EGR(废气再循环)经典论文

EGR

Master’sthesis

performedinVehicularSystems

by

FredrikSwartlingRegnr:LiTH-ISY-EX-3692-2005

15thJune2005

GasflowobserverforDieselEngineswith

EGR

Master’sthesis

performedinVehicularSystems,Dept.ofElectricalEngineeringatLink¨opingsuniversitet

byFredrikSwartlingRegnr:LiTH-ISY-EX-3692-2005

Supervisor:MattiasNyberg

ScaniaCVABJesperRitz´enScaniaCVAB

Examiner:AssistantProfessorErikFrisk

Link¨opingsUniversitetLink¨oping,15thJune2005

Avdelning,InstitutionDivision,DepartmentDatumDate

Spr˚akLanguage

󰀁Svenska/Swedish󰀁Engelska/English

ISBN

Serietitelochserienummer

Titleofseries,numbering

󰀁

URLf¨orelektroniskversion

ISSN

Abstract

Duetostricteremissionlegislation,thereisaneedformoreefficientcon-trolofdieselengineswithexhaustgasrecirculation(EGR).Inparticular,itisimportanttoestimatetheair/fuelratioaccuratelyintransients.Thereforeanewenginegasflowmodelhasbeendeveloped.Thismodeldividesthegasintoonepartforoxygenandonepartforinertgases.Basedonthismodelanobserverhasbeendesignedtoestimatetheoxygenconcentrationinthegasgoingintotheengine,whichcanbeusedtocalculatetheair/fuelratio.Thisobservercanalsobeusedtoestimatetheintakemanifoldpressure.Theadvantageofestimatingthepressure,insteadoflowpassfilteringthenoisysignal,isthattheobserverdoesnotcausetimedelay.

Keywords:EGR,MeanValueEngineModel,Observer,Lambda

v

Preface

Thismaster’sthesishasbeenperformedforScaniaCVABatthedivisionofEngineSoftwareandOBD(NEE)duringthespringof2005.

Thesisoutline

Chapter1Ashortintroductiontothebackgroundandtheobjectivesofthis

thesisChapter2Thebasicsofcombustionchemistry

Chapter3ThemodelonwhichtheobserverisbasedisdescribedChapter4Theobserverdesign

Chapter5MeasurementsthatweredoneintheEGRsystemChapter6Conclusionsandfuturework

Acknowledgment

IwouldliketothankmysupervisorsatScania,JesperRitz´enandMattiasNybergandmyexaminerErikFriskformanyinspiringdiscussionsandyoursupport.ThanksalsotoallthehelpfulpeopleatScania,inparticularDavidElfvikandMatsJennischeatforalwaystakingyourtimetohelpmeandanswermyquestionsaboutenginecontrol.

FredrikSwartlingS¨odert¨alje,June2005

vi

Contents

Abstract

PrefaceandAcknowledgment1

Introduction

1.1Background..........................1.2Objectives...........................1.3Methods............................2

CombustionChemistry

2.1StoichiometricCombustion..................2.2Definitionofλtrue......................2.3DerivationanddefinitionofλO2...............3

Enginemodeling

3.1Introduction..........................3.2Choiceofmodelstates....................3.3Modelstructure......

..................3.3.1Compressor......................3.3.2IntakeManifold....................3.3.3Combustion......................3.3.4ExhaustManifold...................3.3.5EGR.........................3.3.6Turbine........................3.3.7ExhaustSystem....................3.3.8Turbocharger...

..................4

Observerdesign

4.1PropertiesoftheObservedSystem..............4.2DesignMethod........................4.3CalculatingNoiseMatrices....

..............4.3.1CalculatingR.....................4.3.2CalculatingQ.......

..............

vii

vvi112233447799101111121213151517181920

4.4

Observerdesignscomparisons................4.4.1Evaluatingtheneedformultiplelinearizations...4.4.2EvaluatingthepossibilitytocalculateKoff-line...4.5

Evaluation...........................4.5.1Comparisonwithlowpassfiltering.........4.5.2Evaluationofλobserver.............

..5

ValidationofEGRflow

5.1Introduction..........................5.2TheCatalyticConverterExperiment

.............5.2.1TheoreticalBackground...............5.2.2ExperimentalSetup..................5.2.3Results........................5.3Conclusion.............

...........

.

.

6

ConclusionsandFutureWork

6.1Conclusions..........................6.2Futurework..........................

ReferencesNotation

ADerivationofλtrue

viii

23232424242729292929303031333333353739

Chapter1

Introduction

1.1Background

Duetostricteremissionlegislationforheavydutytrucks,manufacturershavecomeupwithnewmethodstoreduceemissions.Onepopularmethodisexhaustgasrecirculation(EGR).

Exhaust Gas Recirculation󰀀

Intake Manifold󰀀Exhaust Manifold󰀀Figure1.1:OverviewofEGRsystem

Thebasicideawithexhaustgasrecirculationistoleadsomeoftheex-haustgasbackintotheengine,asshowninFigure1.1.ThislowersthecombustiontemperatureandleadstoreducedNOxemissionssinceNOxpro-ductioniscloselyrelatedtothepeaktemperatureofthecombustion.Thecombustiontemperaturewillbeloweredbecausetherecirculatedexhaustgas

1

2Introduction

Chapter2

CombustionChemistry

Whendecidinghowmuchfueltoinjectintheengineitisimportanttoknowhowmuchairthereisavailable.Thischapterisashortresumeofthechem-istryofthecombustion,oldwaysofkeepingtrackoftheair/fuelratio,andintheendaproposalofhowtheair/fuelratiocouldbedefinedinawaythatsuitsEGRenginesbetter.

2.1StoichiometricCombustion

Duringinternalcombustion,fuelisburntinthepresenceoftheoxygenintheair,resultinginwaterandcarbondioxideasshowninEq.2.1[1].󰀕b

CaHb+a+

a,

2

󰀕b

H2O+3.773a+

whichshowstherelativeamountof

carboninthefuel.TobalanceEq.2.1,theamountoffuelandairgoingintothereactionhastobeinbalance.Hereairissupposedtohavethecomposition(O2+3.773N2).Whenthisbalancebetweenthefuelmassandtheairmassisachieved,theair/fuelproportionisstoichiometric.ThestoichiometricrelationoffuelandairinEq.2.1isderivedinEq.2.2.

󰀗A

4)(mO2

+3.773mN2)

󰀔

isaround

14.7,i.e.themassoftheairhastobe14.7timeslargerthanthemassofthefuelforthereactiontobebalanced.

Fs

3

4Chapter2.CombustionChemistry

m˙fuel

󰀓A

1−EGR%

EGR%=

m˙egr

(2.4)

m˙fuel

Fs

isthestoichiometricrelationbetweenoxygenandfuel.m˙im,O2

istheoxygenpartoftheflowintotheengine.

󰀗O

4)mO2

󰀔

󰀓O

2.3.DerivationanddefinitionofλO2

5

6

Chapter3

Enginemodeling

3.1Introduction

Inthischapterthemodelthatwillbeusedfortheobserverdesignwillbedescribed.Themodelisanextendedversionofagasflowmodeldevelopedin[5],[6]and[7].Figure3.1andTable3.1showamodeloverviewandexplainthemodel’sinputsignals.

u_egr󰀀W_egr󰀀W_trb󰀀W_eng,in󰀀W_eng,out󰀀W_es󰀀Intake󰀀Manifold󰀀Exhaust󰀀Manifold󰀀u_vgt󰀀Turbine󰀀Exhaust󰀀System󰀀T_im󰀀Turbine shaft󰀀N_eng, delta󰀀T_amb󰀀,󰀀p_amb󰀀

Compressor󰀀W_cmp󰀀Figure3.1:Modelwithinputsandmassflows

7

8Chapter3.Enginemodeling

NengEnginespeed[rpm]

δInjectedfuel

[kg/stroke]TimIntakemanifoldtemperature[K]pambAmbientpressure[Pa]TambAmbienttemperature[K]uegrEGRvalveposition[V]uvgtVGTvaneposition[V]

3.3.Modelstructure9

pim,O2pim,inertpem,O2pem,inertpesntrbIntakemanifoldoxygenpressureIntakemanifoldinertgaspressureExhaustmanifoldoxygenpressureExhaustmanifoldinertgaspressureExhaustsystempressureTurbinespeed[Pa][Pa][Pa][Pa][Pa][rpm]

pamb

,ntrb

󰀏

(3.1)

TheflowcanbedividedintoanoxygenandaninertpartasinEq.3.2and3.3sincethecompositionofpureairiswellknown.Themassoftheoxygenis23%ofthetotalairmass.

Wcmp,O2=0.23Wcmp,totWcmp,inert=0.77Wcmp,tot

(3.2)(3.3)

3.3.2IntakeManifold

Thestateequationforthepressureinallcontrolvolumesarederivedfromtheidealgaslaw.InEq.3.4itisassumedthatallpressurechangescomefromthechangesinmass,notintemperature.

p˙=

RT

MV

m˙

(3.4)

󰀐istheuniversalgasconstant,MthemolecularweightandRisagaswhereR

specificconstantthatdependsonmassofthemolecules.ApplyingEq.3.4totheintakemanifoldgivesthefollowingequationsforp˙im,O2andp˙im,inert:

p˙im,O2=

RO2Tim

10Chapter3.Enginemodeling

(Wcmp,inert+Wegr,inert−Weng,in,inert)(3.6)Vim

where

pim,tot=pim,inert+pim,O2

3.3.3Combustion

Thevolumeflowofairintotheengineis

VdNeng

120RimTim

ηvolismappedfrommeasurementdatawithaxesasinEq.3.9.

ηvol=fηvol󰀗

Npeng,

im

pO2V

mm˙tot

tot=

pO2V

m˙tot=

RinertT

pO2Rinert

pim,O2Rinert+pim,inertRWO2

eng,in,totWeng,in,inert=

pim,inertRO2

120

(3.7)

(3.8)

(3.11)

(3.13)

3.3.Modelstructure11

F

󰀏

,0

s

󰀏

(3.14)

Themassoftheinertgasthatgoesoutoftheengineisthemassoftheinertgasthatgoesintotheengineplusthefuelmassandtheburnedmassoftheoxygen,3.15.

󰀗󰀗

O

Weng,out,inert=Weng,in,inert+Wfuel+minWfuel

cp,exh(Weng,in+Wfuel)

(3.16)

3.3.4ExhaustManifold

Thepressureintheexhaustmanifold,pem,ismodeledinthesamewayastheintakemanifoldpressure.

p˙em,O2=

RO2Tem

Vem

where

(Weng,out,inert−Wegr,inert−Wtrb,inert)(3.18)pem,tot=pem,inert+pem,O2

(3.19)

3.3.5EGR

ThetotalEGRflowismodeledasacompressibleisentropicflowthrougharestriction[1],Eq.3.20.

󰀗

pempim

Wegr,tot=AegrΨ

TemR

,γe

󰀏=

pem

12Chapter3.Enginemodeling

2γe

󰀑

pem

γe+1

󰀖γe+1

󰀗

󰀖

2

γe+1

pempem

≥

󰀕

2

γe−1

pem

=

2

γe−1

(3.22)

TheactiveareafunctionAegrisamapcalibratedfrommeasurementdata,Eq.3.23.

Aegr=f(uegr)(3.23)Thedivisionoftheflowintotwopartsismadeasdescribedearlier.

Wegr,O2=

pem,O2Rinert

pem,O2Rinert+pem,inertRO2

Wegr,tot(3.25)

3.3.6Turbine

Thetotalflowthroughtheturbineismodeledfromamap,Eq.3.26that

dependsonthespeedoftheturbine,thepositionoftheVGTandthepressureratiobetweenpemandpes.

󰀗pem

Wtrb,tot=fWtrb

pem,O2Rinert+pem,inertRO2

Wtrb,inert=

pem,inertRO2

Wtrb,tot(3.27)

Ves

(Wtrb,O2+Wtrb,inert−Wes)

(3.29)

3.3.Modelstructure13

kesRexhTes

(pes−pamb)

(3.30)

wherekesiscalculatedfrommeasurementdata.

3.3.8Turbocharger

Theturbochargerconsistsofaturbineshaft,aturbineandacompressorthatinflictstorqueontheshaft.Thedynamicsintheturbineshaftcomefromthebuildupofmomentofinertia.Themassisacceleratedbythetorquedifferenceoftheturbineandthecompressor.

ωtrb=

1

ωtrb



wheretheefficiency,ηtrb,ismappedfrommeasurementdata.

󰀗pem

ηtrb=fηtrb

󰀗pim

1−

󰀗

pem

γexh



(3.32)

γair

ηcmpωcmp

wheretheefficiency,ηcmp,ismappedfrommeasurementdata.

󰀗pim

ηcmp=fηcmp

−1



(3.34)

14

Chapter4

Observerdesign

4.1PropertiesoftheObservedSystem

Beforestartingdesigningtheobserverthepropertiesofthesystemfromchap-ter3willbeanalyzed.Twothingsthathastobeclarifiedareifthesystemisstableandifitisobservable.Observabilityisneededfortheobservertobeabletoestimatethestatesfromthemeasuredsignals.Inthisanalysisthesystemhasbeenlinearizedinstationaryoperatingpointscoveringthewholeworkingareaoftheengine.Afterlinearizing,linearcontroltheoryhasbeenappliedtothesystemtounderstandthebehavior.Theassumptionismadethatifstabilityandobservabilitycanbeprovenforalllinearizations,thenonlinearsystemwillbestableandobservableintheworkingarea.

Whatconcernsthestability,thesystemisstableinallthelinearizations.

Figure4.1showsanexampleofapoleplacementat1300rpmandδ=150mg/stroke.Thepolediagramlookssimilarforallstationaryoperatingpoints,withonefastpolesomewherebetween-1500and-100.Thisfastpolecomesfromthepim,O2state.Thecombinationofonefastpoleandseveralslowonesgivesthesystemstiffcharacteristics.Thiscancauseproblemwhensolvingthesystemsdifferentialequationsandthelinearizedmodel’sA-matrixisillconditioned.TheA-matrixcausesproblemslaterinthischapter.

Toanalyzetheobservabilityofthesystemtheobservabilitymatrixiscal-culatedasEq.4.1.Iftherankofthismatrixisfull,thesystemisobservable.



C

CA



(4.1)...

CAn−1

Computingthismatrixforthelinearizationsdoesnotgivefullrank,sothismethodcannotprovethatthesystemisobservable.Howeverthereisreasontobelievethatthefactthattheobservabilitymatrixdoesnothavefullrank

15

16Chapter4.Observerdesign

4.2.DesignMethod17

18Chapter4.Observerdesign

4.3.CalculatingNoiseMatrices19

20Chapter4.Observerdesign

4.3.CalculatingNoiseMatrices21

22Chapter4.Observerdesign

4.4.Observerdesignscomparisons23

1126763024212611723761142433119511111

10.93%1.08%4.50%4.07%20.90%1.05%4.33%3.84%30.82%1.03%4.33%3.82%40.75%0.81%4.50%4.46%50.72%0.83%5.01%4.16%

24Chapter4.Observerdesign

41.44%100.87%200.%500.90%

4.5.Evaluation25

26Chapter4.Observerdesign

4.5.Evaluation27

RairTim

󰀏

(4.14)

Adrawbackwiththeconventionalmethodisthatitusesthedifferentiationofpim,whichisanoisysignal.Anotheroneisthatthemassflowsensoritselfhaslowfrequencynoisethatisimpossibletofilterwithoutloosingtoomuchofthedynamicpropertiesofthesignal.

InFigure4.9theoldwayofcalculatingλiscomparedwiththeobservedλ.Thefigureshows100secondsfromanETC.Theλ-signalcalculatedfromthesensorhasbeenfilteredwitha5Hznoncausallowpassfiltertomakeiteasiertoview,butstilltheappearanceoftheobservedsignalismuchbetter.Unfortunatelythereisanoffseterrorbetweentheobservedλandtheconven-

.3.532.521.510.5002040time[s]6080100λλtrue calculated from mass flow sensorObserved λO2Figure4.9:Lambdacalculationcomparison

tionalλ,andthisderivesfromthedifferentmethodsofcalculatingtheEGRflow.Theoffsetcanberemovedwithcalibration,buttherewillstillbesomecaseswherethetheseflowsaredifferent.Awayofremovingtheuncertainty

28Chapter4.Observerdesign

Chapter5

ValidationofEGRflow

5.1Introduction

Theobservedquantitythatwouldbethemostinterestingtovalidateinthisthesisistheoxygenconcentrationintheintakemanifold,sincethisisthemainpurposeoftheobserver.Unfortunatelythelowtemperatureinthein-takemanifoldmadeitimpossibletogetaconcentrationsensortoworkthere.InsteadfocuswasputonvalidatingtheEGRflowmodelduringtransientssincethisisthemostuncertainpartofthemodel.TheEGRflowmodelhasonlybeenvalidatedinsteadystateearlier.ThereasonwhythedynamicsoftheEGRflowmodelhasnotbeenvalidatedisthattheconventionalmethodformeasuringEGRflowisdesignedforaccuratemeasurementinsteadystateonly.PuttingamassflowsensorintheEGRsystemisnotpossible.Thetemperatureistoohighandmassflowsensorsdonotworkwhenthegasisnotclean.Insteadamoreinnovativemethodwasexamined.TheideawiththismethodistoputacatalyticconverterintheEGRsystemandmeasurethepressuredropoverit.Fromthispressuredroptheflowcanbecalculated.

5.2TheCatalyticConverterExperiment

5.2.1TheoreticalBackground

Theideaofusingacatalyticconvertertoproduceapressuredropwaspro-posedby[4].Theparticularitywithusingacatalyticconverterinsteadofasquaredrestrictionisthatinthecasewiththecatalyticconverter,thepressuredropwillhavealinearrelationwiththemassflowforcertainmassflows.Thisphenomenonisduetothefactthattheconverterconsistsofmultiplepipesthatreducestheturbulenceofthegas.ReducingtheturbulenceisanimportantissueintheEGRsystem,sinceitisaveryturbulentenvironment.

29

30Chapter5.ValidationofEGRflow

5.3.Conclusion31

32Chapter5.ValidationofEGRflow

Chapter6

ConclusionsandFutureWork

6.1Conclusions

Anewenginegasflowmodelhasbeendeveloped.Thismodeldividesthegasintoonepartforoxygenandonepartforinertgases.Basedonthismodel,anobserverhasbeendesignedtoobservetheoxygenconcentrationinthegas.Theobservercanalsobeusedtoestimatethemeasuredpressuresintheintakemanifoldandtheexhaustmanifold.Theadvantageofestimatingmeasurablesignalswithanobserverinsteadofusingalowpassfilter,isthattheobserverusestheknowledgeaboutthesystemtopreservethegooddynamicsofasignalwhilereducingthenoise.Whatconcernsthepressureintheintakemanifoldtheobserverinthisthesisestimatesthissignalwiththesamenoiselevelasa2Hzlowpassfilteredsignalwithoutconsiderabletimedelay.Theobservercanthereforewithadvantagereplacealowpassfilter.Thisisnottruefortheexhaustmanifoldpressureestimation,wherethemodelerroristoobigtocompetewithanormalfilter.

AcriticalissuewiththeobserveristheuncertaintyinthemodeloftheEGRflow.IthasnotbeenpossibletovalidatetheEGRmodelduringtransientbehavior.ApartfromtheuncertaintieswiththeEGRflow,λcalculatedwiththeobserverhaveverygoodproperties.ThefactthatλO2,asdefinedinthisthesis,doesn’tusetheERGflowexplicitlygivesamorestablesignalthantheconventionalone.Thissignalissuitableforenginecontrolpurposes.

6.2Futurework

Thereisstillinterestingworkthatcanbedoneinthisarea.Aboveall,mea-surementdatafromrealtrucksisneededtoseehowwellλO2canbeused

33

34Chapter6.ConclusionsandFutureWork

References

[1]J.B.HeywoodInternalCombustionEngineFundamentals.McGrae-hill,

1988[2]A.Gelb,J.F.KasperJr,R.A.NashJr,C.F.Price,A.A.sutherland

Jr.AppliedOptimalEstimation.MassachusettsInstituteofTechnology,1974[3]H.H.RosenbrockState-spaceandmultivariabletheory

[4]F.Ekstr¨omandB.Andersson.PressureDropofMonolithicCatalytic

Converters,ExperimnetsandModeling.SAE2002WorldCongress,De-trit,Michigan,March2002[5]D.Elfvik.ModellingofadieselenginewithVGTforcontroldesignsim-ulations.Master’sthesisIR-RT-EX-0216,DepartmentofSignals,Sen-sorsandSystems,RoyalInstituteofTechnology,Stockholm,Sweden,July2002[6]J.Ritz´enModellingandfixedstepsimulationofaturbochargeddiesel

engine.Master’sthesisLiTH-ISY-EX-3442,DepartmentofElectricalEngineering,Link¨opingUniversity,Link¨oping,Sweden,June2003[7]C.EricsonMeanvaluemodellingofapoppetvalveEGR-system.Mas-ter’sthesisLiTH-ISY-EX-33,DepartmentofElectricalEngineering,Link¨opingUniversity,Link¨oping,Sweden,June2004[8]P.AnderssonandL.ErikssonObesrverbasedfeedforwardair-fuelcon-trolofturbochargedSI-enginesVehicularSystems,ISY,Link¨opingUni-versity,Link¨oping,Sweden[9]P.AnderssonandL.ErikssonMean-valueobserverforaturbochargedSI-engineVehicularSystems,ISY,Link¨opingUniversity,Link¨oping,Swe-den

35

36

Notation

Table6.1:SymbolsusedinthereportValueDescription

SymbolUnit

37

38Notation

imemesdcmptrbengegrintambexhinertO2totIntakemanifoldExhaustmanifoldExhaustsystem

DisplacementvolumepercylinderCompressorTurbineEngine

EGRsystemIntercoolerAmbientExhaust

InertgasfractionOxygengasfractionAllgas

AppendixA

Derivationofλtrue

󰀀

m󰀀egr󰀀m󰀀egr󰀀,󰀀air󰀀

󰀀

m󰀀cmp󰀀,󰀀air󰀀

󰀀m󰀀exh󰀀 󰀀m󰀀exh󰀀,󰀀air󰀀m󰀀fuel󰀀

FigureA.1:Definitionofmassflows

FigureA.1andTableA.1showsthegasflowsaroundtheengine,includ-ingEGR.Inadditiontothetotalflow,thepartoftheflowthatconsistsofpureair,asdefinedinpreviouschapter,isrepresentedasaseparateflow.Thegasfromthecompressorisalwayspureair,soonlyoneflowisneeded.Eq.A.1andA.2arebasicrelationshipsfortheexhaustgascompositionthatarevalidduringsteadystate.InEq.A.2itisassumedthatallthefuelwillbeburned

39

󰀀

󰀀40AppendixA.Derivationofλtrue

m˙cmp,airm˙egrm˙egr,airm˙exhm˙exh,airm˙fuelAirflowfromcompressor

TotalgasflowthroughEGRAirflowthroughEGR

TotalgasflowleavingcylindersAirflowleavingcylindersFuelmassflow

F

󰀏

s

m˙fuel=m˙egr,air+(λmeas−1)

󰀗

A

m˙exh

(A.3)

CombiningEq.A.1,A.2andA.3givesanexpressionform˙egr,air,whichwill

beusedtoderiveλtrue.

󰀔

˙fuelm˙exh,airFsmm˙egr,air=m˙egr

󰀏

󰀓

(λmeas−1)A=m˙egr

m˙cmp,air+m˙fuel+m˙egr

Fs

m˙cmp,air+m˙fuel+m˙egr

⇔m˙egr,air

󰀗

m˙cmp,air+m˙fuel

󰀔

m˙fuel

Fs

󰀔

m˙fuel

󰀓A

m˙cmp,air+m˙fuel

=

41

m˙cmp,air+m˙fuel

λmeasm˙cmp,air(1+=

)1

)λ+m˙egr(λmeas−1)

=

F

s

meas

(A

󰀓A

m˙cmp,air

=

λmeas−EGR%

42

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cFredrikSwartling󰀊Link¨oping,15thJune2005