三相逆變器輸出LC濾波器有效的隱式模型預(yù)測(cè)控制外文文獻(xiàn)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(cè)控制三相逆變器通常用于能量從一個(gè)直流源轉(zhuǎn)移到一個(gè)交流負(fù)載。應(yīng)用在不間斷電源和變頻驅(qū)動(dòng)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(gè)控制器來(lái)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(shí)現(xiàn)零穩(wěn)態(tài)誤差一個(gè)正弦參考，和增加的錯(cuò)誤與參考信號(hào)頻率的增加。同步dq坐標(biāo)系PI控制器和比例諧振調(diào)節(jié)器實(shí)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(gè)

27、缺點(diǎn)是可變開(kāi)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(dòng)態(tài)性能。然而，沒(méi)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(hù)組件。模型預(yù)測(cè)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(cè)控制的一個(gè)主要缺點(diǎn)是，它需要大量的在線計(jì)算。減少計(jì)算需求，稱為明確提出了模型預(yù)測(cè)控制的變體。在明確的模型預(yù)測(cè)控制，使用多參數(shù)優(yōu)化問(wèn)題是解決離線編程。多參數(shù)編程產(chǎn)生一個(gè)查找表，提供最優(yōu)控制行動(dòng)的顯函數(shù)。這種方法減少了在線計(jì)算的數(shù)量。然而，顯式模型預(yù)測(cè)

28、控制不能直接占實(shí)時(shí)變化模型，及其計(jì)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(gè)隱式的MPC解決了在線優(yōu)化問(wèn)題，計(jì)算需求低于明確模型預(yù)測(cè)控制。我們已經(jīng)能夠?qū)崿F(xiàn)計(jì)算需求低于顯式MPC通過(guò)使用隱式MPC與一個(gè)定制的有效集方法單步預(yù)測(cè)地平線。在有效集方法，一個(gè)工作集，這是一組潛在積極約束，維護(hù)和更新的每個(gè)迭代算法。有效集方法的計(jì)算復(fù)雜性呈指數(shù)級(jí)增長(zhǎng)的總數(shù)量限制。在該方案中，我們已經(jīng)能夠這種計(jì)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(gè)單步預(yù)測(cè)地平線。雖然減少數(shù)量的計(jì)算隱式和顯式MPC,在我們的例子中，它進(jìn)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(jiàn)，三相逆變器的原因，它的工作原理與LC濾波器是一個(gè)穩(wěn)定的最小相位系統(tǒng)，不需要很長(zhǎng)的預(yù)測(cè)地平線。出于這個(gè)原因，單步預(yù)測(cè)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(jì)算需求是感興趣的因?yàn)樗试S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(shí)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(wèn)題公式化。該方案將在第四部分討論。模擬結(jié)果歸納負(fù)荷提出了部分VI。第五部分比較了計(jì)算需求所提出的控制方案和明確的政策委員會(huì)。三相逆變器的輸出LC濾波器產(chǎn)生正弦電壓。負(fù)載被認(rèn)為是未知的和平衡的。每條腿的逆變器有兩個(gè)開(kāi)關(guān)在互補(bǔ)工作的模式。逆變器有八個(gè)不同的開(kāi)關(guān)狀態(tài)可以表示為三個(gè)二進(jìn)制開(kāi)

30、關(guān)信號(hào)，每個(gè)逆變器的腿，一個(gè)聲明下面而不是開(kāi)關(guān)信號(hào)。利用狀態(tài)空間平均和離散化，我們獲得以下取樣時(shí)間Ts離散時(shí)間狀態(tài)空間模型基于上述開(kāi)關(guān)信號(hào)我們可以找到以下逆變器的連續(xù)時(shí)間狀態(tài)空間模型：指數(shù)k是采樣時(shí)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(hào)的占空比腿。在獲得上述離散時(shí)間模型，我們也使用在任何瞬間,da,k+db,k+dc,k=1.針衡負(fù)載。二次成本函數(shù)來(lái)調(diào)節(jié)輸出電壓一個(gè)單步預(yù)測(cè)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(gè)障礙，因?yàn)樗蕾囈粋€(gè)未知的負(fù)載。建模中可以找到的細(xì)節(jié)。模型是非線性的，因?yàn)殚_(kāi)關(guān)信號(hào)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(gè)迭代中活躍的設(shè)置方法、拉格朗日乘數(shù)法是計(jì)算和更新工作集。n我們的例子中，我們只有兩個(gè)約束條件，即。，一個(gè)上界和下界的工作周期。止匕外，這兩個(gè)約束也是互補(bǔ)的。，下界和上界約束約束不能同時(shí)活躍。因此，為了避免計(jì)算參與更新管用，我們建議計(jì)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(méi)有約束是活躍的，活躍的上界或下界是活躍的。當(dāng)沒(méi)有約束是活躍的，最優(yōu)工作周期可以計(jì)算使用成

32、本函數(shù)的導(dǎo)數(shù)表達(dá)為da,k和等同為零，計(jì)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(cè)范圍和單相乘以27并且添加22。計(jì)算的顯式計(jì)算MPC控制器，它是實(shí)現(xiàn)優(yōu)化問(wèn)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(gè)二叉搜索樹(shù)的深度等于9。計(jì)算顯式MPC控制器的單步預(yù)測(cè)范圍和單相變成乘120和添加120。比較計(jì)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(jì)算有效而明確的MPC。該方案減少了計(jì)算負(fù)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?jì)算需求的減少可能會(huì)幫助操

33、作在更高的頻率,更便宜的硬件上實(shí)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(shí)，輸出電流估計(jì)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(fù)載10mH和20Q。負(fù)載反應(yīng)時(shí)間為0.02M可以看出，控制器提供了所需的輸出電壓，同時(shí)對(duì)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。可以指出，由于狀態(tài)空間平均使用，而忽略了交換行為，過(guò)濾器目前預(yù)計(jì)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