Modeling of Turbocharged Spark Ignited Engine and Model Predictive Control of Hybrid Turbocharger

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Title:
Modeling of Turbocharged Spark Ignited Engine and Model Predictive Control of Hybrid Turbocharger
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1 online resource (70 p.)
Language:
english
Creator:
Rong, Kang
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University of Florida
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Gainesville, Fla.
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Degree:
Master's ( M.S.)
Degree Grantor:
University of Florida
Degree Disciplines:
Mechanical Engineering, Mechanical and Aerospace Engineering
Committee Chair:
CRANE,CARL D,III
Committee Co-Chair:
DIXON,WARREN E

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Subjects / Keywords:
hybrid -- turbocharger
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
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Mechanical Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

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Abstract:
The idea of a hybrid turbocharger is demonstrated in this thesis. First a battery model and a turbocharged spark ignited(SI) engine is modeled using Simulink. The hybrid turbocharger is obtained by replacing the turbo shaft with a battery, which is connected to the turbine through a generator and to the compressor through a motor. The main idea of the hybrid turbocharger is that the compressor is driven by the battery and the battery is charged by the generator, which is driven by the turbine. Comparisons of the performance of the hybrid turbocharger to the conventional turbocharger and the naturally aspirated engine has been made in a few aspects. The comparison to the naturally aspirated engine shows that the hybrid turbocharger plays a significant role in engine downsizing. In comparison to the conventional turbocharger, it shows that the hybrid turbocharger eliminates the turbo lag. The last step is applying model predictive control (MPC) to the hybrid turbocharger model to minimize the fuel consumption. This is achieved by controlling two inputs of the system. First is controlling the battery output voltage in order to change the compressor speed and influence the air mass flow into the engine. Second is the control of the open angle of the waste gate in order to improve the turbine efficiency and decrease emissions.
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In the series University of Florida Digital Collections.
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Includes vita.
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Includes bibliographical references.
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Description based on online resource; title from PDF title page.
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This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility:
by Kang Rong.
Thesis:
Thesis (M.S.)--University of Florida, 2014.
Local:
Adviser: CRANE,CARL D,III.
Local:
Co-adviser: DIXON,WARREN E.

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lcc - LD1780 2014
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UFE0046795:00001


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MODELINGOFTURBOCHARGEDSPARKIGNITEDENGINEANDMODELPREDICTIVECONTROLOFHYBRIDTURBOCHARGERByKANGRONGATHESISPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFMASTEROFSCIENCEUNIVERSITYOFFLORIDA2014

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c2014KangRong 2

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Specialthankstoeveryonethathelped! 3

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ACKNOWLEDGMENTS IamverygratefultomyadvisorDr.CarlCraneforlettingjointheCIMARgroupandprovidingmewithsuchapreciousopportunitytoworkonthisexcellentproject.SpecialthankstoOlugbengaMosesAnubiandDarsanPatelfortheirwonderfulinstruction,selesshelpandgreatsupporttomeonthisresearch.Thisworkcouldnotbecompletedwithoutyourhelp. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 4 LISTOFTABLES ...................................... 8 LISTOFFIGURES ..................................... 9 ABSTRACT ......................................... 11 CHAPTER 1INTRODUCTION ................................... 12 1.1IntroductionofConventionalEngineChargingMethod ........... 12 1.2IntroductionofHybridTurbocharger ..................... 13 1.2.1HowHybridTurbochargerWorks ................... 13 1.2.2WhyUseHybridTurbocharger ..................... 14 1.3ProblemFormulationandThesisOutline ................... 15 2BATTERYMODELING ................................ 17 2.1BatteryDescription ............................... 17 2.2BatteryModeling ................................ 17 2.2.1MathematicalEquationsofBatteryDischargingandCharging ... 18 2.2.1.1StateofCharge ....................... 18 2.2.1.2DischargingMode ...................... 18 2.2.1.3ChargingMode ........................ 19 2.3SimulinkBatteryModelingandValidation .................. 19 2.3.1SimulinkModel ............................. 19 2.3.2ModelValidation ............................ 20 2.4ChapterConclusion .............................. 20 3TURBOCHARGEDSIENGINEMODELING .................... 22 3.1ModelOverview ................................ 22 3.1.1ModelInput ............................... 22 3.1.2ModelStates .............................. 23 3.1.3ModelConstants ............................ 23 3.2CompressorModeling ............................. 24 3.2.1PressureModel ............................. 24 3.2.2TemperatureModel ........................... 24 3.2.3MassFlowModel ............................ 25 3.2.4EfciencyModel ............................ 26 3.3IntercoolerModeling .............................. 26 3.3.1PressureModel ............................. 27 3.3.2MassFlowModel ............................ 27 5

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3.3.3TemperatureModel ........................... 27 3.3.4ModelValidation ............................ 28 3.4ThrottleModeling ................................ 28 3.4.1MassFlowModel ............................ 28 3.4.2ThrottlePressureModel ........................ 31 3.4.3TemperatureModel ........................... 31 3.5IntakeManifoldModeling ........................... 31 3.6CombustionModeling ............................. 32 3.7ExhaustManifoldModeling .......................... 34 3.7.1MassFlowModeling .......................... 34 3.7.2PressureModeling ........................... 35 3.7.3TemperatureModeling ......................... 35 3.8TurbineModeling ................................ 35 3.8.1MassFlowModeling .......................... 35 3.8.2PressureModeling ........................... 36 3.8.3TemperatureModeling ......................... 37 3.8.4EfciencyModel ............................ 37 3.9ExhaustSystemModeling ........................... 38 3.10WastegateModeling .............................. 40 3.11TurbochargerDynamics ............................ 40 3.12ChapterConclusion .............................. 41 4HYBRIDTURBOCHARGER ............................ 44 4.1HybridTurbochargerSimulinkModel ..................... 44 4.1.1DCMotorModeling ........................... 44 4.1.2HybridTurbochargerModeling ..................... 44 4.2AdvantagesofHybridTurbocharger ..................... 46 4.2.1ComparisonwithConventionalTurbocharger ............ 46 4.2.2ComparisonwithNaturallyAspiratedEngine ............. 47 4.3ChapterConclusion .............................. 48 5INTRODUCTIONTOMODELPREDICTIVECONTROL ............. 49 5.1WhyUseMPC ................................. 49 5.2MPCOverview ................................. 49 5.3MPCDerivation ................................. 50 5.4ChapterConclusion .............................. 53 6MODELPREDICTIVECONTROLOFHYBRIDTURBOCHARGER ....... 54 6.1ModelReduction ................................ 54 6.2ModelLinearization .............................. 54 6.3MPCImplementationInMatlab ........................ 59 6.4MPCWithConstraints ............................. 62 6.4.1OverviewofMPCwithConstraints .................. 62 6.4.2AddConstraintstotheSystem .................... 63 6

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6.5Simulation .................................... 64 6.6ChapterConclusion .............................. 65 7ConclusionandFutureWork ............................ 67 REFERENCES ....................................... 68 BIOGRAPHICALSKETCH ................................ 70 7

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LISTOFTABLES Table page 2-1BatteryParameter .................................. 17 3-1ModelInput ...................................... 23 3-2ModelStates ..................................... 23 3-3ModelConstants ................................... 24 8

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LISTOFFIGURES Figure page 1-1TurbochargedSIengine ............................... 13 1-2Schemeofhybridturbochargerworkow ...................... 15 2-1Batterymodelvalidationindischargemode .................... 20 2-2Batterymodelvalidationinchargemode ...................... 21 3-1Validationofthecompressortemperaturemodel ................. 25 3-2Validationofthecompressormassowmodel .................. 26 3-3Validationoftheintercoolertemperaturemodel .................. 28 3-4ValidationplotforQ-function ............................ 30 3-5Validationofthrottlemassowmodel ....................... 30 3-6Validationofvolumetricefciencymodel ...................... 32 3-7Validationoftorquemodel .............................. 34 3-8Validationofexhaustmanifoldtemperaturemodel ................ 36 3-9Validationofturbinemassowmodel ....................... 37 3-10Validationofturbinetemperaturemodel ...................... 38 3-11Validationofturbineefciencymodel ........................ 39 3-12Validationofexhaustsystemmassowmodel .................. 39 3-13TurbochargedSIenginemodel ........................... 43 4-1HybridturbochargedSIenginemodel ....................... 45 4-2Turbolagelimination ................................. 47 4-3Enginedownsizing .................................. 48 6-1Validationoflinearizedmassowmodel ...................... 57 6-2Validationoflinearizedenginetorquemodel .................... 58 6-3Fuelconsumptionbeforeandafteroptimization .................. 64 6-4Enginetoruquetracking ............................... 65 6-5Requiredbatteryvoltageinput ........................... 65 9

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6-6Requiredwastegateopening ............................ 66 10

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AbstractofThesisPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofMasterofScienceMODELINGOFTURBOCHARGEDSPARKIGNITEDENGINEANDMODELPREDICTIVECONTROLOFHYBRIDTURBOCHARGERByKangRongMay2014Chair:CarlCraneMajor:MechanicalandAerospaceEngineeringTheideaofahybridturbochargerisdemonstratedinthisthesis.Firstabatterymodelandaturbochargedsparkignited(SI)engineismodeledusingSimulink.Thehybridturbochargerisobtainedbyreplacingtheturboshaftwithabattery,whichisconnectedtotheturbinethroughageneratorandtothecompressorthroughamotor.Themainideaofthehybridturbochargeristhatthecompressorisdrivenbythebatteryandthebatteryischargedbythegenerator,whichisdrivenbytheturbine.Comparisonsoftheperformanceofthehybridturbochargertotheconventionalturbochargerandthenaturallyaspiratedenginehasbeenmadeinafewaspects.Thecomparisontothenaturallyaspiratedengineshowsthatthehybridturbochargerplaysasignicantroleinenginedownsizing.Incomparisontotheconventionalturbocharger,itshowsthatthehybridturbochargereliminatestheturbolag.Thelaststepisapplyingmodelpredictivecontrol(MPC)tothehybridturbochargermodeltominimizethefuelconsumption.Thisisachievedbycontrollingtwoinputsofthesystem.Firstiscontrollingthebatteryoutputvoltageinordertochangethecompressorspeedandinuencetheairmassowintotheengine.Secondisthecontroloftheopenangleofthewastegateinordertoimprovetheturbineefciencyanddecreaseemissions. 11

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CHAPTER1INTRODUCTION 1.1IntroductionofConventionalEngineChargingMethodThemostcommontypeofengineisthenaturallyaspiratedengine.Inanaturallyaspiratedengine,airforcombustion(dieselcycleinadieselengine,orspecictypesofOttocycleingasolineenginesnamelygasolinedirectinjection),oranair/fuelmixture(traditionalOttocyclepetrolengines)isdrawnintotheengine'scylindersbyatmosphericpressureactingagainstapartialvacuumthatoccursasthepistontravelsdownwardstowardbottomdeadcenterduringtheintakestroke.Mostautomobilepetrolengines,aswellasmanysmallenginesusedfornon-automotivepurposes,arenaturallyaspirated.Asuperchargedengineisanenginethatusesanaircompressorasthesuperchargertoincreasethepressureordensityofairsuppliedtoaninternalcombustionengine.Thisgiveseachcycleoftheenginemoreoxygen,lettingitburnmorefuelanddomorework,thusincreasingpower.Powerforthesuperchargercanbeprovidedmechanicallybymeansofabelt,gear,shaft,orchainconnectedtotheengine'scrankshaft.Superchargers(andturbochargers)havebeenwidelyappliedtoracingandproductioncars,althoughthesupercharger'stechnologicalcomplexityandcosthavelargelylimitedittoexpensive,high-performancecars.Whenpowerisprovidedbyaturbinepoweredbyexhaustgas,asuperchargerisknownasaturbosuperchargertypicallyreferredtosimplyasaturbochargerorjustturbo.Alargeamountofworkhasalreadybeendoneonthedesignandcontroloftheturbochargedengine,asdescribedin[5],[8],[9],[12].Theworkingprincipaloftheturbochargerisutilizingthehighpressureandtemperatureoftheexhaustgastodrivetheturbine,whichisconnectedtothecompressorthroughashaft,inordertodrivethecompressortoincreasetheairowrateintotheengine.Aturbochargedengineismorepowerfulandefcientthananaturallyaspiratedenginebecausetheturbineforces 12

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moreair,andproportionatelymorefuel,intothecombustionchamberthanatmosphericpressurealone.Figure1-1showstheworkowofhowaconventionalturbochargerworks. Figure1-1. TurbochargedSIengine 1.2IntroductionofHybridTurbocharger 1.2.1HowHybridTurbochargerWorksAhybridturbochargerisanelectricturbochargerconsistingofanultrahighspeedturbine-generatorandanultrahighspeedelectricaircompressor.Theturbineandcompressorarehigh-speedaeromachines,asinaconventionalturbocharger.Theelectricalmotorsrunatspeedsinexcessof120,000rpmandwhenusedasgenerators,generateelectricityatupto98.5%electricalefciency.Highelectricalefciencyisparamount,becausethereisnomechanicallinkbetweentheturbineandcompressor.Inotherwords,hybridturbochargerreferstoaserieshybridsetup,inwhichthecompressorspeedandpowerareindependentfromtheturbinespeedandpower.Thisdesign 13

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exibilityleadstofurtherimprovementsinturbineandcompressorefciency,beyondaconventionalturbocharger. DischargingMode.Whenthedriverdepressesthethrottle,theHTTinitiallyactslikeanelectricsupercharger.Thecompressormotorispoweredfromtheenergystoragemedium,whichinthisthesisisthebattery,allowingittoacceleratetofulloperatingspeedinapproximately500ms.Duringthistransientstage,theenginecontrolunit(ECU)onastandardturbochargedengineusesacombinationofsensorssuchaslambdasensorsandairmassowsensorstoregulatethefuelowrate.InanHTTequippedenginetheECUcandelivertheprecisefuelowrateforcompletecombustionmoreaccurately.Thisisachievedbydirectlycontrollingtheairowrateandboostpressureviacontrolofthecompressorspeed. ChargingMode.Whenthestateofcharge(SOC)[2]ofthebatterydropstosomecertainlevel,thegeneratorstartstochargethebatteryuntiltheSOCreturnstoaxedlevel.Thedischargingandchargingmodewillrepeatagainandagainduringtheworkingprocesstokeepthebatteryinagoodworkingmode,soastokeepthecompressorspeedatahighleveltosupplysufcientairtotheengine.Figure1-2showsthemainideaofthehybridturbochargerandhowitworks. 1.2.2WhyUseHybridTurbochargerEventhoughturbochargingtechnologyhasalreadybeenfullydevelopedandtheturbochargershowsexcellentperformanceinenginedownsizingandincreasingenginepower,itstillhasinevitableshortcomings.Themostobviousoneistheturbolag,whichmeansittakesaverylongtimeforthevehicletoreachtherequiredspeedafterthedriverdepressesthegaspedal.Theideaofthehybridturbochargersolvesthisproblem.Sincethecompressorisnolongerconnecteddirectlytotheturbine,theturboshaftinertiaisnotimportantanymore.Thecompressorisdrivenbythebattery,andisabletoreachfulloperatingspeedinlessthan0.5s.Thisrateofaccelerationeliminatestheturbolagsignicantly. 14

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Figure1-2. Schemeofhybridturbochargerworkow Ontheotherhand,thehybridturbochargerkeepstheadvantageinenginedownsizingwithrespecttothenaturallyaspiratedengine.Theenginewiththehybridturbochargerinstalledcanhaveasmallersizethanordinaryonestoprovideevenmorepowerduetotheincreasedairowrateandhighercombustionefciency. 1.3ProblemFormulationandThesisOutlineTwoproblemshavebeensolvedinthisthesis.TherstoneisthemodelingoftheSIenginewiththehybridturbochargerinstalled.ComparisonwiththenaturallyaspiratedengineandwiththeturbochargedSIenginewillbemadetoshowthatthehybridturbochargerdoesplayanimportantroleinenginedownsizingandeliminatingtheturbolag.ThesecondoneistoapplyModelPredictiveControl(MPC)tothesystemtominimizethefuelconsumptionandinthemeantimepreventthegeneratedengine 15

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torquedeviatingtoomuchfromtherequiredtorque.Thisisachievedbycontrollingthevoltageoutputofthebatteryandtheopenangleofthewastegateatthesametime.Theoutlineofthisthesisisasfollowing: 1. ModelingthebatteryusingSimulink. 2. Developtheconventionalturbochargedenginemodelandvalidateeachcomponentoftheengine. 3. Formthehybridturbochargermodelbyreplacingtheturboshaftwiththebattery. 4. Runsimulationstodemonstratetheperformanceofthehybridturbochargerinenginedownsizingandeliminatingturbolag. 5. Applymodelpredictivecontroltothesystemtominimizethefuelconsumption. 16

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CHAPTER2BATTERYMODELING 2.1BatteryDescriptionTherearealotofproposedbatterymodelsthathavebeenmadepreviously,asdescribedin[2],[3],[4].However,theydonotprovideagoodparameterestimationresultforthisthesiseitherinthebatterydischargingmodeorchargingmode.Thebatteryusedinthisthesistochargethecompressorisasealed50-modulenickelmetalhydride(NiMH)batterypackproviding60.5voltsand6.5Ahcapacity.Inthischapter,onlyonemoduleofthebatterypackismodeledandvalidated.Thespecicvalueofthebatterymoduleisasfollowing(E0isbatteryconstantvoltage(V),Qisbatterycapacity(Ah),Risinternalresistance())[1]: Table2-1. BatteryParameter ParameterValue(Unit) E01.2101(V)Q6.5(Ah)R0.002() 2.2BatteryModelingThebatterymodelisachievedbymakingtheSimulinkmodelaccordingtothemathematicalequationsofthebatterycharginganddischargingmode.Themodelisvalidatedusingthemanufacturer'sdata.Thefollowingassumptionshavebeenmade[1]: Theinternalresistanceisassumedconstantduringthechargeanddischargecyclesanddoesnotvarywiththeamplitudeofthecurrent. Themodel'sparametersarededucedfromthedischargecharacteristicsandassumedtobethesameforcharging. Thecapacityofthebatterydoesnotchangewiththeamplitudeofthecurrent(noPeukerteffect). Thetemperaturedoesnotaffectthemodel'sbehavior. Theself-dischargeofthebatteryisnotrepresented. Thebatteryhasnomemoryeffect. 17

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2.2.1MathematicalEquationsofBatteryDischargingandCharging 2.2.1.1StateofChargeThestateofcharge(SOC)isaveryimportantparameterofthebattery.Itrepresentshowmuchlongerthebatterycandischarge.ThemathematicalequationforSOCisgivenas: SOC=SOCinitial)]TJ /F8 11.955 Tf 13.15 17.94 Td[(Ridt Q(2)whereSOCinitial=theinitialstateofchargeofthebatteryi=thecurrentinthebatteryQ=batterycapacity 2.2.1.2DischargingModeTheproposeddischargemodelcanberepresentedaccuratelybythevoltagedynamicswhenthecurrentvariesandtakesintoaccounttheopencircuitvoltageasafunctionofSOC.Thebatteryvoltageobtainedisgivenby: Vbatt=E0)]TJ /F5 11.955 Tf 11.96 0 Td[(KQ Q)]TJ /F5 11.955 Tf 11.95 0 Td[(itit)]TJ /F5 11.955 Tf 11.95 0 Td[(Ri+Aexp()]TJ /F5 11.955 Tf 9.3 0 Td[(Bit))]TJ /F5 11.955 Tf 11.95 0 Td[(KQ Q)]TJ /F5 11.955 Tf 11.95 0 Td[(iti(2)whereVbatt=batteryvoltage(V)E0=batteryconstantvoltage(V)K=polarisationconstant(V/(Ah))Q=batterycapacity(Ah)it=Ridt=actualbatterycharge(Ah)A=exponentialzoneamplitude(V)B=exponentialzonetimeconstantinverse(Ah))]TJ /F6 7.97 Tf 6.59 0 Td[(1R=internalresistance()i=batterycurrent(A) 18

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i=lteredcurrent(A)Theexponentialzoneofequation(2-1)canbeobtainedbythefollowingequation: _exp(t)=Bji(t)j()]TJ /F5 11.955 Tf 9.3 0 Td[(exp(t)+A(t))(2)whereexp(t)=exponentialzonevoltage(V)i(t)=batterycurrent(A)u(t)=chargeordischargemode 2.2.1.3ChargingModeForaNiMHbattery,afterthebatteryhasreachedthefullchargevoltage,thevoltagedecreasesslowly,dependingonthecurrentamplitude.Thisbehaviorisrepresentedbymodifyingthechargepolarisationresistance.Whenthebatteryisfullycharged,thevoltagestartstodrop.Thisphenomenoncanberepresentedbydecreasingthepolarisationresistancewhenthebatteryisoverchargedbyusingtheabsolutevalueofthecharge(it): Pol.Resistance=KQ jitj)]TJ /F4 11.955 Tf 17.93 0 Td[(0.1Q(2)Thus,themathematicalequationforthechargingmodeis: Vbatt=E0)]TJ /F5 11.955 Tf 11.95 0 Td[(Ri)]TJ /F5 11.955 Tf 11.95 0 Td[(KQ jitj)]TJ /F4 11.955 Tf 17.93 0 Td[(0.1Qi)]TJ /F5 11.955 Tf 11.95 0 Td[(KQ Q)]TJ /F5 11.955 Tf 11.96 0 Td[(itit+exp(t)(2)Now,theSimulinkbatterymodelisreadytobemadeaccordingtothemathematicalequationsforbatterydischargingandchargingmode. 2.3SimulinkBatteryModelingandValidation 2.3.1SimulinkModelThebasicmodelingofthebatteryinSimulinkisbasedonequation(2-1)and(2-4).However,thedetailedmodelingismorecomplicated. 19

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ParameterestimationisperformedinSimulinktoobtainalltheunknownparametersgiventheinputandoutputofthebatteryaccordingtothemanufacturer'sdata.Thenextstepistovalidatethebatterymodel. 2.3.2ModelValidationFigure2-1and2-2showstheresultsofvalidationofthebatterymodelindischargingandchargingmodesrespectively.Itcouldbeobviouslyfoundthatthemodelisvalidatedverywellaccordingtothevalidationresults. Figure2-1. batterymodelvalidationindischargemode 2.4ChapterConclusionThebatteryisaveryimportantcomponentofthehybridturbochargersystem.Inthischapter,aNiMHbatterypackisformedbasedonmathematicalequations,modeled 20

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Figure2-2. batterymodelvalidationinchargemode andvalidatedinSimulink.Accordingtothemodelvalidation,itcanbefoundthattheestimatedparametersofthebatteryprovidereasonableresults.Nowthebatterymodelisreadytobeusedintheenginemodelwhichwillbemadeinthefollowingchapters. 21

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CHAPTER3TURBOCHARGEDSIENGINEMODELING 3.1ModelOverviewInthischapter,ameanvalueenginemodel(MVEM)withturbochargerinstalledispresented.Themodeliscompletedbyrstlycreatingsubsystemsofeachcomponentoftheengineandthenconnectingeachsubsystemstoformthenalenginemodel.Themassowthroughtheengineiscentralinthemodeling,andthusthemodelingisbasedontheairowpath.Theairenterstheenginethroughtheairltertobecleaned.Thenthecleanairentersthecompressorwherethepressureandtemperatureincrease.Theairneedstobecooleddownbeforeenteringtheenginecylindertoavoidknock,andthisprocessisdoneviaaheatexchangercalledtheintercooler.Theamountofairintotheenginecylinderiscontrollerbythethrottleinordertocontroltheengineoutputpower.Thentheairismixedwithfuelintheintakemanifold.Themixtureentersthecylinder,wherecombustiontakesplace.Thepressureandtemperatureincreasessignicantlyaftercombustion.Thehotgas,whichgetsoutoftheengineviatheexhaustmanifold,isthepowertodrivetheturbine.Theturbinethendrivesthecompressortospinatveryhighspeedthroughtheturboshaft.Awastegateisusedtoregulatetheairowintotheturbine.Finallythewastedgasleavestheenginethroughtheexhaustsystem.Allthecomponentswillbemodeledinthefollowingsectionsandnallythewholeenginemodelwillbevalidatedaccordingtoexperimentaldata.Onesimplicationhasbeenmadehere.Theairlterdoesnothavesignicantinuenceonneitherthepressurenorthetemperatureoftheair.Sincethismodelisonlyforsimulation,theairlterwillnotbemodeledinthefollowingsections. 3.1.1ModelInputTheinputintothemodelisshowninTable3-1: 22

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Table3-1. ModelInput NameDescriptionUnit NEnginespeedrpmThrottleangledeguwgWastegateopening-pambAmbientpressurePaTambAmbienttemperatureK Table3-2. ModelStates StateDescriptionUnit pcpressureaftercompressorPaTctemperatureaftercompressorKpicpressureafterintercoolerPaTictemperatureafterintercoolerKpiintakemanifoldpressurePaTiintakemanifoldtemperatureKpeexhaustmanifoldpressurePaTeexhaustmanifoldtemperatureKptpressureafterturbinePaTttemperatureafterturbineK!tcturbochargerspeedrad/s 3.1.2ModelStatesAftersubtractingtheairlterfromtheenginemodel,thesystemcontains11states,includingthepressureandtemperatureaftereachcomponentandtheturbochargerspeed.AllthestatesarelistedinTable3-2: 3.1.3ModelConstantsTable3-3showsalltheconstantsoftheenginemodelthatwillmentionedinthefollowingchapters[11]:Inthefollowingchapters,eachcomponentofthehybridturbochargedenginewillbemodeledintheorderoftheairowpath. 23

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Table3-3. ModelConstants NameDescriptionValue(unit) RGasconstant287(J=(kgK))Heatcapacityratio1.4cpHeatcapacityatconstantpressure1003.4(J=K)QhvHeatingvalueoffuel44106(J/kg)pambAmbientpressure101.7(kPa)TambAmbienttemperature296(K)VcCompressorvolume0.005(m3)VicIntercoolervolume0.005(m3)VimIntakemanifoldvolume0.002(m3)VemExhaustmanifoldvolume0.002(m3)VesExhaustsystemvolume0.01(m3)JTurboshaftinertia0.15(kg=m2) 3.2CompressorModeling 3.2.1PressureModelThedynamicequationforthecompressorcanbederivedfromtherstlawofthermodynamics,andisgivenas: @pc @t=RTc Vc(_mc)]TJ /F4 11.955 Tf 15.2 0 Td[(_mic)(3)whereVc=compressorvolume,_mic=massowratethroughtheintercooler,kg=s_mc=massowratethroughthecompressor,kg=s 3.2.2TemperatureModelIftheexpansionofgasesthroughthecompressorwasisentropic,i.e.c=1,thetemperatureafterthecompressorcouldbemodeledas: Tc=k1Tamb(pc pamb)()]TJ /F6 7.97 Tf 6.58 0 Td[(1)=(3)Despiteitssimplicity,duetothehighefciencyofthecompressorwhichmakestheisentropicapproximationmoreappropriate,thismodelworkswellaccordingtotheexperimentaldata,whichcanbeshownfromFigure3-1: 24

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Figure3-1. Validationofthecompressortemperaturemodel 3.2.3MassFlowModelThecompressormassowdependsmainlyonthecompressorspeedandthepressureratio.Somebasicrequirementsarethatthemassowmustbezerowhentheturboshaftspeediszero,andwhenthereisnopressuredifferencebeforeandafterthecompressor.Onepossiblemodelispresentedas: _mc=k1(1)]TJ /F5 11.955 Tf 13.15 8.08 Td[(pamb pc)+k2!tcr 1)]TJ /F5 11.955 Tf 13.16 8.08 Td[(pamb pc+k3!tc4r 1)]TJ /F5 11.955 Tf 13.15 8.08 Td[(pamb pc+k4!tc(3)wherek1tok4areunknownparameterstobedetermined.However,thismodelisdifculttotunesinceitproducesimaginarynumbersforsomecircumstances.Therefore,anothermathematicalequationisusedtomodelthecompressormassow: ^NT=!tc)]TJ /F4 11.955 Tf 11.95 0 Td[(8104 2104^pr=c)]TJ /F5 11.955 Tf 11.96 0 Td[(b4^NT)]TJ /F5 11.955 Tf 11.96 0 Td[(b5^N2T_mc=b1^pr+b2^p2r+b3^p2r(3)wherec=pc pamb 25

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Inthismodel,b1tob5aredeterminedbyusingthelsqcurvetfunctioninMatlab.Thevalidationshowsagoodresultoftheparameterestimationforthecompressormassowmodel,showninFigure3-2: Figure3-2. Validationofthecompressormassowmodel.Thegroupofpointsrepresentturboshaftspeeds80000RPM,10000RPM,12000RPMand14000RPMrespectivelyfromlefttoright. 3.2.4EfciencyModelTheefciencyisdenedbytheratiooftheisentropicandtheactualspecicinputwork.Themathematicalequationfortheefciencymodelisgivenas: c=(pc pamb))]TJ /F12 5.978 Tf 5.75 0 Td[(1 )]TJ /F4 11.955 Tf 11.95 0 Td[(1 Tc Tamb)]TJ /F4 11.955 Tf 11.96 0 Td[(1(3)Theefciencymodelisdifculttobeestimated,however,equation(3-5)stillsyieldsareasonableresultofthecompressorefciency. 3.3IntercoolerModelingDuetotherstlawofthermodynamics=P RT 26

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Thuswhenthepressureofairincreaseswhenbeingcompressedbythecompressor,theairtemperaturealsorises.Thehightemperatureoftheintakeairintotheenginewillcauseknockinthecylinder.Therefore,theairneedstobecooledandthisisthemainreasonwhytheintercoolerismodeled. 3.3.1PressureModelTheintercoolercanbetreatedasastaticowrestriction.Thedynamicequationfortheintercoolercanbederivedfromtherstlawofthermodynamics,andisgivenas: @pic @t=RTic Vic(_mic)]TJ /F4 11.955 Tf 15.2 0 Td[(_mth)(3)whereVic=intercoolervolume_mic=massowratethroughtheintercooler,kg=s_mth=massowratethroughthethrottle,kg=s 3.3.2MassFlowModelTherelationshipbetweenthepressuredropintheintercoolerandthemassowratehasbeenfoundtotthefollowingequation: pc)]TJ /F5 11.955 Tf 11.96 0 Td[(pic=kTc_m2ic(3)Thenthemassowthroughtheintercoolercanbemodeledas: _mic=r pc)]TJ /F5 11.955 Tf 11.96 0 Td[(pic kTc(3)wherekistheunknownparametertobeestimatedinMatlabusinglsqcurvetfunction.Thevalidationshowsthatthismodeltswellwiththeexperimentaldata. 3.3.3TemperatureModelTheabilityoftheintercoolertolowerthetemperatureofthecompressedairdependsontheintercoolerefciency.Forperfectgastheheatcapacityisafunctionof 27

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thetemperatureonly,andthustheintercoolerefciencycanbeexpressedas:=Tc)]TJ /F5 11.955 Tf 11.95 0 Td[(Tic Tc)]TJ /F5 11.955 Tf 11.95 0 Td[(Tcool (3)Thustheintercoolertemperatureisreadytobeexpressedas: Tic=Tc)]TJ /F10 11.955 Tf 11.95 0 Td[((Tc)]TJ /F5 11.955 Tf 11.95 0 Td[(Tcool)(3)whereTcoolinthisthesisisequaltotheatmosphericpressureTamb. 3.3.4ModelValidationFigure4-1showstheresultoftheparameterestimationoftheintercoolertemperaturemodel.Itcouldbeseenthatthetemperaturemodeltstheexperimentaldatawell. Figure3-3. Validationoftheintercoolertemperaturemodel 3.4ThrottleModeling 3.4.1MassFlowModelIngasolineengines,athrottleisusedtocontroltheairmassowintothecylinders.Thusitisimportanttomodelthethrottlemassowrateprecisely.Themassowthroughthethrottlecanbemodeledliketheowofanidealgasthroughaventuri.A 28

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standardmodelforthistypeofowis _mth=pic p RTicAC(pr)(3)whereA=throttleopeningareaC=dischargecoefcientCdependsontheshapeoftheowarea.(pr)isafunctionofthepressureratiogivenas: (pr)=8>><>>:r 2 )]TJ /F6 7.97 Tf 6.59 0 Td[(1(p2 r)]TJ /F5 11.955 Tf 11.96 0 Td[(p)]TJ /F12 5.978 Tf 5.76 0 Td[(1 r),ifpr>(2 +1) )]TJ /F12 5.978 Tf 5.76 0 Td[(1q 2 )]TJ /F6 7.97 Tf 6.59 0 Td[(1((2 +1)2 )]TJ /F12 5.978 Tf 5.76 0 Td[(1)]TJ /F4 11.955 Tf 11.96 0 Td[((2 +1)+1 )]TJ /F12 5.978 Tf 5.75 0 Td[(1),otherwise(3)wherepristhepressureratiopr=pth picSinceboththeopeningareaAandthedischargecoefcientCdependonthethrottleplateopeningangle,itisreasonabletolumpAandCtogethertoformanotherequationQth()toexpressingtheopeningofthethrottle.TherearemanyvalidatedmodelforQth()accordingtopreviousresearches.Themodelusedinthisthesisisgivenas Qth()=Q1(1)]TJ /F4 11.955 Tf 11.96 0 Td[(cos(a0+a1))+Q0(3)whereQ1,Q0,a1anda0areunknownparametersthatwillbedeterminedbyusingthelsqcurvetfunctioninMatlab.Figure3-4showsthevalidationoftheparametersofthefunctionQth():Nowthemathematicalequationofthrottlemassowratemodelcanbeexpressedasafunctionof,pic,Tthandpim,whichisgivenas: _mth(,pic,Tic,pim)=pic p RTicQth()(pr)(3) 29

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Figure3-4. ValidationplotforQ-function Thethrottlemassowisacentralquantityintheengine.Ithasasignicantinuenceonthecombustionprocess,andthereforedeterminestheoutputpoweroftheengine.Thustheaccuracyofthemassowmodelisimportant.Figure3-5showsthevalidationofthethrottlemassowmodel. Figure3-5. Validationofthrottlemassowmodel.Thisshowsthatthethemodeltstheexperimentaldatawell 30

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3.4.2ThrottlePressureModelSimilarlytothepressuremodeloftheintercoolerandthecompressor,thethrottlepressuremodelcanbederivedfromtherstlawofthermodynamicsandisgivenas: @pth @t=RTic Vim(_mth)]TJ /F4 11.955 Tf 15.2 0 Td[(_mac)(3)whereVim=intakemanifoldvolume_mac=themassowrateintothecylinder 3.4.3TemperatureModelThetemperaturechangeinthethrottleisneglected,whichmeansthetemperatureafterthethrottleisthesameastheoneaftertheintercooler. Tth=Tic(3) 3.5IntakeManifoldModelingTheintakemanifoldiswheretheairandfuelaremixedandisthepathwherethemixtureentersthecylinders.Thepressureandtemperaturearejustconsideredtobetheonesthatareafterthethrottle.Sointhissection,onlythemassowintothecylinderismodeled.Oneoftheparametersthatgovernsthemassowintothecylinderisthevolumetricefciencyvol.Manymathematicalequationshavebeenusedbypreviousresearchersformodelingvol.Inthisthesis,volismodeledasafunctionoftheintakemanifoldpressurepthandtheenginespeedN,whichisgivenas[14]: vol(N,pth)=a0+a1N+a2N2+a3pth(3)Figure3-6showsthevalidationofthevolumetricefciency.Nowthemassowintothecylinderisreadytobemodeledas: _mac=vol(N,pth)VdNpth 120RTth(3) 31

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Figure3-6. Validationofvolumetricefciencymodell whereNistheenginespeedin[RPM]andVdisthedisplacementvolumeoftheenginein[m3]. 3.6CombustionModelingDuringthecombustionprecess,themixtureofairandfuelisburnttogeneratetorqueandpower.Theamountofairintothecylinderaffectstheextensionofthecombustion,sothatitwillinuencetheoutputpoweroftheengine.Inordertoinjectacorrectamountoffuelintotheengine,itisimportanttoknowthetheoreticalproportionofairandfuel,whichiscalledthestoichiometricairtofuelratio A Fs=mac mfc(3)Inthisthesis,thisratioissettobe14.7.Animportantparameteristheratiobetweenthetrueairtofuelratio(A/F)and(A=F)s =(A=F) (A=F)s(3)Whenthereisexcessairinthecombustion(>1),themixtureisreferredtoasleanandwhenthereisexcessfuelinthecombustion(<1),themixtureiscalledrich.An 32

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enginethatrunsunderleanconditionswillemitlargeamountofNOxandifthemixtureisrichtherewillinevitablybeunburnedhydrocarbonsandCOintheexhaustgases.Thus,itisessentialtokeepclosetooneinordertomaintaingoodcatalystfunction,whichwillyieldsthefuelmassowrateas: _mfc=1 14.7_mac(3)Thetorquegeneratedbytheenginedependsontheworkproducedandconsumedintheengine,whichisgivenas[18]: Me=Wig)]TJ /F5 11.955 Tf 11.96 0 Td[(Wp)]TJ /F5 11.955 Tf 11.96 0 Td[(Wf 2nr(3)wherenristhenumberofenginerevolutionspercycle.Inthisthesis,themodelisa2-strokeengine,sonr=2.Wigistheindicatedgrossworkproducedbytheengine,WpisthepumpingworkconsumedandWfisthefrictionworkconsumed.Themathematicalexpressionsforthesethreetermsareasfollows: Wig=Vd_mfuelQhv60 N2 VdeWp=Vd(pem)]TJ /F5 11.955 Tf 11.95 0 Td[(pim)Wf=Vd[0.97+0.15(N 1000)+0.05(N 1000)2](3)whereeisthecombustionefciency.Therearealsomanyvalidatedmathematicalexpressionsfore.Inthisthesis,theequationisgivenasfollowing: in=0.588(1)]TJ /F4 11.955 Tf 11.95 0 Td[(0.392N)]TJ /F6 7.97 Tf 6.58 0 Td[(0.36)ip=0.9301+0.2154pth)]TJ /F4 11.955 Tf 11.95 0 Td[(0.1657pth2e=Cinip(3)wherepthistheintakemanifoldpressureinbarandCisanunknownparametertobeestimatedusingthelsqcurvetfunctioninMatlab. 33

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Theenginetorquemodelisvalidatedaccordingtotheexperimentaldata,whichisshowninFigure3-7. Figure3-7. Validationofenginetorquemodel Thentheoutputenginepowercanbeeasilyexpressedas: P=2MN(3)whereMistheenginetorqueinN_m,Nistheenginespeedinrpm. 3.7ExhaustManifoldModelingThemixtureburntintheenginecylindergeneratesveryhighpressureandtemperatureintotheexhaustmanifold,whichisusedbytheturbinetodrivethecompressor.Thusthepressureandtemperatureoutoftheexhaustmanifoldismodeledhere. 3.7.1MassFlowModelingFirstly,themassowthroughtheexhaustmanifoldismodeledbecauseitwillbeusedtomodelthepressure.Theexhaustmanifoldmassowisjustthesumoftheair 34

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massandfuelmassowthroughtheengine,whichisgivenas: _mem=_mac+_mfuel(3)where_macand_mfuelareexpressedinsection3.6 3.7.2PressureModelingThedynamicsoftheexhaustmanifoldcanbedescribedbythefamiliartankmodelapproach.Thepressurepemisbuiltupbyexhaustmanifoldmassow_memandtemperatureTe,theturbinemassow_mtandthewastegatemassow_mwgwhichwillbemodeledinthefollowingsection. @pem @t=RTem Vem(_mem)]TJ /F4 11.955 Tf 15.2 0 Td[(_mt)]TJ /F4 11.955 Tf 15.19 0 Td[(_mwg)(3) 3.7.3TemperatureModelingTheexhausttemperatureincreaseswithincreasingenginespeed,load,andsparkretard.DifferentcombinationsofthesepropertieshavebeentestedasamodelforTem.CorrelationanalysiswasusedtondacombinationofpowersofNandMthatworksne.Thustheexhausttemperatureisgivenas: Tem=k1M2+k24p N+k3MN(3)wherekiaretheparameterstobedeterminedbyusinglsqcurvetinMatlab.TheexhaustmanifoldtemperaturemodelisvalidatedasshowninFigure3-7 3.8TurbineModeling 3.8.1MassFlowModelingUnlikethecompressor,themassowratethroughtheturbinedoesnotdependontheturboshaftspeed.Accordingtoalargeamountofpreviousresearches,itcanbeaccuratelymodeledbyusingonlythepressureratio,pem=pt.Thebasicrequirementforthemodelingisthatwhenthereisnopressuredifferencethemassowrateneedstobezero.Itturnsoutthatthefollowingmathematicalequationfortheturbinemassow 35

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Figure3-8. Validationofexhaustmanifoldtemperaturemodel makesagoodtwiththeexperimentaldataprovidedbythemanufacturer. _mt=k1(pem pt)+k2r pem pt)]TJ /F4 11.955 Tf 11.95 0 Td[(1(3)Equation(3-29)islinearinparametersk1andk2sothattheparameterscanbeadjustedtomeasureddatabyusingstandardleastsquaremethods.Actually,theparametersareestimatedbyusingthelsqcurvetfunctioninMatlab.Figure3-9showsagoodvalidationresult. 3.8.2PressureModelingSimilartoothercomponents,thepressuremodelingoftheturbinecanalsobederivedfromtherstlawofthermodynamics,whichisgivenas: @pt @t=RTt Ves(_mwg+_mt)]TJ /F4 11.955 Tf 15.19 0 Td[(_mes)(3)where_mesistheexhaustsystemmassowratein(kg/s). 36

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Figure3-9. Validationofturbinemassowmodel 3.8.3TemperatureModelingAswhatwasdonetothecompressor,itispossibletomodeltheturbinetemperatureinthesamewaygivenas: Tt=k1Tem(pt pem)()]TJ /F6 7.97 Tf 6.58 0 Td[(1)=(3)However,thismodeldoesnotholdasexpected.OnepossibleexplanationisthatthegreatheattransferformtheturbinetothesurroundingsmakesthemodelfailtocaptureTt.Thus,anothermodelisintroducedhere,whichshowsagoodtwiththeexperimentaldata. Tt=k1(Tem)]TJ /F5 11.955 Tf 11.95 0 Td[(Tamb)(pt pem)(1)]TJ /F11 7.97 Tf 6.59 0 Td[()=+k2(Tem)]TJ /F5 11.955 Tf 11.95 0 Td[(Tamb)2+k3(3)wherekiareparameterstobedeterminedbyusinglsqcurvetfunctioninMatlab.Figure3-10showsthevalidationresultofthisturbinetemperaturemodel. 3.8.4EfciencyModelTheturbineefciencymodelcanbecalculatedbytheequationgivenas: t=1)]TJ /F7 7.97 Tf 15.84 4.71 Td[(Tt Tem 1)]TJ /F4 11.955 Tf 11.96 0 Td[((pt pem))]TJ /F12 5.978 Tf 5.76 0 Td[(1 (3) 37

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Figure3-10. Validationofturbinetemperaturemodel Theturbineefciencyisimportantsinceitdeterminesthepowerdeliveredtothecompressor.Itisnotclearwhattheefciencyiswhenthereisnomassowthroughtheturbine.Therelationshipbetweentheturboshaftspeedandtheturbineefciencyiscomplicatedandverydifculttomeasure.Asanapproximation,amodelwhichisindependentofturbinespeedisusedinthisthesisgivenas: t=k1r pem pt)]TJ /F4 11.955 Tf 11.96 0 Td[(1+k24r pem pt)]TJ /F4 11.955 Tf 11.95 0 Td[(1+k3(3)wherekiaretheunknownparameterstobeestimatedusingthelsqcurvetfunctioninMatlab.Figure3-11showsthevalidationoftheturbineefciencymodel. 3.9ExhaustSystemModelingThepressuredropfromtheturbinethroughtheexhaustsystemtothesurroundingairissignicant,thereforeitisnecessarytomodelthispressureloss.Theexhaustsystemcanberegardedasatubewithasuddenrestriction.Themathematicalequationforthepressuredropinthistubeisgivenas: pt)]TJ /F5 11.955 Tf 11.96 0 Td[(pamb=k1_mes+k2_m2es(3) 38

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Figure3-11. Validationofturbineefciencymodel Figure3-12. Validationofexhaustsystemmassowmodel Inordertoformtheexhaustsystemmassowratetobeusedforcalculatingturbinepressure,equation(3-35)isredenedasfollowing: _mes=)]TJ /F7 7.97 Tf 11.69 14.85 Td[(k1 k2Tt 2+s (k1 k2Tt 2)2+pt)]TJ /F5 11.955 Tf 11.95 0 Td[(pamb k2(3)ThisexhaustsystemmassowmodelisvalidatedinFigure3-12 39

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3.10WastegateModelingTheturbochargerwilloverspeedveryeasilyathighloads,whichcausesexcessiveboostpressureoreventurbochargerbearingfailure.Iftheturboshaftspeedistoohigh,thecompressorwillconsequentlyspinataveryhighspeed,resultinginhighintakemanifoldpressure,whichwillcauseknockintheenginecylinder.Topreventtheturbinefromoverspeeding,itisnecessarytodeviatesomeamountofexhaustgasesawayfromowingintotheturbinedirectly.Thisisachievedbyusingavalvecalledwastegate.Thiswillkeepthedrivingtorqueandthereforetheturbinespeedatalowerlevelwhenthewastergateisopen.Thewastgatecanbemodeledinasimilarwayasthethrottlemodeling.Equation(3-12)and(3-13)willbeused.TheonlydifferenceisthattheQfunctionwillbereplacedwithafunctionoftheopeningareaofthewastegate.Themathematicalequationforwastegatemodelingisgivenas: Awg=CdAwgmaxuwgAwgmax=D2 4_mwg=pem p RTemAwg(pr)(3)whereCd=wastegateowcoefcient,0.9uwg=theopeningofthewastegate,uwg2[0,1]D=thediameterofthewastegatetubepr=thepressureratiopt=pem 3.11TurbochargerDynamicsAccordingtoNewton'sSecondLawforrotatingsystems,theturbineandcompressorareconnectedbythemathematicalequationgivenas: Tqt)]TJ /F5 11.955 Tf 11.95 0 Td[(Tqc=Jtc_!tc(3) 40

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whereTqtstandsforthedrivingtorqueoftheturbineandTqcisthebrakingtorqueactingonthecompressor.Jtcdenotestheinertiaoftheturboshaftand!tcistherotationalspeedoftheturboshaft.ThetheoreticalmaximumtorquedeliveredbytheturbinedependsontheexhaustmanifoldtemperatureTemandtheratiopem=pt.Iftheprocesswouldbereversible,whichmeanstherewouldnotbeanyfrictionallossesintheturbine,theworkwouldbecalledisentropic.However,sincetheturbinegetsredhotathighloads,thisisnotanisentropiccase.Thustheturbineefciencytisintroducedheretocalculatethetrueportionofpowerdeliveredbytheturbine.Themathematicalequationfortheturbinepowerisgivenas Pt=t_mtcpTem[1)]TJ /F4 11.955 Tf 11.96 0 Td[((pem pt)(1)]TJ /F11 7.97 Tf 6.58 0 Td[(=)](3)Themathematicalequationforcompressorpowercanbemodeledinasimilarway.Sincethecompressorconsumesenergy,thenetamountofproducedpowerisnegative.Moreover,thecompressorisnotideal,sotheefciencycisalsointroducedhere. Pc=_mccpTamb1 c[(pc pamb)()]TJ /F6 7.97 Tf 6.59 0 Td[(1)=)]TJ /F4 11.955 Tf 11.96 0 Td[(1](3)ThetorqueandthepowerareconnectedthroughequationP=Tq!,thustheequationsfortheturbineandcompressortorquesaregivenas: Tqt=t_mtcpTem[1)]TJ /F4 11.955 Tf 11.95 0 Td[((pem pt)(1)]TJ /F11 7.97 Tf 6.58 0 Td[(=)] !tcTqc=_mccpTamb1 c[(pc pamb)()]TJ /F6 7.97 Tf 6.59 0 Td[(1)=)]TJ /F4 11.955 Tf 11.96 0 Td[(1] !tc(3)Substitutingequation(3-41)intoequation(3-38)yieldsadifferentialequationof!jtc.Theturboshaftrotatingspeedcanbecalculatedbysolvingthisdifferentialequationfor!tc. 3.12ChapterConclusionThischaptercoversthemodelingandthevalidationofallthecomponentsintheturbochargedSIengine.Validationresultsshowthateachcomponentworkswell 41

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separately,whichwillprovideareasonableturbochargedenginesystem.Thenextstepistocombinethebatterymodelwiththeenginemodeltoformthehybridturbochargerandmakecomparisonswiththeconventionalturbochargerandthenaturalaspiratedenginetodemonstratetheadvantagesofthehybridturbocharger.Figure3-13showsthetopleveloftheSimulinkmodeloftheturbochargedSIengine. 42

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Figure3-13. TurbochargedSIenginemodel 43

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CHAPTER4HYBRIDTURBOCHARGER 4.1HybridTurbochargerSimulinkModel 4.1.1DCMotorModelingThersttaskistomodelthedcmotorwhichisusedtodrivethecompressor.Therequirementsforthemotorare: Reachthefulloperatingspeedwithinaveryshorttime. Thefulloperatingspeedshouldbeover10000rad=sThemathematicalequationforthedcmotorisgivenas: _!=1 J(ktI)]TJ /F5 11.955 Tf 11.95 0 Td[(b!)_I=1 L()]TJ /F5 11.955 Tf 9.3 0 Td[(RI+V)]TJ /F5 11.955 Tf 11.95 0 Td[(ke!)(4)whereJ=momentofinertiaoftherotor,0.01J=m2b=motorviscousfrictionconstant,0.01(Nms)R=electricresistance,1L=electricinductance,0.1Hke=electromotiveforceconstant,0.001V=(rad=s)kt=motortorqueconstant,2Nm=A 4.1.2HybridTurbochargerModelingThebatterymodelandturbochargedSIenginemodelhavealreadybeencompletedinpreviouschapters.Therefore,itisreadytomaketheenginewiththehybridturbocharger.Thisisdonebyreplacingtheturboshaftwiththebatteryandpowerelectronics.Powerelectronicsconsistofthemotorandthegenerator.Thebatteryisusedtostartthemotortodrivethecompressor.Thegenerator,whichisdrivenbytheturbine,isusedforchargingthebatterywhenthestateofcharge(SOC)ofthebatterydropstoacertainlevel. 44

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Figure4-1. HybridturbochargedSIenginemodel 45

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Figure4-2. HybridTurbochargerworkingprocessshowingthecharginganddischagringmode Inthisthesis,themotorusedismodeledasaDCmotorwhichcanreachthefulloperatingspeed(12000rad/s)inabout0.8s.ThegeneratorinthisthesisisjustpickedfromtheSimPowerSystemDCMachineLibrarywhichispoweredbytheturbinetorque.ThetoplevelSimulinkmodelofthehybridturbochargerisshowninFigure4-1.Theworkingprocessistousethebatterytodrivethemotorinordertodrivethecompressor.WhentheSOCofthebatterydropsto40%,theswitchisturnedontostartthegeneratortochargethebatteryuntiltheSOCreaches80%.Thisrepeatsduringthewholeworkingprocess,whichisshowninFigure4-2.Theinputtothesystemareatmosphericpressure,temperatureandthethrottleangle.Theimportantoutputsaretheenginetorqueandpower. 4.2AdvantagesofHybridTurbocharger 4.2.1ComparisonwithConventionalTurbochargerThemostsignicantadvantageofthehybridturbochargeragainstconventionalonesisthatiteliminatestheturbolag.Turbolagmeansthetimeittakestheenginetogeneraterequiredenginetorque,orinotherwords,thevehiclereachestherequiredspeedafterthedriverdepressesthegaspedal.Theturbolagisresultedfromthe 46

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Figure4-3. Turbolagelimination inertiaoftheturboshaft,whichisthemainreasonthatcausestheturboshafttoreachtherequiredspeedinafewseconds.Thehybridturbochargersolvesthisproblemwellbecausethecompressorisdrivenbythemotordirectly,whichisabletoreachfulloperatingspeedinlessthen1sandindependentoftheturbine.Sincethereisnoshaftbetweenthecompressorandtheturbine,turboinertiaisnotaproblemanymore.Thiscomparisoniscompletedbyusingastepthrottleangleinputtosimulatethecasethatthedriverdepressesthegaspedaltomakethethrottleangleincreasefrom25to35,andcheckthetimeittakesthetwoenginetoreachtherequiredspeed,asshowninFigure4-3.Itiseasytofoundthedifferencebetweenthetimeittakestheengineswiththetwotypesofturbochargerinstalledtoreachtherequiredtorque.Theresultdemonstrateswellthatthehybridturbochargereliminatestheturbolagsignicantly. 4.2.2ComparisonwithNaturallyAspiratedEngineThesecondadvantageofthehybridturbochargeriscomparedtothenaturallyaspiratedengine,sincetheyareabletoeliminatetheturbolag.Thenwhyshouldweusethehybridturbochargerbutnotjustthenaturallyaspiratedengine?Theansweris 47

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Figure4-4. EnginedownsizingwithhybridturbochargerInstalled.Thetwoenginesareinthesamecondition(samethrottleangleandsameload).Thesolidlineshowsa1Lenginewithhybridturbochargerinstalled.Thedashedlineshowsa2Lnaturallyaspiratedengine. thatthehybridturbochargerplaysanimportantroleinenginedownsizing,whichmeanstheenginewiththehybridturbochagerinstalledisabletogenerateequalorevenmorepowerthanthenaturallyaspiratedengineofalargersize.ThisisshownbyFigure4-4.ItcanbeseeninFigure4-4thatwiththehybridturbochargerinstalled,the1Lenginehasaevenlargeroutputpowerandhigherenginespeedthanthe2Lnaturallyaspiratedengine,whichmeanstheenginedownsizesabout50%. 4.3ChapterConclusionInthischapter,comparisonsbetweenthehybridturbochargerwiththeconventionalturbochargerandthenaturallyaspiratedenginehavebeenmade.Itcanbefoundthatthehybridturbochargerhasagreatsignicanceineliminatingtheturbolagandenginedownsizing.Inthenextchapter,thecontrollerwillbemadetocontrolthesystem. 48

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CHAPTER5INTRODUCTIONTOMODELPREDICTIVECONTROL 5.1WhyUseMPCEventhoughPID-controlisnormallyusedinindustry,thecontrolmethodusedinthisthesisismodelpredictivecontrol(MPC),anadvancedmethodofprocesscontrol.Thereasonsareasfollows[19],[21]. MPCallowsthecurrenttimeslottobeoptimized,whilekeepingfuturetimeslotsinaccount. MPChastheabilitytoanticipatefutureeventsandcantakecontrolactionsaccordingly.PIDandLQRcontrollersdonothavethispredictiveability. MPCcanhandlesafetyconstraints. Morethanoneinputandoutput(MIMO-systems)canbehandledusingMPC. 5.2MPCOverviewModelPredictiveControlisanadvancedprocesscontroltechniquewidelyadoptedinindustryasaneffectivemethodtodealwithlargemultivariableconstrainedcontrolproblems.MPCusesamodelofthesystemtopredictitsfuturebehavior,andthenoptimizesaquadraticperformancebasedontheprediction.Themainideaistochoosethecontrolinputbysolvinganonlineoptimalcontrolproblemrepeatedly,aimingatminimizingaperformancecriterionoverafuturehorizon.ThisfuturehorizoniscalledthepredictionhorizonNp,whichmeansthenumberofsamplesonelooksahead.AnotherimportanttermisthecontrolhorizonNc,meaningthenumberofsamplesthattheoptimalinputiscalculatedfor.NpandNcarenotnecessarilythesame.IftheNcisshorterthanNp,thecomplexityoftheproblemisreduced.Inthisthesis,NpispickedtoequaltoNc.TheprocedureoftheMPCisasfollowing:AssumethesystemisrunningduringtheperiodoftimeT.DiscretizethetimeperiodTintoNpiecesofequallength,whichisthesamplingtimeTs=T=N.Thenperformthediscretizationofthecontinuoussystem.Assumestartingattimekwhichisgivenastheinitialcondition,predictthestatesfrom 49

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k+1tok+Np.Theoptimalinputuiscalculatedattimekbysolvingtheoptimalcontrolproblem.Selecttherstelementofuasukandsubstituteitintothedynamicequationtocalculatexk+1,whichisregardedastheinitialconditionofthenextpredictionhorizon.Sincetheinputisoptimizedateachtimestep,nallythebestUwillbeobtained. 5.3MPCDerivationConsideringthedynamicequation: _x=Ax+Buy=Cx+Du(5)Therststepistodicretizethecontinuousequation.Thiscanbecompletedbyusingthec2dfunctioninMatlab.Thediscretizedequationisgivenas: xk+1=Amxk+Bmukyk=Cmxk+Dmuk(5)Substitutexk+1intothestatespaceequationtoobtainxk+2.RepeatthisprocessNptimestoobtainallthepredictedstatesfromxk+1toxk+Np.Thisisgivenasfollows: xk+1=Amxk+Bmukxk+2=A2mxk+AmBmuk+Bmuk+1xk+3=A3mxk+A2mBmuk+AmBmuk+1+Bmuk+2...xk+Np=ANpmxk+ANp)]TJ /F6 7.97 Tf 6.59 0 Td[(1mBmuk+1++AmBmuk+Np)]TJ /F6 7.97 Tf 6.59 0 Td[(2+Bmuk+Np)]TJ /F6 7.97 Tf 6.58 0 Td[(1(5)Putalltheseequationsintomatricestorewritethestatespaceequationas[20] 266666664xk+1xk+2...xk+Np377777775=266666664AmA2m...ANpm377777775xk+266666664Bm0...0AmBmBm...0............ANp)]TJ /F6 7.97 Tf 6.59 0 Td[(1mBmANp)]TJ /F6 7.97 Tf 6.59 0 Td[(2mBm...Bm377777775266666664ukuk+1...uk+Np)]TJ /F6 7.97 Tf 6.59 0 Td[(1377777775(5) 50

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Dene X=266666664xk+1xk+2...xk+Np377777775,U=266666664ukuk+1...uk+Np)]TJ /F6 7.97 Tf 6.58 0 Td[(1377777775(5)andlet Ex=266666664AmA2m...ANpm377777775(5) Fx=266666664Bm0...0AmBmBm...0............ANp)]TJ /F6 7.97 Tf 6.59 0 Td[(1mBmANp)]TJ /F6 7.97 Tf 6.59 0 Td[(2mBm...Bm377777775(5)Nowthestatespaceequationisrewrittenas X=Exxk+FxU(5)Inasimilarway,itiseasytoformtheexpressionfortheoutputstatespaceequation.Itcanbedonebycalculatingxk+1toxk+Npandsubstitutingintothestatespaceequationtoformtheoutputvector,whichisgivenas: 266666664ykyk+1...yk+Np)]TJ /F6 7.97 Tf 6.59 0 Td[(1377777775=266666664CAmCA2m...CANpm377777775xk+266666664CBm0...0CAmBmCBm...0............CANp)]TJ /F6 7.97 Tf 6.59 0 Td[(1mBmCANp)]TJ /F6 7.97 Tf 6.58 0 Td[(2mBm...CBm377777775266666664ukuk+1...uk+Np)]TJ /F6 7.97 Tf 6.59 0 Td[(1377777775(5)Thereforeequation(5-9)canberewrittenas Y=Eyxk+FyU(5) 51

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Nowitisreadytosolvetheoptimalproblem.Thecostfunctionisdesigneddependingonwhattominimize.Ifitisrequiredtominimizetheerrorbetweentheactualoutputandthedesiredoutput,thenthecostfunctionlookslike: J=1 2(NpXs=0jjyk+s)]TJ /F5 11.955 Tf 11.95 0 Td[(rk+sjj2Q+Np)]TJ /F6 7.97 Tf 6.58 0 Td[(1Xs=0jjukjj2P)(5)wherersisthediscretizationofthedesiredtrajectoryr(t)inthecontinuousdomain.Ifwedene ek+s=yk+s)]TJ /F5 11.955 Tf 11.96 0 Td[(rk+s(5)thentheerrormatrixcanbeobtainedas e=266666664yk)]TJ /F5 11.955 Tf 11.96 0 Td[(rkyk+1)]TJ /F5 11.955 Tf 11.96 0 Td[(rk+1...yk+Np)]TJ /F6 7.97 Tf 6.59 0 Td[(1)]TJ /F5 11.955 Tf 11.96 0 Td[(rk+Np)]TJ /F6 7.97 Tf 6.59 0 Td[(1377777775=Y)]TJ /F5 11.955 Tf 11.95 0 Td[(R(5)Nowequation(5-11)canberewrittenas: J=1 2[Eyxk+FyU)]TJ /F5 11.955 Tf 11.95 0 Td[(R]TQ[Eyxk+FyU)]TJ /F5 11.955 Tf 11.96 0 Td[(R]+1 2UTPU(5)whereQandPareweightingfunctions.TheoptimalproblemcanbesolvedbytakingtherstderivativeofJwithrespecttoUandmakingitequaltozero: @J @U=0(5)ThisyieldstoanequationcontainingUandxk.Therefore,theoptimizedinputUcouldbeexpressedbytheinitialstatexkas U=(FTyQF+P))]TJ /F6 7.97 Tf 6.59 0 Td[(1(FTyQR)]TJ /F5 11.955 Tf 11.96 0 Td[(RTyQEyxk)(5) 52

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Sincexkistheinitialstatewhichisgiven,theoptimizedinputvectorUattimekisobtainedbyplugginginthevalueofxk.ThentaketherstelementofU,whichisukoutofthevector: uk=[10...0]U(5)Substitutethevalueofukbackintoequation(5-2)andtogetherwiththevalueofxk,itiseasytocalculatethevalueofxk+1.Thenusexk+1asthenewinitialconditiontorepeattheprocessabovetoobtainuk+1.AfterrepeatingtheprocessforNtimes(Nisdenedpreviously),thebestinputUwhichisoptimizedateachtimestepwillbeobtained. 5.4ChapterConclusionInthischapter,thebenets,introduction,andderivationofMPCisdiscussedindetail.Nowitisreadytoapplythiscontrolmethodtothehybridturbochargersystemtoachievethedesiredgoal. 53

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CHAPTER6MODELPREDICTIVECONTROLOFHYBRIDTURBOCHARGER 6.1ModelReductionInthischapter,theMPCwillbeappliedtothehybridturbochargersystem.Asmentionedatthebeginningofchapter3,theturbochargedSIenginemodelcontains11states,whichistoomanyforMPC.Therefore,modelsimplicationisnecessary.Accordingtopreviousresearches,somestatesdonothavesignicantinuenceonthesystemperformancesoitisreasonabletohavethemtruncated.[17]hasproposedareducedenginemodelwith5states.Therefore,thesimplestproposedmodelforthehybridturbochargerconsistsof6statestogetherwiththestatesofthemotor,whichisgivenasfollows: _!=1 J(ktI)]TJ /F5 11.955 Tf 11.95 0 Td[(b!)_I=1 L()]TJ /F5 11.955 Tf 9.3 0 Td[(RI+V)]TJ /F5 11.955 Tf 11.95 0 Td[(ke!)_pc=RTc Vc(_mc(!,pc))]TJ /F4 11.955 Tf 15.2 0 Td[(_mic(pic,pc))_pic=RTic Vic(_mic(pic,pc))]TJ /F4 11.955 Tf 15.2 0 Td[(_mth(pic,pim))_pim=RTic Vim(_mth(pic,pim))]TJ /F4 11.955 Tf 15.19 0 Td[(_mac(pim))_pem=RTem Vem(_mem(pim))]TJ /F4 11.955 Tf 15.19 0 Td[(_mt(pem,pt))]TJ /F4 11.955 Tf 15.2 0 Td[(_mwg(pt,pem))(6) 6.2ModelLinearizionAccordingtothereducedmodel,allthemassowratefunctionsarenonlinearinthestates.SincethecontrolmethodusedinthisthesisisjustlinearMPC,itisnecessarytolinearizethemodel.Beforethelinearizion,someparametersneedtobesettoconstants. Tc=330K,Tic=302K,Tem=1264Kpt=149kPa,=30,ug=0.7(6) 54

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Linearizioniscompletedaroundtheequilibriumpoint,whichisobtainedbyequalizingallthedifferentialequationstozero. 0=1 J(ktI)]TJ /F5 11.955 Tf 11.96 0 Td[(b!)0=1 L()]TJ /F5 11.955 Tf 9.29 0 Td[(RI+V)]TJ /F5 11.955 Tf 11.96 0 Td[(ke!)0=RTc Vc(_mc(!,pc))]TJ /F4 11.955 Tf 15.19 0 Td[(_mic(pic,pc))0=RTic Vic(_mic(pic,pc))]TJ /F4 11.955 Tf 15.19 0 Td[(_mth(pic,pim))0=RTic Vim(_mth(pic,pim))]TJ /F4 11.955 Tf 15.2 0 Td[(_mac(pim))0=RTem Vem(_mem(pim))]TJ /F4 11.955 Tf 15.2 0 Td[(_mt(pem,pt))]TJ /F4 11.955 Tf 15.19 0 Td[(_mwg(pt,pem))(6)Substitutealltheconstantsintotheequationsandsolveforthesolution.Theequilibriumpointisobtainedas: 2666666666666664!Ipcpicpimpem3777777777777775=26666666666666649628.248.8124.1113.773.4125.73777777777777775(6)Thelinearizedmodelisgivenas: _!=)]TJ /F10 11.955 Tf 9.3 0 Td[(!+200I_I=)]TJ /F4 11.955 Tf 9.3 0 Td[(0.01!)]TJ /F4 11.955 Tf 11.95 0 Td[(10I+10V_pc=5.278pic)]TJ /F4 11.955 Tf 11.96 0 Td[(7.238pc)]TJ /F4 11.955 Tf 11.95 0 Td[(1.185!+224.9_pic=11.866pc)]TJ /F4 11.955 Tf 11.96 0 Td[(12.6pic)]TJ /F4 11.955 Tf 11.95 0 Td[(6.134+294.4_pim=7.321pic)]TJ /F4 11.955 Tf 11.96 0 Td[(0.7274pim+6.14)]TJ /F4 11.955 Tf 11.95 0 Td[(178.4_pem=2.766pim)]TJ /F4 11.955 Tf 11.96 0 Td[(3.864pem)]TJ /F4 11.955 Tf 11.95 0 Td[(3.453uwg+255.9(6) 55

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Inequation(6-5),thebatteryvoltageVandthewastegateopeninguwgaretheinputstothesystemu.Thethrottleangleandalltheconstantsintheequationareconsideredtobethemeasureddisturbanceumd.Thenitisnowpossibletorewriteequation(6-5)instatespaceformas 2666666666666664_!_I_pc_pic_pim_pem3777777777777775=2666666666666664)]TJ /F4 11.955 Tf 9.3 0 Td[(12000000)]TJ /F4 11.955 Tf 9.3 0 Td[(0.01)]TJ /F4 11.955 Tf 9.29 0 Td[(100000)]TJ /F4 11.955 Tf 9.3 0 Td[(1.1850)]TJ /F4 11.955 Tf 9.3 0 Td[(7.238)]TJ /F4 11.955 Tf 9.3 0 Td[(5.278000011.866)]TJ /F4 11.955 Tf 9.3 0 Td[(12.6000000.732)]TJ /F4 11.955 Tf 9.3 0 Td[(0.727000002.766)]TJ /F4 11.955 Tf 9.3 0 Td[(3.86437777777777777752666666666666664!Ipcpicpimpem3777777777777775+266666666666666400100000000)]TJ /F4 11.955 Tf 9.3 0 Td[(3.4533777777777777775264Vuwg375+26666666666666640000224.90294.4)]TJ /F4 11.955 Tf 9.3 0 Td[(6.134)]TJ /F4 11.955 Tf 9.3 0 Td[(178.46.14355.9037777777777777752641375(6)Theoutputofthesystemisthefuelmassow_mfuelwhichisgivenasequation(3-18)and(3-21),andtheenginetorqueMe,whichisgivenasequation(3-22)and(3-23).Thesetwoequationsarealsononlinearinstates,sotheyneedtobelinearizedtoo.Aexpressionfortheairmassowintothecylinderlinearinthestatepimisgivenas[21] _mac=(a0pim+a1)VdN 60RTimnr(6)wherea0anda1areparameterstobeestimatedbyusingthelsqcurvetequationinMatlab.ThevalidationofthelinearizedmodelisshowninFigure6-1. 56

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Figure6-1. Validationoflinearizedmassowintothecylinder HereassumethattheenginespeedisconstantN=3000rpmandtheintakemanifoldtemperatureisconstantTim=302K.Thentheairmassowintothecylindercanbeexpressedlinearlyinthestatepim,soisthefuelmassowratemfuel,givenas _mfuel=k1pim+k2(6)Theotheroutputofthesystemistheenginetorque,givenas Wig=Vd_mfuelQhv60 N2 VdeWp=Vd(pem)]TJ /F5 11.955 Tf 11.95 0 Td[(pim)Wf=Vd[0.97+0.15(N 1000)+0.05(N 1000)2]Me=Wig)]TJ /F5 11.955 Tf 11.96 0 Td[(Wp)]TJ /F5 11.955 Tf 11.96 0 Td[(Wf 2nr(6)Fortheequationtobelinearinstatespimandpem,thesameassumptionhastobemade,thatis,N=3000.Moreover,setthecombustionefciencyetobeaconstant0.3469.Thustheenginetorqueisabletobeexpressedlinearlyinstatespimandpem,whichisgivenas: Me=k3pim+k4pem+k5(6) 57

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Figure3-2showsthevalidationofthelinearenginetorquemodel. Figure6-2. Validationoflinearizedenginetorquemodel Inequations(6-8)and(6-10),k1tok5areallconstantsthatareeasilycalculated.Combiningequations(6-8)and(6-10),itispossibletoformtheoutputmatricesofthesystem,givenas 264_mfuelMe375=26400003.9210)]TJ /F6 7.97 Tf 6.58 0 Td[(5000002.1)]TJ /F4 11.955 Tf 9.3 0 Td[(0.163752666666666666664!Ipcpicpimpem3777777777777775+264)]TJ /F4 11.955 Tf 9.29 0 Td[(3.1310)]TJ /F6 7.97 Tf 6.59 0 Td[(40)]TJ /F4 11.955 Tf 9.3 0 Td[(15.203752641375(6)Nowaccordingtoequations(6-6)and(6-11),itisreadytoformthestatespaceequationforthelinearizedsystemas _x=A0x+B0u+B0mdumdy=C0x+D0mdumd(6) 58

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where x=2666666666666664!Ipcpicpimpem3777777777777775,y=264_mfuelMe375,u=264Vuwg375,umd=2641375(6)Noweverythingisprepared,thusitisreadytoapplyMPCtothesystemaccordingtotheproceduredescribedinChapter5. 6.3MPCImplementationInMatlabTheobjectiveistominimizethefuelconsumptionandthedeviationfromtherequestedenginetorque.Inthisthesis,therequiredenginetorqueMreq=200Nm.Therefore,thecostfunctioncanbeexpressedas: J=(NpXi=1[_mTfuelQf_mfuel+(Me)]TJ /F5 11.955 Tf 11.95 0 Td[(Mreq)TQM(Me)]TJ /F5 11.955 Tf 11.95 0 Td[(Mreq)]+Np)]TJ /F6 7.97 Tf 6.59 0 Td[(1Xi=0(uTQuu)(6)whereQf,QMandQuareweightingfunctionsintheformof Qi=266666664qiIqiI...qiI377777775(6)wherethesubscriptistandsforf,Mandurespectively. 59

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Accordingtotheproceduredescribedinchapter5,therststepisthediscretizationofthecontinuoussystem.ThiscanbecompletedinMatlabbydoing sysC=ss(A0,B1,C0,D1)sysD=c2d(sysC,T)[A,B,C,D]=ssdata(sysD)(6)whereT=0.6sisthesamplingtime.Here,thematricesAandCarethesameastheonesoftheoriginalsystem.TheB1matrixisthecombinationofB0andB0md,andthesamegoeswiththeDmatrix,givenas B1=B0B0md,D1=D0D0md(6)wherematrixD0isjust22zeromatrix.Nowthediscretizationcanbeexpressedas xk+1=ADxk+BDuk+BDmduDwgyk=CDxk+DDmduDwg(6)whereAD=ABD=B1(:,1:2)BDmd=B1(:,3:4)CD=CDD=D1(:,3:4)Followingtheproceduredescribedinchapter5,thepredictionstatespaceequationcanbeexpressedas: X=Exxk+FxU+GxUmdY=Eyxk+FyU+GyUmd(6) 60

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whereEx,FxandEyareofthesameformoftheonesdescribedequations(5-6),(5-7)and(5-9)inChapter5.ThemeasureddisturbancetermGxandGyaregivenas Gx=266666664BDmd0...0ADBDmdBmd...0............ANp)]TJ /F6 7.97 Tf 6.58 0 Td[(1DBDmdANp)]TJ /F6 7.97 Tf 6.59 0 Td[(2DBDmd...BDmd377777775(6) Gy=266666664CDBDmdDDdm0...0CDADBDmdCDBmdDdm...0............CDANp)]TJ /F6 7.97 Tf 6.59 0 Td[(1DBDmdCDANp)]TJ /F6 7.97 Tf 6.59 0 Td[(2DBDmd...CDBDmdDdm377777775(6)Sincetherearetwooutputsofthesystem_mfuelandMewhicharebothinthecostfunction,thereneedstobetwomatricesthatwillseparatethetwooutputs,givenas C1=26666666666410...10377777777775,C2=26666666666401...01377777777775(6)Thusthecostfunctioncanbeexpressednowas J=(C1Eyxk+C1FyU+C1GyUmd)TQf(C1Eyxk+C1FyU+C1GyUmd)+(C1Eyxk+C2FyU+C2GyUmd)]TJ /F5 11.955 Tf 11.96 0 Td[(R)TQM(C1Eyxk+C2FyU+C2GyUmd)]TJ /F5 11.955 Tf 11.96 0 Td[(R)+uTQuu(6) 61

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whereRisthereferencematrix: R=266666664200200...200377777775(6)TaketherstderivativeofJwithrespecttoUandsolvethedifferentialequation: @J @U=0(6)ThenUcanbeexpressedintheinitialstatexk.Sincethesystemhastwoinputs,theoptimizedukshouldbetherstcolumnofthe2byNpmatrixU,givenas: uk=264100...0010...0375U(6)Repeatingtheprocessdescribedinchapter5,itiseasytoobtaintheoptimizedinputU 6.4MPCWithConstraintsInreality,thereshouldbeconstraintsontheinputofthesystem,whichmeansthebatteryvoltageinputandwastegateopeningshouldbebothinareasonablerange.Inthisthesis,theinputconstraintsare 0uv600uwg1(6)Nowitisreadytoaddconstraintstothesystem. 6.4.1OverviewofMPCwithConstraintsWiththesamecostfunction,nowthegoalistosolvetheoptimalproblemsubjecttosomeconstraints,describedas min1 2UTHU+UTFs.jLUb(6) 62

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wherematricesH,F,LandbareformulatedbyC1,C2,Ey,Fy,Gy,Umd,xk,Qfuel,QtorqueandQugivenbefore.ThenextstepistoformthematricesH,F,Landbandapplytheconstraintstothesystem. 6.4.2AddConstraintstotheSystemItisnecessarytorewritetheequation(6-27)toformthematricesLandbinthefollowingway: uv60)]TJ /F5 11.955 Tf 9.3 0 Td[(uv0uwg1)]TJ /F5 11.955 Tf 9.3 0 Td[(uwg0(6)Rewrite(6-29)intomatrixformatas 26666666410)]TJ /F4 11.955 Tf 9.3 0 Td[(10010)]TJ /F4 11.955 Tf 9.3 0 Td[(1377777775264uvuwg375=26666666460010377777775(6)Dene l=26666666410)]TJ /F4 11.955 Tf 9.3 0 Td[(10010)]TJ /F4 11.955 Tf 9.3 0 Td[(1377777775,m=26666666460010377777775(6)NowitisreadytoformtheLandbmatricesas L=266666664ll...l377777775,b=266666664mm...m377777775(6) 63

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ThenextstepistorewritethecostfunctionJtoformthematricesHandF.Basedontheoriginalcostfunction,itiseasytorewriteitinthefollowingform J=1 2UTHU+UTF(6)whereH=FTyCT1QfuelC1Fy+FTyCT2QtorqueC2Fy+QuF=FTyCT1QfuelC1(Eyxk+GyUmd)+FTyCT2QtorqueC2(Eyxk+GyUmd))]TJ /F5 11.955 Tf 11.95 0 Td[(FTyCT2QtorqueRNowusingtheHildrethQuadraticProgrammingproceduredescribedin[19],itisreadytorunthesimulationofthesystemwithconstraints. 6.5SimulationAfterimplementingtheMPCcontroller,itisreadytorunthesimulation.SetthecontrolhorizonandpredicthorizontobethesameNp=Nc=90andrunthesimulationfor90s.Figure6-3andFigure6-4showsthesimulationresults. Figure6-3. Fuelconsumptionafteroptimization TheresultsshowthatthedesignedMPCcontrollerachievesthegoalofminimizingfuelconsumptionandinthemeantimepreventingtheenginetorquefromdeviatingtoomuchfromthedesiredtorque.Figure6-5and6-6showstheoptimizedinputsofthesystem.Itcanbeconcludedthatinthecasethethrottleangleat30andenginespeedat3000rpm,itrequires 64

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Figure6-4. Trackingofthedesiredenginetorque 54.76Vbatteryvoltageand26%wastegateopeningtoobtaintheminimumfuelconsumptionanddeviationfromthedesiredenginetorque. Figure6-5. Therequiredbatteryvoltagetominimizethefuelconsumptionanddeviationfromdesiredenginetorque 6.6ChapterConclusionInthischapter,thehybridturbochargermodeldesignedinChapter4isreducedandlinearizedsothatthelinearMPCcontrollercouldbedesignedandappliedtoit.Thesimulationresultsshowthatthedesignedcontrollerworkswellonthelinearizedsystem 65

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Figure6-6. Therequiredwastegateopeningtominimizethefuelconsumptionanddeviationfromdesiredenginetorque byachievingthegoalofminimizingthefuelconsumptionandandthedeviationoftherealenginetorqueoutput. 66

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CHAPTER7CONCLUSIONANDFUTUREWORKInthisthesis,theSIenginewithahybridturbochargerinstalledisdesignedbybuildingthebatterymodelandeachcomponentoftheturbochargedSIengine.Thecomparisonhasbeenmadebetweenthehybridturbochargerwiththeconventionalturbochargerandthenaturallyaspiratedenginerespectively,demonstratingthetwomainadvantagesofthehybridturbochargerineliminatingtheturbolagandenginedownsizing.ThenthelinearMPCcontrollerisdesignedandappliedtothesimpliedhybridturbochargersystemaftermodellinearizationtorealizetheobjectiveofminimizingthefuelconsumptionanddeviationfromtherequiredenginetorque.Futureworksthatneedstobedonefocusontwoaspects:therstoneistodesignthenonlinearMPCcontrollerwhichcanbeapplieddirectlytothenonlinearhybridturbochargermodelwithoutmodellinearization.Thiswillprovideamoreaccurateresultandcanbeusedinexperimentwithrealhardware.Thesecondone,asmentionedintherstaspect,istoperformthereal-timeMPCbydesigningthenonlinearMPCcontrollerandapplyingittotherealenginemodel,whichhasaverypracticalandimportantsignicance. 67

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REFERENCES [1] OlivierTremblayi,Louis-A.Dessaint,ExperimentalValidationofaBatteryDynamicModelforEVApplications,WorldElectricVehicleJournalVol.3-ISSN2032-6653-2009AVERE [2] RyanC.Kroeze,PhilipT.KreinElectricalBatteryModelforUseinDynamicElectricVehicleSimulations,UniversityofIllinoisatUrbana-ChampaignDepartmentofElectricalandComputerEngineering [3] MinChen,StudentMember,IEEE,andGabrielA.Rincon-Mora,SeniorMember,IEEEAccurateElectricalBatteryModelCapableofPredictingRuntimeandIVPer-formance,IEEETRANSACTIONSONENERGYCONVERSION,VOL.21,NO.2,JUNE2006 [4] OlivierTremblayi,Louis-A.Dessaint,ExperimentalValidationofaBatteryDynamicModelforEVApplications,WorldElectricVehicleJournalVol.3-ISSN2032-6653-2009AVERE [5] LarErikkson,LarsNeilsonModelingofaTurbochargedSIEngine,SAETechnicalPaper2002-01-0374. [6] Guzzella,L.,U.WengerandR.Martin(2000)ICengineDownsizingandPressure-WaveSuperchargingforFuelEconomy,SAETechnicalPaper2000-01-1019. [7] A.Karnik,J.Buckland,andJ.FreudenbergElectronicthrottleandwastegatecontrolforturbochargedgasolineengines,AmericanControlConference,Portland,USA,2005. [8] Muller,Martin,ElbertHendricksandSpencerC.Sorenson(1998).MeanValueModellingofTurbochargedSparkIgnitionEngines.,AESP-1330ModelingofSlandDieselEngines(SAETechnicalPaper980784),125-145. [9] Moraal,PaulandIlyaKolmanovsky(1999).TurbochargerModelingforAutomotiveControlApplications,SAETechnicalPaper1999-01-0908pp.309-322. [10] LarErikksonMeanvaluemodelsforexhaustsystemtemperatures,AnnualReviewsinControl26(2002)129-137 [11] FredrickPetterssonSimulationofaTurboChargedSparkIgnitedEngineLiTH-ISY-EX-3010,DepartmentofElectricalEngineeringofUniversityofLinkoping,2000 [12] JohanBergstrom,JanBrugardSimulationofaTurboChargedSparkIgnitedEngineLiTH-ISY-EX-2081,DepartmentofElectricalEngineeringofUniversityofLinkoping,1999 68

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[13] PerAndersson,LarsErikssonAir-chargeestimationandpredictioninsparkignitioninternalcombustionengines.,InProceedingsoftheAmericanControlConference,pages217221,SanDiego,California,June1999 [14] MrdjanJankovicandSteveW.MagnerAirChargeEstimationinTurbochargedSparkIgnitionEngines,SocietyofAutomotiveEngineers,2004.SAETechnicalPaperNo.2004-01-1366. [15] PerAndersonAirChargeEstimationinTurbochargedSparkIgnitionEngines,LinkopingStudiesinScienceandTechnologyThesisNo.989ISSN0345-7524,2005 [16] MohammadrezaSaeediAMeanValueInternalCombustionEngineModelinMaplesim,DepartmentofMechanicalEngineeringofUniversityofWaterloo,2010 [17] RahulSharma,DraganNesic,Fellow,IEEE,andChrisManzie,Member,IEEEModelReductionofTurbocharged(TC)SparkIgnition(SI)Engines,IEEETRANSACTIONSONCONTROLSYSTEMSTECHNOLOGY,VOL.19,NO.2,MARCH2011 [18] L.Eriksson,S.Frie,C.Onder,andL.GuzzellaControlandoptimizationoftur-bochargedsparkignitedengines,presentedatthe15thTriennialWorldCongr.,Barcelona,Spain,2002 [19] RobertoArgolini,VivianaBloisiOnoptimalcontrolofthewastegateinatur-bochargedSIengine,MastersDegreeProjectStockholm,SwedenJune2007 [20] LiupingWangModelPredictiveControlSystemDesignandImplementationUsingMatlab [21] IdaKristofferssonModelPredictiveControlofaTurbochargedEngine,MasterofScienceThesisPerformedatS3forGeneralMotorsPowertrain,2006 [22] D.AxehillandJ.SjobergAdaptiveCruiseControlforHeavyVehicles,MasterThesis,LinkopingInstituteofTechnology,Linkoping2003. 69

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BIOGRAPHICALSKETCH KangRongreceivedhisBachelorofSciencedegreeinAutomotiveEngineeringin2008inShandongUniversity,Jinan,China.HeisnowpursuinghisMastersofSciencedegreeintheDepartmentofMechanicalandAerospaceEngineeringinUniversityofFlorida.Hisresearchinterestsare:TurobochargedSIenginemodeling,HybridturbochargerdesignandApplicationofnonlinearcontrolandModelPredictiveControl. 70