。三相逆變器的輸出LC濾波器產(chǎn)生正弦電壓。負載被認為是未知的和平衡的。每條腿的逆變器有兩個開關(guān)在互補工作的模式。逆變器有八個不同的開關(guān)狀態(tài)可以表示為三個二進制開

30、關(guān)信號，每個逆變器的腿，一個聲明下面而不是開關(guān)信號。利用狀態(tài)空間平均和離散化，我們獲得以下取樣時間Ts離散時間狀態(tài)空間模型基于上述開關(guān)信號我們可以找到以下逆變器的連續(xù)時間狀態(tài)空間模型：指數(shù)k是采樣時間，和da,k,db,k和直流,k是各自的逆變器的脈寬調(diào)制信號的占空比腿。在獲得上述離散時間模型，我們也使用在任何瞬間,da,k+db,k+dc,k=1.針衡負載。二次成本函數(shù)來調(diào)節(jié)輸出電壓一個單步預(yù)測范圍。然而，它使用成本函數(shù)可以表示的a1,a2,和3品4常系數(shù)取決于和L和c的值,以避免大電流，從而導(dǎo)致輸出電壓峰值和損壞組件，電感電流必須是有界的。電感電流的約束可以表示為電流和電壓的定義。輸出電流

31、被當(dāng)作一個障礙，因為它依賴一個未知的負載。建模中可以找到的細節(jié)。模型是非線性的，因為開關(guān)信號的離散特性Sa某人,Sa通常是采用了狀態(tài)平均技術(shù)用lin-ear近似模型利用逆變器的每條腿的責(zé)任周期。在每個迭代中活躍的設(shè)置方法、拉格朗日乘數(shù)法是計算和更新工作集。n我們的例子中，我們只有兩個約束條件，即。，一個上界和下界的工作周期。止匕外，這兩個約束也是互補的。，下界和上界約束約束不能同時活躍。因此，為了避免計算參與更新管用，我們建議計算所有可能的工作集的成本和選擇成本最低的工作周期是可行的。有三種可能的工作集：沒有約束是活躍的，活躍的上界或下界是活躍的。當(dāng)沒有約束是活躍的，最優(yōu)工作周期可以計算使用成

32、本函數(shù)的導(dǎo)數(shù)表達為da,k和等同為零，計算的數(shù)量參與提出的控制方法，即算法1,該算法所需的集總單步預(yù)測范圍和單相乘以27并且添加22。計算的顯式計算MPC控制器，它是實現(xiàn)優(yōu)化問題使用MPC工具盒。明確MPC的多參數(shù)編程產(chǎn)生274區(qū)域，導(dǎo)致一個二叉搜索樹的深度等于9。計算顯式MPC控制器的單步預(yù)測范圍和單相變成乘120和添加120。比較計算需求，它可以觀察到，該算法控制效率大于5倍顯式的MPC。反相器的輸出LC濾波器。該方案是計算有效而明確的MPC。該方案減少了計算負載利用逆變器的結(jié)構(gòu)模型和約束。模擬表明，該算法執(zhí)行調(diào)節(jié)逆變器的輸出電壓限制濾波器電流和工作周期?？刂破鞯挠嬎阈枨蟮臏p少可能會幫助操

33、作在更高的頻率,更便宜的硬件上實現(xiàn)，或它們之間的權(quán)衡。該方案使用仿真軟件模擬給出的參數(shù)證實，輸出電流估計使用觀察者。提出了一系列隱式控制器的性能感應(yīng)電阻負載10mH和20Q。負載反應(yīng)時間為0.02M可以看出，控制器提供了所需的輸出電壓，同時對應(yīng)限制工作周期和電感電流。最初，濾波電容器試圖吸引大量的電流；但是，它是制約控制器?？梢灾赋?，由于狀態(tài)空間平均使用，而忽略了交換行為，過濾器目前預(yù)計略有違反約束。ControlstrategyofanovelenergyrecoverysystemforparallelhybridhydraulicexcavatorAbstract:Withthehigh

34、fuelprices,thedemandsforenergysavingandgreenemissionofengineeringmachineryhavebeenincreasedrapidly.Duetothecomplexworkingconditionandfrequentloadchanging,theefficiencyofthehydraulicexca-vatorislow.Theaimofthisarticleistoproposeacontrolstrategyforenergyrecoverysystemofhydraulicexcavatordrivenbythepar

35、allelhybridsystem.Themathematicalmodelsofthemaincomponentsandthesimulationmodelsoftheproposedsystemandaconventionalenergyrecoverysystemarebuilt.Then,accordingtotheloadcharacteristic,acontrolstrategybasedontheworkingconditionandstateofchargeofthebatteryisgiven.Theco-simulationforthehybridhydraulicexc

36、avatorsystemisestablished.Theresultsshowthattheproposedenergyrecoverysystemandcontrolstrategycannotonlyimprovetheenergyrecoveryefficiencybutalsoreducefuelconsumptionandemissionofthepowersystem.Keywords：Hydraulicexcavator,hybrid,energyrecovery,boom,controlstrategyEnergyisconsumingupandpollutionismore

37、andmoreseriousintheworld.Withthedevelopmentofworldeconomicconstruction,engineeringmachineryplayanimportantroleinconstruction.Asoneofthemosttypicalequipmentsofengineeringmachinery,thedemandofhydraulicexcavatorisincreasingrapidly.However,only20%oftheengineoutputpowerisutilizedinaconventional-typeexcav

38、ator.Theexcessenergyisconvertedintoheatinthemainthrottlevalve,whichisthemainreasonforthelowefficiencyoftheconventionalhydraulicexcavator.Energysavingisaneffectivemethodtoimprovetheefficiencyofthehydraulicexcavator.So,researchontheenergysavingofhydraulicexcavatorsisverynecessaryandurgent.HoandAhn2pro

39、posedanovelhydraulicenergy-regenerativesystemforexcavatorbasedonaclosed-loophydrostatictransmissionhydraulicaccumulator,andtheresultsindicatedthattherecoveryefficiencyofthedesignedsystemvariedfrom22%to59%.LiuandYaopresentedanimprovedwaytocoordinatelycontrolthefiveindependentvalvesofexcavatorbyincorp

40、oratingtheoff-sidepressuredynamicsintothecontrollerdesign.Energyrecoveryisanotherenergy-savingmethodwhichcanberealizedusinghydraulicorelectricalenergystoragedevices.Theexcessenergyisconvertedtohydraulicorelectricalformandstoredintheenergystorageunit.However,itneedsadditionalcomponentssuchashydraulic

41、pump/motorsortransformerstoreusetherecoveredenergy.Hybridisanewpowersystemwhichcanbeassignedtoserieshybrid,parallelhybrid,ortheircombination.Itiswidelyusedinautomotiveindustry.Tocapitalizeonthebenefitsofusingplug-inhybridelectricvehicles(HEVs),anintelligentenergymanagementsystemwasdeveloped,andtheev

42、aluationresultsdemonstratedthattheproposedenergymanagementsystemiscapableofimprovingthefuelefficiencyofthevehicle.Afuzzylogiccontrolwasutilizedtodesignenergymanagementstrategiesforfuelbatteryhybridvehicle.Basedonthecerebellarmodelarticulationcontrollerandradialbasisfunctionneuralnetworks,Taghavipour

43、aetal.Thehybridsystemcanthoroughlyoptimizethetwoenergyconfigurationsandtakeadvantageofthebenefitsprovidedbythem.Therefore,comparedwiththetraditionalvehicle,HEVnotonlyhasapotentialtoimprovethefuelefficiencybutalsoreducestheemission.Basedonthesuccessfulapplicationofthehybridsysteminautomotiveindustry,

44、itattractsagreatinterestofcompaniesandinstitutesintheworld.Manyresearchesontheapplicationofthehybridtechnologyinhydraulicexcavatorhavebeendone.presentedanewenergy-savinghybridexcavatorusinganelectro-hydrauliccircuitdesigndrivenbyanelectricmotor/generatorforthegenerationofpotentialenergy.analyzedtheb

45、oomcontrolperformanceofthehybridhydraulicexcavatorwithapotentialenergyrecoverysystem.Theexperimentresultsshowthattheproposedcontrolschemecanrecoverthepotentialenergyoftheboomeffectivelywithacceptablecontrolperformance.Recently,researchonthecontrolstrategyandhybridsysteminhybridvehiclehasbeencarriedo

46、ut.However,comparedwithhybridvehicle,theworkingconditionofhydraulicexcavatorvariesperiodicallyinalargerange.Controlstrategyappliedtohybridvehiclesuccessfullyisnotsuitableforhybridhydraulicexcavator.Thisarticlemainlyproposedacontrolstrategyforahybridhydraulicexcavatorenergyrecoverysystemwhichcombines

47、thehydraulicaccumulatorandtheelectricregenerationunittogether.Theproposedsys-temissimulatedbyAMESimsoftware.Theenergyrecoveryefficiencyoftheproposedsystemisclearlyverifiedthroughsimulationresultsincomparisonwiththeconventionalenergyrecoverysystem.Basedontheworkingconditionandstateofcharge(SOC)oftheb

48、attery,thecontrolstrategydesignedforthehybridexcavatorwiththeenergyrecoverysystemcanreducefuelconsumptionandemissionofthepowersystem.Theefficiencyofthehydraulicexcavatorissignificantlyimproved.Thisarticleisorganizedasfollows:section''Structuofetheenergyrecoverysystem'isdevotedtothestruct

49、ureandworkingprocessoftheproposedenergyrecoverysystem.Themathematicalmodelsofthemaincomponentsintheproposedsystemarebuiltinsection''Mathematicmiodeling.'Thesimulationsoftheproposedandconventionalenergyrecoverysys-temaredemonstratedinsection''Simulationoftheboomenergyrecoverysyste

50、m.''Section''Controlstrategyhybridpowersystem'presentsanovelcontrolstrategybasedontheworkingconditionandSOCofthebattery,andtheco-simulationmodelofthewholesystemisalsopresentedinthissection.Finally,conclusionsareprovidedinsection''Conclusion.''Structureoftheenergyr

51、ecoverysystemAnewboompotentialenergyrecoverysystemneedstobedesignedtosatisfythefollowingrequirements:1. Operationofthenewboomenergyrecoverysys-temmustbesimilartotheconventionalhydraulicexcavator.2. Thenewboomenergyrecoverysystemmustachievehigherworkingefficiencyandsavemoreenergywhencomparedwiththeco

52、nventionalenergyrecoverysystem.Figure1presentstheschematicdiagramofthepro-posedboompotentialenergyrecoverysystemforhybridhydraulicexcavator.Itmainlyconsistsofoilsupplysystem,boomcylinder,controlvalves,andenergyregenerationunit.Thepumpisdrivenbytheengineandthemotor.Thepressureoilexportingfromthepumpw

53、assuppliedtotheboomcylindersystem.Whentheboomcylinderpistoniscontracting,theexcessenergyisconvertedintoelectricalenergyandstoredinthebattery.Figure1.Schematicdiagramoftheproposedboomenergyrecoverysystem.1: engine;2:transmissiondevice;3:motororgenerator;4:pump;5:reliefvalve;6:tank;7:electromagneticva

54、lve;8:boomcylinder;9:reversingvalve;10,12:globevalve;11:accumulator;13:variabledisplacementmotor;14:generatorComparedwiththeenginepowerR,themotorpowerPm,andtheloadpowerP,therearethreekindsofworkingconditionsbasedontheloadchange.1. WhenPe.Pi,thepumpisdrivenbytheengine,andtheexcesspoweroftheengineisco

55、nvertedintoelectricalenergybythemotorandstoredinthebattery.Themotorworksasageneratorinthisworkingcondition.2. WhenFePi,electricalenergystoredinthebatteryisusedtodrivethemotor.Theengineandthemotordrivethepumptogether.3. WhenthemotorpowerPe.Pm.R,thepumpisdrivenbythemotorindependently,andtheengineworks

56、intheidlestate.MathematicalmodelingFigure2showsthespeedcharacteristicsofengineinthedifferentcontrolpositions.ItcanbeexpressedbyT=fene,aTwhereTeandneareoutputtorqueandspeedoftheengine,respectively,andaisthepositionspeedofthecontrolrod.Inordertocontroltheengine,speedcharacteristicoftheenginecanbedivid

57、edintoexternalcharacteristicandregulatingcharacteristic.ExternalcharacteristicismatchedbyquadraticcurveTe=kin2e+k2ne+ciwherekiandk2arethequadratictermandmonomialcoefficient,respectively,andciisaconstant.Figure2.Speedcharacteristicsofengine.Figure3.Batterymodel.Whentheengineisinastateofspeedregulatio

58、n,thecharacteristicequationcanbematchedbyastraightline.Assumingthattheslopeofspeedcharacteristiccurveinthedifferentpositionsofthecontrolroddoesnotchange,themathematicalmodelofspeedcharac-teristicisgivenbyne=aenHnLT+nLTe=kane+k3awherenHandnLarethelargestandlowestidlespeedsofengine,respectively;akisth

59、eslopeofthematchingline;andkisaconstantcoefficient.Accordingtotheequationsabove,thespeedoftheenginecanbeadjustedwithinthescopeofitsexternalcharacteristic.BatteryThisarticlemainlystudiesthechargeanddischargeperformanceofthebattery.So,themodelofbatteryissimplifiedandshowninFigure.SOCofthebatteryisgivenbywherehisthechargeanddischargeefficiencyofthebattery;i(t)andCtarethechargecurrentandcapacityofthebattery,respectively;andSOQist