Control oriented modeling and analysis of gas exchange and combustion processes for LTC diesel engine

Applied Thermal Engineering 110 (2017) 1305–1314

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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Research Paper

Control oriented modeling and analysis of gas exchange and combustion processes for LTC diesel engine Tianpu Dong a, Bolan Liu a,⇑, Fujun Zhang a, Yingmin Wang a, Baolin Wang b, Pan Liu a a b

School of Mechanical Engineering, Beijing Institute of Technology, 5 S Zhongguancun St., Beijing, China Ningbo Weifu Tianli Turbocharging Technology Co., Ltd., Ningbo, China

h i g h l i g h t s
The modeling method of low temperature combustion diesel engine was studied.
A dynamic physics based control oriented model to dynamically predict gas exchange and combustion process of a LTC diesel engine was constructed.
Static and dynamic experimental validation of the control oriented model were performed.
The root mean squared error (RMSE) and correlation coefficient (R) were calculated and used to evaluate the validation of the model.

a r t i c l e

i n f o

Article history: Received 30 July 2016 Accepted 1 September 2016 Available online 13 September 2016 Keywords: Diesel Low temperature combustion Gas exchange model Combustion model

a b s t r a c t Diesel low temperature combustion (LTC) has great potential for the realization of ultra low emission of internal combustion engine, which has been widely studied in recent years. Precise control of the LTC combustion is essential for the real applications of LTC concept on diesel engine. Constructing the model which can accurately describe the dynamic characteristics of diesel LTC is the foundation of the modelbased controller design. In this paper, a dynamic physics based control oriented model of low temperature combustion diesel engine is presented. This model is a three-input-three-output physics-based control oriented model and consists of gas exchange sub-model and combustion sub-model. The inputs of the model are fuel rate, EGR opening rate and VGT position. The outputs are intake oxygen mass fraction, CA50 and IMEP. The model has eight states and all the states are able to be measured easily. The model is validated by a large number of steady-state and transient diesel experimental test data. The steady-state and transient validation results show that the model can accurately describe the dynamic characteristics of LTC diesel engine with high accuracy for control applications. Which lays a foundation for model-based controller design and verification of different control algorithms in LTC diesel engine. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Energy and environment problems are the two major challenges facing the human society today. Vehicle is one of the important consumers of petroleum resource, and vehicle emission is one of the main sources of environmental pollution. Reducing internal combustion engine harmful emissions, to meet the requirement of increasing stringent emission regulations around the world is one of the most interesting challenges in the internal combustion engine development. Diesel low temperature combustion (LTC) with EGR dilution has the ability to reduce NOx and Soot emissions while remaining high efficiency In recent years, diesel engine LTC technology has been widely concerned by academy and industry ⇑ Corresponding author. E-mail address: [email protected] (B. Liu). http://dx.doi.org/10.1016/j.applthermaleng.2016.09.001 1359-4311/Ó 2016 Elsevier Ltd. All rights reserved.

and has become an important direction of the research of diesel engine combustion theory and technology [1–3]. Due to the effect of chemical reaction dynamics, the effective control of diesel LTC is considered as the most important challenge for the application of LTC in vehicle engine [4,5]. Combustion timing control is a main problem for diesel LTC combustion control [6–10]. The combustion timing affects the fuel economy, combustion stability, in-cylinder peak pressure and emission [9]. Due to the influence of mixed gas chemical kinetic reaction rate, diesel LTC is very sensitive to the temperature, pressure and composition of the intake charge and the fuel physicochemical properties. In order to control diesel LTC combustion timing, a number of control strategies and approaches have been used. The traditional PID control method and the model based control method are two mainly used methods. Feedback closed loop control based on incylinder pressure signal is widely used in diesel low temperature

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Nomenclature ATDC CA CA50 CA10 EGR ECU EVO EVC HCCI IMEP IVO IVC

after top dead center crank angle crank angle of 50% heat release crank angle of 10% heat release exhaust gas recirculation engine control unit exhaust valve open exhaust valve close homogeneous charge compression ignition indicated mean effective pressure Intake valve open Intake valve close

LTC MPC NOx PID RMSE R SOC SNS UEGO VGT

low temperature combustion model predictive control nitrogen oxide proportion integration differentiation root mean squared error correlation coefficient start crank angle of combustion smart NOx sensor universal exhaust gas oxygen variable geometry turbocharger

combustion control and the control algorithm is mainly empirical PID [6,11,12]. In this control method, one or several combustion parameters are selected as the feedback signal, such as CA50, IMEP or maximum in-cylinder pressure. Model based control using physical or data driven engine models is a popular pathway, essentially resulting from the large on-board computing power available on the modern engine control unit (ECU) [5,13]. For model based control of diesel LTC, accurate control oriented simulation model is required to understand the dynamics of engine gas exchange variations and combustion state variations. With the development of modern control theory, more and more new control algorithm have gradually been applied in diesel engine control. In recent years, study on gas exchange modeling for diesel LTC combustion control has made some progress [5,13–16]. All these works will contribution to the LTC combustion control. To accurately predict the combustion process, a precise combustion model is a necessity. A control oriented one zone model was used in [7,10,17,18] to model and control the combustion phasing of the blended-fuel HCCI engine. In [13], a control oriented charge mixing and two zone HCCI combustion model was constructed based on the assumption that the in-cylinder charge is divided into the wellmixed and unmixed zones. The model was validated against the GT-Power simulation data and experimental data. In [8], a physics based correlation model was developed to model the combustion timing and ignition delay of the partially combustion. Based on the model, the model predictive control (MPC) controller was designed and validated. A simple, analytical, control oriented and physically-based model for prediction of combustion timing during PCCI combustion was developed and validated in [19], but the gas exchange model was not designed. In this work, a control oriented physical model of diesel LTC is developed and validated. Based on the diesel LTC combustion mechanism, the gas exchange dynamic model which can reflect the characteristics of the diesel gas exchange, and the combustion prediction model which can predict the combustion characteristics of the diesel LTC are detailed described in Section 2. Section 3 describes the experimental engine setup process. The evaluation method of model validation and the validation results of the model are discussed in Section 4 and the conclusions are summarized in Section 5.

affected. The key and foundation to realize the accurate modelbased control of the diesel LTC is to construct control oriented diesel LTC prediction model with high accuracy, high noise immunity and good response. In the following, according to the characteristics of diesel LTC engine, the physical model of LTC diesel engine is constructed by using the method of the modular modeling and the staged modeling.

2. Control-oriented modeling

T em Rem  ðW ei þ W f Þðcem T exh  T em Þ þ W egr ðT em  cem T em Þ T_ em ¼ pem V em ð6Þ þ W t ðT em  cem T em Þ

The high accuracy control oriented model is very important for the model-based controller design. However, as the diesel LTC combustion process is complicated, it is very difficult to build an accurate model. If the accuracy of the model is insufficient, the transient control effect of the combustion will be significantly

2.1. Gas exchange sub-model In this paper, an electronically controlled high pressure common rail diesel engine with cooling high pressure EGR system and VGT system is studied. The diesel engine gas exchange system consists of intake manifold, exhaust manifold, VGT system, EGR system, cooling system and cylinder system. Detailed description of all these gas exchange subsystem are given in the following sections. 2.1.1. Intake and exhaust manifold Using the control volume method, based on the mass and energy conservation as well as ideal gas law, the intake and exhaust manifold dynamic model can be derived as follows [20]:

p_ im ¼

 Rim T im
W c þ W egr  W ei V im

 Rim T im  F_ Oim ¼ W egr ðF Oem  F Oim Þ þ W c ðF Oc  F Oim Þ pim V im

ð1Þ ð2Þ


 T im Rim  W egr cim T egr T im þW c ðcim T ic T im ÞþW ei ðT im  cim T im Þ T_ im ¼ pim V im ð3Þ Using the similar modeling approach, the dynamics of the pressure, temperature and oxygen mass fraction of the exhaust manifold can be derived as follows:

p_ em ¼

 Rem T em
W eo  W t  W egr V em

Rem T em ðF Oe  F Oem ÞW eo F_ Oem ¼ pem V em

ð4Þ ð5Þ

where, pim , T im and V im are the pressure, temperature and volume of the intake manifold, respectively; pem , T em and V em are the pressure, temperature and volume of the exhaust manifold, respectively; T egr

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is the gas temperature after the EGR cooler; T ic is the gas temperature after the intercooler; T exh is the temperature of the exhaust gas; W c , W t , W egr are the mass flow rate of the compressor, turbine and EGR, respectively; W ei is the total mass flow from the intake manifold into the cylinder; W eo is the mass flow out from the cylinder; Rim and Rem are the gas constant of the intake manifold and exhaust manifold; cim , cem are the specific heat ratio of the gas in the intake manifold and in the exhaust manifold. F Oim is the intake manifold oxygen mass fraction; F Oem is the exhaust manifold oxygen mass fraction; F Oc is the oxygen mass fraction in atmosphere; F Oe is the oxygen mass fraction out from the cylinder. 2.1.2. Cylinder Assuming that the engine speed is as a known input, the total mass flow from the intake manifold into the cylinder can be modelled by using speed density equation:

Ne V d pim gv ol 120Rim T im

W ei ¼

ð7Þ

where, N e is the engine speed; V d is the cylinder displacement volume; gv ol the volumetric efficiency of the cylinder, which is the function of speed and intake manifold pressure.

gv ol ¼ f ðpim ; Ne Þ

ð8Þ

According to the mass conservation, the mass flow rate out from the cylinder can be given as:

W eo ¼ W ei þ W f  W rg

ð9Þ

The fuel mass flow into the cylinder can be calculated as

Wf ¼

106 ud Ne ncyl 120

ð10Þ

where, ud is the fuel rate; ncyl is the number of cylinders. Oxygen fuel ratio in the cylinder before the start of combustion can be calculated by the following equation

kO ¼

W ei F Oim W f ks

ð11Þ

where, ks is the stoichiometric ratio of the oxygen mass and the fuel mass. Assuming that the fuel is completely burned in the combustion process, the oxygen mass fraction of the exhaust gas out from cylinder is given by the mass balance as

F Oe ¼

W ei F Oim  W f ks W eo

ð12Þ

At the intake valve closing (IVC) moment, the oxygen mass fraction in the cylinder can be derived as

F Ocyl ¼

mei F Oim þ mrg F Oe mei þ mrg

W eegr þ W iegr W egr þ W c þ W f

W egr ¼

f ðuegr ÞAegr;: max pem pffiffiffiffiffiffiffiffiffiffiffiffiffi wegr ðPegr Þ Ra T egr

ð14Þ

2.1.3. EGR system At the end of a combustion cycle, a part of exhaust gas flow through the VGT into atmosphere and the other part flow through the EGR valve into the intake manifold, in which EGR gas is mixed with fresh air. After that the mixed gas flow into the cylinder when the intake valve is open, which will influence the next combustion

ð15Þ

where Aegr;max is the max flow area of the EGR valve. f ðuegr Þ is the flow coefficient, which is the function of the EGR valve opening. Pegr is pressure ratio, Pegr ¼ pim =pem .

8 vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !ffi u cegr þ1 >  c cegr1 2 > >u 2cegr cegr cegr egr 2 > t > ; P  P P > t > t t cegr þ1 < cegr 1 wegr ðPegr Þ ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > > >  ccegr þ1  c cegr1 > 1 > > cegr c 2þ1 egr ; Pt 6 c 2þ1 egr : egr

ð16Þ

egr

The EGR valve actuator is modelled as follows

 d 1  uegr ¼ uegrPWM ðt  sdeg r Þ  uegr dt segr

ð17Þ

where uegrPWM is the control signal of the EGR actuator. segr is the time constant associated with the EGR valve structure. sdeg r is the time delay. 2.1.4. Coolers There are two coolers in the air path system: the intercooler and the EGR cooler. Usually the pressure drops across the coolers is neglected and mass accumulation in coolers is not taken into consideration. The temperature of the gas passing through the intercooler and the EGR cooler can be calculated by using the linear heat exchanger effectiveness [21]:

T ic ¼ T c ð1  gc;i Þ þ gc;i T coolant

ð18Þ

T egr ¼ T em ð1  gc;e Þ þ gc;e T coolant

ð19Þ

where, T c is the temperature of the gas flow through the compressor; T em is the gas temperature before the EGR valve; T coolant is the coolant temperature; gc;i , gc;e are the cooling efficiency of the intercooler and the EGR cooler. 2.1.5. VGT system The behavior of the VGT turbocharger is modelled in time domain. According to Newton’s second law, the speed of the turbocharger can be derived as [22,23]

d P g  Pc xt ¼ t m dt J t xt

ð20Þ

where, J t is the inertia. According to the first law of thermodynamics, neglecting the heat transfer between the gas and the wall, the power delivered by the turbine gives

ð13Þ

where, mrg is the mass of the residual gas in the cylinder; mei is the gas mass flow into the cylinder. The total exhaust gas rate (RGF) of the gas in the cylinder at the IVC moment can be described as

RGF ¼

cycle. The EGR flow rate can be approximately calculated by a nozzle orifice equation, and can be simplified as



Pt ¼ gt W t cp;em T em

pem 1 pamb

1c cem ! em

ð21Þ

Similarly, the power required to drive the compressor can be calculated by

Pc ¼

1

gc

" W c cp;c T amb

pc pamb

ccc1 c

# 1

ð22Þ

where, gt , gc are the isoentropic efficiency of the turbine and the compressor, respectively; cem , cc are the specific heat ratio of the gas in the exhaust manifold and the compressor; pc is the pressure after the compressor; pamb is the atmospheric pressure. The outlet temperature of the compressor can be calculated by using the second law of thermodynamics:

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" T c ¼ T amb 1 þ

1



gc

pc pamb

ccc1 c

!# 1

ð23Þ

The exhaust gas flow rate through from VGT system can be approximated by the nozzle flow equation:

Wt ¼

f ðuegr ÞAt;max pem pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi wt ðPt Þ Rem T em

ð24Þ

where, At;max is the maximum effective area of the VGT. f ðuegr Þ is the effective flow area of the VGT nozzle, which is the function of the VGT position. Pt is the expansion ratio of the turbine, Pt ¼ pamb =pem .

8 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2

t  c c1 ct þ1 > > ct ct > > c21 P  Pt ct ; Pt > c 2þ1 t < t t t wt ðPt Þ ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi >  cct þ1  c c1 t > > 1 > : ct c 2þ1 t ; Pt 6 c 2þ1 t t

where uv gtPWM is the control signal of the VGT actuator. sv gt is the time constant associated with the VGT valve structure. sdv gt is the time delay. 2.2. Combustion sub-model The thermodynamic process analysis of combustion in the cylinder is carried out in stages. The intake valve opening (IVO) time is selected as the starting point for calculation and the exhaust valve closing (EVC) timing is selected as the end of the calculation. The beginning and the ending of each stage are controlled by the valve timing which is regarded as the known input. On the assumption that the in-cylinder fuel, fresh air and residual gas are uniformly premixed at the IVC, according to the mass conservation, energy conservation and ideal gas state equation, the states of the mixed gas in a combustion cycle of diesel LTC engine are calculated. 2.2.1. Intake process When the intake valve is open, the mixed gas in the intake manifold flow into the cylinder through the intake valve. The total mass flow from the intake manifold into the cylinder can be calculated by formula (8). After the intake valve closing, due to the limitation of technical conditions, the temperature and pressure in the cylinder are not easy to be measured. Instead, the temperature and pressure of the intake manifold are usually measured. The pressure and temperature in the cylinder at IVC moment can be calculated by the following empirical fitting formulas [17].

T 0:005 im

T soc ¼ T mix

ð26Þ

!

pim

ð27Þ

  U0:1488 N0:0850 e T iv c ¼ 0:0073T 2im þ 1:4829T im þ 110:3672  0:0092 1 þ vegr ð28Þ After the intake valve closed the fresh air, the EGR gas, the fuel and the residual gas are mixed in the cylinder. The temperature of the mixed gas in the cylinder T mix can be calculated according to the enthalpy balance.


 cp;mix mair þ megr þ mf þ mrg T mix
 ¼ cp;iv c mair þ megr þ mf T iv c þ ncp;rg mrg T rg

ð29Þ

ð30Þ

2.2.2. Isentropic compression process Assuming that the compression process of the diesel engine is a polytropic process, the temperature and the pressure in-cylinder before the combustion can be calculated according to polytropic relation.

t

 d 1  uv gt ¼ u ðt  sdv gt Þ  uv gt dt sv gt v gtPWM

N 0:027 U0:046 e

T mix


 cp;iv c mair þ megr þ mf T iv c þ ncp;rg mrg T rg
 ¼ cp;mix mair þ megr þ mf þ mrg

ð25Þ

The VGT actuator dynamics are modelled as a first order system with a time delay

piv c ¼

where, cp is the specific heat capacity at constant pressure. n is the equivalent correction factor of the residual exhaust gas heat loss and the estimation bias of the cp . The temperature of the mixture can be calculated by the formula (13)

psoc ¼ piv c

V iv c V soc

cic 1

ð31Þ



c V iv c ic V soc

ð32Þ

where, cic is the average specific heat capacity ratio of the mixture for the compression process. V iv c , V soc are the cylinder volume at the crank angle of the IVC and SOC, respectively. 2.2.3. Constant volume combustion process When the mixture in-cylinder is compressed to a small fraction of its initial volume, the combustion is initiated and the cylinder pressure and temperature rise rapidly. The start of combustion (SOC) can be predicted by a variety of models [6,8,10,18,19], such as multi-dimensional CFD models, multi-zone models, and single zone models. For real-time control, a compromise between the accuracy of model and the computation time is required. Models based on Arrhenius-type correlation can be used to predict SOC of LTC engine which is relatively accurate. It depends on incylinder gas temperature, residual gas rate, fuel and oxygen concentrations. Replacing the fuel equivalence ratio with oxygen fuel ratio in-cylinder F Ocyl , the combustion starting point of diesel LTC can be derived by the following formula:

Z

hsoc

hiv c

1 1 Aa Ne F bOcyl RGF b2

exp


E  dh ¼ 1

ð33Þ

a

RT

The CA10 is used to replace the SOC, and T soc is used to replace T in Eq. (6), CA10 can be approximately estimated by the following equation

1 CA10 ¼ hiv c þ Aa Ne F bOcyl RGF b2 exp

Ea RT soc

ð34Þ

When the CA10 is derived, the CA50 can be predicted by using a fitted correlation

CA50 ¼ ða1 F Ocyl þ a2 ÞCA10 þ ða3 RGF þ a4 Þ

ð35Þ

where, a and m are setting parameters. h is the crank angle. h0 is crank angle at the start of combustion. Dh is the whole combustion duration. Based on the formula (8), the CA50 of diesel LTC can be accurately described by the prediction model. Indicated mean effective pressure (IMEP) is a very important index for diesel. The IMEP model is essential to estimate the indicated torque of a diesel LTC engine. Many researchers have tried to improve the IMEP prediction at different engine operating conditions [24–26]. For IMEP estimation, the key lies in the calculation of thermal efficiency. The combustion of the LTC engine is approximately regarded as a constant volume combustion process. The thermal efficiency can be calculated based on the compression ratio and adiabatic index. On this basis, the correction of the

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combustion phase and the correction of the oxygen fuel ratio are added to obtain the prediction model of the IMEP:



V IVC IMEP ¼ mf LHV f 1  V TDC

  a4 2  a1 CA50 þ a2 CA50 þ a3 exp þ a5 F Ocyl

Table 1 Experimental engine specifications.

ð36Þ

In the combustion process, the average gas temperature incylinder rises to the highest temperature from that of SOC, the highest temperature can be calculated by the following formula:

T comb ¼ T soc þ

gc mf LHV f cv ;iv c ðmair þ megr þ mf Þ þ cv ;rg mrg

ð37Þ

The pressure in-cylinder at the end of combustion can be obtained based on the ideal gas state equation:

peoc ¼ piv c

V iv c T eoc Reoc V eoc T mix Riv c

ð38Þ

2.2.4. Polytropic expansion process Similar to the compression stroke, the pressure and temperature of the burned gas at exhaust valve opening (EVO) are obtained by using polytropic relation:



V eoc V ev o

T ev o ¼ T eoc pev o ¼ peoc

V eoc V ev o

ce 1

ce

ð39Þ

ð40Þ

where, ce is the average specific heat capacity ratio for the expansion process. V eoc is the cylinder volume at the end of combustion. V ev o is the cylinder volume at the EVO. 2.2.5. Exhaust process When the exhaust valve is open, the exhaust gas flow into the exhaust manifold through the exhaust valve. Assuming that this process is a polytropic process, the temperature of the exhaust gas and residual gas in-cylinder can be calculated by using polytropic relation

T rg ¼ T ev o



k 1 V ev o e V ev c

ð41Þ

where, V ev c is the cylinder volume at exhaust valve close (EVC). The mass of residual gas in-cylinder can be obtained according to the ideal gas state equation:

mrg ¼

pEVC V EVC Rem T EVC

ð42Þ

Based on the above analysis, the complete model which is able to accurately describe the gas exchange process and combustion process of diesel LTC was constructed. This model is a threeinput-three-output physics-based control oriented model which consists of three inputs (uegr , uv gt and ud ) and three outputs (kO , CA50 and IMEP). 3. Experimental engine setup The experimental test was carried out on a four-cylinder common-rail turbocharged diesel engine. The specifications of the test engine are listed in Table 1. The original diesel engine in the system is equipped with a fixed ratio turbocharger and hot high pressure EGR system. The air system of original diesel engine was upgraded by replacing the turbocharger with a variable

Engine type

VMR 425DOHC

Bore  stroke Displacement volume Compression ratio Intake valve open (IVO) Intake valve close (IVC) Exhaust valve open (EVO) Exhaust valve close (EVC) Rate power Max. torque Injection system Injector

92 mm  94 mm 2.499 L 17.5:1 344.4°CA ATDC 115.6°CA ATDC 114°CA ATDC 328°CA ATDC 105 kW@4000 r/min 320 Nm@2000 r/min Bosch common rail 6  /0.14 mm, 145°

geometry turbocharger (VGT) and adding an EGR intercooler before EGR valve. The experimental setup and also the data acquisition system on it are shown in Fig. 1. For the high pressure EGR system, the EGR gas is directly from the exhaust manifold and introduced to the intake manifold. Then, the EGR gas is mixed with the fresh charge in intake manifold. When the intake valve is open, the mixed gas flow into the cylinder through the valve. The fuel temperature and coolant temperature are controlled by a digital thermostatic apparatus. The temperature of the fresh air through the compressor is controlled by the intercooler. The EGR gas temperature is controlled by the EGR cooler. The temperature of the charge can be set to a desired value by using a closed-loop controller. The intake manifold pressure is adjusted by the compressor driven by a VGT system. The EGR gas mass flow rate is adjusted by the EGR valve. The air path is controlled by a self-developed air-path aided control system. Therefore the intake pressure, intake temperature, intake mass flow rate of fresh air and EGR rate can be adjusted under different diesel engine operating conditions. A Bosch ETKBypass ECU is used to control the injection parameters. Injection parameter Calibration and monitoring are done by using INCK. The parameters such as fuel injection quantity, injection timing and rail pressure can be adjusted flexibly according to different conditions. The speed and the load of the engine are regulated by using a CAMA CW440eddy current dynamometer. The EGR rate is calculated by the ECM’s EGR 5230 Analyzer. The EGR 5230 directly determines the EGR rate by measuring the O2, oxidizable concentrations and pressure in the intake and exhaust of the engine under test. Two UEGO (universal exhaust gas oxygen) sensor are installed on the intake manifold and exhaust manifold, respectively. The oxygen concentrations can be measured by the UEGO sensors. The EGR rate can be calculated by the following formula

%EGRv ¼

O2air  O2int  100 O2air  O2exh

ð43Þ

where, O2air is the oxygen concentration in ambient air; O2int is the oxygen concentration in intake gas; O2exh is the exhaust oxygen concentration. One Kistler 6056A integrated glow plug in-cylinder pressure transducer is installed in cylinder to trace real-time cylinder pressure during combustion. The encoder connected to crankshaft in the front of the engine samples the cylinder pressure every 0.2 degrees of crank angle. The DEWETRON 5000 combustion analysis system is used to process cylinder pressure sampling and combustion state parameters estimation, such as heat release rate (HRR), cumulative heat release, crank angle of start of combustion (SOC), CA50, and indicated mean effective pressure (IMEP). The dSpace MicroAutobox is used for the sensor signal collection and real-time model calculation. The control systems can communicate with data acquisition system via CAN bus. NOx concentration in

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Fig. 1. Four-cylinder VM common-rail testbench schematic.

the exhaust gas is measured by using a smart NOx sensor (SNS) while soot concentration can be sampled by an AVL 415S smoke meter.

4. Experimental validation The physical model created above is empirically validated with data collected on the experimental engine testbench. Two types of experimental data were collected: stationary data and transient data. Table 2 presents the steady-state operating conditions of the diesel engine used in this study. Two different parameters are calculated and used to evaluate the validation of the model: root mean squared error (RMSE) and correlation coefficient (R). The RMSE for steady-state between the testbench measured value and the model estimated value are calculated as

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn 2 i¼1 ðxi  yi Þ RMSE ¼ n

ð44Þ

And the R can be calculated as

Pn   i¼1 ðxi  xÞðyi  yÞ R ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn 2 Pn  2 i¼1 ðxi  xÞ  i¼1 ðyi  yÞ

Fig. 2 shows the intake oxygen mass fraction model predicted values versus experimental values at various steady-state operation conditions. The model predicted values were calculated by Eq. (2). As shown in figure, the R and RMSE of the intake oxygen mass fraction between model predicted value and experimental values are 0.995 and 0.21%, respectively. Fig. 3 shows the comparison between the experimental actual exhaust oxygen mass fraction and model predicted exhaust oxygen mass fraction. The model predicted values are calculated by Eq. (6). The R and RMSE of the experimental values and model calculated values are 0.994 and 0.39%, respectively. As seen from the two figures, it demonstrated that the model constructed above can accurately estimate the intake and exhaust oxygen mass fraction of the diesel engine at steady-state operation conditions. Fig. 4 indicates the CA50 model predicted value versus experimental value at steady-state operating conditions. It can be seen from the figure that the errors of the actual CA50 and model estimated CA50 are small. The R and the RMSE of the model calculated value and the bench test values are 0.991 and 0.34°CA ATDC, respectively. Fig. 5 shows the IMEP model predicted values versus experiment values at various steady-state operation conditions. It indicates from the figure that the R of IMEP at various engine

ð45Þ

where xi and yi are the two sets of parameters to be compared, namely, the model predicted values and experimental values in this  is the paper.  x is the average value of model predicted values; y average value of experimental values. i is an operating point for steady-state condition, and is a time sample for transient condition. n is the number of measurement.

Table 2 Steady-state operating conditions (100 points). Parameter/unit

Value

Engine speed (rpm) EGR rate (%) Injection timing (°C) Fuel mass (mg/cycle) Coolant temperature (°C) Fuel temperature (°C) Intake manifold pressure (kPa)

1500–2000 0–50 7  15 10–30 70–80 35–42 87–150

Fig. 2. Model predicted values versus experimental values of the F Oim at various steady-state operation conditions.

T. Dong et al. / Applied Thermal Engineering 110 (2017) 1305–1314

Fig. 3. Model predicted values versus experimental values of F Oem at various steadystate operation conditions.

Fig. 4. CA50 model predicted values versus experimental values at various steadystate operation conditions.

Fig. 5. IMEP model predicted values versus experimental values at various steadystate operation conditions.

operating conditions is 0.993 and the RMSE is 0.023 MPa. Based on the above analysis, it is demonstrated that the CA50 and IMEP of the diesel engine can be accurately estimated by the model.

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Compared with the gas exchange model, the combustion model has a poor estimation precision at steady-state operating conditions. That is because there are many parameters influencing the combustion and the combustion process of diesel LTC is too complex. But the R of each parameter is greater than 0.9 whereas the RMSE of all the parameters is relatively small. Therefor, the accuracy of the model can meet the control requirements under steady-state conditions. To validate the transient response and accuracy of the model under transient operating conditions, the fuel rate variations and the intake oxygen mass fraction variations are selected since these two parameters are the main variables that affect the combustion of the diesel LTC. Fig. 6 shows the transient response during the fuel rate step from 6 mg/cycle to 14 mg/cycle, with the diesel engine operates at 1500 r/min, 100 MPa injection pressure, 11°CA ATDC injection timing. It can be seen from the figure that there is a good agreement between model predicted and experimental CA50 and IMEP during the fuel rate steps. The R and RMSE of the CA50 between the calculated values and experimental values are 0.989 and 0.472°CA ATDC, respectively. Similarly, the R and RMSE of the IMEP are 0.983 and 0.03 MPa, respectively. Fig. 7 illustrates the transient response during the fuel rate step from 9 mg/cycle to 16 mg/cycle, with the diesel engine operates at 1750 r/min, 100 MPa injection pressure, 11°CA ATDC injection timing. It denotes that there is a good fitting between predicted values and experimental values of CA50 and IMEP during fuel rate step. The R and RMSE of CA50 between model calculation value and experimental value are 0.985 and 0.552°CA ATDC. While the R and RMSE of IMEP are 0.987 and 0.026 MPa. Fig. 8 illustrates the comparison between the model predicted data and engine test data of the CA50 and IMEP during the fuel rate step from 11 mg/cycle to 22 mg/cycle, with the diesel engine operates at 2000 r/min, 100 MPa injection pressure, 11°CA ATDC injection timing. It can be seen from the figure that the model estimate values have a good agreement with the experimental data. The R and RMSE of CA50 are 0.988 and 0.359°CA ATDC, respectively. While the R and RMSE of the IMEP are 0.987 and 0.048 MPa. The intake oxygen mass fraction is an important state that affects the combustion of the LTC diesel engine [27–29]. Figs. 9– 11 show the transient response during the intake oxygen mass fraction steps at 1500 r/min, 1750 r/min and 2000 r/min. The intake oxygen mass fraction is accurately controlled by the coupling control of EGR and VGT. Fig. 9 compares the model transient response with that of the experiment when the intake oxygen mass fraction is changed from 20% to 14.2% at 1500 r/min, baseline IMEP of 0.374 MPa, 15 mg/ cycle fuel rate. It can be seen from the figure that the model estimated data of CA50 and IMEP are in good agreement with that of experiment test. The R and RMSR of CA50 are 0.983 and 0.417°CA ATDC, respectively. While the R and RMSE of IMEP are 0.982 and 0.053 MPa, respectively. Fig. 10 compares the model predicted transient response with that of the experiment when intake oxygen mass fraction is changed from 20% to 12%, at an engine operating condition of 1750 rpm, baseline IMEP of 0.472 MPa, and constant fuelling (18 mg/cycle). The F Oim step will result in a decrease in the IMEP (0.33 MPa) due to the unstable engine operation in LTC mode. The CA50 was step from 10.7°CA ATDC to 16.5°CA ATDC. At this transient operating condition, CA50 can be predicted by the model with the R less than 0.981 and RMSE less than 0.375°CA ATDC. Meanwhile, IMEP can be predicted with the R is 0.989 and the RMSE is 0.036 MPa. Fig. 11 illustrates an intake oxygen mass fraction step change at an engine operating condition of 2000 r/min, baseline IMEP of 0.37 MPa, and constant fuelling (13 mg/cycle). The intake oxygen mass fraction was stepped from 20.2% to 12.7%. The IMEP was

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Fig. 6. Comparison between predicted and experimental of the CA50 and IMEP. During the fuel rate step at 1500 r/min.

Fig. 7. Comparison between predicted and experimental of the CA50 and IMEP during the fuel rate step at 1750 r/min.

Fig. 8. Comparison between predicted and experimental of the CA50 and IMEP during the fuel rate step at 2000 r/min.

decreased from 0.37 MPa to 0.27 MPa, and the CA50 was increased from 12.0°CA ATDC to 21.6°CA ATDC. The R and RMSE of CA50 are 0.977 and 0.873°CA ATDC. While, the R and RMSE of IMEP are 0.981 and 0.047 MPa. Based on the above analysis, it shows that the model can capture the dynamic characteristics and predict CA50 and IMEP with relatively small error when the fuel rate and the intake oxygen

mass fraction step variation occurs under different transient conditions of the LTC diesel engine. Compared with the steady-state condition, there is a smaller R and a larger RMSE for CA50 and IMEP, respectively. That means the estimation accuracy of the model is decreased under transient conditions. But the values of R between the model predicted data and experimental data of the CA50 and IMEP are greater than 0.9, and the values of RMSE for CA50 and

T. Dong et al. / Applied Thermal Engineering 110 (2017) 1305–1314

Fig. 9. Comparison between predicted and experimental of the CA50 and IMEP during the intake oxygen mass fraction steps at 1500 r/min.

Fig. 10. Comparison between predicted and experimental of the CA50 and IMEP during the intake oxygen mass fraction steps at 1750 r/min.

Fig. 11. Comparison between predicted and experimental of the CA50 and IMEP during the intake oxygen mass fraction steps at 2000 r/min.

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IMEP are smaller than 0.9°CA ATDC and 0.053 MPa, respectively. The fidelity of the model meets the requirements of the model based controller design. 5. Conclusions and future work Based on the dynamic characteristics analysis of LTC diesel engine, the control oriented model, that can detailed describe the dynamics of the gas exchange and combustion process, has been developed. The diesel engine gas exchange model was developed by using the modular modeling method. The gas exchange submodel of diesel engine system consists of the intake manifold, the exhaust manifold, the VGT turbocharger system, the EGR system, cooler system and the cylinder. The detailed dynamic model of these subsystems were described in this paper. A single zone combustion model was constructed by using the phased modeling method. The combustion cycle was broken down into five stages that include air charge process, isentropic compression, constant volume combustion, polytropic expansion, exhaust process. The sub-models that describe the dynamic characteristics of each part were developed. The entire model was obtained by coupling the individual sub-models. Static and dynamic validation of the entire model were performed by using the experimental data. The R and RMSE were calculated and used to evaluate the validation of the model. The static validation results show that the combustion model has slightly larger prediction errors than gas exchange model, but that they are still with satisfactory ranges. Dynamic validation were done using dynamic measurements data, consisting of steps in the fuel rate and intake oxygen mass fraction. The dynamic validation results show that the constructed model can capture the transient dynamics with an acceptable error. The model developed in this paper can be used to design the diesel LTC controller. In future work, the model described in this paper will be further validated under different operating conditions. In addition, this model will be used to design the modelbased controller and control the diesel LTC on-line. Acknowledgement The authors are thankful the support of Diesel Engine Development Program of MIIT (DEDP-1004) and Fundamental research Foundation of Beijing Institute of Technology under Grant No. 3030012211428. References [1] M. Yao, Z. Zheng, H. Liu, Progress and recent trends in homogeneous charge compression ignition (HCCI) engines, Prog. Energy Combust. Sci. 35 (5) (2009) 398–437. [2] S. Saxena, I.D. Bedoya, Fundamental phenomena affecting low temperature combustion and HCCI engines, high load limits and strategies for extending these limits, Prog. Energy Combust. Sci. 39 (5) (2013) 457–488. [3] X. Lu, D. Han, Z. Huang, Fuel design and management for the control of advanced compression-ignition combustion modes, Prog. Energy Combust. Sci. 37 (6) (2011) 741–783. [4] S. Imtenan, M. Varman, H.H. Masjuki, et al., Impact of low temperature combustion attaining strategies on diesel engine emissions for diesel and biodiesels: a review, Energy Convers. Manage. 80 (2014) 329–356.

[5] P. Divekar, Q. Tan, Y. Tan, et al. Nonlinear model reference observer design for feedback control of a low temperature combustion diesel engine, in: 2015 American Control Conference (ACC), IEEE, 2015, pp. 13–18. [6] F. Yang, J. Wang, G. Gao, et al., In-cycle diesel low temperature combustion control based on SOC detection, Appl. Energy 136 (2014) 77–88. [7] M. Bidarvatan, M. Shahbakhti, S.A. Jazayeri, et al., Cycle-to-cycle modeling and sliding mode control of blended-fuel HCCI engine, Control Eng. Practice 24 (2014) 79–91. [8] G. Ingesson, L. Yin, R. Johansson, et al., Simultaneous control of combustion timing and ignition delay in multi-cylinder partially premixed combustion, SAE Int. J. Engines 8 (5) (2015) 2089–2098. [9] G. Ingesson, L. Yin, R. Johansson, et al., A model-based injection-timing strategy for combustion-timing control, SAE Int. J. Engines 8 (2015-01-0870) (2015) 1012–1020. [10] K. Ebrahimi, C. Koch, Model predictive control for combustion timing and load control in HCCI engines, SAE Technical Paper 2015-01-0822, 2015. [11] A.P. Carlucci, D. Laforgia, S. Motz, et al., Advanced closed loop combustion control of a LTC diesel engine based on in-cylinder pressure signals, Energy Convers. Manage. 77 (2014) 193–207. [12] C. Fang, F. Yang, M. Ouyang, et al., Combustion mode switching control in a HCCI diesel engine, Appl. Energy 110 (2013) 190–200. [13] S. Zhang, G. Zhu, Z. Sun, A control-oriented charge mixing and two-zone HCCI combustion model, IEEE Trans. Veh. Technol. 63 (3) (2014) 1079–1090. [14] X. Zeng, J. Wang, A physics-based time-varying transport delay oxygen concentration model for dual-loop exhaust gas recirculation (EGR) engine air-paths, Appl. Energy 125 (2014) 300–307. [15] P. Chen, J. Wang, Control-oriented model for integrated diesel engine and aftertreatment systems thermal management, Control Eng. Practice 22 (2014) 81–93. [16] J. Wahlström, L. Eriksson, Modelling diesel engines with a variable-geometry turbocharger and exhaust gas recirculation by optimization of model parameters for capturing non-linear system dynamics, Proc. Inst. Mech. Engineers, Part D: J. Automobile Eng. 225 (7) (2011) 960–986. [17] M. Shahbakhti, C.R. Koch, Physics based control oriented model for HCCI combustion timing, J. Dyn. Syst. Meas. Contr. 132 (2) (2010) 021010. [18] K. Ebrahimi, C. Koch, A. Schramm, A control oriented model with variable valve timing for HCCI combustion timing control, SAE Technical Paper 2013-010588, 2013. [19] D.G. Van Alstine, L.E. Kocher, E. Koeberlein, et al. Control-oriented PCCI combustion timing model for a diesel engine utilizing flexible intake valve modulation and high EGR levels, in: 2012 American Control Conference (ACC), IEEE, 2012, pp. 2060–2065. [20] T. Dong, F. Zhang, B. Liu, et al., Model-based state feedback controller design for a turbocharged diesel engine with an EGR system, Energies 8 (6) (2015) 5018–5039. [21] L. Guzzella, A. Amstutz, Control of diesel engines, Control Syst., IEEE 18 (5) (1998) 53–71. [22] M. Ammann, N.P. Fekete, L. Guzzella, et al., Model-based control of the VGT and EGR in a turbocharged common-rail diesel engine: theory and passenger car implementation, SAE Technical Paper 2003-01-0357, 2003. [23] M. Jung, R.G. Ford, K. Glover, et al., Parameterization and transient validation of a variable geometry turbocharger for mean-value modeling at low and medium speed-load points, SAE Technical Paper 2002-01-2729, 2002. [24] R. Omran, R. Younes, J.-C. Champoussin, et al., New indicated mean effective pressure (IMEP) model for predicting crankshaft movement, Energy Convers. Manage. 52 (12) (2011) 3376–3382. [25] K. Min, J. Chung, E. Kang, et al., Individual cylinder IMEP estimation using a single cylinder pressure sensor for light-duty diesel engines, SAE Technical Paper 2014-01-1347, 2014. [26] R. Finesso, E. Spessa, Y. Yang, Fast estimation of combustion metrics in DI diesel engines for control-oriented applications, Energy Convers. Manage. 112 (2016) 254–273. [27] U. Asad, M. Zheng, Efficiency & stability improvements of diesel low temperature combustion through tightened intake oxygen control, SAE Int. J. Engines 3 (1) (2010) 788–800. [28] J. Meyer, S. Midlam-Mohler, S. Yurkovich, In-cylinder oxygen concentration estimation for diesel engines via transport delay modeling, in: Proceedings of the 2011 American Control Conference, IEEE, 2011, pp. 396–401. [29] S. Nakayama, T. Fukuma, A. Matsunaga, et al., A new dynamic combustion control method based on charge oxygen concentration for diesel engines, SAE Technical Paper 2003-01-3181, 2003.