Modelling of the Exhaust Gas Recirculation

Original Article

Proc IMechE Part D:J Automobile Engineering115 IMechE 2015Reprints and permissions:sagepub.co.uk/journalsPermissions.navDOI: 10.1177/0954407015586700pid.sagepub.com

Modelling of the exhaust gasrecirculation rate based on thein-cylinder pressure measurement fora passenger car diesel engine

Jihyun Ryu, Jaesung Chung and Myoungho Sunwoo

AbstractThis paper proposes a modelling of the exhaust gas recirculation rate using the in-cylinder pressure sensor for a passen-ger car diesel engine. Traditional modelling approaches for the exhaust gas recirculation rate normally use variableswhich are measured for a long intakeexhaust air path so that a time delay is inevitable. In addition, the model structureis complex, since many non-linear or unmeasurable variables such as the volumetric efficiency and the efficiency of theexhaust gas recirculation cooler have to be considered in the model. The proposed exhaust gas recirculation rate modelis based on the in-cylinder pressure measurement which provides instantaneous information about combustion.Therefore, when this information is used, it is able to model the exhaust gas recirculation rate with a fast response com-pared with traditional modelling approaches. Furthermore, the proposed model can have a simple model structure sincethe model does not require consideration of the non-linear or unmeasurable parameters of the air path. The proposedexhaust gas recirculation rate model was integrated into an engine control unit and validated through engine experi-ments on various operating conditions.

KeywordsExhaust gas recirculation, in-cylinder pressure, modelling, control, diesel engine

Date received: 15 November 2014; accepted: 8 April 2015

Introduction

Emission and energy restrictions have been strength-ened as interest in the environment has increased. Inorder to meet these strengthened emission and energyregulations, many technologies such as common-raildirect injection, variable-geometry turbochargers(VGTs) and exhaust gas recirculation (EGR) have beendeveloped.

Among those technologies, the EGR system is a rep-resentative technology for reducing the nitrogen oxide(NOx) emissions.

14 The EGR system involves recircu-lating a portion of the exhaust gas from an exhaustmanifold into the cylinders. When the amount of EGRgas increases in the cylinder, the combustion tempera-ture decreases owing to the reduced available oxygenconcentration and the raised heat capacity. As a result,the NOx emissions (which are sensitive to the combus-tion temperature) decrease.58 Nevertheless, other emis-sions such as carbon monoxide (CO) and particulatematter increase.911 In addition, the reduced thermal

efficiency degrades the engine performance parameterssuch as the fuel efficiency and the output torque.10,12

Therefore, it is important to control the amount ofEGR gas to optimize these trade-off correlations.

Conventional engine control systems use the rate ofmass (fresh-)air flow (MAF) as a reference variable tocontrol the fresh air and the EGR gas. However, themass flow rate of the EGR gas can change even thoughthe MAF rate is constant because of the MAF sensorlocated upstream of the compressor. Therefore, it is noteasy to control the fresh air and the EGR gas with onlythe MAF sensor. Nevertheless, the EGR rate can

Department of Automotive Engineering, Hanyang University, Seoul,

Republic of Korea

Corresponding author:

Myoungho Sunwoo, Department of Automotive Engineering, Hanyang

University, 222 Wangsimni-ro, Seongdong-gu, Seoul 133-791, Republic of

Korea.

Email: [email protected]

at Brunel University London on June 18, 2015pid.sagepub.comDownloaded from

represent directly the amount of EGR gas in the mix-ture of fresh air and EGR gas, and so it is a moreappropriate variable to control the mixture of fresh airand EGR gas precisely.

It is difficult to measure the EGR gas with a sensorbecause the conditions of the EGR path are too harshto install a sensor. Since the temperature and the pres-sure of the exhaust gas are high, and since particulatematter also causes problems such as sensor fouling,using a sensor is not suitable for the EGR systembecause of the sensors durability.10,13 Consequently, amodel is required to estimate the EGR rate.

Traditional EGR rate modelling approaches usevalues that are measured along the long intakeexhaustair path,14 and so a time delay is inevitable. In addition,the modelling is difficult and the model structureis complex, since many non-linear or unmeasurablevariables such as the valves effective area or the effi-ciency of each component are considered for themodel.1519

Based on the in-cylinder pressure measurement, it ispossible to obtain the physical values for the EGR ratemodel directly with a fast response. Furthermore, theEGR rate model can be simplified even more, since itdoes not consider the non-linear elements such as theefficiency or the valves effective area of each compo-nent. Desantes et al.20 introduced MAF rate estimationfor the EGR rate using the in-cylinder pressure sensor.They proposed a regression model for estimating thecylinder air charge. However, although this model issimple and its computational time is short, it cannotguarantee accuracy of the model outside its modellingrange since the model is based on an empirical modeland not a physical model.

In this study we propose an EGR rate model basedon the in-cylinder pressure measurement. The proposedmodel is based on the physical model to improve themodel accuracy, and this model has a fast responsesince it uses the in-cylinder pressure measurements asan input. The proposed model was integrated into theengine control unit (ECU) and validated through sev-eral engine cell tests. Furthermore, EGR rate controltests were also carried out to validate the feasibility ofthe proposed model.

Experimental environment

Experimental apparatus

The environment for the engine experiments isdescribed in Figure 1. The target engine is a 2.2 l inlinefour-cylinder common-rail diesel engine for a passengercar with high-pressure EGR, low-pressure EGR andVGT systems, as shown in Figure 2. Table 1 lists thedetailed engine specifications. The engine is connectedto an eddy-current dynamometer which controls theengine speed and the load. The maximum errors insome key parameters of the engine experiments arelisted in Table 2.

Four glow plug-type in-cylinder pressure sensorswere installed in each cylinder. These sensors were pro-duced by Continental. AVL INDICOM and the cylin-der pressure analysis system (CyPAS) are used toacquire the in-cylinder pressure data. The in-cylinderpressure at every 0.1 C is obtained using INDICOM.Based on this measurement, it is used for offline analy-sis to determine the crank angle (CA) interval, which isone of the parameters for EGR rate modelling. The

Figure 1. Overview of the experimental apparatus.NI: Natonal Instruments; EC: eddy current; ECU: engine control unit; CyPAS: cylinder pressure analysis system.

2 Proc IMechE Part D: J Automobile Engineering


CyPAS calculates parameters such as the polytropiccoefficient and the heat release for online estimation ofthe EGR rate. This process is described in more detailin the section on the CyPAS.

Additional sensors such as thermocouples and pres-sure sensors are used to monitor the engine states viacRIO, and the intercooler is equipped with an electricvalve to control the temperature of the intake manifold.The EGR rate and other emissions such as NOx andCO are measured with a HORIBA MEXA-1600D

exhaust gas analyser. As shown in Figure 3, all mea-surements are transmitted to VN1630 by controllerarea network (CAN) communication so that they aremonitored and logged through a personal computer.An in-house ECU was used for engine control with anin-house software platform (AUTOSAR-Ready).21,22

An MPC5554 was used as the microcontroller for theECU. The EGR rate model was implemented in theECU by the autocode generation method usingMATLAB/Simulink.

Cylinder pressure analysis system

Figure 4 represents the structure of the CyPAS. TheCyPAS measures in-cylinder pressure informationaccording to the CA position. After the measured in-cylinder pressure is filtered and pegged, the parametersused for the EGR rate model are calculated and trans-mitted to the ECU through CAN communication.

The constants used in this paper are given in Table 3.The in-cylinder pressure is filtered with a hardware

low-pass filter with a cut-off frequency of 3 kHz and

Figure 2. Schematic diagram of the air system of a diesel engine equipped with high-pressure EGR, low-pressure EGR and a VGT.HP-EGR: high-pressure exhaust gas recirculation; LP-EGR: low-pressure exhaust gas recirculation VGT: variable-geometry turbocharger.

Table 1. Specifications of the target diesel engine.

Parameter Value

Engine type Inline, double overhead camshaftNumber of cylinders 4Injector type PiezoelectricCooling type Water cooledBore 85mmStroke 96mmDisplacement volume 2199 cm3

Compression ratio 16.0:1Firing order 1342Intake valve open timing 10 CA BTDCIntake valve closed timing 28 CA ABDCExhaust valve open timing 54 CA BBDCExhaust valve closed timing 4 CA ATDC

CA: crank angle; BTDC: before top dead centre; ABDC: after bottom

dead centre; BBDC: before bottom dead centre; ATDC: after top dead

centre.

Table 2. Maximum errors of the key parameters.

Parameter Maximum error

Engine speed 2 r/minEngine load (brake mean effective pressure) 0.3 barCoolant temperature 0.1 C

Ryu et al. 3


filtered again with a SavitzkyGolay23 filter to removenoise. The measured pressure signal has an offsetbecause of the thermal shock of the piezo element;therefore, it is removed using the two-point referencingmethod.24

After the filtering and pegging process, the CyPAScalculates the parameters for the EGR rate model suchas the differential in-cylinder pressure between two spe-cific CA positions, the polytropic coefficient and theheat release. If the compression process is assumed tobe adiabatic, then the polytropic coefficient k is derivedfrom

PaVka =PbV

kb

and therefore

k=log Pa=Pb log Vb=Va 1

The polytropic coefficient is assumed to be knownand constant; to ensure this, it was checked and foundto be reasonably constant for all operating conditions.

The rate of heat release is calculated from the in-cylinder pressure25 according to

dQ

du=

g

g 1PcyldV

du+

1

g 1VdPcyl

du2

The heat release can be obtained by integrating the rateof heat release to obtain the in-cylinder temperature.

EGR rate model

The proposed EGR rate model is shown in Figure 5. Inorder to obtain the EGR rate, the total mass of mixedgas is determined on the basis of the in-cylinder pres-sure measurement. The specific heat and the intakemanifold temperature are used to determine the totalmass of mixed gas. However, these parameters cannot

Figure 3. Structure of the DAQ system.sig.: signal: CAN: controller area network; Elec.: electrical; Comm.: communication; CyPAS: cylinder pressure analysis system; ECU: engine control

unit; PC: personal computer.

Figure 4. Structure of CyPAS.

Table 3. Values of the constants used in this paper.

Symbol Description Units Value

k polytropic coefficient 1.4R Universal gas constant kJ/kg K 0.287Va In-cylinder volume at a m

3 0.0004Vb In-cylinder volume at b m

3 0.000 12Vint Intake manifold volume m

3 0.002



be measured directly, and so they are obtained withempirical models using some measurable parameterssuch as the intake manifold pressure, the engine speed,the injected fuel mass and the MAF rate.

Definition of the EGR rate

The mixed gas in the cylinder is composed of fresh airand EGR gas. By the law of mass conservation, thetotal mass of mixed gas is expressed as the sum of themass of fresh air and the mass of EGR gas accordingto

mtot=mair+mEGR 3The equation that defines the EGR rate, which is the

proportion of the amount of exhaust gas to the totalamount of mixed gas taken into the engine, is given by

FEGR= 1mairmtot

3100 4

The mass of fresh air is calculated using the enginespeed and the MAF rate, which is measured with theMAF sensor. However, measuring the total mass ofmixed gas directly is difficult owing to the harsh envi-ronment of the EGR path, and so a model is required.

Determination of total mass of mixed gas

When the intake valve and the exhaust valve are closed,the cylinder is regarded as a closed system, which meansthat there is no mass change. On the assumption thatthe in-cylinder temperature at a specific CA is known,the total mass mtot of mixed gas is expressed using theideal-gas equation

PuVu=mtotRTu

and therefore

mtot=PuVuRTu

5

However, piezoelectric-type in-cylinder pressure sen-sors have a sensor voltage drift due to thermal shock,so that there is offset in the measurement signal.Although the pressure signal has an offset, the pressuredifference between the two CA positions is constant.Therefore, the total mass of mixed gas could be deter-mined using the DP method based on this pressuredifference.19

DP method. As shown in Figure 6, the in-cylinder pres-sure increases when the piston moves from a to b

Figure 5. Block diagram of the EGR rate estimation algorithm.EGR: exhaust gas recirculation.

Figure 6. Piston movement during the compression stroke.

Ryu et al. 5


during a compression stroke. If this process is assumedto be adiabatic, then from

PaVka =PbV

kb

the in-cylinder pressure at b is expressed as

Pb =VaVb

kPa 6

Also

DP=Pb Pa 7If the mixed gas is assumed to be an ideal gas, then

from

PaVa=mtotRTa

the in-cylinder pressure at a is represented as

Pa=mtotRTa

Va8

By substituting the in-cylinder pressure at a fromequation (8) into

DP=PaVaVb

k1

9

the difference in the in-cylinder pressures isexpressed as

DP=mtotRTa

Va

VaVb

k1

10

Finally, by rearranging equation (10), the total massof mixed gas is expressed as

mtot=DP VaRTa

VaVb

k1

111

Cylinder temperature at a. In equation (11), the total massof mixed gas is obtained from the pressure difference,the cylinder temperature at a and other constants suchas the ideal-gas constant, the cylinder volume and thepolytropic coefficient. The in-cylinder pressure differ-ence is measured with the in-cylinder pressure sensor,and other constant values are known. Nevertheless, it isdifficult to measure the cylinder temperature directly,and so the cylinder temperature at a should beestimated.

In this study, the cylinder temperature at a wasdetermined on the basis of heat release analysis duringthe compression stroke. After integrating the rate ofheat release (which is represented in equation (2)) fromthe CA with the intake valve closed (IVC) to the CA ata, the heat release between IVC and a is calculatedfrom

Q=

aIVC

dQ

dudu 12

Since the cylinder temperature at IVC is assumed toequal the temperature of the intake manifold in an idealintake process,20 the heat generated during that periodcan be expressed as

Q= cmtot Ta Tint 13By combining equations (12) and (13), the cylinder

temperature at a is expressed as

Ta=Q

cmtot+Tint 14

By substituting the cylinder temperature at a fromequation (14) into equation (11) and rearranging, thetotal mass of mixed gas is expressed as

mtot=1

Tint

DP VaR

VaVb

k1

1 Q

c

( )15

As shown in equation (15), the intake manifold tem-perature needs to be known in order to calculate thetotal mass of mixed gas. However, mass-produced pas-senger cars are generally not equipped with a sensor formeasuring the intake manifold temperature. Therefore,on the basis of the ideal-gas equation,26 the intakemanifold temperature is modelled as

Tînt=PintVintmîntR

16

Additionally, in order to validate this model, anintake manifold temperature sensor was added for thepurpose of correlation. The intake manifold pressurecan be measured with a boost pressure sensor, and themass of gas in the intake manifold is estimated usingthe empirical model, which is expressed as

mînt = f Pint,WairN

= a1 + a2 Pint+ a3

WairN

17

In equation (15), the intake manifold temperature,the cylinder pressure difference and the heat release canbe measured, and we already know other constantparameters such as the gas constant, the polytropiccoefficient and the cylinder volume at each position.However, the specific heat is unknown because it is dif-ficult to measure or calculate. Therefore, by consider-ing some parameters that affect the process (the enginespeed, the injected fuel mass, the MAF rate, the intakemanifold pressure and the temperature), an empiricalmodel is suggested in this study according to

c= c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 3 Pint Tint mf m

2f N N

2 Wair W2air N

2W2air 1h i

18In particular, the engine speed, the fuel injection

quantity and the MAF rate are dominant factors of thespecific heat, and so quadratic factors for them are



included. The calibrated values of constants are asshown in Table 4.

Modelling results

In order to determine the CA interval for the DPmethod and to identify the modelling parameters,engine cell tests were conducted in a total of 60 testcases. At each given case of 20 operating conditions asshown in Figure 7, the MAF set point was changedfrom the nominal point to the nominal point 6 50mg/stroke. At this time, the load was changed from 2 barto 8 bar. Even though the operating conditions of theengine were constant, the NOx emissions can changebecause of external environmental factors such as thecoolant temperature and the ambient pressure; there-fore, the MAF set point was changed to consider theeffects of one of the external environmental factors ofthe MAF rate.

The CA positions of a and b for the DP method weredetermined with the in-cylinder pressure measurementdata at every 0.1 CA from INDICOM to minimize thecycle-by-cycle variation and the polytropic coefficientvariation. These results are shown in Table 5 andTable 6 respectively, and so the interval was selected as100 CA ATDC at a and 40 ATDC at b to minimizethe variations.

The modelling results for the intake manifold tem-perature are shown in Figure 8 with an r.m.s. error(RMSE) of 3.03K and R2=0.9091. Figure 9 showsthe modelling results for the specific heat, which is

Table 4. Values of the constants for the specific heat model.

Constant Value

C1 9.00C2 4.29 3 10

22

C3 7.31 3 102

C4 3.99 3 1023

C5 1.79 3 1022

C6 5.22 3 1026

C7 4.28 3 1022

C8 7.22 3 1024

C9 9.83 3 10211

C10 3.15 3 1021

Figure 7. Operating conditions of the engine for modellingparameter identification.str: stroke; rpm: r/min.

Table 6. Mean absolute errors due to polytropic coefficient variation for different intervals.

Crank angle at a Mean absolute error (%) due to polytropic coefficient variation for the following crank angles at b

140 120 100 80 60 40

IVC 74.016 16.952 7.825 4.545 3.764 3.152140 22.525 6.649 3.751 2.936 2.452120 8.801 3.924 2.465 1.955100 3.033 1.344 1.05880 1.706 1.00860 0.769

IVC: intake valve closed.

Table 5. Mean absolute errors due to cycle-by-cycle variation for different intervals.

Crank angle at a Mean absolute error (%) due to cycle-by-cycle variation for the following crank angles at b

140 120 100 80 60 40

IVC N 44.553 18.379 8.340 3.810 1.620140 66.809 22.262 9.512 4.144 1.731120 31.046 10.116 4.051 1.626100 14.560 4.511 1.68580 6.439 1.85660 2.519

IVC: intake valve closed.

Ryu et al. 7


represented in equation (18) with an RMSE of0.2751 kJ/kgK.

With the previous modelling results for the intakemanifold temperature and the specific heat, the EGRrate was modelled using the experimental data. Figures10 and 11 show the modelling results. As shown inFigure 11, the EGR rate from the proposed modelshows a similar tendency to that of the measured EGRrate with an RMSE of 0.8199% and R2=0.9763 evenwhen the operating conditions were changed.

Experimental validation

The EGR rate model was integrated into an ECU. Inorder to validate the proposed EGR rate model, severalengine experimental tests were carried out.

Steady-state experimental results

The operating conditions of steady-state validationexperiments differ from those of the modelling

Figure 8. Modelling results for the intake manifold temperature.

Figure 9. Modelling results for the specific heat.



experiments. The engine speed and the brake meaneffective pressure (BMEP) were changed as shown inFigure 12.

Figures 13 to 15 show the validation experimentresults for steady-state tests. Figure 13 shows the vali-dation results for the EGR rate. As shown in Figure 13,the modelled EGR rate shows a similar tendency to thatof the measured EGR rate with R2=0.9611 and anRMSE of 0.6015%. The maximum difference betweenthe measured value and the modelled value is 1.35%.Figure 14 and Figure 15 show the steady-state valida-tion results for the intake manifold temperature and the

specific heat respectively. The maximum percentageerrors are 2.19% for the intake manifold temperatureand 7.18% for the specific heat; the RMSEs are 3.60Kand 0.13 kJ/kgK respectively.

Transient experimental results

The proposed EGR rate model was also validated intransient operating conditions. Figures 16 and 17 showthe transient experimental results for the EGR rate.The first transient test was carried out at a fixed enginespeed of 1500 r/min with a step change in the BMEP asfollows: 4 bar ! 6 bar! 8 bar! 6 bar ! 4 bar. EachBMEP was retained for 60 s. The other operating

Figure 10. Modelling results for the EGR rate.EGR: exhaust gas recirculation.

Figure 11. Evaluation of the linearity between the measuredEGR rates and the modelled EGR rates.EGR: exhaust gas recirculation.

Figure 12. Operating conditions for the validation tests in thesteady state.rpm: r/min.

Ryu et al. 9


conditions were not changed during the test. As shownin Figure 16, the errors between the measured EGRrate and the estimated EGR rate for the transient statewere within 4%.

Additionally, the model performance in the transientstate was evaluated during the changes in the MAF setpoint. In the previous validation tests, the operatingconditions were determined by the engine speed andthe BMEP. However, even though the operating

conditions were kept constant, the MAF rate changedin practice. When the MAF set point increases, theMAF rate also increases so that the mass of EGR gasis reduced. Consequently, the EGR rate decreases. Theset point of the MAF was step changed as follows:(nominal point 50) mg/stroke ! nominal point mg/stroke ! (nominal point + 50) mg/stroke ! nominalpoint mg/stroke ! (nominal point 50) mg/stroke.Each set point of the MAF was retained for 40 s with a

Figure 13. Steady-state validation results for the EGR rate.rpm: r/min; BMEP: brake mean effective pressure; EGR: exhaust gas recirculation.

Figure 14. Steady-state validation results for the intake manifold temperature.



fixed engine speed and a fixed BMEP. Figure 17 showsthe transient estimation results of the EGR rate. Theerror of the EGR rate was within 5% across the wholetest period.

Case study: EGR rate control

The feasibilities of the proposed EGR rate model forEGR rate control were also validated with a simplefeedforward and proportionalintegral (PI) feedbackcontroller.

Structure of the controller

Figure 18 shows the structure of EGR rate control.The feedforward controller generates a desired EGRvalve position based on the engine speed and the injec-tion quantity. The set-point generator generates the

desired EGR rate according to the operating conditionsof the engine such as the engine speed and the injectionquantity. Each generated value from the look-up table(LUT) was based on experimental data from thesteady-state tests for modelling.

Experimental results

EGR rate control was conducted with several enginetests.

First, the EGR rate was controlled following thedesired EGR rate which was changed at fixed operatingconditions. This test was performed to check whetherthe EGR rate could be controlled at the fixed point ofoperation without any problem. Figure 19 shows theresults for EGR rate control when the EGR rate setpoint was changed as follows: 15% ! 20% ! 15%. Inthis test, each EGR rate set point was retained for 60 s,

Figure 15. Steady-state validation results for the specific heat.

Figure 16. Transient validation results for the EGR rate with a step change in the BMEP at an engine speed of 1500 r/min.BMEP: brake mean effective pressure; EGR: exhaust gas recirculation.

Ryu et al. 11


and the operating conditions were fixed at an enginespeed of 1500 r/min and a BMEP of 4 bar. As shown inFigure 19, the EGR rate from the proposed modelshowed a rise time of 0.6 s while the measured EGRrate took 3 s to respond to the set-point change; thisresulted from the relatively long sampling line of thegas analyser.

Subsequently, another EGR rate control test wascarried out with changing operating conditions. The

EGR rate tracked the set point which is generated onthe basis of an LUT according to the operating condi-tions. Figure 20 shows the transient control results witha fixed BMEP of 4 bar when the engine speed was chan-ged as follows: 1250 r/min ! 1500 r/min ! 1250 r/min.The desired EGR rate was changed as follows: 20% !15% ! 20%. The maximum rise time of the EGR ratefrom the proposed model was 1.4 s, and that of themeasured EGR rate was 5.5 s.

Figure 17. Transient validation results for the EGR rate with a step change in the MAF set point at an engine speed of 2000 r/minand a BMEP of 4 bar.MAF: mass air flow; EGR: exhaust gas recirculation.

Figure 18. Structure of the EGR rate controller.EGR: exhaust gas recirculation; PI: proportionalintegral; HP-EGR: high-pressure exhaust gas recirculation.



Figure 19. Transient control results for the EGR rate with a step change in the set point at an engine speed of 1500 r/min andBMEP of 4 bar.EGR: exhaust gas recirculation; HP-EGR: high-pressure exhaust gas recirculation.

Figure 20. Transient control results for the EGR rate with a step change in the engine speed at a BMEP of 4 bar.BMEP: brake mean effective pressure; EGR: exhaust gas recirculation.

Ryu et al. 13


Summary

In this section, we confirmed the feasibility of EGRrate control using the proposed EGR rate model with asimple feedforward and PI feedback controller as a casestudy. Through the engine experiments under bothfixed operating conditions and changed operating con-ditions, we validated that the EGR rate from the pro-posed model can be used as a feedback variable forcontrolling the amount of EGR gas.

Conclusions

In this paper, the EGR rate model based on the in-cylinder pressure measurement was proposed for apassenger car diesel engine. The conclusions aresummarized as follows.

1. The total mass of mixed gas was determined onthe basis of the DP method. The intake manifoldtemperature and the specific heat for calculation ofthe total mass of mixed gas were determined frommodels. In addition, the cylinder temperature wascalculated from the heat released during the com-pression stroke.

2. The steady-state data for modelling were obtainedby changing the engine speed, the fuel injectionquantity and the MAF rate. With these data, mod-elling was conducted so that the parameters of eachmodel were identified. As a result, the EGR ratemodelling results showed high linear correlationcompared with the measured EGR rates with anRMSE of 0.8199% and R2=0.9763.

3. The proposed EGR rate model was implementedon a real-time embedded system and validated withseveral engine experiments. The steady-state testresults were similar to the measured EGR rateswith an RMSE of only 0.6015% and R2=0.9611.Transient-state tests were also conducted andshowed that the error was within 5% throughoutthe whole test period.

4. Additionally, EGR rate control tests were con-ducted as a case study to validate the feasibility ofthis model. Through these tests, we verified thatthe proposed EGR rate model is appropriate forthe feedback control variable.

5. However, the proposed model did not consider theeffect of internal EGR. Therefore, in order toimprove the accuracy of the model, the internalEGR should be considered when modelling theEGR rate. Furthermore, the EGR rate model usesthe in-cylinder pressure sensor. Thus, in order toapply this model, installation of an in-cylinderpressure sensor is inevitable. However, this prob-lem will be solved since several mass-produced in-cylinder pressure sensors are now available forapplications, and some automotive manufacturershave already implemented an in-cylinder pressuresensor in their vehicles.27,28

Declaration of conflict of interest

The authors declare that there is no conflict of interest.

Funding

This research was financially supported by the BK21plus program (grant number 22A20130000045) underthe Ministry of Education in the Republic of Koreatogether with the National Research Foundation ofKorea grant funded by the Korean Ministry ofEducation, Science and Technology (grant number2011-0017495). In addition, the research was financiallysupported by the Industrial Strategic TechnologyDevelopment Programs (grant numbers 10039673 and10042633) of the Ministry of Knowledge Economy.Finally, this work was supported through the EnergyResource Research and Development Program (grantnumber 2006ETR11P091C) under the Ministry ofKnowledge Economy in the Republic of Korea.

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Appendix 1

Notation

c specific heat (kJ/kg K)F fraction (%)m mass (kg)N speed of the engine (r/min)P pressure (kPa)Q net heat release (kJ)T temperature (K)u valve position (%)V volume (m3)W mass flow rate (mg/stroke)g ratio of the specific heats ()e percentage error (%)u crank angle (deg)

Superscripts

^ estimated value mean value

Subscripts

a predefined crank angle at position aair fresh airb predefined crank angle at position bcyl cylinderEGR exhaust gas recirculationf fuelint intake manifoldtot total

Abbreviations

BMEP brake mean effective pressureCA crank angleCAN controller area networkCO carbon monoxideCyPAS cylinder pressure analysis systemECU engine control unitEGR exhaust gas recirculationIVC intake valve closedLUT look-up tableMAF mass (fresh-)air flowNOx nitrogen oxidesPI proportionalintegralRMSE root mean square errorVGT variable-geometry turbocharger

Ryu et al. 15


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Modelling of the Exhaust Gas Recirculation