Mean Value Engine Model

of a

Heavy Duty Diesel Engine

Jonas Biteus

Vehicular SystemsDepartment of Electrical Engineering

Linkopings universitet, SE-581 83 Linkoping, SwedenWWW: www.vehicular.isy.liu.se

E-mail: biteus@isy.liu.se

May 29 2002Published in December 2004

Avdelning, InstitutionDivision, Department

DatumDate

Sprak

Language

� Svenska/Swedish

� Engelska/English

�

RapporttypReport category

� Licentiatavhandling

� Examensarbete

� C-uppsats

� D-uppsats

� Ovrig rapport

�URL for elektronisk version

ISBN

ISRN

Serietitel och serienummerTitle of series, numbering

ISSN

Titel

Title

ForfattareAuthor

SammanfattningAbstract

NyckelordKeywords

A first implementation of a mean value engine model (MVEM) of a Heavy DutyDiesel (HDD) engine is described in this report. Framework and sub models aredescribed. Where applicable ISO standards are followed. Verification againststatic measurements shows maximum model errors of about 6% for mass flow andinlet/exhaust manifold pressures.

Vehicular Systems,Dept. of Electrical Engineering581 83 Linkoping

Written: May 2002

Published: Dec. 2004

—

LITH-ISY-R-2666

1400-3902

http://www.vehicular.isy.liu.se

Mean Value Engine Model of a Heavy Duty Diesel Engine

Medelvardesmodell av en dieselmotor for tunga lastbilar

Jonas Biteus

×

×

mean value engine model, MVEM

Contents

1 Introduction 7

1.1 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.3 Simulation Environment . . . . . . . . . . . . . . . . . . . . . . . 7

1.4 Name Convention . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.5 Simulation Structure . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.6 Reversible vs. Non Reversible . . . . . . . . . . . . . . . . . . . . 9

1.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2 Standard Sub Models 9

2.1 Control Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2 Heat Exchanger . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3 Variable Restriction . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.4 Quadratic Restriction . . . . . . . . . . . . . . . . . . . . . . . . 10

3 Specific Sub Models 11

3.1 Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.2 Turbo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.3 Intercooler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.4 Inlet Manifold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.5 Combustion Chamber . . . . . . . . . . . . . . . . . . . . . . . . 14

3.6 Exhaust Manifold . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.7 EGR System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.8 Exhaust Brake . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.9 Exhaust Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4 Identification 17

5 Validation 18

5.1 Static Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

5.2 Dynamic Simulation . . . . . . . . . . . . . . . . . . . . . . . . . 18

6 Model Errors and Further Improvements 23

6.1 Further Measurements . . . . . . . . . . . . . . . . . . . . . . . . 24

6.2 Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

References 24

A EGR Valve Angle Model 25

A.1 Experiment and Experimental Setup . . . . . . . . . . . . . . . . 25

A.2 Model Construction . . . . . . . . . . . . . . . . . . . . . . . . . 25

A.3 Identification and Validation . . . . . . . . . . . . . . . . . . . . 26

B Notation 28

C Simulink blocks 30

1 Introduction

1.1 Acknowledgments

This work has been supported by Scania AB, Department of Software and Di-agnostics, Sweden.

1.2 Objectives

The objectives are to construct an accurate model of a HDD engine. The modelshould be able to predict effects of mechanical and/or control system changesin the engine. Primary the model should be used to test and verify OBD (onboard diagnostic) systems.

A framework for the model that supports automatic or semi automatic identi-fication and verification should be implemented.

An object oriented approach should be used to construct the model.

1.3 Simulation Environment

The model is implemented in Simulink/Matlab. The model is to a large extentobject oriented. In simulink, a component library has been created. From thecomponent library the engine model is implemented.

1.4 Name Convention

Components are abbreviated with a two or three lowercase letters subindex. Ifseveral sub indices are required, the second is spelled with a first upper caseletter. When sub indices cannot be used, e.g., Matlab code, every subindex firstletter is upper case.

Control volumes are named after the component upstream, e.g., control volumefi is after the filter restriction.

In appendix B notations used in the model are described.

1.5 Simulation Structure

The model can be described in state variables and flows. From the states incontrol volumes up, i.e., upstream, and down, i.e., downstream, of a component,it is possible to calculate the flow F thru the component. The flow can be dividedinto flow in and out of a component. The nominal flow direction defines up anddown.

By having a strict order of “control volume – component – control volume –component” with flows as connectors, an object oriented system is achieved.

Figure 1 shows a schematic overview of the system including components ab-breviations.

7

im

engOut

em

engIn

tu

fi

icIn/OutcoIn/Outfi

tu eb

eb ep

co

egrIn/OutEgr

eng

co

tu

tb

eng

Exhaust brake Exhaust pipeTurbin

Compressor IntercoolerFilter

Combustion ChamberExhaust manifold Inlet manifold

W,�,�

W,�,�

W,�,� W,�,�

W,�,�

W,�,�

W,�,� W,�,�

W,�,�

M

MM

n

n

Æ

Fig

ure

1:Sc

hem

atic

over

view

ofen

gine

mod

el.

8

1.6 Reversible vs. Non Reversible

During normal non faulty operation, there is no need for reversible systems.Therefore, it is assumed that all flows are positive. Reversible components areconstructed from non reversible with a case system, e.g., if pup < pdown in aquadratic restriction Wreversible = −Wnon reversible where Wx is mass flow [kg/s].

1.7 References

MVEM:s have been implemented before. Several articles and reports describingthe basic ideas are available. Some articles with relevant results are (Guzzellaand Amstutz, 1998) for physical modeling and (Muller, 1998) for regressionanalyze modeling.

At Vehicular Systems at Linkopings universitet, several master’s theses that de-scribe MVEM have been published. Most noticeable are (Brugard and Bergstrom,1999; Pettersson, 2000), available at www.fs.isy.liu.se.

2 Standard Sub Models

In this section the “standard” sub models are described. These models formthe model library.

2.1 Control Volume

The control volume is based on energy- and mass-conservation. State variablesare energy and mass of gas components. The standard volume is implementedwith two components, air and exhaust gas.

The model for a control volume with inlets i and outlets j is

U =∑

i

νi −∑

j

νj − Q Energy balance

mair =∑

i

Wi(1 − χi) −∑

j

Wj(1 − χcv) Mass balance air

mexh =∑

i

Wiχi −∑

j

Wjχcv Mass balance exhaust

m = mair + mexh Total mass

χcv =mexh

mMass fraction

p =RU

V cvPressure

T =U

mcvEnergy – Temp. relation

9

ρ =p

TRDensity

cv = cvAir(1 − χcv) + cvExhχcv

cp = cpAir(1 − χcv) + cpExhχcv

νj = cpWjT ∀j Energy flow outQ = f(·) Heat losses.

The heat losses can be static or dynamic and be positive (energy decreases) ornegative (energy increases).

2.2 Heat Exchanger

The heat exchanger decreases the energy flow. The model is

Tout = Tin − η(Tin − Tsurr)νout = cpUpWTout,

where η is the efficiency of the heat exchanger and Tsurr the surrounding tem-perature.

2.3 Variable Restriction

The variable restriction uses the pressure ratio pdown

pupand mapped area A(u) to

evaluate mass flow. The model is

W = A(u)pup√

TupRup

Ψ(pdown

pup, γup)

Ψ(Π, γ) =

√2γ

γ−1

(Π

2γ − Π

γ+1γ

)if Π ≥

(2

γ+1

) γγ−1

√γ(

2γ+1

) γ+1γ−1

else,

where u is the control signal.

2.4 Quadratic Restriction

The quadratic restriction is based on a quadratic relationship between pres-sure drop and mass flow. It is a simplified version of the variable restriction.Restrictor constant kres depends on area, wallfriction etc. The model is

pup − pdown =kresW

2

ρup

ρup =pup

RupTup.

10

3 Specific Sub Models

The specific sub models used in the engine model are described in this section.For the control volumes, in- and outlet symbols are defined.

3.1 Filter

The filter model should describe the pressure losses inflicted by the air filter.

Restriction

The filter is modeled as a standard restriction with constant kfi.

Filter Control Volume

IN : [ν,W, χ]Tfi

OUT : [ν,W, χ]TcoIn

Qfi = 0.

3.2 Turbo

The turbo is divided into three parts; compressor, turbine and turboshaft.

Two different turbo models have been implemented. The first uses physicalrelations and compressor and turbine efficiency and mass flow maps from themanufacturer. The turbo speed is considered a state variable. However, dueto inaccuracy in maps and disturbances, it was not possible to achieve correctstatic turbo speeds.

The second turbo model is based on the same physical relations but developedwith regression analysis. In this model the turbo speed is considered an input.

To be able to use the compressor and turbine maps the pressure ratios and turbospeed have to be normalized. Normalization is implemented in the simulationlibrary. For more information about the normalization see (Marberg, 1999).

Compressor – Model I

The model is based on thermodynamic energy transformation described in(Guzzella and Amstutz, 1998). Compressor efficiency and mass flow are takenfrom manufacturer data that have been inter- and extrapolated with GT-Powerand algorithms developed by Scania (Marberg, 1999).

11

The model for the compressor is

W = fw(pup

pdown, ntb) (1a)

T = Tup(1 +1η(µ − 1) (1b)

M =WcpUpTup

ηntb(µ − 1)

η = fe(pup

pdown, ntb)

µ =(

pdown

pup

) γup−1γup

νout = cpUpWT.

Compressor – Model II

A second model based on thermodynamic energy transformation but developedwith regression analysis has been implemented. The model is based on relationsdescribed in (Muller, 1998) and implemented on a turbo charged SI engine in(Brugard and Bergstrom, 1999; Pettersson, 2000).

The model for mass flow is

W = k1(1 − pup

pdown) + k2ntb

√1 − pup

pdown+ k3ntb

4

√1 − pup

pdown+ k4ntb,

where k1,2,3,4 are constants. The model for the temperature out is

Tout = s1W2 + s2Wntb + s3n

2tb + s4Tup,

where s1,2,3,4 are constants. Note that these models depends on the same vari-ables as model equation (1a) and (1b).

Compressor Control Volume

IN : [ν,W, χ]TcoOut

OUT : [ν,W, χ]TicIn

Qco = 0.

Turbine – Model I

A model based on thermodynamic energy transformation as described in (Guzzellaand Amstutz, 1998) has been implemented.

Compressor efficiency and mass flow are taken from manufacturer data thathave been inter- and extrapolated with GT-Power and algorithms developed byScania (Marberg, 1999).

12

The turbine model is

W = fw(pup

pdown, ntb)

T = Tup(1 − η(µ − 1))

M =WcpUpTinη

ntu(1 − µ)

η = fe(pup

pdown, ntb)

µ =(

pdown

pup

) γup−1γup

νout = cpUpWT.

Turbine – Model II

The second model is based on thermodynamic energy transformation but de-veloped with regression analysis. The model is based on relations described in(Muller, 1998) and implemented on a turbo charged SI engine in (Brugard andBergstrom, 1999; Pettersson, 2000). It should be noted that this model is basedon similar assumptions as the algorithms developed in (Marberg, 1999).

The model for mass flow is

W =pdown√pup2t1

[−t2 +

√t22 + 4t1

(pup

pdown− t3

)],

where t1,2,3 are constants, found from a least square fit of

pup

pdown= t1

(W√

Tup

pdown

)2

+ t2W√

Tup

pdown+ t3,

w.r.t. t1,2,3.

Due to lack of sensors in the exhaust system, TtuOut is not modeled. However,this is not very important because of the low restrictions down stream theturbine. Note that if an exhaust brake is used, this assumption does not hold.

Turbine Volume

IN : [ν,W, χ]TtuOut

OUT : [ν,W, χ]Teb

Qtu = 0.

Turboshaft

Friction is assumed to be included in the turbine efficiency mapping. The modelfor the turboshaft is

Jtbdntb

dt

2π

60= Mtu − Mco − Mfr,

13

where Mfr is assumed zero.

3.3 Intercooler

The intercooler model should describe the heat exchange and restriction in theintercooler.

Restriction

Modeled as quadratic restriction with constant kic.

Heat Exchanger

Modeled as a heat exchanger with constant ηic. It is assumed that TicSurr isconstant.

3.4 Inlet Manifold

The inlet manifold collects gases from the intercooler and the EGR (exhaustgas recycling) system. The walls of the inlet manifold have a relatively hightemperature which will lead to negative heat losses. In this first implementationthe heat losses are assumed zero.

Control Volume

IN : [ν,W, χ]TicOut, [ν,W, χ]TegrOut

OUT : [ν,W, χ]TengIn

Qim = 0.

3.5 Combustion Chamber

The combustion chamber models the mean value of the in cylinder combustion.Most notable is that fuel is added, temperature increased, and the amount ofexhaust gas increased.

The theoretic volumetric efficiency is modeled with ηvolEm.

14

The model for the combustion chamber is

Wout = Win + Wfuel

Win =ρupVdncylNeng

2 ∗ 60ηvolEmηvol

Wfuel =δncyl

2 ∗ 60Neng

Wair = Win(1 − χup)

λ =Wair/Wfuel

(A/F )s

T = Tup + ftemp(δ,WengIn)

χout =

{1 if λ < 1λ−1 else

νout = cpTWout

ρup =pup

RupTup

ηvolEm =rc

rc − 1− 1

γup(rc − 1)

(pdown

pup+ γup − 1

)

ηvol = fvol(Neng,pdown

pup)

cp = cpAir(1 − χout) + cpExhχout

cv = cvAir(1 − χout) + cvExhχout.

Note, in the first implementation of the model, it is assumed that χout = 1.

3.6 Exhaust Manifold

The exhaust manifold divides gases to turbine and EGR system. The wallsof the exhaust manifold have a relative low temperature which will lead toheat losses. In this first implementation the heat losses are assumed zero. Aregression model for the energy losses in the exhaust manifold is described in(Muller, 1998). However, this model has not been implemented.

IN : [ν,W, χ]TengOut

OUT : [ν,W, χ]TtuIn, [ν,W, χ]TegrIn

Qem = 0.

3.7 EGR System

The model of the EGR system has not been validated. To be able to validatethe system, more measurements are needed, see Section 6. In this section twodifferent types of EGR systems are considered. Both uses a EGR variablerestriction to restrict EGR flow and EGR cooler to gain a high density EGRflow. Additional pressure drop is created with a throttle or a venturi.

15

EGR Variable Restriction

The EGR valve is modeled as a variable restriction. In the model it is assumedthat EGR valve angle, αegr, can be predicted from EGR control signal, uegr. Inthe fault free case this is correct, since pneumatic actuators are designed to belinear, i.e., αegr = f(legr) and legr ∝ uegr. However, in some cases hysterics cancause large deviation from linearity. In Appendix A the linearity of the actuatoris analyzed.

EGR Cooler

The EGR cooler is modeled as a standard heat exchanger. The constant is ηegr

and it is assumed that TegrSurr is constant.

EGR throttle

The EGR throttle is used to maintain a positive pressure drop over the EGR.The throttle is positioned between the intercooler and inlet manifold.

The throttle is modeled as a variable restriction.

Venturi

The venturi system is used to maintain a positive pressure drop over the EGR.The EGR flow is added to the main flow at the minimum area of the venturi.At this point the pressure is at minimum. After this point a diffusor is used torecover the pressure.

It has not been possible to find a working model for the venturi system. Follow-ing is a suggestion of a venturi model used to model pdownEgr, i.e., the pressuredownstream the EGR variable restriction, used to predict Wegr with the modelfor the EGR variable restriction. See Fig. 2 for a schematic overview of theventuri system with EGR.

Wout

downppt

egrWpdownEgr

pup

W

Figure 2: Schematic overview of a venturi system.

16

If non choked flow is assumed, a venturi can be modeled as

W = Apup√

TupRup

Ψ[pt

pup, γup] (2)

Ψ[Π, γ] =√

2γ

γ − 1

(Π

2γ − Π

γ+1γ

).

If it is assumed that the venturi can be model as a quadratic restriction, W canbe calculated

W =

√ρpup − pdown

k.

Further assume that Wegr << W , then (2) can be solved numerically for pt

pt = f(pup,Wegr, Tup).

Now pt can be used as pdownEgr and a model for the venturi-EGR system hasbeen achieved.

3.8 Exhaust Brake

Exhaust Brake Variable Restriction

The exhaust brake has not been implemented but can be modeled as a variablerestriction. For a good implementation it is necessary to model the temperaturedrop over the turbine.

Exhaust Brake Volume

IN : [ν,W, χ]Teb

OUT : [ν,W, χ]Tep

Qeb = 0.

3.9 Exhaust Pipe

Exhaust Pipe Restriction

The exhaust pipe is modeled as a quadratic restriction with constant kep.

4 Identification

To identify the sub models least square optimization of has been used. The dataused is from the static mapping of a HDD engine without EGR.

17

5 Validation

The validation has only been performed against static data, due to the problemswith accurate EGR models. The data used is from the static mapping of a HDDengine without EGR. Figure 3 shows the static points used for simulation andidentification. Simulation of the points marked with “o” failed due to simulationproblems.

In these simulations the second turbo model has been used. Note that in datato this model are Neng, ntb, and δ.

5.1 Static Validation

Simulations have been performed for the major part of the stationary points.Figure 4, 6, and 8 shows simulated and reference values for Wfi, pim, and pem

in static points. Relative error is shown in Fig. 5, 7, and 9. As can be seen inthe figures, the maximum relative error is about 6%.

5.2 Dynamic Simulation

The model has not been validated against dynamic measurements.

Figure 10, 11 and 12 shows step responses for the model. Note that these figuresare only presented to show that the system works for dynamic references. Thereferences are Neng, δ, and ntb. To obtain stability, Neng and ntb are low passfiltered.

1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 20000

500

1000

1500

2000

2500

Neng

[rpm]

Men

g [Nm

]

Not simulated

Figure 3: Static measurements points in Neng and Meng.

18

0500

10001500

20002500

1000

1200

1400

1600

1800

20000.1

0.2

0.3

0.4

0.5

0.6

Meng

[Nm]Neng

[rpm]

Wfi [k

g/s]

SimulationReference

Figure 4: Measured and simulated Wfi.

1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 20000

1

2

3

4

5

6

Neng

[rpm]

Rel

. err

or (

%)

0 500 1000 1500 2000 25000

1

2

3

4

5

6

Meng

[Nm]

Rel

. err

or (

%)

Figure 5: Relative error for simulated Wfi sorted w.r.t. Neng and Meng respec-tively.

19

0500

10001500

20002500

1000

1200

1400

1600

1800

20001

1.5

2

2.5

3

Meng

[Nm]Neng

[rpm]

p im [1

05 Pa]

SimulationReference

Figure 6: Measured and simulated pim.

1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 20000

1

2

3

4

5

6

Neng

[rpm]

Rel

. err

or (

%)

0 500 1000 1500 2000 25000

1

2

3

4

5

6

Meng

[Nm]

Rel

. err

or (

%)

Figure 7: Relative error for simulated pim sorted w.r.t. Neng and Meng respec-tively.

20

0500

10001500

20002500

1000

1200

1400

1600

1800

20001

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

Meng

[Nm]Neng

[rpm]

p im [1

05 Pa]

SimulationReference

Figure 8: Measured and simulated pem.

1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 20000

2

4

6

8

Neng

[rpm]

Rel

. err

or (

%)

0 500 1000 1500 2000 25000

2

4

6

8

Meng

[Nm]

Rel

. err

or (

%)

Figure 9: Relative error for simulated pem sorted w.r.t. Neng and Meng respec-tively.

21

0 1 2 3 4 5 6 7 80.98

0.99

1

1.01p fi [1

05 Pa]

reference

0 1 2 3 4 5 6 7 81

1.5

2

2.5

3

p im [1

05 Pa]

reference

0 1 2 3 4 5 6 7 81

2

3

4

p em [1

05 Pa]

t [s]

reference

Figure 10: Step response for pfi, pim and pem.

0 1 2 3 4 5 6 7 80.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

W [k

g/s]

t [s]

fiturefer

Figure 11: Step response for Wfi.

22

0 1 2 3 4 5 6 7 81200

1400

1600

1800

2000

n eng [r

pm]

0 1 2 3 4 5 6 7 80

0.5

1

1.5

2x 10

−4

δ [m

g/st

roke

]

0 1 2 3 4 5 6 7 86

7

8

9x 10

4

t [s]

n tb [r

pm]

Figure 12: Reference values for the step response.

6 Model Errors and Further Improvements

The most notable model errors and model defects are listed below. Listed arealso suggestions for how these defects can be removed.

EGR: No accurate model of the EGR system has been implemented.

In Section 3.7, an EGR model is described. This model has to be testedand verified during static and dynamic measurements.

Heat losses: Heat losses have not been implemented. The heat losses withlarge impact on the system are the losses in inlet- and exhaust manifolds.The heating of gases in inlet manifold and cooling of gases in exhaustmanifold will impact the dynamic behavior of the system.

In (Muller, 1998) a model for the exhaust manifold heat losses is described.This model can be implemented in the engine model. To validate themodel, dynamic measurements are needed. During a step response thetime constants for the heat losses are visible.

Turbo: The turbo speed is assumed to be an input in the second model.

It seems difficult to implement a good turbo speed model. Note that(Pettersson, 2000) failed in the implementation of dynamic turbo. A suc-cessfull implementation is described in (Muller, 1998).

When performing tests in test cells the turbo speed can be seen as input.If the turbo speed can’t be measured, a solution is to map the turbo speed

23

and use this as input to the model. The turbo dynamics can partly be re-produced with low pass filtering, i.e., time constant found w.r.t. turboshaftinertia.

Low mass flow: For low mass flows the simulations fails.

This is a numerical problem that has to be isolated.

6.1 Further Measurements

For a complete validation of the model, the measurements in Table 1 have tobe performed.

Table 1: Required measurements.Type EGR Description Identified parametersStatic Closed Mapping of engine. kfi, {k, s}co, ttu, {k, η}ic,

ηvol, kep

Static Nominal Mapping of engine. {η,A}egr

Dynamic Closed Step responses. Qim, Qem (Validation: Vx

etc.)Dynamic Nominal Transient cycle. Complete validation

6.2 Sensors

Besides the “standard” sensors the following variables have to be measured.

• ntb – Turbo speed.

• αegr – The true angle of the egr valve. The angle has to be measuredto be able to validate a correct relationship between actuator signal andvalve angle.

From the ECU, δ, α, uegr and sensor data have to be collected.

References

J. Brugard and J. Bergstrom. Modeling of a turbo charged spark ignited engine.Master’s thesis, Linkopings universitet, SE-581 83 Linkoping, 1999.

I. Guzzella and A. Amstutz. Control of diesel engines. IEEE Transactions onAutomatic Control, 7:53–, 1998.

J. Marberg. Turbinmappar for GT-powersimulering. Technical Report M17/577,1999. Internal Scania report.

M. Muller. Mean value modelling of turbocharged spark ignition engines. SAE,(980784), 1998.

F. Pettersson. Simulation of a turbo charged spark ignited engine. Master’sthesis, Linkopings universitet, SE-581 83 Linkoping, 2000.

24

A EGR Valve Angle Model

Note: Some parts of this text have been removed due to corporate secretes.

The amount of EGR gases in inlet manifold are predicted with the EGR model.In the model it is assumed that EGR valve angle, αegr, can be predicted fromEGR control signal, uegr. In the fault free case this is correct, since pneumaticactuators are designed to be linear, i.e., αegr = f(legr) and legr ∝ uegr. However,in some cases hysterics can cause large deviation from linearity.

In this section the results from a test of the EGR linearity are presented. Notethat this is only a first experiment and its conclusions are not fully proved.

A.1 Experiment and Experimental Setup

Figure 13 shows a schematic overview of the experimental setup. The EGR valveis moved by the EGR arm. The EGR arm is connected to the EGR actuator.An inductive length sensor is attached to the EGR arm. For relatively smallangles there is a linear relationship between actuator and sensor. The sensor isattached to minimize the angle.

The sensor was not correctly adjusted before experiment. The result of this isthat for large EGR valve angles the sensor give constant values. The limit isabout 49◦, closed valve is x∗∗.

A.2 Model Construction

The model objective is to predict αegr from uegr. Figure 14 shows the trigono-metric problem.

The sensor is linear and l is found from sensor signal yegr,

l = lmin +1

0.32(yegr − min(yegr)).

Minimum lmin = x and maximum lmax = x. The angle β is with law of cosines,

β(l) = arccosa2 + b2 − l2

2ab,

where a = x and b = x. Since minimum αegr = 0 and β(lmin) = x,

αegr(l) = β(l) − x.

Maximum αegr = x. The model for the EGR actuator is

legr(t) = C1uegr(t + d) + C2,

where C1,2 and d are constants. The time delay is introduced to model time lagin the actuator. The time lag d is identified with least square minimization.

Note that the valve is closed for values below x − x%uegr. It is fully open forvalues above x − x%uegr. The effects from this is not in the model. The lowerplot of Fig. 15 shows this effect for low values.

∗∗Corporate secret.

25

αEGR arm

EGR flow

EGR valve

EGR actuatorEGR sensor

Figure 13: Schematic overviewof experimental setup.

αegr

lb

a

β

Figure 14: Trigonometric prob-lem.

A.3 Identification and Validation

A transient cycle is used for identification and validation. Figure 15 shows EGRcontrol signal and measured EGR valve angle. Solid line is EGR control signaland dashed line is measured EGR valve angle. As noted above the sensor islimited to 49◦. Figure 16 shows four different time windows during a transientcycle. Solid lines are measured length. Dashed lines are model prediction. Thetime windows are marked in Fig. 15 with “*”.

The data from time window two is used to identify the model described inSection A.2. The time windows are chosen so that the EGR valve is open duringthe entire time window. All time windows are used to validate the model. Themodel is identified with least square minimization. The time lag is xs.

The model prediction for time window four has a bias fault. The model predic-tion is good for time window two and three.

26

0 200 400 600 800 1000 1200 1400 1600 18000

20

40

60

80

100α [°]u

egr [%]

120 125 130 135 140 145 1500

10

20

30

40

50

t [s]

Figure 15: Solid line is EGR control signal and dashed line is measured EGRvalve angle. The time windows used to identify the model are marked with “*”.

420 430 440 450 460 470 480 490 5000

20

40α [°]α estimate

705 710 715 720 725 730 7350

20

40

1535 1540 1545 1550 1555 1560 1565 15700

20

40

1640 1660 1680 1700 1720 1740 17600

20

40

t [s]

Figure 16: EGR valve angle. Measured and simulated.

27

B Notation

In the following table notations used in the model is described. See Table 2 fordescription of abbreviations.

Symbol Value Description UnitPHYSICAL PROPERTIES

component x ∈ {air, exh}cpX Con Spec. heat capacity, constant pressure J/(kgK)cvX Con Spec. heat capacity, constant volume J/(kgK)Rx cpX − cvX Gas constant J/(kgK)γx cpX/cvX - -

FLOWF [W, ν, χ]T Flow between control volumes -W Var Mass flow kg/sν Var Energy flow J/sχ Var Amount of exhaust gas [0,1]

CONTROL VOLUMEmair S.Var Mass of air kgmexh S.Var Mass of exhaust gas kgχ Var Amount of exhaust gas -U S.Var Internal energy Jmair Var Change of air mass kg/smexh Var Change of exhaust gas mass kg/s

U Var Change of energy J/sp Var Pressure PaT Var Temperature KV Con Volume m3

Q Var Heat losses WFILTER

kfi Con Restrictor constant Pas2/(m3kg)COMPRESSOR

fw Map Compressor flow kg/sfe Map Compressor efficiency -M Var Compressor moment NmFin Var Flow in to compressor -Fout Var Flow out of compressor -

INTERCOOLERkic Con Restrictor constant Pas2/(m3kg)TicSurr Tamb Cooler temperature Kηic Con Cooler efficiency -

COMBUSTION CHAMBERδ Act Amount of injected fuel kg/strokeα Act Ignition angle radρim Var Density in inlet manifold kg/m3

continued on next page

28

continued from previous page

Symbol Value Description UnitVd Con Displacement volume (1 cylinder) m3

Vcyl Con Cylinder volume (1 cylinder) m3

rc x Compression ratio −ηvolEm Var Theoretic volumetric efficiency −ηvol Map Volumetric efficiency −ftemp Map Temperature increase Kncyl x Number of cylinders −Neng Var Engine speed rpmλeng Var Air/fuel equivalence ratio −(A/F )s Con Stoichiometric air to fuel ratio. −

EGRTegrSurr Con Cooler temperature Kηegr Con Cooler efficiency −Aegr Map Effective area of EGR valve opening m2

uegr Act EGR valve control-signal -αegr Var EGR valve angle radlegr Var Length of egr actuator m

TURBINEfw Map Turbine flow kg/sfe Map Turbine efficiency −M Var Turbine moment NmJtb Con Turbo inertia s2Nmutb Act Turbo variable geometry signal -

EXHAUST PIPEkep Con Restrictor constant Pas2/(m3kg)

Table 2: Abbreviations used in this report.Abbreviation ExplanationAct ActuatorCon ConstantCV Control VolumeECU Electronic Control UnitEGR Exhaust Gas RecirculationHDD Heavy Duty DieselMVEM Mean Value Engine ModelOBD On Board DiagnosticsRPM Revolutions Per MinuteS.Var State variableVar VariableVGT Variable Geometry Turbo-chargerVNT Variable Nozzle Turbine

29

C Simulink blocks

The main parts of the simulink models are included in this appendix. Figure 17shows the top level of the engine model. Figure 18 shows the first layer, itincludes the inlet , see Figure 19, the combustion chamber, see Figure 20, andthe outlet, see Figure 21. The models are collected in a simulink library shownin Figure 22.

NEng

delta

Engine

0

Display

Data Collection

Clock

input.NEng

input.delta

Figure 17: The top level of the simulink model.

30

The

sys

tem

can

be

anal

ysed

in s

tate

san

d flo

ws.

Sx

repr

esen

t Sta

te x

, and

Fx

flow

x.

S =

[p,T

,x]^

TF

= [W

,v,x

]^T

p: P

ress

ure

in v

olym

e [P

a]T

: Tem

pera

ture

in v

olym

e [K

]x:

Am

ount

of e

xhus

t gas

in v

olym

e/flo

w [0

,1]

W: M

assf

low

in fl

ow [k

g/s]

v: E

nerg

yflo

w in

flow

[J/s

]

S,F

:s a

re c

olle

cted

in "

Dat

a C

olle

ctio

n"

OB

S. T

he s

ubm

odel

s ar

e lin

ked

to th

e lib

rary

eng

inem

odel

Lib

Do

not e

dit t

he s

ubm

odel

dire

ctly

. Edi

t thr

ough

the

libra

ry.

Mc

Mt

nTb

Tur

boS

haft

1

0.1s

+1

Tra

nsfe

r F

cn(w

ith in

itial

out

puts

)1

1

0.1s

+1

Tra

nsfe

r F

cn(w

ith in

itial

out

puts

)

SD

own

ntb

SU

p

Tsu

rrIC

Mc

Fou

t

Inta

ke

[SC

o]

ntb

SD

own

SU

p

uTur

b

FIn Mt

Exh

aust

FO

ut

FIn

Nen

g

delta

uAlp

ha

Tsu

rrE

GR

Aeg

r

SU

p

SD

own

Eng

ine/

Egr

SIc

pRef

delta

ref

delta

Bos

st p

ress

ure

cont

roll

[nT

b]

[nE

ng]

0

par.

TS

urrI

c

inpu

t.TS

urrE

gr

inpu

t.pC

o

inpu

t.nT

b

inpu

t.Alp

ha

inpu

t.AE

gr

inpu

t.pA

mb

0

inpu

t.TA

mb

2

delta1

NE

ng

Figure 18: The first layer of the engine model. It includes the inlet, combustion,and finally outlet parts.

31

2

Fout

1

McSDown

SUp

Tsurr

Fout

Fin

Non−Rev Restrictor and HEInter cooler

SDown

SUp

F

Non−Rev Restrictionfi restriction

SDown

SUp

ntb

Mc

FcompOut

FcompIn

Compressor Regression

Fin1

Fout1

S

2−comp volyme 1in/1out1co, compressor volyme

Fin1

Fout1

S

2−comp volyme 1in/1outfi, filter volyme

[Mc]

[FIcOut]

[SCo]

[FIcIn]

[FCoOut]

[SFi]

[FCoIn]

[FFi]

4

TsurrIC

3

SUp

2

ntb

1

SDown

Figure 19: The inlet side of the engine-model.

2

SDown

1

SUp

SQ

heat losses1

SQ

heat losses

SDown

SUp

delta

N

uAlpha

FengOut

FengIn

Combustion chamber

Fin1

Fin2

Fout1

Q

S

2−comp volyme 2in/1outinlet manifold

Fin1

Fout1

Fout2

Q

S

2−comp volyme 1in/2outexhaust manfold

[SEm]

[FEngIn]

[SIm]

[FEngOut]

[0,0,0]

[0,0,0]

7

Aegr

6

TsurrEGR

5

uAlpha

4

delta

3

Neng

2

FIn

1

FOut

Figure 20: The central combustion part of the engine-model. Notice that thisconfiguration of the engine does not include a EGR system.

32

2

Mt

1

FIn

SDown

SUp

ntb

Mc

FcompOut

FcompIn

Turbin Regression

SDown

SUp

F

Non−Rev Restrictionexhaust pipe restriction

Fin1

Fout1

S

2−comp volyme 1in/1out1exhaust pipe

[SEp]

[Mt]

[FTuIn]

[FTuOut]

[FEp]

4

uTurb

3

SUp

2

SDown

1

ntb

Figure 21: The outlet side of the engine-model.

33

"HIGH" LEVEL SUBMODELS"LOW" LEVELS SUBMODELS

x gamma

gamma

SDown

SUp

A

TSurr

Fout

Fin

Var. estrictor & HEMc

Mt

nTb

TurboShaft

SDown

SUp

ntb

Mc

FcompOut

FcompIn

Turbin/Compressor

SDown

SUp

ntb

Mc

FcompOut

FcompIn

Turbin Regression

F1 T

Standard F to T

W

T

x

F

Standard F calculation

Fin1

Fin2

Fout1

Fout2

Q

S

Standard 2−comp volyme 2in/2out Old systems

SDown

SUp

A

F

Non−Rev Variable restrictor

SDown

SUp

Tsurr

Fout

Fin

Non−Rev Restrictor and HE

SDown

SUp

F

Non−Rev RestrictionFin

Tsurr1

FOut

Non−Rev Heat exchanger

Data Collection Small

Data Collection

SDown

SUp

ntb

Mc

FcompOut

FcompIn

Compressor Regression

SDown

SUp

delta

N

uAlpha

FengOut

FengIn

Combustion chamberFin1

Fin2

Fout1

Q

S

2−comp volyme 2in/1out

Fin1

Fout1

Fout2

Q

S

2−comp volyme 1in/2out

Fin1

Fout1

S

2−comp volyme 1in/1out

Figure

22:T

helibrary

includingthe

sub-models

usedto

constructthe

engine-m

odel.34