Analytical Model of a Compression Ignition Engine for
Control Analysis & Real-Time Simulations
Olivier Grondin†‡, Jean Maquet†, Christophe Letellier†, Houcine Chafouk‡
†CORIA - UMR 6614, Université & INSA de Rouen, Avenue de l’Université - BP 12, 76801 Saint-Etienne du Rouvray -
France, Emails: name@coria.fr, Telephone: +33 (0)2 32 95 37 04, Fax: +33 (0)2 32 95 97 21
‡IRSEEM, Avenue Galilée, 76800 Saint Etienne du Rouvray - France, Emails: olivier.grondin@esigelec.fr,
houcine.chafouk@esigelec.fr, Telephone: +33 (0)2 32 91 58 58, Fax: +33 (0)2 32 91 58 59
Abstract—This paper presents a direct injection (DI) diesel
engine model based on the filling and emptying approach with a
crank angle resolution. The model includes a variable geometry
turbocharger (VGT), an exhaust gas recirculation valve (EGR)
and a modern injection system. A detailed crankshaft inertial
model is used to reproduce engine speed variations. Model inputs
are EGR valve position, VGT position and injection system
settings (injection timing, fuel mass). Pressure and temperature
inside plenums (manifolds and cylinders), engine speed, indicated
torque may be taken as model outputs. The purpose of
this work is to provide a flexible compression ignition engine
model in order to help engineers in control system development.
The model is designed to fulfill demands on electronic control, it
can be used as an engine simulator : off-line control algorithms
testing as well as real-time simulations are possible.
Keywords—Diesel engines, modeling, filling and emptying
method, control analysis, real-time simulations.
I. INTRODUCTION
More than one century after Dr. Rudolf Diesel’s invention,
the compression ignition engine remains one of the
most efficient internal combustion engine for ground vehicle
applications. Increasing demands on driveability, emission
reduction and efficiency lead to a progressive introduction of
electronic actuators. Variable geometry turbocharger, EGR
valve and modern injection systems (common-rail, HEUI,...)
allow a better control of air, EGR and fuel masses fed to
the cylinder. A topical concern with diesel engines is to
exploit potential benefits provided by advanced electronics
hardware. In order to understand engine behavior with electronic
actuators and to test control algorithms, engine models
for off-line or real-time simulations are required. Modeling
of internal combustion engines involves researchers from
many fields. In the development of diesel engine models
we may distinguish three main steps : (i) thermodynamic
models based on first and second law analysis used since
1950, (ii) empirical models introduced in early 1970s [1] and
(iii) physically-based non linear models for both engine simulation
and control design introduced during the past twenty
years. For comprehensive reviews on Diesel engine modeling
see [2], [3]. In this paper we focus on cylinder-bycylinder
engine models (CCEM) [4]. This model, based on
the filling and emptying concept [5] gives an accurate prediction
of in-cycle engine state evolution (in-cylinder pressure,
instantaneous crankshaft speed,...). That is the reason why
CCEM are well suited for studying transient fuelling control
and for fault diagnostic applications [6].
The next section gives the reader a set of equations to
form an overall multi-cylinder compression ignition engine
fitted with modern actuators. This section is divided in three
parts : (i) the air and EGR path, (ii) the cylinder model (including
heat transfer and heat release) and (iii) the engine
dynamic model. Section III describes the setup for real-time
simulation and results are compared with experimental data
recorded on a test cell. As a conclusion we consider future
model improvements and the possible issues that can be investigated
with the proposed engine model.
II. THE DIESEL ENGINE MODEL
A. Engine structure & model hypothesis
We study a multi-cylinder direct injection diesel engine.
A turbocharger is fitted to the engine to improve its low
power density. The turbocharger consists of a compressor
powered by a variable geometry turbine. This system allows
a good boost pressure for all range of turbocharger speed.
The engine is also equipped with an EGR valve. Note that
exhaust gas recirculation is the most useful way to reduce
NOx emissions. The valve is located between the exhaust
and intake manifolds and is controlled to reintroduce the adequate
fraction of burned fuel (EGR fraction setpoints are
usually mapped according to engine speed and mass of fuel
injected per cycle [7]).
Engine plenums (cylinders, intake and exhaust manifolds)
are modelled as separate thermodynamic systems containing
gases at uniform state. With respect to the filling and
emptying method, mass, temperature and pressure of gas are
calculated using first law and mass conservation. The main
simplifying assumptions for this model are :
• ideal gases with constant specific heats;
• effects of heat transfer through intake and exhaust manifolds
are neglected;
• the engine cylinder wall temperature Twall is supposed
to be steady and homogenous;
• compressor inlet and turbocharger outlet temperatures
and pressures are assumed to be equal to ambient pressure
pa and temperature Ta.
The schematic diagram of the engine is shown in Fig. 1.
Note that parameters u¤ refer to model control inputs. Pa-......