Model development for intake gas composition controller design for commercial vehicle diesel engines with HP-EGR and exhaust throttling

Mechatronics 44 (2017) 6–13

Contents lists available at ScienceDirect

Mechatronics journal homepage: www.elsevier.com/locate/mechatronics

Model development for intake gas composition controller design for commercial vehicle diesel engines with HP-EGR and exhaust throttlingR Ádám Bárdos∗, Huba Németh Department of Automobiles and Vehicle Manufacturing, Budapest University of Technology and Economics, 6 Stoczek St, building J, H-1111 Budapest, Hungary

a r t i c l e

i n f o

Article history: Received 1 August 2016 Revised 31 January 2017 Accepted 3 April 2017

Keywords: Diesel engines Exhaust throttle Exhaust gas recirculation (EGR) Air-path

a b s t r a c t Developers of modern diesel engines have to face rigorous restrictions in emission of nitrogen-oxides and particulate matter. Among several methods (DPF, SCR, improved injection etc) which are used to handle these exhaust gas components precise control of the cylinder charge composition seems to be a cost effective solution. The oxygen concentration of the intake gas has a significant impact on the combustion process hence on the pollutant formation. Moreover the precise adjustment of the cylinder charge oxygen concentration can be used to control low temperature combustion processes. The amount of the backflowing exhaust gases is limited by the pressure difference on the EGR duct. To solve this problem the authors suggest the use of novel exhaust brakes with extended functionality: backpressure adjustment for the precise control of the intake gas composition. This way arbitrary EGR rates can be achieved in any engine operation point. For the implementation of such a function the design of an intake manifold oxygen controller is needed, where the control inputs are the EGR valve and the exhaust throttle. This paper demonstrates the development of a control oriented model of the air path system as the first step of this task. The model considers three balance volumes in the air path and has five state variables. Its performance has been evaluated and validated with engine dyno measurements on a medium duty diesel engine. © 2017 Elsevier Ltd. All rights reserved.

1. Introduction Current and next generation emission standards (eg Euro 6 and US EPA 13) include significant limitations. The most challenging for engine developers are especially the reduction of particulate matter (PM) and nitrogen oxide contents of the exhaust gases. Basically there are two possibilities to achieve this: exhaust gas aftertreatment and the reduction of raw emissions. The use of a diesel particle filter (DPF) to reduce the PM emission of a diesel engine results in higher fuel consumption caused by the generated backpressure and the filter regeneration. Selective catalytic reduction (SCR) catalysts are expensive and reach their nominal efficiency only in a limited exhaust gas temperature range. The required urea and its reservoir further increase the costs and reduce the space available

R

This paper was recommended for publication by Associate Editor Roger Dixon. Corresponding author. E-mail addresses: [email protected] (Á. Bárdos), [email protected] (H. Németh). ∗

http://dx.doi.org/10.1016/j.mechatronics.2017.04.002 0957-4158/© 2017 Elsevier Ltd. All rights reserved.

for the fuel tanks. Due to the above disadvantages diesel engine development today aims to reduce aftertreatment system size [1]. To handle NOx and PM formation during the combustion process the precise adjustment of the intake charge oxygen concentration is an effective tool [2] and can be achieved by exhaust gas recirculation (EGR). Current EGR systems concentrate mostly on controlling EGR rates thereby ignoring the quality of the recirculated exhaust gases. The advantages of taking the intake manifold oxygen concentration into consideration is described in [3]. A detailed overview of the relatively complex effects of the exhaust gases on combustion can be found in [4]. Moreover, with higher EGR rates and therefore lower intake manifold oxygen concentrations, the realization of different types of low temperature combustions (LTC) will be possible. For details see [5] and [6]. In addition, synergies of advanced combustion systems by reducing low load NOx are revealed in [7]. Consequently the proposed control model calculates the intake gas oxygen concentration as performance output variable to eliminate the above mentioned limitations of current systems controlling EGR rate.

Á. Bárdos, H. Németh / Mechatronics 44 (2017) 6–13

Nomenclature Tc,in Tamb Tet,out pc,in t pim

Compressor inlet temperature [K] Ambient temperature [K] Exhaust throttle outlet temperature [K] Compressor inlet pressure [Pa] Time [s] Intake manifold pressure [Pa ] 

R

Specific gas constant of air

Tim Vim

Intake manifold temperature [K] Intake manifold volume [m3 ]   Compressor mass flow rate kg s

σc σ egr σ ei κ ηt

EGR mass flow rate

J kg·K

 kg  s

Mass flow rate into the cylinders Adiabatic exponent of air [-] Turbocharger efficiency [-]

 kg  s



J kg·K



cp

Air specific heat at constant pressure

ηv

Engine volumetric efficiency [-] Engine speed [ 1s ] Engine displacement [m3 ] Number of revolutions per cycle [-] Intake manifold oxygen volume fraction [-] Air oxygen volume fraction [-]

ne Vd i xO2 ,im wO2 ,air Mair MO2 xO2 ,em pem Tem Vem

σ eo σt Hl Keo

σf

cd,egr Aegr

σ t,red ct kt pto xO2 ,eo KL0 Tto Vto Kt cd,et Aet

σ et T

Air average molar mass [g/mol] Oxygen molar mass [g/mol] Exhaust manifold oxygen volume fraction [-] Exhaust manifold pressure [Pa] Exhaust manifold temperature [K] Exhaust manifold volume [m3 ]   Engine outflowing mass flow rate kg s

 

Turbine mass flow rate kg s Diesel lower heating value [J/kg] Engine outflowing enthalpy   ratio [-] Fuel mass flow rate kg s EGR valve discharge coefficient [-] EGR valve geometrical flow area [m2 ]

 

Reduced turbine mass flow kg s Turbine mass flow model parameter [-] Turbine mass flow model parameter [-] Turbine outlet pressure [Pa] Engine outlet gas oxygen volume fraction [-] Stoichiometric air to fuel ratio [-] Turbine outlet temperature [K] Volume between turbine and exhaust throttle [m3 ] Turbine temperature drop constant [-] Exhaust throttle discharge coefficient [-] Exhaust throttle geometrical flow area [m2 ]   Mass flow rate through the exhaust throttle kg s Validation cycle length [s]

The mass flow of the backflowing exhaust gases acting as dilutants is governed by the pressure difference through the EGR duct. In case of a high-pressure exhaust gas recirculation system (HPEGR) this results from the turbocharger and engine cooperation and cannot be chosen arbitrarily. Therefore the maximum amount of dilutant in the cylinder charge is limited. With the use of an exhaust throttle the pressure difference can be adjusted and low intake gas oxygen concentrations essential for LTC become achievable. The vanes of a variable geometry turbine can also be used for exhaust backpressure generation for HP-EGR as presented in [8]. On the other hand exhaust throttles are common compo-

7

nents of commercial vehicle diesel engines used mainly as endurance brakes. However, to fulfil the requirements as endurance brakes, exhaust throttles have only two states: fully opened and fully closed. In this work the authors suggest the use of the exhaust brake in an extended functionality, providing precise control of the intake gas composition. For this purpose an accurate tracking position controlled exhaust throttles are needed with intermediate positions (see [9]). Additionally, such exhaust throttles have numerous alternative applications eg brake blending, exhaust gas thermomanagement etc, see [10]. Moreover, the use of an exhaust throttle leads to a cost effective and more reliable solution compared to VGT turbochargers. There are several alternative placements of throttle valves in the engine intake and exhaust system, eg upstream or downstream to the compressor etc. Models for EGR rate increase with intake throttling are presented in [11–13]. Preliminary investigations show that Bárdos and Németh [14], taking the maximum cylinder charge into consideration, the most advantageous placements of the throttling is downstream to the turbine. Similar advantages of exhaust side throttling in low pressure EGR systems are shown in [15]. Based on the above results this paper gives a novel propose for the EGR rate increase through exhaust throttling. In recent years for the MIMO control problem of precisely adjusting the air-path parameters (eg gas mass flow rate, boost pressure etc) with the numerous new actuators (eg VGT, bypass valves etc) several control approaches were developed. Model Predictive Control (MPC) techniques were successfully applied in [16]. The highly nonlinear model of a two-stage turbocharged diesel engine air path was linearized by feedback in [17]. H-infinity techniques were employed for a three-input-three-output problem in [18]. A hybrid robust air-path control was developed in [19] for diesel engines running conventional and LTC combustion modes. For handling the pollutant formation and the combustion process the precise adjustment of the cylinder charge composition is necessary. To solve this problem a control method is proposed which can adapt the intake gas oxygen concentration to a targeted level with the actuation of the EGR valve and if necessary additionally the exhaust throttle. As it is revealed from the above discussion of air-path controllers a wide variety of control techniques are available for physics-based, mean-value, nonlinear models. Moreover, calibration effort can be minimized on different engines with the use of a model based on first engineering principles, hence, a model-based controller is targeted. The model described below is the first step toward this aim. In this paper a physics-based, mean-value, nonlinear model will be described. Three balance volumes were chosen: the intake manifold, the exhaust manifold and the volume between the turbine and the exhaust throttle. The model has five state variables, two control and two measured disturbance inputs. The model validation was carried-out based on engine dyno measurements with a medium-duty diesel engine. The test cycle was taken from the World Harmonized Transient Cycle (WHTC). In Section 2 the engine air path system and the experimental setup will be introduced. The modelling aims and requirements are laid down in Section 3 followed by the modelling assumptions in Section 4. The model is introduced in detail in Section 5 and is converted for the controller design to state space form in Section 6. The validation measurements are described in Section 7. Finally, concluding remarks are given in Section 8. 2. System description and experimental setup The model was validated on a common rail, medium-duty commercial vehicle, turbocharged and intercooled diesel engine. The engine was equipped with a cooled HP-EGR system. The exhaust throttle valve was installed directly downstream of the turbine,

8

Á. Bárdos, H. Németh / Mechatronics 44 (2017) 6–13

Fig. 1. Engine layout.

which provides the minimum volume between the engine exhaust valves and the throttle flap in order to minimize pressure rise times. The layout of the test engine is shown in Fig. 1. The engine was installed on an engine test bench where all the operating parameters of the engine relevant for the system model were measurable. The intake manifold oxygen concentration was measured with an UEGO (Universal Exhaust Gas Oxygen) sensor the signal of which was corrected due to the boost pressure change. 3. Modelling aims and requirements The modelling goals have a major impact on the complexity and the mathematical form of the model. The model developed in this paper will be the base of an intake manifold oxygen concentration controller. Therefore the following requirements were laid down on the basis of this control-oriented intended usage: R1 The model description must be based on the chemistry and thermodynamics of the engine air path system and the model variables and parameters must be of physical relevance. R2 A deterministic input-output model must be specified. R3 The model should be restricted to the index-1 model class. That is, the model should be a set of differential algebraic equations (DAEs), where the algebraic equations can be inserted into the differential ones. R4 The model should be represented in state space form. R5 The model should be capable of describing the dynamics of the intake manifold oxygen concentration within a deviation of 10% from the measurement in the whole operation domain of the engine. The accuracy should be evaluated as L2 error. 4. Simplifying assumptions and input constraints Simplifying assumptions have been made to reduce model complexity and to reach modelling goals. A1 The potential energy is neglected. A2 Constant physical and chemical properties are assumed over each balance volume of the model, such as specific heat, specific gas constant and adiabatic exponent etc. A3 The adiabatic exponent, the specific gas constant and consequently the specific heat of the air and the exhaust gas are equal, which is a good assumption because diesel engines operate with a lean mixture. A4 There are no mass and energy storage effects in the combustion chamber.

A5 The fluids can be modelled as an ideal gas. A6 The temperature of the outflowing gas from the receiver is equal to the receiver’s temperature. A7 The inlet temperature and pressure of the compressor is equal to the ambient temperature and pressure: Tc,in = Tamb and pc,in = pamb . A8 The outlet pressure of the turbine is equal to the ambient pressure: pet,out = pamb . 5. System model The model described below was derived from the preliminary model published in [20] with further development, completion and the omission of the pneumatic booster system. In the engine air path system three balance volumes were chosen: the intake manifold (I.), the exhaust manifold (II.) and the volume between the turbine and the exhaust throttle (III.) (each depicted by dashed lines in Fig. 1). 5.1. Equations for the intake manifold balance volume For the balance volume pressures the isothermal equation was defined based on the mass conservation and the ideal gas law. The heat loss through the walls can be neglected due to the small temperature differences. The EGR gas temperature does not differ significantly from the air temperature flowing out of the intercooler since it is cooled by the engine coolant. Moreover, it was found in [11] that a dynamic model does not improve the model quality, therefore the temperature was treated as a constant seeking of simplicity. The intake manifold has two mass flow inlets from the compressor and from the EGR valve and one mass flow outlet to the cylinders so the differential equation for the pressure state was formulated as follows:

dpim R · Tim = · [σc + σegr − σei ]. dt Vim

(1)

The compressor mass flow rate was computed based on the formula suggested in [8]. The overall efficiency of the turbocharger was treated as a constant which is a good approximation and provides a simple model structure compared to more detailed turbocharger models, eg see [21].

 κ −1  ηt · σt · c p · Tem · ppemto κ − 1   κ −1  σc = pim κ Rκ κ −1 Tamb ·

pamb

−1

(2)

Á. Bárdos, H. Németh / Mechatronics 44 (2017) 6–13

The engine can be modelled as a positive displacement pump, so the induced gas mass flow rate into the cylinders is formulated in the following form:

σei = ηv ·

(3)

The intake manifold oxygen volume fraction can be written as:



·

wO2 ,air Mair MO2

   − xO2 ,im σc + xO2 ,em − xO2 ,im σegr .

(4)

The exhaust pressure was defined in the isothermal form where the mass flow from the engine (σ eo ) was defined as the sum of the engine inlet mass flow rate (σ ei ) and the fuel flow rate σ f provided by the EDC (Electronic Diesel Control).

dpem R · Tem = · [σeo − σt − σegr ] dt Vem

(5)

The exhaust temperature cannot be treated as a constant because its value depends on the engine load. Several models for the exhaust manifold temperature have been developed (see eg [22]) but for our goals these models are too complex for use in a control-oriented model. Therefore the exhaust manifold temperature was calculated from the intake gas and the fuel enthalpy.

c p · σei · Tim + σ f · Hl · Keo c p · σeo

(6)

The EGR valve flow is assumed to be subsonic due to low pressure differences between the exhaust and the intake manifold. A hybrid mode is generated by the checkvalve in the EGR loop. If the exhaust gas flow is pem > pim then the EGR mass flow is calculated as [23]:

σegr = cd,egr · Aegr · √



pem

R · Tem

·



2 · pim · 1− pem

p  im

pem

,

(7)

otherwise:

σegr = 0.

(8)

Turbines in turbomachinery can be approximated as orifices. Therefore the reduced mass flow rate through the turbine can be defined with the help of a simplified two parameter model as suggested in [23]. Hence one can obtain the actual mass flow rate as follows:



p

σt = √ em ct 1 − Tem

p kt em

pto

.

dpto R · Tto = · [σt − σet ], dt Vto

where the turbine outlet temperature is obtained as a constant fraction of the turbine inlet temperature as follows:

(9)

(13)

The mass flow rate through the exhaust throttle remains subsonic during the EGR rate increasing operation. Sonic conditions may occur during exhaust brake operations [10]. Therefore the mass flow rate through the exhaust throttle can be calculated with the orifice equation for subsonic conditions as follows:

σet = cd · Aet · √

pto

R · Tto



·

xO2 ,eo =

σei + σ f

.

(11)

pto



.

(14)

Three balance volumes are designated in the nonlinear model and for each one of them one differential equation for the pressure state was defined. For the intake and the exhaust manifolds an additional differential equation was added for the oxygen concentrations to allow the calculation of the dilution effect of the exhaust gas in the intake manifold. The state vector consists of the states of the intake manifold pressure, the exhaust manifold pressure, the pressure of the volume between the turbine and the exhaust throttle and the exhaust and intake manifold oxygen concentrations as follows:



x = pim

pem

pto

xO2 ,im

xO2 ,em

T

.

(15)

The input vector contains the EGR valve and the exhaust throttle flow areas:



u = Aegr

Aet

T

.

(16)

The measurable disturbance vector includes the engine speed and the fuel mass flow respectively:



T σf .

6.2. The state equations

wO2 ,air Mair MO2

amb

6.1. Definition of model vectors

dxO2 ,em R · Tem = · [σeo (xO2 ,eo − xO2 ,em )], dt Vem pem

where the oxygen volume fraction of the engine outlet flow can be calculated with the following algebraic equation:

p

A natural form of system representation for control engineering is the state space form. In such model structures, originating from first engineering principles, state variables are the set of the conserved extensive quantities in the process system [24]. Most theories and techniques in control system design and analysis both in linear [25] and nonlinear [26] control theory, are based on state space models. Therefore, in accordance with the predefined modelling aims and requirements R4 and to facilitate the future controller design the above defined nonlinear model will be converted into state space form.

d = ne

(10)



2 · pamb · 1− pto

6. System model in state space form

The exhaust manifold oxygen volume fraction equation is formulated as:

σei xO2 ,im − σ f KL0

(12)

Tto = Kt · Tem .

5.2. Equations for the exhaust manifold balance volume

Tem =

5.3. Equation for the balance volume between the turbine and the exhaust throttle The pressure state equation for the third balance volume is

pim V · ne · d . R · Tim i

dxO2 ,im R · Tim = dt Vim pim

9

(17)

The sonic flow condition of the EGR valve and the exhaust throttle and the EGR checkvalve adds hybrid modes to the model. However, in order to arrive at the simplest form of the model the state space equation will be given for the nominal hybrid mode. After inserting the constitutive equations into the differential conservation balances the state space model can be obtained in an

10

Á. Bárdos, H. Németh / Mechatronics 44 (2017) 6–13

input-affine form.

⎡ p˙ im ⎢ p˙ em ⎢ p˙ to ⎣

⎤

⎡ f (x, d, r )⎤ ⎡g (x, d, r ) 1 11 ⎥ ⎢ f2 (x, d, r )⎥ ⎢g21 (x, d, r ) ⎥ = ⎢ f3 (x, d, r )⎥ + ⎢ 0 ⎦ ⎣ ⎦ ⎣ x˙ O2 ,im f 4 ( x, d, r ) g41 (x, d, r ) x˙ O2 ,em f 5 ( x, d, r ) 0

g32 (x, d, 1 ) = −

⎤

0 0 ⎥ g32 (x, d, r )⎥u ⎦ 0 0

(18)

R · Tim · Vim



1−

·



pem pto

 pem kt  pto R ·κ κ −1

· ·

p

c p ·ηv · R·Tim ·ne · 2

·

im

Vd i

· Tamb ·

ηv · R·Tim ·ne · pim pamb



im κ −1

κ

Vd i

·

·

−1

+σ f

(19)





(20)

f 2 ( x, d, 1 ) =

im

p

im

Vd i

+σ f

f 5 ( x, d, 1 ) = ·

p

im

Vd i

wO2 ,air Mair − xO2 ,im MO2



1−

 pem kt pto

pim R·Tim



· ne ·

ηv ·



· ne ·

c p ·σei ·Tim +σ f ·Hl ·Keo

p

c p · ηv · R·Tim ·ne · im

⎛ ⎝

Vd i

+σ f



Vem · pem

ηv ·

pim R·Tim

· ne ·

Vd i

ηv ·

⎞⎤

·



cd,egr ·



2 · pim · pem · R ·

p

c p · ηv · R·Tim ·ne · im

=−

Vd i

+σ f

Vem

(21)

f 3 ( x, d, 1 ) =

c p ·σei ·Tim +σ f ·Hl ·Keo

p

im

Vd i

+σ f



 · 1−

 pim  pem

.

 · pem · ct

p

c p · ηv · R·Tim ·ne · im

Vd i

+σ f

Vd i

+ σf





,

(25)

(26)

ηv ·



pim V · ne · d + σ f · R · Tim i

pim R·Tim

· ne ·

Vd i

wO2 ,air Mair MO2

+ σf

−

(27)

(28)



(23)

R5×2

where the D11 ∈ and D12 ∈ are zero matrices. C is determined by the application circumstances of the model. For example, on the test bed used all the state variables were measured directly, therefore C ∈ R5×5 can be equal to the identity matrix. For vehicle applications of the proposed intake manifold oxygen controller some sensors should be substituted by observers to provide a cost effective solution. The performance output is the intake manifold oxygen concentration based on the modelling aim and it is generated from the measured output as:

z= 0

Vto

   kt  1 − ppem  to · , V p  c p ·ηv · R ·Timim ·ne · id ·Tim +σ f ·Hl ·Keo



−1

6.3. The measured output and the performance equations

R5×2

The elements of the third state equation: c p · ηv · R·Tim ·ne ·

−1

κ

Since the output is linear with respect to the state vector, the measured output is written as the following linear equation

(22)

R · Kt ·

pto

− xO2 ,em ⎠⎦.

+σ f

c p ·σei ·Tim +σ f ·Hl ·Keo

 pem κ −1

· xO2 ,im − σ f · KL0 ·

y = Cx + D11 d + D12 u, g21 (x, d, 1 )

 κ κ−1

·

· Tim + σ f · Hl · Keo

Vd i

pim R·Tim

pim pamb

· cp ·



  Tim · xO2 ,em − xO2 ,im · cd,egr · pem · Vim · pim

·

pim V · ne · d + σ f − pem · ct · · ηv · R · Tim i ⎞    kt ⎟  1 − ppem ⎟  to ·  ⎟, Vd pim c · η · ·n · ·T + σ ·H ·K p v e eo im ⎠ f l  R·Tim i

 c p · ηv · R·Tim ·ne ·



c p · ηv ·

R·



Vem

(24)

The elements of the fifth state equation are:

·Tim +σ f ·Hl ·Keo

c p · ηv · R·Tim ·ne ·

.

im

The elements of the second state equation:

R·

 · pamb

pto



R ·κ κ −1 · Tamb ·



im

Vd i

+σ f

 V p c p · ηv · R·Tim ·ne · id +σ f

 V p c p · ηv · R·Tim ·ne · id +σ f

p

Vd i

  R · 2·pim · 1 −  pim   pem pem . ·   c p ·ηv · Rp·Timim ·ne · Vid ·Tim +σ f ·Hl ·Keo

2·p pim Tim · cd,egr · pem  R · pemim · 1 − pem g11 (x, d, 1 ) = · . Vim  c p ·ηv · Rp·Timim ·ne · Vid ·Tim +σ f ·Hl ·Keo

c p ·ηv · R·Tim ·ne ·

amb

cp ·

g41 (x, d, 1 ) =

pim V − ηv · · ne · d , Vim i

 

p

im

ηt · pem · ct · 



pto

·Tim +c p ·σ f ·Hl ·Keo

p



1−

R · Tim f 4 ( x, d, 1 ) = · Vim · pim

· ηt · pem · ct ·

−1

p

c p ·σei ·Tim +σ f ·Hl ·Keo c p · ηv · R·Tim ·ne ·

The elements of the fourth state equation:



κ −1 κ

   2 · R · Kt · 

where r : Rn → N is a piecewise constant switching function mapping from the state space to N. The integer set N is finite, i.e. q N = 1, 2, . . . , n, where n = i=a ni is the total number of hybrid modes and ni is the number of the individual hybrid modes of a subsystem (n = 2 × 3 = 6). Let the value of the switching function mapping r be 1 for the nominal hybrid mode. The nonlinear state functions with all constitutive relations inserted for the nominal hybrid mode. The elements of the first state equation are given as:

f 1 ( x, d, 1 ) =

cd,et · pto Vto

0

0

1



0 y.

(29)

7. Model validation The model verification and validation was performed in MATLAB/Simulink environment. The parameters used in simulations are listed in Table 1.

Á. Bárdos, H. Németh / Mechatronics 44 (2017) 6–13

11

Table 1 List of parameters. Parameter name

Symbol

Value

Unit

Adiabatic exponent Air mean molar mass Air oxygen mass fraction Ambient temperature Ambient pressure Diesel lower heating value Diesel stoichiometric air consumption EGR valve discharge coefficient Engine displacement Engine volumetric efficiency Exaust manifold volume Exhaust throttle discharge coefficient Intake manifold temperature Intake manifold volume Number of revolutions per cycle Oxygen molar mass Parameter for engine-out temperature Specific gas constant Turbocharger efficiency Turbine mass flow model parameter 1 Turbine mass flow model parameter 2 Volume between exh. manifold and throttle

κ

1.4 28.96 0.232 300 105 43 14.5 0.195 0.003922 0.82 0.0051 0.501 315 0.0133 2 32 0.25 287 0.273 −0.48 2.74 × 10−5 0.0045

– kg/kmol – K Pa MJ/kg kg/kg – m3 – m3 – K m3 – kg/kmol – J/kg∗ K – – – m3

Mair wO2 ,air Tamb pamb Hl KL0 cd,egr Vd

ηv

Vem cd,et Tim Vim i M O2 Keo R

ηt

kt ct Vto

Fig. 2. Comparison of the modelled and measured quantities in the World Harmonized Transient Cycle (from 990 to 1150 s).

The model performance was evaluated in the EU legally prescribed World Harmonized Transient Cycle (WHTC). For comparison a section of the cycle from 990 to 1150 s is shown. The engine operation points of the complete WHTC cycle for the investigated engine are depicted in Fig. 2. The motoring points were measured and depicted with zero loads because the applied eddy current brake cannot produce negative torques. It can be seen that engine speeds over 1500 RPM are quite rare. In these medium engine speeds the boost pressure is often higher than the exhaust manifold pressure without exhaust throttling. High number of low load points can also be observed. Consequently the test cycle provides the opportunity to take advantage of the EGR rate increase by the exhaust throttling, and the low air-fuel ratio does not limit its utilization in low load cases. The EGR valve and exhaust throttle areas were actuated based on predefined lookup tables. The EGR valve is fully opened at low loads and gradually closes at high loads. The exhaust throttle is nearly closed at low loads and low speeds and gradually opens with increasing load and speed.

A good fit of the modelled signals can be observed. The intake and exhaust manifold signals follow the measurement with a delay. This is caused by the unmodelled dynamics of the turbocharger which is calculated by algebraic equations. The inclusion of the turbocharger dynamics in the differential equations would lead to unacceptably complex model structures and a large number of model states which is contradictory to the control oriented application aim. Based on R5 the fitting of the performance variable is desired. In order to show the accuracy of the model the deviation of the intake manifold oxygen concentration was evaluated as rootmean square errors in the validation cycle based on the following expression:

 εxim =

1 T

T 0



xim,m − xim xim,m

2 dt

(30)

12

Á. Bárdos, H. Németh / Mechatronics 44 (2017) 6–13 Table 2 Comparison of controller performance and its requirements. No

Requirement

Limit

Model performance

R1 R2 R3 R4 R5

First engineering principle based model Deterministic model Index-1 class model State space model RMS error

True/False True/False True/False True/False 10%

True True True True 6.9%

The duration of the entire cycle was 160 s and the suffix ’m’ denotes the measured value. The compliance of the predefined requirements in Section 2 is summarized in Table 2. All the predefined requirements have been met. Therefore the model can be used for the intended intake manifold oxygen concentration controller design. 8. Summary and conclusion The legal frameworks for commercial vehicle diesel engines forces engine developers to constantly utilize new tools to reduce engine emissions and fuel consumption. A possible way of emission limitation is influencing the combustion process through exhaust gas recirculation. This is a well-known method for nitrogen oxide reduction and can also be applied for the realization and control of low temperature combustion processes. The widely used control of the EGR-rate does not give accurate information about the inlet gas composition. For this reason the use of the intake manifold oxygen concentration as a controlled variable is targeted. Moreover, in high pressure EGR systems the amount of the backflowing exhaust gases is limited by the pressure ratio between the intake and exhaust manifold. Consequently the required level of oxygen concentration cannot be reached despite the wideopen EGR valve. In these cases the exhaust throttle valve, which is a common component on commercial vehicle diesel engines, can generate the accurate backpressure to adjust the amount of the recirculated exhaust gases arbitrarily. Accordingly an intake manifold oxygen concentration controller is targeted. Towards these aims a physics-based, control-oriented model for commercial vehicle diesel engines equipped with a high-pressure EGR system and exhaust throttle was designed in this paper. After defining the modelling requirements simplifying assumptions were made to ensure as compact a model as possible. First engineering principle based model equations were described for three balance volumes resulting in five state variables. The equations were converted to state space form to facilitate controller synthesis. The model was validated by engine dyno measurements with a section of the World Harmonized Transient Cycle, which shows a good fit of the intake manifold oxygen concentration. All the predefined requirements were fulfilled. Hence, an intake gas composition controller design with high-pressure EGR and exhaust throttling will be possible using the developed model. Supplementary material Supplementary material associated with this article can be found, in the online version, at 10.1016/j.mechatronics.2017.04.002. References [1] Körfer T, Ruhkamp L, Herrmann O, Linssen R, Adolph D. Verschärfte anforderungen an die luftpfadregelung bei nutzfahrzeugmotoren. MTZ - Motortechnische Zeitschrift 2008;69(11):958–65. doi:10.1007/BF03227504. [2] Herrmann OE. Emissionsregelung bei nutzfahrzeugmotoren über den luftund abgaspfad, Aachen: Technische Hochschule; 2005. Ph.D. thesis. http:// publications.rwth-aachen.de/record/52065.

[3] Bessai C, Stölting E, Gratzke R. Virtueller sauerstoff-sensor im einlasskrümmer eines dieselmotors. MTZ - Motortechnische Zeitschrift 2011;72(11):874– 81. doi:10.1365/s35146- 011- 0189- x. [4] Ladommatos N, Abdelhalim S, Zhao H, Hu Z. The dilution, chemical, and thermal effects of exhaust gas recirculation on diesel engine emissions - part 4: effects of carbon dioxide and water vapour. SAE Technical Paper 971660. SAE; 1997. doi:10.4271/971660. [5] Akihama K, Takatori Y, Inagaki K, Sasaki S. Mechanism of the smokeless rich diesel combustion by reducing temperature. SAE Technical Paper 2001-010655. SAE; 2001. doi:10.4271/2001-01-0655. [6] Rebecchi P. Fundamentals of thermodynamic for pressure-based lowtemperature premixed diesel combustion control, Holzgarten Str. 16, 70174 Stuttgart: Universität Stuttgart; 2013. Ph.D. thesis. http://elib.uni-stuttgart.de/ opus/volltexte/2013/8276. [7] Johnson TV. Review of diesel emissions and control. Int J Engine Res 2009;10(5):275–85. doi:10.1243/14680874JER04009. [8] Ammann M, Fekete N, Guzzella L, Glattfelder A. 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. SAE; 2003. doi:10.4271/2003- 01- 0357. [9] Ahmed FS, Laghrouche S, Bagdouri ME. Analysis, modeling, identification and control of pancake DC torque motors: application to automobile air path actuators. Mechatronics 2012;22(2):195–212. http://dx.doi.org/ 10.1016/j.mechatronics.2012.01.004. www.sciencedirect.com/science/article/pii/ S09574158120 0 0 050. [10] Bárdos Á, Szimandl B, Németh H. Feedforward LQ servo backpressure controller for engine exhaust throttle. 14th mini conference on vehicle system dynamics, identification and anomalies (VSDIA 2014); 2014. [11] Wahlström J, Eriksson L. Modeling of a diesel engine with intake throttle, VGT, and EGR. Tech. Rep., LiTH-R-2976. SE-581 83 Linköping, Sweden: Department of Electrical Engineering, Linköpings Universitet; 2010. https://www.fs.isy.liu. se/Publications/Reports/10_R_2976_JWLE.pdf. [12] van Nieuwstadt M. Coordinated control of EGR valve and intake throttle for better fuel economy in diesel engines. SAE Technical Paper 2003-01-0362. SAE; 20 03. doi:10.4271/20 03- 01- 0362. [13] Friedrich I, Liu CS, Oehlerking D. Coordinated EGR-rate model-based controls of turbocharged diesel engines via an intake throttle and an EGR valve. In: 2009 IEEE vehicle power and propulsion conference; 2009. p. 340–7. doi:10. 1109/VPPC.2009.5289828. [14] Bárdos Á, Németh H. EGR support investigation on a diesel engine. A ˝ Jövo˝ Jármuve 2011;3–4:48–53. http://jovojarmuve.hu/content/imageup/cikk_ pdf/c675bcbb9ef694cb4bd5d670357bae8e.pdf. [15] Nyerges Á, Németh H. Low pressure intake throttle and exhaust brake support assessment on the low pressure loop exhaust gas recirculation on medium duty diesel engines. 14th mini conference on vehicle system dynamics, identification and anomalies (VSDIA 2014); 2014. [16] Huang M, Nakada H, Butts K, Kolmanovsky I. Robust rate-based model predictive control of diesel engine air path. In: 2014 American control conference; 2014. p. 1505–10. doi:10.1109/ACC.2014.6859220. [17] Liu Y, Zhou J, Fiorentini L, Canova M, Wang YY. Control of a two-stage turbocharged diesel engine air path system for mode transition via feedback linearization. In: 2016 American control conference (ACC); 2016. p. 5105–11. doi:10.1109/ACC.2016.7526163. [18] Yang Z, Winward E, Zhao D, Stobart R. Three-input-three-output air path control system of a heavy-duty diesel engine. IFAC-PapersOnLine 2016;49(11):604–10. http://dx.doi.org/10.1016/j.ifacol.2016.08.088. 8th {IFAC} symposium on advances in automotive control {AAC} 2016 Norrköping, Sweden, 20–23 June 2016. [19] Wang J. Hybrid robust air-path control for diesel engines operating conventional and low temperature combustion modes. IEEE Trans Control Syst Technol 2008;16(6):1138–51. doi:10.1109/TCST.2008.917227. [20] Bárdos Á, Németh H. Control oriented air path model for compressed air boosted diesel engines. Periodica Polytechnica Transportation Engineering 2013;41(1):3–12. doi:10.3311/PPtr.7093. [21] Moraal P, Kolmanovsky I. Turbocharger modeling for automotive control applications. SAE Technical Paper 1999-01-0908. SAE; 1999. doi:10.4271/ 1999- 01- 0908. [22] Eriksson L. Mean value models for exhaust system temperatures. Technical Paper Series (2002-01-0374). SAE; 2002. doi:10.4271/2002- 01- 0374. [23] Guzzella L, Onder CH. Introduction to modeling and control of internal combustion engine systems. 2nd ed. Berlin Heidelberg: Springer Verlag; 2010. doi:10.1007/978- 3- 642- 10775- 7.

Á. Bárdos, H. Németh / Mechatronics 44 (2017) 6–13 [24] Hangos K, Bokor J, Szederkényi G. Analysis and control of nonlinear process systems. Springer; 2004. doi:10.1007/b97665. [25] Bokor J, Gáspár P, Szabó ZB. Robust control theory with automotive applications. Budapest: Typotex Kiadó; 2012. ISBN 978-963-279-788-5. [26] Slotine J-JE, Li W. Applied nonlinear control. Englewood Cliffs (N.J.): Prentice Hall; 1991. ISBN 0-13-040890-5.

13

Ádám Bárdos was born in Ózd, Hungary, in 1986. He received the Diploma in Mechanical Engineering in 2010 from the Budapest University of Technology and Economics. He is currently lecturer for the Department of Automobiles and Vehicle Manufacturing of Budapest University of Technology and Economics (BUTE).