MODELING AND CONTROL OF SI AND SI-HCCI HYBRID
COMBUSTION ENGINES
By
Xiaojian Yang

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Mechanical Engineering
2011

ABSTRACT
MODELING AND CONTROL OF SI AND SI-HCCI HYBRID COMBUSTION ENGINES
By
Xiaojian Yang
As a special combustion mode of internal combustion (IC) engines, homogeneous charge
compression ignition (HCCI) combustion has the potential to meet the increasingly stringent
emissions regulations with improved fuel economy. In order to take advantage of this
combustion mode, the traditional spark ignition (SI) engine needs to operate in both SI and HCCI
modes, and the combustion mode transition between the SI and HCCI combustions is inevitable.
It is fairly challenging to operate the engine in the two distinct combustion modes, and it is even
more difficult to have smooth combustion mode transition between the two modes due to the
distinct engine operational parameters over the two combustion modes and the cycle-to-cycle
residual gas dynamics. In this research, the modeling and control of the combustion mode
transition problem were studied for a multi-cylinder engine with dual-stage valve lift and
electrical variable valve timing (VVT) systems.

In order to describe engine continuous time and event-based dynamics a mixed time-based and
crank-based engine model was developed. The continuous dynamics of engine air-handling
system and crankshaft were modeled by traditional time-based mean value models; and the
engine combustion process was modeled as a function of crank angle (crank-based) using the
two-zone combustion modeling approach. The developed combustion model is capable of

ii

simulating the SI, HCCI, and SI-HCCI hybrid combustion modes. This unique modeling
approach made it possible for the engine model to be simulated in real-time in a dSPACE based
hardware-in-the-loop (HIL) system, due to its low computational throughput. The developed
engine model was calibrated and validated using the simulation results from the corresponding
one-dimensional GT-Power engine model in the dSPACE based HIL engine simulation
environment.

Through HIL simulations using the developed engine model, a multistep SI to HCCI combustion
mode transition strategy was incrementally developed. It takes several engine cycles (typically
five) to complete the combustion mode transition. During the combustion mode transition, a
model based linear quadratic (LQ) engine MAP (intake manifold absolute pressure) tracking
controller was used to maintain the air-to-fuel ratio in the desired range by regulating the engine
throttle; the DI (direct injection) fuel quantity of individual cylinder was controlled via iterative
learning control (ILC); and spark ignitions were maintained to enable the SI-HCCI hybrid
combustions; The other engine parameters, such as the intake/exhaust valve timing and lift,
external EGR (exhaust gas recirculation) valve opening were controlled in an open loop. The
entire control strategy was validated in the developed HIL simulation environment. The
simulation results demonstrated the effectiveness of the proposed control strategy under both
constant and transient engine operating conditions. It can be concluded that smooth combustion
mode transition is achievable for IC engines using dual-stage valve lift and electrical VVT
systems as the valve actuation systems.

iii

Copyright by
Xiaojian Yang
2011

iv

TO MY PARENTS AND FAMILY

v

ACKNOWLEDGMENTS
This dissertation would not have come into existence without the generous support and
encouragement of many people. There are no words sufficient to express my gratitude to them.
First and foremost, I would like to express my profound gratitude to my advisor, Dr.
Guoming Zhu, for his continued support and guidance for my research work, and generous help
with my life during the past four years. His comprehensive knowledge of automotive control
theory and application inspired me and led me into this interesting area, and I learned a lot. Dr.
Guoming Zhu also encouraged me to read and write many technical papers, and improved my
reading and writing skills at the same time. These skills are very important to me, not only for my
Ph.D. study, but also for my future career.
I would also like to acknowledge my committee members: Dr. Clark Radcliffe, Dr. Harold
Schock, and Dr. Hassan Khalil, for their helpful discussions and insightful comments during my
dissertation work, as well as for the knowledge they shared with me in their lectures that were
essential for me to make progress throughout my Ph.D. program. Having this committee for my
dissertation was a great privilege.
Further thanks are extended to past and current graduate students and other lab personnel
who helped me considerably with many aspects of my research work: Xuefei Chen, Andrew
Huisjen, Taotao Jin, Gary Keeney, Mittal Mayank, Stephen Pace, Xing Rao, Zhen Ren, Cody
Squibb, Tom Stuecken, Yuxin Zhang.
Lastly, I am overly grateful for my parents and my wife, for their never-ending love and
encouragement. I want to dedicate this dissertation to them. I also want to dedicate this dissertation
to my precious daughter, Yuning Yang, and wish her a splendid future.

vi

LIST OF CONTENTS
LIST OF TABLES .......................................................................................................................... x
LIST OF FIGURES ....................................................................................................................... xi
NOTATIONS ............................................................................................................................... xiv
CHAPTER 1
INTRODUCTION .......................................................................................................................... 1
1.1
New Technologies and Challenges ............................................................................. 1
1.1.1
Engine downsizing.......................................................................................... 1
1.1.2
HCCI combustion ........................................................................................... 2
1.2
Related Work............................................................................................................... 4
1.2.1
HCCI capable engine control.......................................................................... 4
1.2.2
SI-HCCI hybrid combustion mode ................................................................. 6
1.2.3
Related control methods ................................................................................. 7
1.2.4
HIL engine simulation .................................................................................... 8
1.2.5
Engine modeling ............................................................................................. 9
1.3
Dissertation Contributions ........................................................................................ 10
1.4
Dissertation Outline ...................................................................................................11
CHAPTER 2
DUAL-STAGE TURBOCHARGED SI ENGINE MODELING USING MIXED MEAN VALUE
AND CRANK BASED METHOD............................................................................................... 13
2.1
Introduction............................................................................................................... 13
2.2
Engine Configuration and GT-Power Model ............................................................ 14
2.3
Mean Value Models for Engine Air Handling System.............................................. 18
2.3.1
Valve model .................................................................................................. 18
2.3.2
Manifold filling dynamic model ................................................................... 18
2.3.3
Crankshaft dynamic model ........................................................................... 19
2.3.4
Turbine and compressor models ................................................................... 19
2.4
Crank Based One-Zone SI Combustion Model ........................................................ 22
2.4.1
Crank based methodology............................................................................. 22
2.4.2
Gas exchange process modeling ................................................................... 24
2.4.3
Fueling dynamics and air-to-fuel ratio calculation ....................................... 26
2.4.4
One-zone SI combustion model.................................................................... 27
2.4.5
Engine torque computation ........................................................................... 29
2.5
Model Validation Using GT-Power Model ............................................................... 30
2.6
Conclusions............................................................................................................... 33
CHAPTER 3
CONTROL ORIENTED SI-HCCI HYBRID COMBUSTION MODEL FOR AN HCCI
CAPABLE INTERNAL COMBUSTION ENGINE .................................................................... 35
3.1
Introduction............................................................................................................... 35
3.2
Engine Architecture and GT-Power Model............................................................... 37

vii

3.3
3.4

3.5
3.6

3.7

3.8

SI-HCCI Hybrid Combustion Model Architecture ................................................... 40
Revisit the Gas Exchange Process ............................................................................ 42
3.4.1
Gas exhaust process ...................................................................................... 43
3.4.2
Residual gas recompression in NVO ............................................................ 46
3.4.3
Gas exchange behavior in PVO .................................................................... 47
3.4.4
Air intake process ......................................................................................... 48
One-zone HCCI Combustion Model ........................................................................ 50
Two-zone SI Combustion Model .............................................................................. 51
3.6.1
Two-zone assumptions.................................................................................. 52
3.6.2
Governing equations ..................................................................................... 53
3.6.3
Solutions of two-zone model ........................................................................ 54
Model Validation Using GT-Power........................................................................... 55
3.7.1
Comparison between two-zone and one-zone model ................................... 56
3.7.2
Two-zone SI combustion model validation .................................................. 60
3.7.3
One-zone HCCI combustion model validation............................................. 65
3.7.4
The impact of external EGR ......................................................................... 67
Conclusions............................................................................................................... 68

CHAPTER 4
IMPLEMENTATION OF ENGINE MODEL IN THE HIL SIMULATION ENVIROMENT .... 70
4.1
Introduction............................................................................................................... 70
4.2
From Mathematic Equations to Simulink Model...................................................... 71
4.2.1
Build engine in Simulink .............................................................................. 71
4.2.2
Model solution in Simulink .......................................................................... 73
4.3
Model Implementation in HIL Simulator ................................................................. 76
4.3.1
The engine simulator hardware..................................................................... 76
4.3.2
HIL simulation system architecture .............................................................. 77
4.4
Engine HIL Simulations............................................................................................ 80
4.4.1
Transient performance of engine with dual-stage turbocharger ................... 81
4.4.2
SI to HCCI combustion mode transition....................................................... 84
4.5
Conclusions............................................................................................................... 88
CHAPTER 5
SI AND HCCI COMBUSTION MODE TRANSITION CONTROL .......................................... 89
5.1
Introduction............................................................................................................... 89
5.2
The Control Problem Formulation............................................................................ 90
5.2.1
Control target of the combustion mode transition ........................................ 91
5.2.2
Existing one-step combustion mode transition ............................................. 92
5.3
Control Architecture of Multistep Combustion Mode Transition............................. 96
5.4
IMEP Regulation for DI Fuel Quantity Control ....................................................... 98
5.4.1
Sensitivity analysis of engine IMEP ............................................................. 99
5.4.2
DI fuel quantity control for learning mode ................................................. 100
5.4.3
DI fuel quantity control for transient mode ................................................ 100
5.5
Air-to-Fuel Ratio Control ....................................................................................... 101
5.5.1
Tracking reference of engine MAP............................................................. 101
5.5.2
Control oriented MAP model...................................................................... 103

viii

5.5.3
LQ optimal controller synthesis.................................................................. 104
5.6
HIL Simulation Results and Analysis ..................................................................... 106
5.6.1
SI-HCCI hybrid combustion mode ............................................................. 107
5.6.2
Air-to-fuel ratio control............................................................................... 108
5.6.3
DI fuel quantity control with iterative learning mode .................................111
5.6.4
Engine torque performance comparison ......................................................114
5.6.5
Engine performance during the throttle tip out operation............................116
5.7
Conclusions..............................................................................................................119
CHAPTER 6
CONCLUSIONS AND FUTURE WORK ................................................................................. 120
6.1
Conclusions............................................................................................................. 120
6.2
Recommendations for Future Work ........................................................................ 121
BIBLIOGRAPHY....................................................................................................................... 123

ix

LIST OF TABLES
Table 1.1: Features for different combustion model ..................................................................... 10
Table 2.1: Dual-stage turbocharged SI engine specification......................................................... 15
Table 2.2: Engine setting for both full and half load simulation .................................................. 30
Table 2.3: Dual-stage turbocharger setting for full/half load simulation...................................... 31
Table 3.1: HCCI capable engine specification.............................................................................. 38
Table 3.2: Calibration of ηEVC for low stage exhaust valve profile............................................... 45
Table 3.3: Calibration of ηEVC for high stage exhaust valve profile.............................................. 46
Table 3.4: Calibration of ηIVC for low stage intake valve profile .................................................. 49
Table 3.5: Calibration of ηIVC for high stage intake valve profile................................................. 49
Table 5.1: Engine control parameters for SI and HCCI combustion modes................................. 91
Table 5.2: Engine performance comparisons for different control strategies ..............................115

x

LIST OF FIGURES
Figure 1.1: HCCI combustion operation range............................................................................... 3
Figure 1.2: MFB in SI-HCCI hybrid combustion mode transition process.................................... 6
Figure 2.1: Dual-stage turbocharged SI engine configuration...................................................... 15
Figure 2.2: GT-Power engine model diagram............................................................................... 16
Figure 2.3: SI combustion related events and phases ................................................................... 23
Figure 2.4: Operating status of LP compressor for full load simulation....................................... 32
Figure 2.5: Correlation plots of the HIL and GT-Power simulation results.................................. 33
Figure 3.1: HCCI capable engine configuration ........................................................................... 38
Figure 3.2: GT-Power combustion model..................................................................................... 39
Figure 3.3: SI-HCCI hybrid combustion related events and phases............................................. 40
Figure 3.4: SI-HCCI hybrid combustion model diagram ............................................................. 42
Figure 3.5: In-cylinder pressure trace in gas exchange process.................................................... 43
Figure 3.6: Two-zone SI combustion model................................................................................. 52
Figure 3.7: In-cylinder gas pressure and temperature traces: correlations between GT-Power
model, two-zone SI combustion model and one-zone SI combustion model............................... 57
Figure 3.8: Burned zone gas temperature: correlation between GT-Power and two-zone SI
combustion models ....................................................................................................................... 59
Figure 3.9: In-cylinder gas temperature without combustion; unburned zone gas temperature:
correlation between GT-Power and two-zone SI combustion models .......................................... 59
Figure 3.10: In-cylinder pressure traces for different engine load at 3000rpm: correlations
between GT-Power and two-zone SI models................................................................................ 61
Figure 3.11: In-cylinder temperature traces for different engine load at 3000rpm: correlations
between GT-Power and two-zone SI models................................................................................ 61
Figure 3.12: Two-zone SI combustion model correlations: total in-cylinder gas mass Mt, residual
gas mass Mr, peak in-cylinder pressure Pmax and crank position of Pmax ...................................... 62
xi

Figure 3.13: Two-zone SI combustion model correlations: peak in-cylinder gas temperature Tmax,
peak unburned zone temperature TU-max, charge temperature at IVC TIVC and IMEP................ 63
Figure 3.14: Correlations between the peak unburned zone temperature TU-max and in-cylinder
gas temperature at IVC TIVC for NVO at different engine speed .................................................. 64
Figure 3.15: Correlations between the peak unburned zone temperature TU-max and in-cylinder
gas temperature at IVC TIVC for PVO at different engine speed................................................... 64
Figure 3.16: In-cylinder pressure and temperature traces: correlations between the one-zone
HCCI combustion model and GT-Power model ........................................................................... 66
Figure 3.17: One-zone HCCI combustion model correlations: peak in-cylinder pressure Pmax,
peak in-cylinder gas temperature Tmax, in-cylinder gas temperature at IVC TIVC and crank position
of SOHCCI.................................................................................................................................... 67
Figure 3.18: In-cylinder gas temperature traces for different external EGR rate ......................... 68
Figure 4.1: Simulink engine model - layout of each subsystem ................................................... 72
Figure 4.2: Dialogue box for fuel injection system ...................................................................... 73
Figure 4.3: Transient performance of the turbocharger shaft rotational speed: comparison
between different times of iteration using single step multiple iteration approach ...................... 75
Figure 4.4: The dSPACE hardware............................................................................................... 76
Figure 4.5: System architecture of the integrated HIL simulation environment .......................... 78
Figure 4.6: Simulated engine signals displayed on oscilloscope.................................................. 79
Figure 4.7: Snapshot of HIL simulation platform......................................................................... 80
Figure 4.8: Control architecture for transient response simulation of the SI engine with dual-stage
turbocharger .................................................................................................................................. 81
Figure 4.9: Transient response of relative air-to-fuel ratio and fuel pulse width.......................... 83
Figure 4.10: Responses of engine torque and intake manifold pressure....................................... 83
Figure 4.11: Responses of the turbocharger shafts’ rotational speed of each stage ...................... 84
Figure 4.12: In-cylinder pressure traces in SI-HCCI transition.................................................... 86
Figure 4.13: Combustion parameter settings in SI-HCCI transition............................................. 87

xii

Figure 4.14: Combustion performance in SI-HCCI transition...................................................... 87
Figure 4.15: MFB profiles in SI-HCCI transition with hybrid mode ........................................... 88
Figure 5.1: Steady state combustion characteristics of SI and HCCI modes................................ 92
Figure 5.2: Engine responses of one-step combustion mode transition strategy.......................... 93
Figure 5.3: Combustion performance of one-step combustion mode transition strategy ............. 94
Figure 5.4: SI to HCCI combustion mode transition control events and schedules ..................... 97
Figure 5.5: SI to HCCI combustion mode transition control diagram.......................................... 97
Figure 5.6: IMEP sensitivity with FDI input for the SI-HCCI hybrid combustion mode.............. 99
Figure 5.7: The target MAP operational range and MAP tracking reference ............................. 102
Figure 5.8: Combustion performances with and without SI-HCCI hybrid combustions ........... 107
Figure 5.9: Engine performances with and without MAP tracking control................................ 109
Figure 5.10: Adjustment of weighting matrix R in cost function (5.12)......................................110
Figure 5.11: Correction of DI fuel quantity after iterative learning.............................................111
Figure 5.12: Combustion performances with and without ILC ...................................................113
Figure 5.13: Engine knock index (dP/dθ) with and without ILC ................................................114
Figure 5.14: Engine torque performances of different control strategies ....................................114
Figure 5.15: In-cylinder gas pressure profiles during SI to HCCI combustion mode transition .115
Figure 5.16: Engine responses during Tip out operation .............................................................117
Figure 5.17: Engine torque response during tip out operation.....................................................118

xiii

NOTATIONS
Symbol

Description

Unit

Δθ

Predicted burn duration

deg

ηcomp

Thermal efficiency of compressor

ηHCCI

Combustion efficiency in HCCI combustion mode

ηIN

Volumetric efficiency of the intake process

ηSI

Combustion efficiency in SI combustion mode

ηturb

Thermal efficiency of turbine

θ

Current crank position

deg ACTDC

θST

Spark timing in degree after combustion TDC

deg ACTDC

θINTM

Intake valve timing at peak lift

deg AGTDC

θEXTM

Exhaust valve timing at peak lift

deg BGTDC

κ

Heat capacity ratio

λ

Normalized air-to-fuel ratio

Πlift

Peak lift of intake/exhaust valve

mm

ϕTPS

Engine throttle position

%

ϕacc

Acceleration pedal position

%

ϕEGR

External EGR valve opening

%

xiv

2

Ac

Instant cylinder inner surface area

m

Av

Cross area of valve flow

m

bETC

Damping ratio of throttle plate

cETC

Torque constant of throttle drive motor

Cd

Valve discharge coefficient

Cp

Specific heat for constant pressure

kJ/kg·K

Cv

Specific heat for constant volume

kJ/kg·K

e

Specific internal energy

kJ/kg

FDI

Direct injection (DI) fuel pulse duration

(ms/cycle)

FFB, FFF

Feedback/feedforward portions of FDI

(ms/cycle)

FILC

ILC portion of DI pulse duration

(ms/cycle)

h

Specific enthalpy

kJ/kg

HLHV

Lower heating value

kJ/kg

i

Indexes of ILC iteration

IETC

Actuator current of electric throttle control (ETC) system

A

Je

Rotational inertia of the engine crankshaft

Kg.m

Jturbo

Rotational inertia of the turbocharger shaft

Kg.m

k

Index of sampling time for time based control logic

2

xv

N.m/A

2
2

kETC

Spring constant of throttle plate

mcomp

Gas mass flow rate through compressor

g/s

min

Inlet gas mass flow rate

g/s

mout

Outlet gas mass flow rate

g/s

mturb

Gas mass flow rate through turbine

g/s

mv

Mass flow rate across the valve

g/s

M

Mass of gas mixture

g

MB

Mass of burned zone gas mixture in SI combustion

g

Mf

Fuel mass of each cylinder per engine cycle

g

Mr

Mass of residual gas

g

Mt

Total mass of in-cylinder charge

g

MU

Mass of unburned zone gas mixture in SI combustion

g

Ne

Engine speed

rpm

P

Instant in-cylinder gas pressure

bar

Pamb

Ambient pressure

bar

Pdown

Valve downstream pressure

bar

PEM

Gas pressure at exhaust manifold

bar

PIM

Gas pressure at intake manifold

bar

xvi

Pm

Gas pressure at manifolds, or connecting pipes

bar

Pup

Valve upstream pressure

bar

Q

Heat transfer to combustion chamber surface

kJ/deg

r

Radius of throttle plate

m

R

Gas constant

kJ/kg·K

T

Instant in-cylinder gas temperature

K

Tamb

Ambient temperature

K

TB

Gas temperature of burned zone in SI combustion

K

TU

Gas temperature of unburned zone in SI combustion

K

Tm

Gas temperature at manifolds, or connecting pipes

K

Te

Engine brake torque

N.m

Tl

Engine load torque

N.m

V

Instant cylinder volume

m

VB

Volume of burned zone gas mixture in SI combustion

m

Vd

Engine displacement

m

Vm

Volume of intake manifold

m

VU

Volume of unburned zone gas mixture in SI combustion

m

w

The average in-cylinder gas velocity

m/s

x

Mass fraction burned

3
3
3
3

xvii

3

xEGR

EGR gas fraction in engine intake manifold

MAP

Intake manifold absolute pressure

bar

IMEP

Indicated mean effective pressure

bar

IMEPref

IMEP learning reference used in ILC

bar

ACTDC

After combustion TDC

BGTDC

Before gas exchange TDC

DI

Direct injection

EGR

Exhaust gas recirculation

EMP

Exhaust manifold pressure

EVC

Exhaust valve closing

EVO

Exhaust valve opening

HCCI

Homogeneous charge compression ignition

HIL

Hardware in the loop

HP

High pressure

IC

Internal combustion

ILC

Iterative learning control

IVC

Intake valve closing

IVO

Intake valve opening

LP

Low pressure

MBT

Minimal advance for the best torque

MFB

Mass fraction burned

MFR

Mass flow rate

xviii

PFI

Port fuel injection

PID

Proportional, integral, and derivative

SI

Spark ignition

SOHCCI

Start of HCCI combustion

TDC

Top dead center

VVA

Variable valve actuation

VVT

Variable valve timing

WOT

Wide open throttle

xix

CHAPTER 1
INTRODUCTION

1.1 New Technologies and Challenges
The imminent energy crisis and the increasingly stringent emission and fuel economy
regulations of automobiles are key factors to promote the research and development of many new
engine technologies in the past decade that increase internal combustion (IC) engine system
complexity significantly. Among these technologies engine downsizing using single or dual-stage
turbocharger and homogeneous charge compression ignition (HCCI) combustion are two
promising ones.
1.1.1

Engine downsizing
Downsized engine has higher power density (small displacement), leading to improved

fuel economy ([1] and [2]). Turbocharger is widely used in downsized IC engines, but it leads to
slow engine response due to turbo lag [3], which reduces the competitiveness of turbocharged
vehicles in the market. Smaller turbocharger reduces turbo lag, but at the same time, it limits the
engine boost pressure at high engine speed. Dual-stage turbocharger system has been proposed
recently in [4], [5], and [6] due to its potential of covering wide range of engine operational
conditions with reduced turbo lag. However the control of a dual-stage turbocharged engine is
fairly complicated. The dynamics of two turbochargers staged in series interact with each other,
which is different from the dual turbocharger engine with two turbochargers connected in parallel.
Furthermore, the turbo system and combustion chamber are connected in a closed loop. The
product of the combustion process, exhaust gas, is the energy input to the turbo system; the
1

compressor utilizes the turbo output mechanical energy to generate pressurized intake charge; the
intake gas pressure, or in other words, the boost pressure, is directly associated with the
combustion efficiency. High boost pressure leads to high combustion efficiency and engine power
density [7], but it could also lead to heavy engine knock [8]. Some technologies are introduced to
suppress the engine knock, such as high dilution combustion using external EGR (exhaust gas
recirculation) gas [8], dual fueling technology [9], and closed-loop combustion control using
in-cylinder ionization signal ([10] and [11]) or pressure signal ([12] and [13]). These technologies
greatly increase the engine control system complexity, and make it necessary to develop model
based control strategies.
1.1.2

HCCI combustion
HCCI combustion is another promising technology [14]. The flameless nature of the HCCI

combustion and its capability of high dilution operation lead to low combustion temperature. As a
result, the formation of NOx (nitrogen oxides) can be significantly reduced [15]. Furthermore,
HCCI combustion is capable of un-throttled operation that greatly reduces engine pumping loss
and improves fuel economy ([16] and [17]).
On the other hand, HCCI combustion has its own limitations. As illustrated in Figure 1.1, it
is limited at high engine load due to the audible knock ([18] and [19]); and at low load due to
misfire caused by the lack of sufficient thermal energy to trigger the auto-ignition of the gas-fuel
mixture during the compression stroke ([20] and [21]). In fact, HCCI can be regarded as a type of
engine operating mode rather than a type of engine [22]. In order to take advantage of the HCCI
combustion mode in an IC engine, other combustion mode, such as spark ignited (SI) combustion,
is required at high load, at high speed [23], at ultra-low load (such as idle), and at certain operating
conditions, such as at cold start [24].

2

Figure 1.1: HCCI combustion operation range

It is fairly challenging to operate the engine in two distinct combustion modes, and it is
even more difficult to have smooth combustion mode transition between the SI and HCCI
combustions, because the favorable thermodynamic conditions for one mode are always adverse to
the other [25]. For example, high intake charge temperature is required in the HCCI mode to
initiate the combustion, while in the SI mode it leads to reduced volumetric efficiency and
increased knock tendency [26]. For this reason, engine control parameters, such as intake and
exhaust valve timings and lifts, throttle position, and EGR (exhaust gas recirculation) valve
opening, are regulated at different level between these two combustion modes. During the
combustion mode transition, these engine parameters need to be changed rapidly. However, the
physical actuator limitations on response time prevent them from completing their transitions
3

within the required duration, specifically, within one engine cycle [27]. The multi-cylinder
operation makes it even more difficult [28]. Accordingly the combustion performance during the
transition cannot be maintained unless proper control strategy is applied.

1.2 Related Work
In order to tackle the challenges and implementing these new technologies to IC engines,
more attentions have been paid to the researches for advanced control strategies, such as model
based control. In this dissertation, control oriented models are presented for the dual-stage
turbocharged engine and the HCCI capable SI engine. Furthermore, the model based control
strategies were studied for the combustion mode transition control of the HCCI capable SI engine.
1.2.1

HCCI capable engine control
To realize the HCCI combustion in production IC engines, it has two challenges regarding

the engine controls. One is the control of the HCCI combustion process, where the challenge is
mainly due to the cycle-to-cycle residual gas dynamics; the other is the combustion mode
transition control, which is a major concentration of this dissertation.
The control of the HCCI combustion process has been widely studied for different engine
configurations in past decades. Among these studies, the combustion timing control is of the
greatest interest, due to the lack of direct combustion trigger in the HCCI combustions. In [29],
stable HCCI combustion timing was achieved at different engine speeds by regulating the engine
VVT (variable valve timing) through a PID (proportional, integral, and derivative) control with
gain scheduling. Shaver ([30], [32], and [32]) realized stable combustion timing and work output
performances via closed-loop residual gas quantity control, for an HCCI capable engine equipped
with a camless VVA (variable valve actuation) system. Ravi developed a model based combined

4

feedback, feedforward and integral control strategy to track desired load-phasing trajectories of the
HCCI combustions ([33] and [34]), where the pilot fueling during recompression phase of the
HCCI combustions is used as the control knob. Robust HCCI combustions were also achieved for
transient operating conditions through control strategies as described in [35], [36], and [37]. These
advanced control strategies make the HCCI combustion feasible in practical IC engines, but they
bring challenges to the combustion mode transition at the same time, which is inevitable for
production engines with the HCCI combustion mode [38].
In order to implement the HCCI combustion technology in production engines, in recent
years, the combustion mode transition control has become an interesting topic in the HCCI engine
research. In [39] and [40], smooth mode transitions between the SI and HCCI combustions were
realized for a single cylinder engine equipped with the camless VVA system. However, the
camless VVA system itself is still not feasible for mass production due to its high cost and package
issues. In [41], smooth combustion mode transition was realized for a single cylinder GDI engine
equipped with VVT system. In [42], a VVT system with dual-stage lifts was used on a
multi-cylinder engine for studying the mode transition. Experimental results showed the potential
of achieving smooth mode transition by controlling the throttle opening timing and the DI (direct
injection) fuel quantity. However, satisfactory engine performance during the mode transition was
not accomplished due to the lack of control strategies.
The SI-HCCI hybrid combustion mode as described in [43] and [44] can be observed
during the mode transition between the SI and HCCI combustions. It was discovered in [25] that
the control of the SI-HCCI hybrid combustion mode is the key to achieve smooth combustion
mode transition for engines equipped with the VVT system. Accordingly, this dissertation mainly
focuses on the modeling and control development of the hybrid combustion mode.

5

1.2.2

SI-HCCI hybrid combustion mode
The SI-HCCI hybrid combustion starts in SI combustion mode with a relatively low heat

release rate; and once the thermodynamic and chemical conditions of the unburned gas satisfy the
start of the HCCI (SOHCCI) combustion criteria, the combustion continues in the HCCI
combustion mode, which is illustrated by the dashed curves of mass fraction burned (MFB) shown
in Figure 1.2. During an ideal SI to HCCI combustion transition process, the percentage of SI
combustion (ST to SOHCCI, see Figure 1.2) decreases gradually while the HCCI combustion
percentage (SOHCCI to end of combustion or MFB = 1) increases gradually [45]. For the HCCI to
SI combustion transition, the process is reversed. This hybrid combustion mode transition process
allows using conventional cam phase system since the required cam phase will change gradually.

Mass Fraction Burned

1
0.8
0.6
SOHCCI
0.4
0.2
0
-60

SI mode
HCCI mode
SI-HCCI Hybrid mode

ST
-40

-20

0
20
40
60
Crank angle (deg ACTDC)

80

100

120

Figure 1.2: MFB in SI-HCCI hybrid combustion mode transition process
"For interpretation of the references to color in this and all other figures, the reader is referred to
the electronic version of this dissertation."
6

During the combustion mode transition, the engine thermodynamic conditions are between
the SI and HCCI modes. The typical control strategies of both SI and HCCI combustion modes
cannot be applied under the transitional conditions, due to the lack of control variables [25].
However, the SI-HCCI hybrid combustion mode is feasible under the transitional conditions.
Implementing the hybrid combustion mode during the combustion mode transition, the engine
performances such as the IMEP (indicated mean effective pressure) can be controlled by the spark
ignition, fuel quantity, and intake/exhaust valve timings. The multistep mode transition control
strategy developed in this dissertation is based on the SI-HCCI hybrid combustion mode.
1.2.3

Related control methods
The SI-HCCI hybrid combustion mode control is studied in this dissertation for the first

time, to achieve smooth SI to HCCI combustion mode transition, for an HCCI capable SI engine
equipped with dual-stage turbocharger system. For the control development, three control methods
were utilized. They are linear quadratic (LQ) tracking control, iterative learning control (ILC), and
PI (proportional and integral) control.
LQ tracking control minimizes a quadratic tracking error over a given time period based
upon the LQ optimal control theory, where a nonzero reference signal is given, see [46], [47], and
[48]. In this dissertation, this method is used to make the engine MAP (intake manifold absolute
pressure) track the desired reference during the combustion mode transition. As a result, the
air-to-fuel ratio of each engine cylinder can be maintained within the desired range, which makes
the engine IMEP (indicated mean effective pressure) controllable through regulating DI (direct
injection) fuel quantity.
ILC is a feedforward control method [49] with numerous applications, such as in [50] and
[51]. In this dissertation, to eliminate the significant cylinder-to-cylinder and cycle-to-cycle

7

variations of the engine IMEP during the mode transition, ILC was applied to the DI fuel quantity
of individual cylinder. The motivation of using this method is mainly due to the repetitive nature of
the combustion mode transition process.
PI control is a popular feedback control method. In this dissertation, it is combined with the
ILC to smooth the combustion mode transition process under transient engine load conditions.
The control methods discussed above are well known in theory, but to apply them to the
specific application a validation approach is required and the HIL engine simulation is adopted.
1.2.4

HIL engine simulation
The HIL simulation is a powerful tool used in the development and validation of a complex

real-time embedded control system, such as an engine control system. Utilizing the appropriate
engine model, an HIL simulator, such as the dSPACE engine simulation system, is capable of
providing various engine output signals based upon the control signals provided by the engine
controller at different engine operational conditions [46]. Development of an engine control
system using the HIL simulation environment could reduce cost and shorten development cycle.
Therefore, HIL simulations are widely used in the automotive industry for power-train system
research and development [53]. To take the advantage of the HIL simulation, a control oriented
engine model is required.
In order to provide high resolution engine signals, the HIL simulator always runs with a
very short time step. Accordingly the model needs to be updated within a given short period. For
example, if the in-cylinder pressure signal is updated every crank degree, the combustion model
calculation needs to be completed every crank degree, which is corresponding to 56 microseconds
when engine speed is 3000 rpm. The requirement of real-time simulation limits the complexity of
the control oriented engine model.

8

1.2.5

Engine modeling
For control strategy development, zero dimensional mean value engine models are widely

used, see [54] through [58], due to their simplicity and low simulation throughput. For the engine
air handling system or crankshaft dynamics, mean value models are accurate enough since the
piston reciprocating movement has less impact on these subsystems than on the combustion
process. Therefore, the mean value modeling approach is also used for these subsystems in this
dissertation. The disadvantage of the mean value engine modeling is that it does not provide
detailed information about engine combustion process, such as in-cylinder gas pressure,
temperature, and ionization signals, which have been widely used for closed-loop combustion
control ([59], [60] and [61]). The in-cylinder pressure rise (dP/dθ) is a key indicator for detecting
engine knocks [62].
In order to explore the details about the engine combustion process, multi-zone, three
dimensional CFD (computational fluid dynamics) models with detailed chemical kinetics are
presented in [63], [64] and [65], and they are able to precisely describe the thermodynamic,
fluid-flow, heat transfer, and pollutant formation phenomena of the HCCI combustion. Similar
combustion models have also been implemented into commercial codes such as GT-Power [66]
and Wave. However, these models with high fidelity cannot be directly used for control strategy
development since they are too complicated to be used for real-time simulations, but they can be
used as reference models for developing simplified (or control oriented) combustion models for
control purpose.
For real-time HIL simulations, it is necessary to develop a type of combustion model with
its complexity inter-between the time based mean value models and the CFD models. This
motivates the combustion modeling work presented in this dissertation. The 0D (zero dimensional)

9

crank based combustion model is selected for this dissertation. Table 1.1 compares the capability
of this modeling method with the other two.
Table 1.1: Features for different combustion model
0D time based
combustion model
Implementation tool

0D crank based
combustion model

1D & 3D CFD
combustion model

Matlab/Simulink

Matlab/Simulink
and HIL simulator

GT-Power, Wave
and Fluent

Time cost per cycle

Micro seconds

Real-time

Minutes to hours

One-zone

Yes

Yes

Yes

Two-zone

No

Yes

Yes

Multi-zone

No

No

Yes

Chemical concentration

No

No

Yes

Gas-fuel mixing model

No

No

Yes

In-cylinder flow dynamics

No

No

Yes

IMEP

Yes

Yes

Yes

In-cylinder pressure

No

Yes

Yes

In-cylinder temperature

No

Yes

Yes

Ionization signal

No

Yes

No

1.3 Dissertation Contributions
This research begun with modeling the dual-stage turbocharged SI engine. A mixed
time-based and crank-based modeling method was used. The engine air-handling system was
modeled in a time-based mean-value approach, and SI combustion process was modeled as
functions of engine crank angle. The same modeling approach was then applied to model the
HCCI capable SI engine. The developed combustion model is capable of simulating the SI, the
10

HCCI and the SI-HCCI hybrid combustion modes. Both engine models were calibrated and
validated by the corresponding GT-Power models. Afterwards the engine models were
implemented and validated in the dSPACE based HIL simulation environment.
The HCCI capable SI engine control was studied in the developed HIL simulation
environment. A multistep control strategy was developed to achieve smooth combustion mode
transition between the SI and HCCI combustion modes. The HIL simulation results demonstrated
the effectiveness of the developed control strategy under both constant and transient engine
operating conditions.
The dissertation has the following major contributions:


The mixed time-based and crank-based engine models were developed for a dual-stage
turbocharged SI engine and an HCCI capable SI engine. They are capable of real-time
simulation with accuracy comparable to the relatively high fidelity GT-Power model.



The SI-HCCI hybrid combustion process was modeled for the first time using a mixed
two-zone and one-zone combustion models. The SI and HCCI combustions are special
cases in the SI-HCCI hybrid combustion model.



Smooth SI to HCCI combustion mode transition was demonstrated using multistep control
strategy, where the SI-HCCI hybrid combustion mode was implemented to relax the charge
temperature requirement, LQ optimal tracking control was used to regulate the charge
air-to-fuel ratio at desired range so that the engine IMEP can be regulated through DI fuel
quantity control, and the IMEP of each engine cylinder was regulated through iterative
learning control of the DI fuel quantity of the corresponding cylinder.

1.4 Dissertation Outline
The material presented in this dissertation is organized into six chapters. In Chapter 2, the

11

dual-stage turbocharged SI engine model is developed using the mixed time-based and
crank-based method; the model is also validated with the corresponding GT-Power model. In
Chapter 3, the SI-HCCI hybrid combustion mode is defined and the corresponding model is
presented along with the gas exchange process model; the model validation results are also
discussed. In Chapter 4, the implementation of the developed model into the real-time HIL
simulation environment is depicted with the proposed numerical approach; the HIL simulation
results are presented to introduce the control study for the following chapter. In Chapter 5, the
challenges of the SI to HCCI combustion mode transition are analyzed and the multistep
combustion mode transition control strategy is presented with HIL validations. In Chapter 6,
conclusions and future work are drawn.

12

CHAPTER 2
DUAL-STAGE TURBOCHARGED SI ENGINE MODELING USING
MIXED MEAN VALUE AND CRANK BASED METHOD

2.1 Introduction
Downsized engine using dual-stage turbocharger has been discussed in the previous
chapter for its high power density and ability to cover wide range of engine operational conditions
[6]. However dual-stage turbocharger may lead to extreme engine operational conditions. For
instance, the engine load could reach 30 bar IMEP (indicated mean effective pressure) with 3 bar
MAP (intake manifold absolute pressure), which could result in heavy engine knock that can’t be
ignored. Using the external cooled EGR gas to reduce combustion temperature and the rate of
in-cylinder pressure rise is introduced in [11]. VVT technique is also recommended to adjust the
effective compression ratio at high load to suppress the engine knock. Flex fuel, such as ethanol, is
also an effective way to reduce engine knock ([67] and [68]).
These technologies require sophisticated engine control strategies, such as model-based
control, to operate the engine at its most efficient conditions, which requires a control oriented
engine model for the control strategy development and validation. This control oriented model has
to be accurate enough to include detailed engine dynamics, and capable of being simulated in
real-time at the same time. A mixed mean value and crank based engine model is proposed and
developed in this chapter. The engine model contains both time based engine dynamics, such as
crankshaft dynamics, and crank based engine combustion process.

13

This chapter is organized as follows. In Section 2.2 the engine configuration and its
GT-Power model are discussed. In Section 2.3 the time based mean value models of the engine air
handling system are presented. Section 2.4 provides the governing equations of combustion
process as a function of the crank angle. Model validation is accomplished in Section 2.5.

2.2 Engine Configuration and GT-Power Model
Figure 2.1 shows the downsized three-cylinder engine with cooled EGR and dual-stage
turbocharger. The HP (high pressure) turbocharger, connected to the engine intake and exhaust
manifolds, is smaller than that of the LP (low pressure) turbocharger. Accordingly, the HP
compressor has a smaller capacity of air mass flow rate than the LP one. A bypass valve is
connected to the HP compressor, and it is used to match the air mass flow rate of both compressors.
Each stage of turbine is equipped with solenoid controlled continuously adjustable waste-gate. An
intake cooler is connected between the HP compressor and intake manifold. Unlike traditional
engines, this engine utilizes intake throttles located close to the three intake runners between the
intake manifold and intake ports to improve transient responses. The engine also features dual
intake and exhaust valves with independent variable valve timing (VVT) control. Both cam
phasing actuators are adjustable in the range of 20 crank degrees. The EGR cooler and
controllable EGR valve in Figure 2.1 composes the external EGR system of the engine. Cooled
EGR gas can be re-circulated through the external EGR system back to cylinder, and acts as inertia
gas to cool down the combustion temperature. The engine is also equipped with dual fuel injection
systems: port fuel injection (PFI) and direct injection (DI), and can be operated with any blend of
ethanol and gasoline.

14

Bypass Valve

Throttle
Actuator

Intake
Cooler
LC

HC

EGR
Valve

Intake Manifold
PFI

EGR
Cooler
DI
LT

HT
Exhaust Manifold

LP Waste-gate

HP Waste-gate

Figure 2.1: Dual-stage turbocharged SI engine configuration

Table 2.1: Dual-stage turbocharged SI engine specification
Engine parameter

Model value

Bore/stroke/con-rod length

83mm/73.9mm/123mm

Compression ratio

13.5:1

Intake valve/exhaust valve diameter

31.4mm/22.5mm

Throttle diameter

3×48mm

Intake manifold/exhaust manifold volume

2.0L/0.57L

Inertia of HP-stage turbocharger shaft

3.807E-6kg.m

Inertia of LP-stage turbocharger shaft

2.7E-5kg.m

2

2

15

Figure 2.2: GT-Power engine model diagram
16

The key engine geometry dimensions are listed in Table 2.1. The actual engine is still under
development. Accordingly a GT-Power engine model was developed corresponding to the engine
configuration shown in Figure 2.1 as the baseline for the engine control system development in the
early stage of the research.
GT-Power is commercial software for vehicle powertrain system modeling and simulation.
It is widely used in the automotive industry. It features an object-based code design, which allows user
to build an engine part by part, module after module. As shown Figure 2.2, the layout of the GT-Power
engine model is consistent with the engine configuration in Figure 2.1. The parameters of each engine

component can be specified individually by editing the property dialogue box of the corresponding
block. Most of the key parameters were given by the engine manufacturer, such as the intake and
exhaust valve lifts.
The GT-Power model is mainly based on one-dimensional fluid dynamics, representing the flow
and heat transfer in the piping and other flow components of an engine system [66]. It takes relatively long
time (sometimes, in hours) for the model solution to converge and provides the steady state performance of
the engine. This makes it impossible to use the GT-Power model for real-time engine simulation.
Furthermore, GT-Power is capable of providing accurate steady state simulation results but relatively weak
in transient simulations. Therefore, GT-Power modeling tools are usually used to estimate steady state
engine performance.
To meet the requirements of the real-time HIL simulation, a control oriented engine model was
developed in Matlab/Simulink with “C” S-functions to be implemented into dSPACE or Opal-RT based
HIL simulators. The GT-Power model introduced in this section was used to calibrate and validate the
engine model developed in the remaining chapter.

17

2.3 Mean Value Models for Engine Air Handling System
This section describes mathematical subsystem models for those engine subsystems whose
averaged dynamic behaviors are required for control purpose, even though they are functions of
engine reciprocating phenomenon. All parameters and variables used in these models are functions
of time t.
2.3.1

Valve model
The valve model, described below, is used for the intake throttle, the HP and LP waste-gate,

and EGR valve since these actuators share same physical characteristic. Assuming that the spatial
effects of the connecting pipes before and after these valves are neglected and their
thermodynamic characteristics are isentropic expansion [69], the governing equation of the valve
model is
Pup

mv  Cd Av

RTup

 Pdown 

 Pup 





(2.1)

where


  x  



2 x(1  x),
1

2

if

,

if

1  x 1
2
x 1
2

(2.2)

Cd is the valve discharge coefficient; Av is the valve open area; Pup and Tup are the valve upstream
pressure and temperature; Pdown is the valve downstream pressure; and mv is the mass flow rate
across the valve. Note that both Cd and Av are functions of the valve opening angle θv.
2.3.2

Manifold filling dynamic model
This model is mainly used for the intake and exhaust manifolds, inter-compressor and

inter-turbine pipes. The receiving behavior is assumed to be an adiabatic process in these

18

manifolds [69]. Their thermodynamic states are uniform over the entire manifold volume and the
manifold temperature is averaged over one engine cycle for this mean value model. Then the
governing equation for the manifold filling dynamics is

dPm RTm

 min  mout 
dt
Vm

(2.3)

where Pm is the manifold pressure; Tm is the manifold temperature; Vm represents the manifold
volume; min and mout are the inlet and outlet air mass flow rates, respectively.
2.3.3

Crankshaft dynamic model
Based upon Newton theory, assuming a rigid crankshaft, it can be derived as

dN e 60 Te  Tl

dt
2 J e

(2.4)

where Je is the rotational inertia of the engine crankshaft; Te and Tl are the engine brake torque and
load torque, respectively. Note that in future simulations, Tl is generated by an engine
dynamometer model controlled by a PID feedback controller to maintain the desired engine speed.
2.3.4

Turbine and compressor models

The turbocharger is modeled using the so-called energy conservative equations based upon
its steady state compressor and turbine maps, which can be found in [6] and [70]. Notice that the
turbo mass flow rate (MFR) and shaft speed in the turbo mapping equations given below are in the
so-called reduced form, to make the turbo maps applicable for all inlet conditions. Without this
conversion, it would require different turbo maps for each combination of inlet pressure and
temperature [71].
Both turbine and compressor dynamics are described below in equations (2.5) to (2.12),
where Pin and Tin are either turbine or compressor inlet pressure and temperature; Pout and Tout are
19

either turbine or compressor outlet pressure and temperature; Nturbo is the turbocharger shaft
speed in rpm; and η denotes thermal efficiency.
1) Turbine mapping: Turbine maps (fturb and f’turb) in equations (2.5) and (2.6) are used

to calculate the reduced MFR mturb and thermal efficiency ηturb based on pressure ratio across the
turbine and the reduced turbo shaft speed. The actual MFR can be calculated from the reduced
MFR mturb by
 P N
 P
mturb  fturb  in , turbo  in
 Pout
Tin  Tin



(2.5)

and
 Pin Nturbo 
,

 Pout
Tin 




turb  fturb 

(2.6)

2) Compressor mapping: Compressor maps (fcomp and f’comp) in equations (2.7) and (2.8)

are used to calculate the compressor pressure ratio and thermal efficiency ηcomp based on reduced
MFR mcomp and reduced turbo shaft speed by
 mcomp Tin N

Pout
 f comp 
, turbo 

Pin
Pin
Tin 



(2.7)

 mcomp Tin N

, turbo 

Pin
Tin 



(2.8)

and

comp  fcomp 

3) Temperature calculation: The outlet temperature of the turbine or compressor can be

calculated based upon:

20

 1

Tout  Pout 


Tin  Pin 



(2.9)

Notice that equation (2.9) assumes isentropic gas expansion and compressing process for
either turbine or compressor. However, the actual physical process is not isentropic, leading to
more enthalpy remaining in the gas due to thermal efficiency, which makes the actual outlet
temperature higher than that given by equation (2.9), but the difference is relatively small.
Simulation results presented in Figure 2.5 show an acceptable correlation between GT-Power
results and the temperature calculated using equation (2.9). Therefore, this assumption is
acceptable.
4) Turbine power calculation: The power generated by turbine, denoted as Eturb, is

calculated by

 P
Eturb  mturbC pturbTin 1   out
  Pin


 1 
  






(2.10)

5) Compressor power calculation: The power required to drive compressor, denoted as

Ecomp, is calculated by

 P
1
Ecomp  mcomp C p
Tin  out
comp
 Pin


 1

 

 1





(2.11)

6) Power balance on turbocharger shaft: The power balance on the turbocharger shaft is

calculated by

Eturb  Ecomp  J turbo Nturbo

dNturbo
dt

where Jturbo is the rotational inertia of the turbocharger shaft.
21

(2.12)

2.4 Crank Based One-Zone SI Combustion Model

This section presents the mathematic model of the SI combustion model based on the
one-zone assumption of the in-cylinder gas-fuel mixture.
2.4.1

Crank based methodology

The purpose of the combustion process modeling is to correlate the trapped in-cylinder gas
properties, such as air-to-fuel ratio, trapped EGR gas mass, in-cylinder gas pressure and
temperature, to the combustion characteristics such as misfire, knock, burn duration, and IMEP.
The developed combustion model will be combined with the mean value air handling system
model to construct the entire engine model used for model-based control strategy development and
validation of the dual-stage turbocharger engine. Note that the combustion model also needs to
meet the real-time HIL simulation requirements.
Some combustion related parameters in the combustion model are updated every crank
degree, such as in-cylinder gas pressure and temperature, while the others, such as IMEP and
air-to-fuel ratio are updated once every engine cycle at the given crank position. The latter reflects
cycle-to-cycle dynamics of the combustion process. Overall they are all discrete functions of
engine crank position θi, which is different from the mean value model presented in the last section,
where the parameters are continuous functions of time t.
There are many motivations of using the crank based modeling approach. The first is due to
the fact that most combustion characteristics are usually functions of the crank angle, such as burn
duration and peak pressure location; and the second is that the entire combustion process is divided
into several combustion phases associated with certain events as a function of crank position. As
shown in Figure 2.3, these events are intake valve closing (IVC), spark ignition timing (ST),
exhaust valve opening (EVO), exhaust valve closing (EVC), and intake valve opening (IVO). The

22

in-cylinder behaviors (such as pressure, temperature, etc.) are modeled differently during each
combustion phase that is defined between two combustion events.

In-cylinder pressure (bar)

35
In-cylinder pressure
Intake valve profile
Exhaust valve profile

30
25
20
15
10
5
0

IVC

-100

ST

0

EVO

IVO

100
200
300
Crank angle (deg)

EVC

400

500

Figure 2.3: SI combustion related events and phases

The crank based modeling approach has its own limitation, too. During the real-time
simulation the entire model needs to be executed within the time period associated with the desired
update period (for example, one crank degree). This leads to short computational time window at
high engine speed. For instant, 3000 rpm of engine speed corresponds to 56 micro seconds for one
crank degree, while 6000 rpm corresponds to only 28 micro seconds. If the upper limit of engine
speed is set to 6000 rpm, in order to avoid the overrun during the simulation, the computation of
the combustion model must be completed within 28 micro seconds. This limits the complexity of
the combustion model.
In Figure 2.3, the combustion phase starts from ST and ends with EVO. The gas exchange

23

process from EVO to IVC and compression process from IVC to ST are also important to the
combustion process, since the gas-fuel mixture is prepared during these two phases.
2.4.2

Gas exchange process modeling
1) EVO to IVO: After the exhaust valve is opened, the in-cylinder gas isentropically

expands in the engine cylinder, exhaust ports and manifold, and this phase is called gas exhaust.
Simply assume the in-cylinder pressure in this phase equals the exhaust manifold absolute pressure
(EMP) PEM

P(i )  PEM

(2.13)

where θi is the current crank position. The in-cylinder gas temperature is calculated by
 1
 

 P
T (i )  T ( EVO )   EM 
 P( EVO ) 

(2.14)

where T(θEVO) and P(θEVO) are the temperature and pressure at the crank position of exhaust
valve closing, and they are derived from the combustion phase.
2) IVO to EVC: this phase is usually called valve overlap phase. During this phase the

intake valve starts to open while exhaust valve is closing. The opening of both valves makes the
flow dynamics more complicated and difficult to model. For simplicity, assume the in-cylinder gas
pressure equals the mean value of the pressures in exhaust manifold and intake manifold. That is,
P  PIM
P (i )  EM
2

(2.15)

where PIM is the intake manifold absolute pressure. The gas temperature can be calculated same as
in the last phase

24

 1

 P  PIM  
T (i )  T ( IVO )  EM

 2 P( IVO ) 

(2.16)

In addition, at EVC the residual gas mass is calculated based on ideal gas law as follows,
Mr 

P( EVC )V ( EVC )
T ( EVC ) R

(2.17)

3) EVC to IVC: during this phase fresh air is trapped into engine cylinder. The in-cylinder

pressure is mainly influenced by intake manifold pressure but not always equal to it. It can be
calculated by:

P (i )  PIM  IN

(2.18)

where ηIN is actually the volumetric efficiency of the intake process, and it is a function of engine
speed Ne and engine load PIM. In-cylinder gas temperature is calculated by
 1

P   
T (i )  T ( EVC )  IM IN 
 P( EVC ) 

(2.19)

Additionally, the total mass of in-cylinder gas mixture for the compression and combustion phases
is calculated at IVC also based on ideal gas law as follows,

Mt 

P( IVC )V ( IVC )
P V ( IVC )
  IN IM
T ( IVC ) R
T ( IVC ) R

(2.20)

4) IVC to ST: This phase is the compression phase without combustion. The governing

equations of this phase are also based on the isentropic law of ideal gas. They are

 V (i 1 ) 
P (i )  P(i 1 ) 

 V (i ) 
and

25



(2.21)

 V (i 1 ) 
T (i )  T (i 1 ) 

 V (i ) 

 1
(2.22)

where V(θi) is the cylinder volume at crank position V(θi) and is calculated by

1
  B2S
L cos(i )
L2
1
 

 sin 2 (i ) 
V (i )   
2
 2 r 1 S
 4
S2



(2.23)

Note that r is compression ratio; L is connecting rod length; S is piston stroke; B is piston bore. The
values of these parameters can be found in Table 2.1.
2.4.3

Fueling dynamics and air-to-fuel ratio calculation

As shown in Figure 2.1, the engine is equipped with dual fueling systems: DI and PFI. The
vaporization and mixing of DI fuel is complicated and difficult to be modeled in a zero dimension
model. The combustion model simply assumes that the total DI fuel of every cycle is completely
vaporized and well mixed with the in-cylinder air. On the other hand, the DI fueling has less
dynamic influence on engine combustion, since the DI fuel injected in current engine cycle has
negligible impact on the combustion of next cycle if combustion is normal. Whereas for the PFI
fuel, the vaporization and mixing inside the engine cylinder are nearly complete, but the wall
wetting phenomena of the PFI fuel spray on the intake port and the back of the intake valve
introduces cycle-to-cycle dynamics and affects the engine transient performance seriously. It must
be modeled in the engine model.
The wall wetting phenomena of the PFI fuel injection can be described in such a way that
only part of the injected fuel (β·Minj, 0< β<1) enters the cylinder while the rest of the fuel
((1-β)·Minj) remains on the surface of the intake port and the back of intake valves. Then the total
fuel injected into the cylinder consists of the fuel directly injected into the cylinder and the fuel

26

vapor (α·Mres, 0< α<1) from fuel mass stored from previous injection. Wall wetting phenomenon
leads to the most important dynamics in PFI fuel mass calculation, which affects engine transient
performance significantly [72]. The governing equation of the wall wetting dynamics is


M fuel  k     M res  k  1    M inj  k 


 M res  k   1     M res  k  1  1     M inj  k 


(2.24)

where k is the index representing engine cycle number, k indicates current engine cycle and k-1
indicates the last engine cycle; Mfuel is the quantity of fuel mass flowed into the cylinder; Mres is
the quantity of fuel mass left on the port and the back of intake valves; Minj is the amount of fuel
injected by the PFI injector for the given engine cycle; coefficients α and β are functions of engine
coolant temperature, engine speed and load.
The engine gas exchange behavior introduces dynamics to the air-to-fuel ratio calculation
too, since a substantial part of the burned gas remains inside the cylinder, especially at low load.
This gas fraction carries the air-to-fuel ratio of the previous engine cycle to the current one.
Therefore, the air-to-fuel ratio is model cycle-by-cycle below

[ k ] 

 f [k ]  M t [k ]  M r [k  1]  [k  1]  M r [k  1]
M t [k ]

(2.25)

where λ is the normalized air-to-fuel ratio of gas mixture inside engine cylinder after IVC; λf is the
normalized air-to-fuel ratio of fresh charge in current cycle, and it is defined as

 f [k ] 

M t [k ]  M r [k  1]
M fuel [k ](1   )

(2.26)

and σ is stoichiometric air-to-fuel ratio of the fuel.
2.4.4

One-zone SI combustion model

In the SI combustion mode, the start of combustion is forced by the spark ignition, which
27

can be controlled at any desired crank position ST. After ST the mass fraction burned of trapped
fuel can be represented by the S-shaped Wiebe function [73] as

   
x(i )  1  exp  a  i ST
   SI






m 1 





(2.27)

where ΔθSI is the predicted burn duration of SI combustion mode (a calibration parameter of
engine speed, engine load (MAP) and coolant temperature); and m is the Weibe exponent (m=2
was used in the model). Coefficient a depends on how the burn duration ΔθSI is defined. If ΔθSI is
specified as 10% to 90% MFB, a is calculated by
1
1 m  1



a    ln(1  0.9)  m  1    ln(1  0.1)  m  1 





(2.28)

Assuming both burned and unburned gases are evenly mixed in one zone, the SI
combustion process is simplified into a heat transfer with volume change process of entire
in-cylinder gas. The in-cylinder gas temperature can be calculated by
 V (i 1 ) 
T (i )  T (i 1 ) 

 V (i ) 

 1  M H
SI f LHV  x (i )  x (i 1 )   Q (i )


M t Cv

(2.29)

where ηSI is function of engine speed and engine load, calibrated by matching the calculated IMEP
with that given by GT-Power; and Q represents the heat transfer between the in-cylinder gas and
cylinder inner surface. Only convection was considered in the model, since for gasoline engine the
heat transfer due to radiation is relatively small in comparison with the convective heat transfer [3].
Woschni correlation model ([38] and [74]) is used to calculate the heat transfer term,
Q(i )  Ac hc T (i 1 )  Tw 

where hc is called Woschni correlation, and it can be written as
28

(2.30)

hc  cB m 1P m wmT 0.751.62m N e

(2.31)

The coefficients c and exponent m in equation (2.31) can be used to correlate the simulation results
to the experimental data, or GT-Power simulation results; c=0.54 and m=0.8 were found to have
good correlation for the model in this research.
There are two terms in the right hand of equation (2.29). The first term represents an
isentropic compressing or expanding process, while the second term calculates the temperature
rise due to the heat transfer during the combustion. Therefore, the complicated thermodynamic
process of the combustion is simplified into an isentropic volume change process without heat
exchange in one crank degree period and the heat absorption from combusted fuel without volume
change in an infinitely small time period. Based on the updated gas temperature from equation
(2.29), the gas pressure can be calculated by applying ideal gas law to the in-cylinder gas as
follows,

P (i )  P(i 1 ) 
2.4.5

V (i 1 ) T (i )

V (i ) T (i 1 )

(2.32)

Engine torque computation

The equations presented in the last sub-sections provide a complete profile of in-cylinder
gas pressure of each engine cycle. Based on this pressure profile and the cylinder volume profile,
the engine IMEP (indicated mean effective pressure) can be calculated by a simple integration

PIMEP 

1 i  719
  P i   V i   V i 1  


Vd i  0





(2.33)

where Vd is the cylinder displacement; and
Vd  V  BDC   V TDC 

At last engine torque output is calculated by

29

(2.34)

Te 

60n( PIMEP  PFMEP )Vd
2 N e

(2.35)

where PFMEP is the friction mean effective pressure and n is the quantity of engine cylinders.

2.5 Model Validation Using GT-Power Model

The crank based combustion model was assembled with the mean value air handling model
to build the entire control oriented engine model. Chapter 4 provides details about how they are
assembled and implemented into the HIL simulator. To validate the developed engine model, HIL
simulations were performed and results were compared with those from GT-Power model.
Table 2.2 lists some key parameters of the engine setup, and Table 2.3 shows how the
dual-stage turbocharger was adjusted for different engine conditions. Both full and half load
engine simulations were performed for engine speeds between 1000 and 5000 rpm with a 500 rpm
increment. The fuel quantity was controlled in a closed-loop to maintain stoichiometric air-to-fuel
ratio for all simulations, and engine spark timing was adjusted to MBT timing [75] for all
simulations, too. The same parameter set was used for both GT-Power engine model and the
developed engine model in all simulations.
Table 2.2: Engine setting for both full and half load simulation
Actuator Parameter

Setting

Intake valve timing (peak valve lift)

460° ACTDC

Exhaust valve timing (peak valve lift)

260° ACTDC

EGR valve duty

0

Intake throttle opening

Full: 90°; half: 20°

Air-to-fuel ratio

stoichiometric

30

Table 2.3: Dual-stage turbocharger setting for full/half load simulation
Engine speed
(rpm)

HP Waste-gate (°)

LP Waste-gate (°)

Bypass valve (°)

Full

Half

Full

Half

Full

Half

1000

0

90

0

90

0

0

1500

1.5

2.7

0

90

0

0

2000

3.5

3.2

0

90

0

0

2500

4.5

3.6

0.5

90

0

0

3000

4

3.8

1.8

90

0

0

3500

90

3.5

3.4

90

90

0

4000

90

90

4.1

15

90

90

4500

90

90

6

18

90

90

5000

90

90

7.8

24

90

90

In Table 2.3 the waste-gates and bypass valve positions of the dual-stage turbocharger were
selected to achieve the best engine performances while maintaining the stability of the compressor
and turbo systems. For instance, for the full load simulations, the LP compressor always operates
within the surge and over speed limits of its compressor map to maintain stable engine operations
without damaging itself, as shown Figure 2.4. Note that for this downsized engine, high boost
pressure is desired to achieve maximum engine torque output at full load, and as a result, the LP
compressor tends to operate at the region close to its surge limit to have the best performance.
Figure 2.5 presents the correlations of the engine torque; IMEP, MAP, and EMP (exhaust
manifold pressure). Good correlations were found for most of the simulated conditions over
engine speed and load ranges except for a few simulation points that are outside of the ±10% range.
One can easily find that the EMP is the worst among the four compared parameters shown in
Figure 2.5. This is mainly due to the simplification of turbine dynamics in the real-time HIL
31

simulations. From Table 2.3 one can see that when engine speed is higher than 3500 rpm at full
load condition, and 4000 rpm for half load condition, the HP waste-gate and bypass valve are fully
opened, and the dual-stage turbocharger system switches to a mode utilizing LP turbine only. To
simplify the computation, the HIL Simulink model neglects the pressure drop across the HP
turbine when the LP turbine only mode is activated. In the GT-Power model this dynamics is well
modeled since in this case there exists a small pressure drop across the HP turbine. In fact, this
pressure drop increases as the increment of engine load, leading the HP turbo shaft to rotate, which
increases EMP. Therefore, the GT-Power model simulates this small pressure drop in the pure LP
mode, providing more accurate results of EMP than those provided by HIL simulations. On the
other hand, the small errors of EMP in HIL simulations do not affect engine simulation accuracy
significantly in the LP turbine only mode since there is almost no additional boost provided by the
HP compressor due to the fully opened bypass valve.

overspeed limit
2.6

Pressure Ratio

2.4
2.2 surge limit
2

4500
3500
4000
3000
2500

1.8

5000

2000

1.6
1.4

1000

1.2
1

0

1000
0.005

0.01
0.015
0.02
0.025
0.5
Reduced Mass Flow Rate (kg/s.K /kPa)

0.03

Figure 2.4: Operating status of LP compressor for full load simulation

32

40
IMEP of HIL (bar)

Torque of HIL (N.m)

400
300
200
100
0

0

EMP of HIL (bar)

MAP of HIL (bar)

2
1
2
MAP of GT-Power (bar)

10
0

Half load
Full load
4

3

0

20

0

200
400
Torque of GT-Power (N.m)

4

0

30

3
2
1
0

4

20
40
IMEP of GT-Power (bar)

0

2
EMP of GT-Power (bar)

4

Figure 2.5: Correlation plots of the HIL and GT-Power simulation results

2.6 Conclusions

In this chapter, governing equations for the combustion process and subsystems of a
dual-stage turbocharged SI engine are presented with certain assumptions. The steady state HIL
(Hardware-In-the-Loop) simulation results are also compared with the corresponding GT-Power
simulation results with satisfactory correlations. The following are the three key conclusions.


Using mean value modeling technique for engine air handling subsystems and crank based

33

modeling method for combustion process is an effective way to model both continuous and
discrete engine dynamics.


One-zone combustion assumption simplifies the SI combustion process modeling. By
separating the volume change and the fuel heat release in each crank degree, the in-cylinder
gas pressure and temperature can be calculated using two independent equations.



The developed engine model is capable of real-time simulations with modeling accuracy close
to that of the one dimensional GT-Power model.

34

CHAPTER 3
CONTROL ORIENTED SI-HCCI HYBRID COMBUSTION MODEL FOR
AN HCCI CAPABLE INTERNAL COMBUSTION ENGINE

3.1

Introduction

As discussed in chapter 1, the HCCI combustion has potentials to reduce engine out NOx
(nitrogen oxides) emissions with the improve fuel economy. However, it has its limitations, too.
The HCCI combustion is limited at high engine load due to the audible knock [62] and at low load
due to misfire caused by the lack of sufficient thermal energy to trigger the auto-ignition of the
gas-fuel mixture late in the compression stroke [76]. In fact, HCCI can be regarded as a type of
engine operating mode rather than a type of engine [22]. In order to take advantage of the HCCI
combustion mode in an internal combustion engine, the SI combustion mode is still required for
those engine operational conditions between the medium load and high load. The HCCI
combustion mode can be used for these operational conditions between low load and medium load
[77]. Typically, it is between 2.5 bar and 5.5 bar IMEP. For engine load conditions below the low
limit, spark ignition is activated again to avoid misfired combustion [78]. Therefore, the HCCI
capable engine needs to switch its combustion modes between the SI and HCCI combustions
frequently under the practical vehicle operational conditions. However, the combustion mode
transition is an open issue that prevents utilizing the HCCI combustion technology. To address this
issue, a crank based SI-HCCI hybrid combustion model ([45] and [79]) will be presented in this
chapter for the control research of the combustion mode transition.

35

Using the crank based engine modeling method introduced in the last chapter, a more
detailed two-zone SI combustion model was developed and is presented in this chapter. The
simulation results of the two-zone SI combustion model demonstrate that there exists an SI-HCCI
hybrid combustion mode, which starts with SI combustion and ends with HCCI combustion.
During the SI combustion phase, the burned gas applies work to the unburned gas and triggers
HCCI combustion of the unburned gas-fuel mixture under certain conditions. Controlling this
hybrid combustion process has the potential to have a smooth combustion mode transition, and the
HIL simulation results presented in the next chapter demonstrate its feasibility of improving the
quality of combustion mode transition. In this chapter, the two-zone SI combustion model is also
combined with an one-zone HCCI combustion model with updated gas exchange model to model
the SI-HCCI hybrid combustion, where both SI combustion and HCCI combustion are two special
operating modes of the SI-HCCI combustion.
This chapter is organized as follows. In Subsection 3.2 the HCCI capable engine is
introduced and a GT-Power combustion model is presented as the baseline model for the
calibration and validation of the modeling work in this chapter. The SI-HCCI hybrid combustion
model architecture is described in Subsection 3.3 to demonstrate the modeled hybrid combustion
process and the mode transition between the SI and HCCI combustions. In Subsection 3.4 the gas
exchange model is modified based upon the model described in the last chapter. Subsection 3.5
presents the dynamic equations used for the HCCI combustion phase; and Subsection 3.6
describes the two-zone SI combustion model as well as the governing equations under the
two-zone assumptions. Some steady state simulation results of the developed model are shown in
Subsection 3.7 with comparison to those obtained from the GT-Power simulations.

36

3.2

Engine Architecture and GT-Power Model

Figure 3.1 shows the engine architecture used for modeling the SI and HCCI combustion
modes transition control. It features four cylinders with an external EGR system, dual cam shaft
capable of independent timing control of both intake and exhaust valves. The air handling system
of this engine is much simpler than the one studied in the last chapter due to the absence of
turbocharger system. Intake throttle is installed at intake pipe upstream of the intake manifold. The
engine is also equipped with the dual fuel injection system, PFI and DI, to facilitate the combustion
study. The major specifications of the engine are given in Table 3.1. According to these parameters
one can find that this engine configuration is very close to a typical SI engine, except for the cam
and valve systems. Both intake and exhaust cam shafts have two stages of lift profiles, the high and
low stages. For both cam shafts, the maximum lift is 9 mm for high stage and 5 mm for the low
stage. The engine valve timings can be adjusted independently with a fairly large range of ±40°
crank angle for both cam shafts. This cam design enables the engine to operate in the SI
combustion mode with high volumetric efficiency, and in the HCCI combustion mode with more
internal residual gas and less pumping loss due to the possibility of un-throttled combustion.
Compression ratio of 9.8 shown in Table 3.1 might be a little low for the HCCI combustion. In
future, higher compression ratio will be adopted to extend the HCCI operation range at light load
conditions, such as the idle condition.
The air handling system shown in Figure 3.1 is actually a simplification of the system
presented in Figure 2.1. All governing equations of the air handling system are the same as those
listed in the last chapter. Therefore, they will not be repeated in this chapter and only the
combustion model will be presented in detail.

37

Figure 3.1: HCCI capable engine configuration

Table 3.1: HCCI capable engine specification
Engine parameter

Model value

Bore/stroke/con-rod length

86mm/86mm/143.6mm

Compression ratio

9.8:1

Intake/exhaust valve diameters

31.4mm/22.5mm

Intake/exhaust valve lifts of high stage

9mm/9mm

Intake/exhaust valve lifts of low stage

5mm/5mm

Intake/exhaust valve timing range

±40°/±40°

Intake/exhaust valve lifts lash

0.2mm/0.25mm

38

For the SI-HCCI combustion study, a GT-Power model as shown in Figure 3.2 was also
developed, but only for studying the combustion process. It will be used as the baseline model to
calibrate the combustion related parameters and validate the combustion performance for the
developed model. In order to validate the combustion model without the influence of the engine air
handling system, the engine air handling dynamics was not included in the GT-Power combustion
model. Furthermore, only one cylinder is modeled, since the combustion process is assumed to be
the same for all cylinders with different combustion phase.

Figure 3.2: GT-Power combustion model

39

3.3

SI-HCCI Hybrid Combustion Model Architecture

As discussed in Subsection 3.1, three combustion modes have been proposed for the HCCI
capable engine. They are SI, HCCI, and SI-HCCI hybrid combustion modes. In the rest of this
chapter, a zero dimensional crank based combustion model will be developed to model the three
combustion modes.

In-cylinder pressure
Exhaust valve lift
Intake valve lift

30

20

ST
EVO

IVC

EVC

IVO

5

Valve lift (mm)

In-cylinder pressure (bar)

40

10

0

SOHCCI
-100

0
TDC

100

200

300

400

500

0

Crank angle (deg ACTDC)
Figure 3.3: SI-HCCI hybrid combustion related events and phases

To understand the characteristic of each combustion mode, the combustion related events
and phases of an IC engine are shown in Figure 3.3. Comparing with Figure 2.3, there is one
additional event in Figure 3.3. That is the SOHCCI (start of HCCI combustion). Furthermore, both
ST and SOHCCI are marked in the boxes with dashed frame to distinguish them from other events,
since the occurrences of these two events depend on the combustion mode. The other events exist
for any 4-stroke internal combustion engine. Accordingly, the main difference among each
40

combustion mode lies on the phase between IVC and EVO. When the SOHCCI event does not
occur in this phase, the engine is operated at the SI combustion mode; and when the SOHCCI
event occurs before the SI event, the engine is operated at the HCCI combustion mode; while the
SI-HCCI hybrid combustion mode occurs inter-between the HCCI and SI combustion modes.
Note that both SI and HCCI combustion modes are special cases of the SI-HCCI hybrid
combustion mode. In fact, there is a fourth mode, in which both SI and SOHCCI do not occur in
the combustion phase, or SOHCCI happens very late in that phase. The fourth mode is unexpected
and needs to be avoided since it means misfire or partial combustion. The diagram in Figure 3.4
illustrates the model architecture and explains how the combustion modes switch between each
other. The most important criterion of the mode switch is Arrhenius integration ARI ([73], [80],
and [81]), which can be represented by
 Ea 




b 
ARI   i Ax a xox e RT  d
f
IVC

(3.1)

where xf and xox are unburned fuel and oxidizer mass fractions; exponents a and b are the influence
factors; multiplier A and Arrhenius activation energy Ea can be obtained by matching the
experimentally determined rates of burning. The SOHCCI crank position is defined as the crank
angle for 1% fuel burned under HCCI combustion. Accordingly once ARI exceeds 1 the
combustion model switches to HCCI mode. The Arrhenius integration in equation (3.1) starts at

θIVC, and is reset at θEVO. During this period the integration is updated every crank degree. The
gas temperature T in equation (3.1) is a key parameter that affects the rising speed of ARI
significantly. If spark ignition never happens, the variable T in equation (3.1) equals to in-cylinder
gas temperature; while during the SI combustion phase T equals to unburned gas temperature TU,

41

which will be calculated by a two-zone SI combustion model presented in this chapter. This is also
the main motivation of developing the two-zone SI combustion model, since the one-zone SI
combustion model presented in the last chapter does not provide this information.
In Figure 3.4, there are three subroutines in the entire combustion model, the gas exchange
model, the one-zone HCCI and two-zone combustion models. In the rest of this chapter, these
sub-models will be investigated in great details.

   1

   IVC
   EVO

ARI  0



ARI  
AR    d
IVC

ARI  1

   ST

Figure 3.4: SI-HCCI hybrid combustion model diagram

3.4

Revisit the Gas Exchange Process

In HCCI capable engines, the gas exchange process is more complicated than that in SI
42

combustion engines [82], and it affects the combustion timing and duration significantly. Both
positive valve overlap (PVO) and negative valve overlap (NVO) might happen in the entire engine
operating range depending on the valve control strategy. Figure 3.3 shows the case of NVO, in
which IVO comes later than EVC and creates a recompression profile on the in-cylinder pressure
signal. Furthermore the low stage lift profiles of both intake and exhaust valves allow the valve
timing to shift in a large range. The gas exchange model introduced in last chapter cannot be used
here, since it cannot deal with the large range of valve timing. A new gas exchange model is
required.

In-cylinder pressure (bar)

6

RPM=4000, MAP=1bar, EMP=1bar, EVC=340 , IVO=380 , IVC=-116
GT-Power model
Two-zone model

5
4
3

IVC

EVO

EVC

IVO

100
200
300
Crank angle ( ACTDC)

400

2
1
0

-100

TDC

500

Figure 3.5: In-cylinder pressure trace in gas exchange process

3.4.1

Gas exhaust process

The gas exhaust phase corresponds to the phase from EVO to IVO for PVO and the phase
from EVO to EVC for NVO. In this phase, the in-cylinder gas mixture is expanding in the cylinder,
43

exhaust runner and manifold. The in-cylinder pressure drops quickly but not instantaneously down
to the level of the exhaust manifold pressure. It normally takes a few crank degrees for the
in-cylinder pressure to approach the exhaust manifold pressure. One can find this dynamic delay in
Figure 3.5. It is difficult to model this dynamics using simple dynamic equations for real-time
simulations. For simplicity, a first order transfer function is used to approximate this dynamic
process as

P( z ) 

1   EVO

1   EVO  z 1

PEM ( z )

(3.2)

where z is the unit delay operator; τEVO is the time constant for exhaust valve opening;
The entire gas exhaust process is not an isentropic process because of the heat transfer
during the process. However, the entire process is divided into each crank degree, and the process
in such small period as a crank degree is also divided into two stages. The first stage is
approximated as an isentropic process without heat exchange, and it occupies the duration of one
crank degree. Heat exchange happens in the second stage, which occupies an infinitely small time
period. Using this method, the computational error is negligible, while the model is as simple as
 1

 P(i )  
Q(i 1 )
T (i )  T (i 1 ) 


M (i 1 )Cv
 P (i 1 ) 

(3.3)

By investigating the pressure trace provided by the GT-Power model shown in Figure 3.5,
one can find that during the late stage of the gas exhaust phase the in-cylinder pressure increases
significantly, and it finally reach 1.9 bar at EVC, much bigger than the exhaust manifold pressure
(1 bar in this case). There are two causes. One is that the exhaust valve is almost closed during the
late stage and restricts gas from leaving the cylinder; and the other is that the EVC timing is before
gas exchange TDC in the case. This phenomenon cannot be ignored, since P(θEVC) is used to

44

calculate residual gas mass Mr, and Mr will affect HCCI combustion timing and duration
significantly. This pressure rise dynamics can also be modeled by a first order transfer function

P( z ) 

1   EVC

1   EVC  z 1

PEM ( z ) EVC

(3.4)

where ηEVC is the predicted pressure ratio at EVC, and it is mostly affected by engine speed, EVC
timing and exhaust valve lift. A 3D table of the ηEVC calibration was derived based upon the
GT-Power simulations. As shown in Figure 3.2, this model yield a good match between the
pressure traces provided by GT-Power model and the two-zone combustion model, especially at
the EVC timing.

Table 3.2: Calibration of ηEVC for low stage exhaust valve profile
RPM

1000

2000

3000

4000

5000

300

1.26

1.4

1.49

1.62

1.72

310

1.31

1.46

1.57

1.72

1.78

320

1.32

1.49

1.63

1.79

1.88

330

1.3

1.49

1.64

1.79

1.9

340

1.25

1.39

1.51

1.68

1.77

350

1.13

1.23

1.31

1.41

1.48

360

1

1.01

1.04

1.04

1.12

370

0.9

0.91

0.83

0.85

0.8

380

0.82

0.77

0.69

0.7

0.63

390

0.75

0.68

0.62

0.61

0.54

θEVC

45

Table 3.3: Calibration of ηEVC for high stage exhaust valve profile
RPM

1000

2000

3000

4000

5000

300

1.53

1.74

1.91

2.01

2.28

310

1.57

1.8

2

2.17

2.34

320

1.6

1.88

2.08

2.33

2.4

330

1.57

1.87

2.13

2.45

2.44

340

1.47

1.78

2.03

2.27

2.36

350

1.27

1.47

1.67

1.83

2.05

360

1.03

1.11

1.19

1.29

1.4

370

0.89

0.88

0.86

0.87

0.87

380

0.77

0.73

0.7

0.66

0.66

390

0.68

0.64

0.6

0.55

0.54

θEVC

3.4.2

Residual gas recompression in NVO

Negative valve overlap (NVO) is often used to regulate the HCCI combustions. There are
two main advantages. One is to reform the pilot fuel injected during this phase (between EVC and
IVO in Figure 3.3) into short carbon chain molecules (pyrolysis) [83], as a result the active energy

Ea in equation (3.1) can be reduced; and the other is to regulate the residual gas temperature. As a
result the in-cylinder gas temperature at IVC can be optimized for desired SOHCCI timing. The
first effect is difficult to model using governing equations. In [63] and [83], the influence of
recompression on Ea is correlated by experimental data. In this chapter, this effect is ignored until
experimental data is available. For the second effect, it is modeled as follows.

46

 V (i 1 ) 
T (i )  T (i 1 )  

 V (i ) 

 1


Q(i 1 )
M (i 1 )Cv

(3.5)

and


 V (i 1 ) 
P (i )  P(i 1 )  

 V (i ) 

(3.6)

Another important parameter calculated in this phase is the residual gas mass. It is
calculated based upon ideal gas law, and updated once per engine cycle at EVC for NVO.

M r  M ( EVC ) 
3.4.3

P( EVC )  V ( EVC )
R  T ( EVC )

(3.7)

Gas exchange behavior in PVO

The gas exchange behavior during the phase from IVO to EVC for the PVO is also very
complicated. Since both intake and exhaust valves are partially opened in this phase, residual gas
and fresh charge can flow in many ways depending on the pressure ratio across each valve. For
simplification, assume gas exchange across exhaust valve is terminated in this phase; part of
residual gas can flow to intake port, but finally it flows back into cylinder during the rest of the
intake process. Based upon this assumption, the mass of residual gas for PVO case can be
calculated by equation (3.8) at IVO instead of EVC for NVO, and gas exchange of this phase is
actually a part of the air intake process.

M r  M ( IVO ) 

P ( IVO ) V ( IVO )
R  T ( IVO )

(3.8)

This modeling approach may result in slight error for Mr. Fortunately, the PVO only occurs
during the SI combustion process, and in this case the influence of residual gas to the entire engine
performance is much less than that during the HCCI combustion process which usually involves
the NVO strategy. On the other hand, the multiplier ηEVC can also be calibrated to match the test
47

data or the high resolution simulation data. For this paper the GT-Power simulation data is used to
calibrate the entire combustion model.
3.4.4

Air intake process

The air-intake process starts from IVO and ends at IVC. It is also a process of in-cylinder
gases mixing. During this phase the fresh charged air, injected fuel vapor, and residual gas are
assumed to be mixed homogeneously, which is the modeling assumption for combustion. At the
same time, the in-cylinder pressure drops to the pressure level of intake manifold. A first order
transfer function is also used in this model.

P( z ) 

1   IVO

1   IVO  z 1

 PIM ( z )

(3.9)

and

T (i ) 

M f  Cv f  T f  M a  Cva  TIM  M r  Cvr  Tr
M f  Cv f  M a  Cv f  M r  Cvr

(3.10)

where τIVO is the transition time constant for intake valve opening; Ma is the fresh charge mass
(note that it could be the mixture of fresh air and external EGR gas); Cv is specific heat; Tr is the
temperature of residual gas, and it can be calculated by the same approach used in equation (3.3).
During the late stage of the air intake phase, the in-cylinder pressure is also increased, see
Figure 3.5. This phenomenon is the same as that in exhaust phase. The same approach is used.

P( z ) 

1   IVC

1   IVC  z 1

PIM ( z ) IVC

(3.11)

where ηIVC is the predicted pressure ratio at IVC, and it is function of engine speed, IVC timing
and exhaust valve lift. The calibration of ηEVC was derived by the GT-Power model. Good match
has been illustrated in Figure 3.5 too.

48

Table 3.4: Calibration of ηIVC for low stage intake valve profile
RPM

1000

2000

3000

4000

5000

460

0.792

0.713

0.646

0.586

0.53

480

0.848

0.784

0.723

0.661

0.597

500

0.908

0.86

0.812

0.743

0.652

520

0.956

0.931

0.901

0.801

0.672

540

0.995

0.986

0.981

0.848

0.699

560

1.016

1.012

1.057

0.911

0.748

580

1.057

1.051

1.145

1.01

0.833

600

1.113

1.13

1.262

1.162

0.975

θIVC

Table 3.5: Calibration of ηIVC for high stage intake valve profile
RPM

1000

2000

3000

4000

5000

460

0.709

0.621

0.557

0.505

0.46

480

0.783

0.705

0.645

0.594

0.542

500

0.859

0.801

0.75

0.7

0.646

520

0.927

0.892

0.857

0.816

0.768

540

0.986

0.972

0.96

0.938

0.902

560

1.021

1.033

1.042

1.051

1.044

580

1.074

1.094

1.106

1.139

1.175

600

1.155

1.185

1.213

1.244

1.307

θIVC

49

3.5

One-zone HCCI Combustion Model

The HCCI combustion is modeled under the one-zone assumption due to its flameless
nature. Fuel and air are assumed to be premixed homogeneously throughout the entire cylinder;
thermodynamic characteristics such as pressure and temperature are uniformly distributed in the
cylinder. Accordingly only the mean value of in-cylinder gas pressure and temperature will be
modeled.
Unlike the SI combustion, there is no direct trigger (spark ignition) of the HCCI
combustion. The fast heat release process of the HCCI combustion is actually triggered by a very
slow chemical reaction of the gas-fuel mixture during the compression phase after IVC. The most
common practice in control oriented modeling of the HCCI combustion is to assume the chemical
reaction process is governed by single rate Arrhenius equation,

AR(i ) 


Ea 


R T (i ) 
b
A  x a  xox  e
f

(3.12)

where AR is the rate of disappearance of unburned fuel and other parameters have been explained
in equation (3.1). As mentioned earlier in this chapter, the integration of the Arrhenius function is
used to estimate the SOHCCI timing. The SOHCCI timing is the timing separates the slow
chemical reaction with the fast one. During the fast combustion phase the fuel mass fraction
burned can also be approximated by the Wiebe function,

   
x(i )  1  exp   a  i SOHCCI
   HCCI






m 1 





(3.13)

where the burn duration ΔθHCCI is given by

 HCCI  k  T ( SOHCCI )



50

2
3

Ea
1
3R Tm
3
 Tm  e

(3.14)

where k is a scaling constant; Ea is activation energy of the fuel; and Tm is the mean valve of HCCI
combustion temperature. It is calculated by

Tm  T ( SOHCCI ) 

 HCCI M f hLHV [1  x( SOHCCI )]
(3.15)

M t Cv

At last in-cylinder pressure and temperature are calculated by

 1 
HCCI M f hLHV  x(i )  x(i 1 )   Q (i )

 V (i 1 ) 
T (i )  T (i 1 ) 

 V (i ) 



M t Cv

(3.16)

and
P (i )  P(i 1 )

V (i 1 ) T (i )

V (i ) T (i 1 )

(3.17)

where ηHCCI is a function of engine speed and fuel mass, it was calibrated by matching the
calculated IMEP provided by the GT-Power model.

3.6

Two-zone SI Combustion Model

During the SI combustion the spark ignited flame front divides the in-cylinder gas mixture
into two zones, the burned zone and unburned zone, as shown in Figure 3.6. The temperature of the
unburned zone is quite different from that of the burned zone as seen in Figure 3.6. However, this
difference is ignored in the one-zone SI combustion model discussed in the last chapter, where a
mean value of temperature is used for entire in-cylinder gas. This may not lead to large modeling
error for the SI combustion, in which the temperature difference does not impact much on the
combustion model parameters such as in-cylinder pressure. However, for the SI-HCCI hybrid
combustion, the unburned zone temperature is a key parameter for predicting the start of the HCCI
combustion. The expansion of the burned zone during the initial SI combustion process applies
work to the unburned zone. As a result it makes the unburned zone temperature rise faster, and

51

causes HCCI combustion in the unburned zone. On the other hand, the two-zone SI combustion
model is closer to the nature of the SI combustion process. These are the motivations for
developing this two-zone combustion model.
3.6.1

Two-zone assumptions

Work

Heat
transfer

Enthalpy
flux

Chemical
reaction

Unburned zone

Spark

P, TU
P, TB
B/2

rf
Burned zone
Flame front
Figure 3.6: Two-zone SI combustion model
For modeling simplicity, some assumptions have been made to the two-zone SI
combustion process.


The fuel, air, and residual gas charges are uniformly premixed at IVC.



In the two-zone model, the gas mixture pressure is assumed to be evenly distributed
throughout both burned and unburned zones.



During each given crank degree, a portion of gas-fuel mixture is transferred from the
52

unburned zone to the burned zone. The amount of the gas-fuel mixture is defined by the burn
rate of fuel, which is prescribed by the Wiebe function.


In each step of engine crank degree, the flow of each zone is assumed to be in steady state.



The total heat transfer between in-cylinder gas mixture and the cylinder inner surface is
calculated by equation (2.30) same as that in the one-zone model, except the gas temperature
T in that equation is replaced by the average temperature of both burned and unburned zones,
which is calculated by
T



xCvBTB  (1  x)CvU TU
xCvB  (1  x)CvU

(3.18)

The heat transfer between the burned and unburned zones is neglected.

3.6.2

Governing equations

After spark ignition, the burned zone is created. Both the burned and unburned zones can
be regarded as control volumes. Mass, enthalpy, and work exchange between these two control
volumes, and also between the control volumes and the surrounding cylinder wall. According to
the first law of thermodynamics [84], the energy balance equation of the burned zone is
represented by
d ( M B eB )
dV
dx dM B
hU
 P B  xQ   SI H LHV M f

d
d
d
d

(3.19)

The subscription B and U represent the burned and unburned zones, respectively. The energy
balance equation of unburned zone is
d ( MU eU )
dV
dMU
 P U  (1  x)Q 
hU
d
d
d

(3.20)

Apply the ideal gas law [84] to the burned zone and get
PVB
 M B  xM t
RTB

53

(3.21)

Apply the ideal gas law to the unburned zone and get
PVU
 MU  (1  x) M t
RTU

(3.22)

Additionally, the cylinder geometry yields
VB  VU  V
3.6.3

(3.23)

Solutions of two-zone model

Equations (3.19) to (3.23) constitute the complete governing equations of the two-zone
combustion model. There are five unknowns:
 X1  VB (i )
 X  V ( )
U i
 2

X 3  TB (i )

 X  T ( )
 4 U i
 X 5  P(i )


And they can be computed by solving equations (3.19) to (3.23) using the iterative method as
described in equation (4.3) based on the information computed in last crank position

VB (i 1)

VU (i 1 ) TB (i 1 ) TU (i 1 ) P(i 1 ) x(i 1 ) 

T

and the MFB of current crank

position x(i ) , which is given by the Wiebe function. The initial conditions are the thermodynamic
states at the end of the compression phase, and they are
X 0
 1
X 0
 2
 0
 X3
 0
X 4

X 0
 5

0
 V ( ST )
 T ( ST )
 T ( ST )
 P( ST )

Therefore, differential equations (3.19) to (3.23) can be converted to

54

 a1 X1  b1 X 3
a X  b X
 2 2 2 4

 X1 X 5 X 3
 X X X
 2 5 4
 X1  X 2




c1

 c2
 c3
 c4

(3.24)

 c5

where
a1
b1
a2
b2
c1
c2
c3
c4
c5






P i 1 
x i  M t Cv
P i 1 
1  x i   M t Cv



  SI H LHV M f dx(i )  P i 1 VB (i 1 )  x(i )Q(i )
 M t x i 1  CvTB i 1   M t dx(i )CpTU i 1 
 P i 1 VU (i 1 )  M t dx(i )CpTU i 1 
 M t 1  x i 1   CvTU i 1   1  x(i )  Q(i )


 x i  M t R
 1  x i   M t R


 V i 

Equation (3.24) was solved analytically using Matlab symbolic toolbox, and the rational
solution was used for numerical solution of the algebraic equations set (3.24) in the HIL simulation.
Note that due to the nonlinearity of equations (3.21) and (3.22) the solutions are not unique and
they consume large portion of HIL simulator throughput. After implementing the model into the
dSPACE HIL simulator for real-time simulations, the two-zone engine model can be simulated at
the engine speed up to 5000 rpm without overrun, while the one-zone model can be simulated up to
10000 rpm. Fortunately the possible operating range of the two-zone model (SI-HCCI hybrid
mode) is between 1000 and 5000 rpm.

3.7

Model Validation Using GT-Power

Since the GT-Power does not support SI-HCCI hybrid combustion modeling, the hybrid
55

combustion mode cannot be directly validated. In this section only the sub-models are validated
with the GT-Power combustion model. The hybrid combustion mode will be validated by the
actual engine test data in next stage of the research.
3.7.1

Comparison between two-zone and one-zone model

To validate the developed two-zone SI and one-zone HCCI combustion models, two
combustion simulations were conducted using both models. In the SI combustion model used for
the simulations, gas exchange model is from this chapter, whereas the combustion model is from
the last chapter. The operational conditions for both simulations were selected as following. In the
first simulation, engine speed was set to 2000 rpm, and intake manifold absolute pressure (MAP)
was set to 1.0 bar as full load condition. In the second simulation engine speed was at 5000 rpm
with MAP equals to 0.4 bar to simulate the low load condition. The valve strategies are also
different, NVO for the first one (EVC=IVO=360° ACTDC), whereas PVO is used for the second
one (EVC=380° ACTDC, IVO=340° ACTDC). Same simulations were also completed by the
GT-Power combustion model as the baseline for the comparison. Simulation results are plotted in
Figure 3.7 to Figure 3.9. Note that the abbreviation ACTDC represents after TDC, and TDC stands
for top dead center of piston movement.
Figure 3.7 shows the in-cylinder pressure and temperature traces. The temperature
provided by the two-zone SI combustion model is the average temperature of both burned and
unburned zones, and it is given by equation (3.18). From Figure 3.7 one can find that the
simulation results of both one-zone and two-zone combustion models have good matches with the
GT-Power model results except some small difference of the temperature traces at gas exchange
process. The comparisons partially validate both modeling methods.

56

70

GT-Power, RPM=2000, MAP=1.0bar, NVO
Two-zone, RPM=2000, MAP=1.0bar, NVO
One-zone, RPM=2000, MAP=1.0bar, NVO
GT-Power, RPM=5000, MAP=0.4bar, PVO
Two-zone, RPM=5000, MAP=0.4bar, PVO
One-zone, RPM=5000, MAP=0.4bar, PVO

In-cylinder pressure (bar)

60
50
40
30
20
10
0

-100

0

100

200

300

400

500

-100

0

100

200

300

400

500

Mean in-cylinder temperature (k)

2500

2000

1500

1000

500

Crank position ( ACTDC)
Figure 3.7: In-cylinder gas pressure and temperature traces: correlations between GT-Power
model, two-zone SI combustion model and one-zone SI combustion model

57

The simulation results in Figure 3.7 also show close matches between one-zone and
two-zone combustion models. However they are governed by different equations. In the two-zone
model five equations were used, whereas in the one-zone model only two equations were used.
After investigating all the equations used. It is found that the five equations (3.19) to (3.23) of the
two-zone model are derived based on energy conservation and mass conservation of the entire
in-cylinder gas; on the other hand, the two equations (2.29) and (2.32) of the one-zone model can
also guarantee the energy conservation and mass conservation. So they are based on the same
physical principle, but the two-zone model provides more information.
Figure 3.8 and Figure 3.9 demonstrate how the two-zone SI combustion model divided the
in-cylinder gas temperature profile into two temperature profiles: the burned zone temperature in
Figure 3.8 and unburned zone temperature in Figure 3.9, which one-zone model is not capable to
do. Both temperature profiles show good match with the GT-Power simulation results. It further
confirms the effectiveness of the two-zone model.
In Figure 3.9 unburned zone temperatures are also compared with the in-cylinder gas
temperature simulated without combustion. It shows that before spark ignition (ST=-17° ACTDC
in this case), the three temperatures are the same; but after spark ignition, the unburned zone
temperature rises faster than the one without SI combustion. This is due to the work applied by the
burned zone gas. The Arrhenius integration in equation (3.1) is more sensitive to higher unburned
zone temperature, which indicates that the slow chemical reaction before the SOHCCI can be
accelerated by the raised temperature. Accordingly if the unburned zone gas temperature can be
controlled, the SOHCCI timing of the hybrid combustion model can also be controlled.

58

Burned zone temperature (k)

3000

RPM=2000, MAP=1bar, ST=-17 , =1, EVC=360 , IVO=360
GT-Power model
Two-zone model

2500
2000
1500
1000
500
-100

0

100
200
300
Crank position ( ACTDC)

400

500

Figure 3.8: Burned zone gas temperature: correlation between GT-Power and two-zone SI
combustion models

Unburned zone temperature (k)

900

RPM=2000, MAP=1bar, ST=-17 , =1, EVC=360 , IVO=360
GT-Power model
Two-zone model
No combustion

800
700
600
500
400
300

-100

-80

-60

-40
-20
0
20
Crank position ( ACTDC)

40

60

Figure 3.9: In-cylinder gas temperature without combustion; unburned zone gas temperature:
correlation between GT-Power and two-zone SI combustion models
59

3.7.2

Two-zone SI combustion model validation

The two-zone SI combustion model was firstly validated at 3000 rpm of engine speed and
in three different engine load conditions: PIM = 0.4, 0.7 and 1.0 bar corresponding to low load,
medium load and full load conditions. The combustion durations at the three conditions are
different, spark timings were set to MBT (Minimal advance for the Best Torque) for each condition.
The valve strategy is PVO. Fairly good correlations of both pressure and temperature can be found
in Figure 3.10 and Figure 3.11.
To validate the combustion model in wider engine operating range, more simulations were
conducted. In those simulations, engine speed sweeps from 1000 rpm to 5000 rpm with 1000 rpm
increment interval; engine load also ranges from low load, medium load to full load conditions.
Both PVO and NVO valve strategies were used, for PVO: IVO=340° ACTDC and EVC=380°
ACTDC; while for NVO: IVO=380° ACTDC and EVC=340° ACTDC. To simplify the validation,
only some key parameters were recorded and plotted in Figure 3.12 and Figure 3.13. Actually
these key parameters listed in Figure 3.12 and Figure 3.13 outline the profiles of the pressure,
temperatures (burned and unburned).
From Figure 3.12 and Figure 3.13, one can find all pressure related parameters, like IMEP,
Pmax and the crank position of Pmax, have fairly good correlations with the GT-Power results;

whereas for the temperature related parameters, the errors are relatively larger, but still within
±10% of their normal reachable range. One possible reason is that the gas property parameters
such as Cv and R used in these two models are different. In the GT-Power model these parameters
are functions of not only the gas temperature but also the gas chemical composition. While in the
two-zone model chemical composition is not considered due to simplified real-time modeling.

60

In-cylinder pressure (bar)

70
GT-Power model, MAP=0.4bar
Two-zone model, MAP=0.4bar
GT-Power model, MAP=0.7bar
Two-zone model, MAP=0.7bar
GT-Power model, MAP=1.0bar
Two-zone model, MAP=1.0bar

60
50
40
30
20
10
0

-100

0

100
200
300
Crank position ( ACTDC)

400

500

Average in-cylinder temperature (K)

Figure 3.10: In-cylinder pressure traces for different engine load at 3000rpm: correlations
between GT-Power and two-zone SI models

GT-Power model, MAP=0.4bar
Two-zone model, MAP=0.4bar
GT-Power model, MAP=0.7bar
Two-zone model, MAP=0.7bar
GT-Power model, MAP=1.0bar
Two-zone model, MAP=1.0bar

2500
2000
1500
1000
500
-100

0

100
200
300
Crank position ( ACTDC)

400

500

Figure 3.11: In-cylinder temperature traces for different engine load at 3000rpm: correlations
between GT-Power and two-zone SI models
61

Another low correlation parameter is the residual gas Mr. for NVO it is fairly good, but for
PVO the correlation becomes worse. As explained in section 3.4, the gas exchange process of PVO
is complicated and difficult to be modeled accurately [85]. Fortunately, this only happens to PVO,
which is only used for the SI combustion mode. The modeling error of Mr in the SI combustion
mode has less impact on the combustion timing and duration than it has in the HCCI mode. Since
in the SI mode: combustion timing is controlled by spark ignition input from engine controller,

Mr, two-zone model

800
600
400
200
0

0

500

20

), two-zone model

60
40
20
0

20

40

60

80

0

20

NVO

0

60

80

Mr, GT-Power

15
10
5
0

10

(P

Pmax, GT-Power

40

20

max

Pmax, two-zone model

40

PVO

80

0

60

0

1000

Mt, GT-Power

80

(P

Mt, two-zone model

while combustion duration is mainly decided by engine load and speed.

20

), GT-Power

max

Figure 3.12: Two-zone SI combustion model correlations: total in-cylinder gas mass Mt, residual
gas mass Mr, peak in-cylinder pressure Pmax and crank position of Pmax
62

TU-max, two-zone model

Tmax, two-zone model

1000

2500
2000
1500
1000
1000

1500

2000

2500

800
600
400
400

500
400
300
200
100
0

0

200

800

1000

Tu-max, GT-Power
IMEP, two-zone model

TIVC, two-zone model

Tmax, GT-Power

600

400

TIVC, GT-Power

15
10
5
0

0

5

10

15

IMEP, GT-Power

Figure 3.13: Two-zone SI combustion model correlations: peak in-cylinder gas temperature
Tmax, peak unburned zone temperature TU-max, charge temperature at IVC TIVC and IMEP

Even Figure 3.13 does not show very good correlations on TIVC and TU-max that are of
great interest in the study of the SI-HCCI hybrid combustion, Figure 3.14 and Figure 3.15
demonstrate fairly good consistency when both temperatures vary with the engine speed.
Furthermore, in Figure 3.14 and Figure 3.15 strong correlation is also found between TIVC and
TU-max. It indicates that the unburned zone temperature can be regulated by adjusting TIVC

through valve timing control.
63

950
900

430

850

TIVC, GT-Power

380

TIVC, Two-zone

800

TU-max, GT-Power 750
TU-max, Two-zone

330

500

TU-max (k)

Charge temperature at IVC - TIVC (k)

480

1000 1500 2000 2500 3000 3500 4000 4500 5000 5500

Engine speed (rpm)

Figure 3.14: Correlations between the peak unburned zone temperature TU-max and in-cylinder

TIVC, GT-Power
380

TIVC, Two-zone

950

TU-max, GT-Power

900

TU-max,Two-zone
360

850

TU-max (k)

Charge temperature at IVC - TIVC (k)

gas temperature at IVC TIVC for NVO at different engine speed

800
340

500

750

1000 1500 2000 2500 3000 3500 4000 4500 5000 5500

Engine speed (rpm)

Figure 3.15: Correlations between the peak unburned zone temperature TU-max and in-cylinder
gas temperature at IVC TIVC for PVO at different engine speed

64

3.7.3

One-zone HCCI combustion model validation

Figure 3.16 shows that the one-zone model can simulate the HCCI combustion process as
well as the GT-Power model. For this simulation, 16 mg of fuel was injected into each cylinder
every engine cycle to generate 5.02 bar IMEP at 2000 rpm, which is close to the upper load
limitation of the HCCI combustion. Note that for the HCCI combustion the engine load is not
decided by MAP but by the injected fuel quantity due to the un-throttled operation. The valve lift
profiles of both intake and exhaust were switched to the low stage ones since the decrease in
exhaust valve lift makes it possible to trap more internal residual gas with NVO and the decrease in
intake valve lift enables un-throttled engine operation.
The HCCI combustion timing is also sensitive to the intake and exhaust valve timings.
Proper valve timing selections lead to improved combustion quality. For instance, in the
simulation results presented in Figure 3.16, intake valve timing was advanced to make the
effective compression ratio smaller to avoid engine knock at the upper load limitation of the HCCI
combustion. The simulations were extended for different valve timings, and these results were
compared with the GT-Power simulation results shown in Figure 3.17 with good correlation.

65

50

RPM=2000, FUEL=16mg, IN=420deg, EX=290deg, IMEP=5.02bar
5

30

3

20

2

1

0

-100
-100

0
0

100
100

200
200

300
300

400
400

500
500

Valve lifts (mm)

4

10

In-cylinder pressure
(bar)

40

0

In-cylinder temperature (k)

2500
One-zone model
GT-Power model
Intake valve lift
Exhaust valve lift

2000
1500
1000
500
0

-100

0

100

200

300

400

500

Crank position ( ACTDC)
Figure 3.16: In-cylinder pressure and temperature traces: correlations between the one-zone
HCCI combustion model and GT-Power model

66

RPM=2000; FUEL=16mg; IN=420, 460deg; EX= 250, 270, 290deg
3000

Tmax of one-zone model

P max of

one-zone mode

80
60

2000

40

1000

20
0

0

20
40
60
P max of GT-Power

0

80

SOHCCI of
one-zone model

400

200

0

1000
2000
Tmax of GT-Power

3000

50

one-zone model

TIVC of

600

0

0

200
400
TIVC of GT-Power

0

-50
-50
0
50
SOHCCI of one-zone model

600

Figure 3.17: One-zone HCCI combustion model correlations: peak in-cylinder pressure Pmax,
peak in-cylinder gas temperature Tmax, in-cylinder gas temperature at IVC TIVC and crank
position of SOHCCI

3.7.4

The impact of external EGR

The impact of the EGR percentage to the hybrid combustion modes was also investigated
through steady-state simulations. HCCI combustions have much shorter burn duration than that of
SI combustions. This leads to high peak in-cylinder pressure and temperature, as shown in Figure

67

3.16. High peak in-cylinder pressure leads to high engine efficiency if it occurs at a proper timing
(5 to 10 crank degree after TDC), whereas high in-cylinder temperature is an adverse condition for
NOx emissions. However, the HCCI combustion is capable of operating with higher EGR rate than
that of the SI combustion. Figure 3.18 demonstrates how the cooled EGR rate affects the
in-cylinder gas temperature. The simulation results in Figure 3.18 were completed with 3.7 bar
IMEP, where the exhaust valve timing, spark timing and fuel quantity were adjusted to maintain a
constant IMEP (3.7 bar) and SOHCCI (0° ACTDC) for each simulation. Simulation results show
that the higher EGR rate the lower the peak in-cylinder gas temperature.

In-cylinder temperature (K)

2500
EGR rate=12.1%
EGR rate=26.6%
EGR rate=36.8%
EGR rate=44.5%

2000

1500

1000

500
-100

0

100
200
300
Crank postion ( ACTDC)

400

500

Figure 3.18: In-cylinder gas temperature traces for different external EGR rate

3.8

Conclusions

In this chapter, the SI-HCCI hybrid combustion model was developed based on the
two-zone SI combustion model and the one-zone HCCI combustion model. The gas exchange

68

model was also updated for improved accuracy. As two special operational modes of the SI-HCCI
hybrid combustion, the SI combustion and the HCCI combustion modes were simulated in HIL
simulation system respectively. Simulation results were also compared with the corresponding
GT-Power ones. The following are the conclusions:


Both one-zone and two-zone SI combustion models provide accurate simulations of the
in-cylinder gas pressure and average temperature of both burned and unburned zones at
different engine operational conditions.



The two-zone SI combustion model is more accurate than the one-zone model for simulating
in cylinder temperatures of both burned and unburned zones. Note that the unburned zone gas
temperature of the SI combustion is related to TIVC (in-cylinder gas temperature at IVC) and
is the key factor of simulating the start of the HCCI combustion (SOHCCI) that can be
controlled by adjusting the intake and exhaust valve timings.



The gas exchange model has higher accuracy for negative valve overlap (NVO) than positive
valve overlap (PVO). It is proper to be used for the SI-HCCI hybrid combustion.



The one-zone HCCI combustion model is proper for the HCCI combustion modeling as part
of the SI-HCCI hybrid combustion



Cooled external EGR gas can be used to reduce in-cylinder gas temperature during the HCCI
combustion process.

69

CHAPTER 4
IMPLEMENTATION OF ENGINE MODEL IN THE HIL SIMULATION
ENVIROMENT

4.1 Introduction

The engine sub-models introduced in Chapters 2 and 3 can be used to conduct offline
simulations individually for validation purpose. To simulate the entire engine model, the model
needs to be implemented into a HIL simulation environment for real-time simulation.
As mentioned in Chapter 1, real-time HIL simulation is a powerful tool for engine control
strategy development and validation. With the HIL simulations, the initial engine control strategy
calibration can be generated and control implementation issues can be resolved. This chapter
explores how the mathematic engine sub-models presented from the last chapters are integrated
into an engine model, and implemented into the dSPACE based HIL simulation environment.
This chapter is organized as follows. Section 4.2 discusses the integration of the entire
Simulink engine model module-by-module in the Matlab/Simulink environment; the methods of
model solutions are presented in this section, too. In Section 4.3 the integrated Simulink engine
model will be implemented into the dSPACE HIL simulation environment. In Section 4.4 results of
two transient simulations are presented based upon the HIL simulations to validate the transient
performance of the developed engine model. At last, conclusions are drawn in Section 4.4.

70

4.2 From Mathematic Equations to Simulink Model

This section discusses the integration of the mathematic equations in Chapters 2 and 3 into
a entire engine model, used for the HIL simulations, in Simulink.
4.2.1

Build engine in Simulink

The engine model was assembled module-by-module. Figure 4.1 shows the layout of these
sub-models used for assembling the Simulink engine model. Each block represents an engine
subsystem. Signals transferred between these blocks are the state variables calculated by the
governing equations embedded inside each block. The governing equations are presented in the
last two chapters. These sub-models were also calibrated and validated separately. Simulink
dialogue box is used to input the sub-model calibrations, see Figure 4.2 for an example. The
functionality of each sub-model can be tested individually by applying signals to the input ports
and observing the output signals.
Integrating the Simulink engine model in such a way makes it easy to change the engine
model configurations. The engine model shown in Figure 4.1 is for the dual-stage turbocharger 3
cylinder SI engine in Chapter 2. It takes only hours to convert this engine model into an HCCI
capable 4 cylinder engine model in Chapter 3 due to the module architecture.

71

Figure 4.1: Simulink engine model - layout of each subsystem

72

Figure 4.2: Dialogue box for fuel injection system

4.2.2

Model solution in Simulink

The entire engine model consists of more than hundred mathematic equations. Some of
them are nonlinear differential equations. To solve these equations analytically is almost
impossible. In Simulink these equations are solved by numeric method. Typically, the differential
equations in the engine model can be written in a simple form as

x  f  x

73

(4.1)


where x is the state space of the engine model and x represents the time derivative of x. One way

to solve the above differential equation is to use the iterative method with first order approximation,
where the above equation can be approximated by the following
x(t  t )  x(t )
 f  x(t ) 
t

(4.2)

where Δt is the time step for the numeric solution. x(t  t ) is the updated state and x(t) is the
known current state. Accordingly f (x(t)) is known since x(t) is known. Therefore, the solution can
be approximated by
x(t  t )  x(t )  f  x(t )  t

(4.3)

The solution can also be represented in discrete time domain (z domain) as
1
1

x( z )  x( z )  f  x( z )  t
z
z


(4.4)

where z is a delay operator. In fact, majority of the nonlinear differential equations are solved in
such way with either variable step or fixed step. Our Simulink engine model is numerically solved
by this approach and that is why there are many unit delay blocks (1/z) in the Simulink engine
model; see Figure 4.1. The crank based combustion model was solved based on the same concept
as discussed above but the time step Δt is replaced by crank angle step Δθ. For this engine model,
the crank step Δθ equals to one crank degree.
Note that in equation (4.3), as time step Δt approaches 0 x(t  t ) approaches x(t).
Accordingly small Δt leads to high accuracy. However Δt cannot be too small due to the
computational throughput limitation. Currently in the Simulink engine model Δt is fixed at 1.0 ms,
and for most subsystems this time step is acceptable, but for system like turbocharger smaller time
step could be required. To reduce the step size for a specific subsystem, multiple iterations within
single time step is used.

74

To implement multiple iterations in single time step, equation (4.3) is rewritten as



xi 1 (t  t )  xi (t )  f xi (t )

 t
m

i  0,1, (m  1)

(4.5)

and
x0 (t )



x(t )

(4.6)

x(t  t )  x m (t  t )

where m is the specified iteration number in one time step. Figure 4.3 illustrates how m affects the
transient performance of the Simulink engine model. The simulation in Figure 4.3 was conducted
with Δt = 5ms, and m = 10 and shows proper accuracy without adding a lot of computational
throughput. Note that it is difficult to implement multiple iterations in single step directly in
Simulink. In the Simulink engine model, the sub-model of the dual-stage turbocharger was
programmed in C language, and compiled as an S-function and called by Simulink block, because
it is easy to execute a particular piece of code for multiple times in C language.

Turbocharger speed (kRPM)

180
160
140
120
2 time's iteration
10 time's iteration
30 time's iteration

100
80

8

9

10

11
12
13
Simulation time (s)

14

15

16

Figure 4.3: Transient performance of the turbocharger shaft rotational speed: comparison
between different times of iteration using single step multiple iteration approach
75

4.3 Model Implementation in HIL Simulator

The Simulink engine model developed has three tasks: the 1.0 ms time step task for the
mean value sub-models (such as the engine air handling subsystem), the crank based task for the
combustion model, and the cycle based task for sub-models like the fuel wall wetting dynamics.
The crank based and the cycle based tasks are independent of simulation time step. To simulate
these three tasks in a parallel way, crank and cycle based interrupts need to be generated. A
dSPACE HIL simulator was selected for the engine simulations. This section introduces the
functionality of the dSPACE HIL system and discusses the implementation of the Simulink engine
model in the dSPACE HIL simulation environment for engine real-time simulations.
4.3.1

The engine simulator hardware

A dSPACE PX20 was selected for the real-time simulation, see Figure 4.4. A DS-1006
microprocessor board was used as the simulation engine, and a DS-2211 automotive application
board along with other I/O boards was used to form the HIL simulator.
The most important feature of dSPACE systems is that the Simulink block diagram can be
auto-coded into C and compiled to be executed in the dSPACE system. Also, there are many
Simulink block libraries that make the programming fairly easy.

Figure 4.4: The dSPACE hardware
76

4.3.2

HIL simulation system architecture

Figure 4.5 shows the system architecture of the HIL simulation system. For simplicity, not
all the signals and subsystems are included in the diagram. It is only used to explain how the
Simulink engine model was implemented in the HIL simulation environment. In Figure 4.5, the
ECU (engine control unit) in the upper area of the diagram is the engine control target of the HIL
simulation, and it is not the focus of this chapter. All blocks below the ECU block are from the HIL
simulator. In the center it is the engine model, the main sub-models were displayed. On the output
side of the engine model, signal conditioning block converts all computed parameters to real
engine signals that the ECU can recognize. On the input side of the engine model, signal
preprocessing block translate all ECU control signals back to the parameters that engine model can
recognize.
During the HIL simulations, the time based mean value sub-models are executed in
real-time at a fixed time step (1.0 ms). Among these sub-models, the engine crankshaft dynamic
model as described by equation (2.4) provides the engine speed. Based on the modeled engine
speed, engine crank signal (720 pulses per cycle), TDC signal (2 pulses per cycle) and cam signal
(1 pulse per cycle) are generated using the dSPACE hardware, as shown in Figure 4.6. The signals
are sent to synchronize the HIL simulator with the ECU. At the same time, crank and CAM signals
are looped back to the HIL simulator as input signals to generate interruptions for crank and cycle
based simulations. During the interruptions, crank based and cycle based interruption sub-model
routines are executed. The interruption triggered by crank signal has the top priority in the
interruption queue, since the crank based routine needs to be executed within a specific crank
angle.
Figure 4.6 presents a snapshot of the oscilloscope signals during the HIL simulation,

77

in-cylinder pressure and temperature signals are the output from this HIL simulation. A picture of
the entire HIL engine simulation platform is shown in Figure 4.7. One can find that some auxiliary
instruments like the oscilloscope and host PC are required to facilitate the real-time HIL
simulations.

ECU

Fuel pulse
Spark timing
Throttle duty
Valve timing
EGR duty
.
.
.

Crankshaft
CAM

Tbrake Crank

Fuel inject Mfuel
Air intake
MEGR

Nengine

Mair

Combustion

CAM
TDC
Crank
P(θ)
T(θ)

EGR
Valve

Air exhaust

Control Signal
Measurements

Control Oriented Engine Model

(DS-2211 APU)

(DS-1006 CPU)

x(θ)
PIM(t)
.
.
.

Engine Signal
Conditioning
(DS-2211 APU)

Figure 4.5: System architecture of the integrated HIL simulation environment

78

Figure 4.6: Simulated engine signals displayed on oscilloscope

79

Figure 4.7: Snapshot of HIL simulation platform

4.4 Engine HIL Simulations

In order to demonstrate the transient performance of the developed engine model,
turbocharger lag simulation and the SI-HCCI combustion mode transition simulation were
performed. The simulation results motivated the control study in the next phase of the research.

80

4.4.1

Transient performance of engine with dual-stage turbocharger

Two transient simulation responses were performed using the developed HIL simulation
environment, one with feedforward fuel control and the other without. Both simulations utilize
closed-loop fuel control with a PID control strategy. The transfer function of the feedforward
controller is:
M FF  s  g  N e   s

PIM  s 
  s 1

(4.7)

where g is a function of engine speed, Ne, implemented as a lookup table; τ is the time constant of
feedforward fuel control. The control system block diagram is shown in Figure 4.8.
Note that except for the fuel control, all the other engine control parameters remained
unchanged for both simulations. Engine speed was at 2500 rpm with 10% throttle and the MBT
spark timing. The control reference of the air-to-fuel ratio was set at stoichiometric ratio when a
step throttle of 90% was applied, which sets the throttle to WOT (wide open throttle). The
waste-gates of both stages are closed when the throttle was opened. As a result, the engine started
switching from the partial load to the full load condition.

Figure 4.8: Control architecture for transient response simulation of the SI engine with dual-stage
turbocharger

81

The corresponding engine dynamic responses, plotted in Figure 4.9, show that the
feedforward fuel control provides additional fuel output to improve transient response. With the
feedforward fuel control, the engine air-to-fuel ratio response settles within 1 second, while
without the feedforward fuel control it takes about 4 seconds. The corresponding engine torque
settling time decreases from 2.11 seconds without feedforward control to 1.29 seconds with the
feedforward control, which is significant. One can see this improvement of transient response in
Figure 4.10.
From Figure 4.9 it can be observed that even with feedforward control, during the
transition operation there exists an impulsive overshoot of the relative air-to-fuel ratio, which
indicates that lean combustion occurs right after the step throttle and last for a few engine cycles.
This is mainly due to the special engine architecture. As mentioned in Chapter 2, the engine
throttle locates between the intake manifold and engine head. The lack of volume between the
engine throttle and the intake valve leads to a rapid increment of engine volumetric efficiency
when the throttle is suddenly opened. From Figure 4.10, one can see that the corresponding MAP
also drops at the same time due to the rapid increment of air flow to engine cylinders, which
reduces the air mass in the intake manifold. This makes it difficult to control the air-to-fuel ratio
precisely.
As shown in Figure 4.11, during the transient operation, both stages of turbochargers
accelerate. Obviously, the HP-stage turbocharger has faster transient response since it has a smaller
size with small shaft rotational momentum. This is an advantage of the dual-stage turbocharger
system, which can used to reduce turbo lag. One can also find both engine torque and boost
pressure increase rapidly at beginning due to the quick response of the HP-stage turbocharger and
then the response slows down when the LP-stage turbocharger plays the main role.

82

Relative
air-to-fuel ratio

1.6

w/o feedforward
with feedforward

1.4
1.2

Fuel pulse width
(ms)

1
15

5

10

15

20

10

15

20

combined
feedback
feedforward

10
5
0

5

Time (ms)
Figure 4.9: Transient response of relative air-to-fuel ratio and fuel pulse width

Engine torque (N.m)

MAP (bar)

2.5
2
w/o feedforward
with feedforward

1.5
300

5

10

15

20

200
100
0

with feedforward
w/o feedforward
5

10

15
Time (s)

Figure 4.10: Responses of engine torque and intake manifold pressure
83

20

Turbocharger speed (krpm)

200

160

120

80
Speed of LP Turbocharger
Speed of HP Turbocharger
40

5

10

15

20

Simulation time (s)
Figure 4.11: Responses of the turbocharger shafts’ rotational speed of each stage

4.4.2

SI to HCCI combustion mode transition

To demonstrate the effectiveness of the SI-HCCI hybrid combustion mode for mode
transition, an SI-HCCI mode transition process was simulated by two different strategies. One uses
the hybrid combustion mode and the other switches from the SI to HCCI combustion mode in one
step. Figure 4.12 shows the in-cylinder pressure traces generated in simulations using the two
strategies. The pressure profiles vary significantly from cycle to cycle during the mode transition
for both strategies. The engine control parameters used for the simulations are spark timing, fuel
quantity, intake and exhaust valve timings and lifts. For the simulation results presented in Figure
4.12, these control parameters were adjusted manually to have the best (smooth) transition. To
obtain smooth combustion mode transition for the entire engine operating range, advanced control
strategy will be developed in the next stage of the research.

84

In the mode transition simulations, 26 engine cycles of combustions were simulated and
recorded for both control strategies. Engine speed was set to 2000 rpm throughout the entire
process. In the first 15 cycles, engine was operated in the SI mode and 12 mg (per cycle) of
gasoline was injected to each cylinder; spark timing was set to be -23° ACTDC; intake and exhaust
valve timings (at peak lift position) were set to 440° ACTDC and 270° ACTDC, respectively; and
the lifts of both valves were in the high stage. Starting at engine cycle 16, the combustion mode
transition from the SI to HCCI combustion modes was initiated. At cycle 16 both intake and
exhaust valves switched to low stage mode, but the valve timing change was limited to 10 crank
degrees per cycle due to the continuing operation of the electric variable valve timing actuating
system. Note that10 crank degrees per cycle were for the engine operated at 2000 rpm. The valve
speed limitation varies as a function of engine speed. Also at cycle 16, spark was eliminated for the
control strategy without hybrid combustion mode and the control parameters were adjusted to
make the HCCI combustion possible with minimal IMEP variation. On the other hand, for the
hybrid combustion mode transition, spark was kept on in cycles 16, 17 and 18 and advanced. After
cycle 19 the spark was cut. At cycle 19, the intake and exhaust valves also reached their target cam
phase positions and stopped moving. Throughout the entire mode transition process, fuel mass was
adjusted to minimize the IMEP fluctuation. All selected control parameters can be found in Figure
4.13.
In Figure 4.14, some key combustion performance parameters are shown. Engine IMEP is
the most important performance parameter for the mode transition since the less IMEP variation is,
the less the engine brake torque variation or the smoother the combustion mode transition. For the
one step transition, the IMEP drop is significant right after spark ignition was eliminated, see
cycles 16 and 17. Note that during mode transition, the in-cylinder gas mixture can’t reach

85

appropriate temperature for the HCCI combustion at IVC with or without hybrid mode of
combustions, see TIVC trace in Figure 4.14. If spark were cut at this engine cycle, the SOHCCI
timing would be retarded significantly. It can be observed from Figure 4.12 and Figure 4.14. The
retarded SOHCCI timing leads to large IMEP reductions, or even misfires under certain extreme
conditions. Therefore, the spark assistant HCCI combustion, or the hybrid HCCI combustion, is a
necessary tool for smooth mode transition. Based upon Figure 4.12 the hybrid combustion mode
exists in cycles 16, 17 and 18 and the IMEP variation is significantly reduced, comparing to the
one-step mode transition. Figure 4.15 shows the MFB profiles of the SI-HCCI hybrid combustions
during the mode transition and illustrate how the combustion timing changes during the process.

40

w/ hybrid mode
w/o hybrid mode

In-cylinder pressure
(bar)

35
30

Hybrid
HCCI

25

SI

20
HCCI

15
10
5
0

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

Crank position (deg)
Figure 4.12: In-cylinder pressure traces in SI-HCCI transition

86

1.45
x 10

4

Fuel mass
(mg/cycle)

13
12
11

w/ hybrid mode
w/o hybrid mode

-25
-30
-35
-40
500

10

350

5

200
13

14

15

16

17

18

19

20

21

0
22

Cycle number

SOHCCI
( ACTDC)

IMEP
(bar)

Figure 4.13: Combustion parameter settings in SI-HCCI transition

4
w/ hybrid mode
w/o hybrid mode

3
40
20
0

TIVC (k)

450
400
350
13

14

15

16

17
18
Cycle number

19

20

Figure 4.14: Combustion performance in SI-HCCI transition
87

21

22

Valve lifts
(mm)

Valve timings
( ACTDC)

ST
( ACTDC)

10

1

MFB of fuel

0.8
0.6
Cycle 15: SI mode
Cycle 16: hybrid mode
Cycle 17: hybrid mode
Cycle 18: hybrid mode
Cycle 19: HCCI mode
Cycle 20: HCCI mode

0.4
0.2
0
-40

-20

0

20
40
Crank position (deg)

60

80

100

Figure 4.15: MFB profiles in SI-HCCI transition with hybrid mode
4.5 Conclusions

This chapter describes the implementation of the developed engine model into the MSU
dSPACE HIL simulation system. HIL simulations were conducted for both steady state and
transient engine operations. The following is a list of conclusions:


The mixed mean value and crank based engine model is feasible for the dSPACE based
real-time HIL simulation.



The dual-stage turbocharger configuration is capable of reducing turbo lag.



The feedforward fuel control improves the transient performance of the closed loop control of
the dual-stage turbocharged engine.



The SI-HCCI hybrid combustion mode can be realized during the combustion mode transition,
and it is capable of reducing the engine torque variations during the mode transition.

88

CHAPTER 5
SI AND HCCI COMBUSTION MODE TRANSITION CONTROL

5.1 Introduction

In order to take advantage of the HCCI combustion mode, a traditional SI engine needs to
operate in both SI and HCCI modes, and the mode transition between the SI and HCCI
combustions is necessary. It is fairly challenging to operate the engine in the two distinct
combustion modes, and it is more difficult to have smooth combustion mode transition between
the two modes due to the distinct engine operational parameters over the two combustion modes
and the cycle-to-cycle residual gas dynamics ([86] and [87]). The control problem becomes even
more complicated for a multi-cylinder engine studied in this project.
In recent years, more and more attentions have been paid to the mode transition control
between the SI and HCCI combustions. In [39] and [40], smooth mode transitions between the SI
and HCCI combustions are realized for a single cylinder engine equipped with the camless VVA
system. However, high cost and package issues prevent the implementation of the camless VVA
system in production engines [88]. In [42] a VVT (variable valve timing) system with dual-stage
lifts was used on a multi-cylinder engine for studying the mode transition. Experimental results
showed the potential of achieving smooth mode transition by controlling the throttle opening
timing and the DI (direct injection) fuel quantity. However, satisfactory mode transition was
accomplished due to the lack of the robust mode transition control strategy.
In this chapter a multistep SI to HCCI combustion mode transition control strategy was

89

developed using the HIL simulation environment developed in the last chapters. It takes several
engine cycles to complete the combustion mode transition. During the combustion mode transition,
a model based linear quadratic (LQ) tracking control ([89] and [90]) of engine MAP was used to
maintain the air-to-fuel ratio in the desired range by regulating the engine throttle; the DI fuel
quantity of individual cylinder was controlled via iterative learning control ([91] and [92]); and
spark ignitions were maintained to enable the SI-HCCI hybrid combustion mode during the mode
transition; the other engine parameters, such as the intake/exhaust valve timing and lift, external
EGR (exhaust gas recirculation) valve opening are controlled in an open loop. The entire control
strategy is also validated in the HIL simulation environment. The simulation results demonstrated
the effectiveness of the proposed control strategy under both constant and transient engine
operating conditions.
This chapter is organized as follows. Section 5.2 discusses the control problem of the
combustion mode transition. In Section 5.3, the development of the multistep combustion mode
transition strategy is described, along with the control architecture. The details of the DI fuel
quantity control are given in Section 5.4, and the following section introduces the air-to-fuel ratio
control. In section 5.6, HIL engine simulation results are presented, compared, and discussed for
the validation of the proposed control strategies. Conclusions are finally drawn in Section 5.7.

5.2 The Control Problem Formulation

This section discusses the control target of the mode transition between the SI and HCCI
combustion modes. The challenges of achieving the control target were found during the study of
the simple one-step mode transition strategy. Based on the finding, a more complex control
strategy is developed in the next section.

90

5.2.1

Control target of the combustion mode transition

In this chapter, the combustion mode transition is studied for the engine operated at 2000
rpm with 4.5 bar IMEP. Table 5.1 lists the engine parameters associated with the SI and HCCI
combustions. These parameters are optimized for the steady state engine performance with the best
fuel economy that satisfies the engine knock limit. That is, the maximum pressure rise rate (dP/dθ)
is less than or equal to 3 bar per crank degree. It can be seen in Table 5.1 that the optimized engine
control parameters are quite different between the SI and HCCI combustion modes. Due to
actuator dynamics, some of these parameters can be adjusted within one engine cycle, such as θST,
FDI and Πlift; and some of them cannot.
Table 5.1: Engine control parameters for SI and HCCI combustion modes
Mode

SI

HCCI

-36

none

ϕEGR (%)

3

26

IETC (A)

0.84

5

FDI (ms/cycle)

2.06

1.6

θINTM (deg AGTDC)

70

95

θEXTM (deg BGTDC)

100

132

9

5

Parameter
θST (deg ACTDC)

Πlift (mm)

The combustion characteristics are also quite different between these two combustion
modes as illustrated in Figure 5.1. For example, the HCCI combustion has higher peak in-cylinder
91

pressure comparing with that of the SI combustion, due to the fast fuel burn rate. Most likely, it
also has a recompression phase due to negative valve overlap (NVO), while the SI combustion
does not. The goal of the combustion mode transition is to transfer the combustion mode without
detectable engine torque fluctuation by regulating the engine control parameters, or in other words
to maintain the engine IMEP during the combustion mode transition.

35
HCCI mode
SI mode

25
20
15
10

0.6
0.4
0.2

5
0

0.8
Mass fraction burned

In-cylinder pressure (bar)

30

1

0
200
400
Crank angle (deg ACTDC)

0

-50
0
50
Crank angle (deg ACTDC)

Figure 5.1: Steady state combustion characteristics of SI and HCCI modes

5.2.2

Existing one-step combustion mode transition

In order to investigate the control problem of the combustion mode transition, the control
strategies development starts with one-step transition strategy. That is to directly change the
control references of all engine control parameters from the SI mode to the HCCI mode, in one
engine cycle. HIL simulations of the one-step transition strategy were conducted and key engine
variables are plotted in Figure 5.2 and Figure 5.3.
92

80

5
600
600

700
700

800
800

900
900

1000
1000

1100
1100

1300
1300

1400
1400

100

50

0.6
70

 (%)

1200
1200

0.8
MAP
throttle opening

0.4
600
600

700
700

800
800

900
900

1000
1000

1100
1100

1200
1200

60
50

30
1.4

1300
1300

1400
1400

cylinder #1
cylinder #2
cylinder #3
cylinder #4

40
600

700

800

900

1000

1100

1200

1300

1400

600

700

800

900 1000 1100
Time (ms)

1200

1300

1400

1.2


7
6

1
MAP
(bar)

8

1
0.8
0.6

 lift (mm)

100

9

Figure 5.2: Engine responses of one-step combustion mode transition strategy

93

0

 TPS (%)

INTM ( AGTDC)
EXTM ( BGTDC)

exhaust valve
intake valve
valve lift

120

TIVC ( K)

450
400

(deg ACTDC)

350

SOHCCI

cylinder #1
cylinder #2
cylinder #3
cylinder #4
700

800

900

1000

1100

1200

1300

1400

600

700

800

900

1000

1100

1200

1300

1400

600

700

800

900 1000 1100
Time (ms)

1200

1300

1400

40
20
0
5

IMEP (bar)

600

4
3
2

Figure 5.3: Combustion performance of one-step combustion mode transition strategy

By analyzing the simulation results in Figure 5.2 and Figure 5.3, the control problems of
the combustion mode transition are summarized as following.


Extreme rich conditions of gas-fuel mixture (see the response of λ) are found for all
cylinders at the first engine cycle after the valve lift switch of Πlift. This indicates the lack of
fresh air charge in the engine cylinders.



Fairly lean conditions of the gas-fuel mixture are observed at the cycles following the first

94

one after the switch of Πlift due to the fast increment of the engine MAP.


The thermodynamic condition (TIVC) of the first few engine cycles after the combustion
mode switch is below the required condition for HCCI combustions due to the response
delay of the valvetrain actuators (see θINTM and θEXTM).



The combustion timings (θSOHCCI) of the first few engine cycles after the combustion
mode switch are retarded corresponding to the thermodynamic condition (TIVC). It could
lead to unstable HCCI combustions, and even misfire in the worst case.



Cylinder-to-cylinder variations were observed at combustion related variables during the
mode transition since the adjustments of Πlift, θINTM and θEXTM affect all engine cylinders
globally while each cylinder is undergoing different stroke.



Slight oscillations were found to combine with the first order response delays of TIVC and
θSOHCCI. This is a strong indication of the cycle-to-cycle residual gas dynamics of the
HCCI combustions.
Engine IMEP cannot be maintained as illustrated in Figure 5.3. Thereby it is very difficult

to achieve smooth combustion mode transition in one step, due to all the issues described above.
To solve the problems and reduce the fluctuation of the engine IMEP response during the mode
transition, a multistep mode transition scheme with some control strategies was proposed. The
corresponding control architecture will be presented in the next section.

95

5.3 Control Architecture of Multistep Combustion Mode Transition

The multistep combustion mode transition strategy was proposed by inserting a few
SI-HCCI hybrid combustion cycles between the SI and HCCI combustions. As illustrated in
Figure 5.4, five engine cycles are reserved for bridging the SI and HCCI combustions.
During the transitional cycles some engine parameters are adjusted in an open loop
according to the schedule shown in Figure 5.4. At the end of cycle 2, the intake/exhaust valve lift
Πlift switches from high lift to low, and the control references of ϕEGR, θINTM and θEXTM are set to
those of the steady state HCCI combustion mode as listed in Table 5.1. Cycles 1 and 2 are used for
engine throttle control. They provide enough time for the engine MAP to be adjusted due to the
impacts of Πlift switching from high to low. Spark timing θST of each cylinder was kept constantly
during the transitional cycles and was eliminated at the end of cycle 5.
Throughout the transitional cycles, the engine control parameters IETC and FDI were
regulated in time-based control with 1 ms sampling rate and cycle-based control logics,
respectively. The corresponding control algorithm will be described in the next two sections.
Under the regulations of the engine parameters, the combustion characteristics during the
transitional engine cycles are different from those of the typical SI and HCCI combustion modes.
The combustions at cycles 1 and 2 are still in SI combustion mode, but the air-to-fuel ratio might
not be stoichiometric and most likely is lean due to the throttle (IETC) control. During cycles 3 to 5,
engine charge temperature TIVC is higher than that of the SI mode and lower than the desired
temperature of the HCCI mode. Under such condition, during cycles 3 to 5 the engine is operated
in the SI-HCCI hybrid combustion mode with the help of the maintained spark ignitions.

96

Figure 5.4: SI to HCCI combustion mode transition control events and schedules

IMEP

λ(i+1) IMEP(i+1)

PI Control
(Feedback)

FFB
+

FFF(i)
Memory IMEP(i)
λ(i)

ILC Control

FILC

FDI

+

FFF(i+1)
θST
ϕEGR
θINTM
θEXTM
Πlift

Scheduled
Open-loop
Control

MAP
ϕTPS

IETC

LQ Control

Prototype Engine Controller

Crank-Based
Combustion
Model

Time-Based
Air Handling
Model
HIL Engine
Simulator

Figure 5.5: SI to HCCI combustion mode transition control diagram
97

Figure 5.5 shows the control diagram of the multistep combustion mode transition
controller and its interface with the HIL engine simulator. The multistep combustion mode
transition is activated as engine IMEP switches from above IMEPref (IMEPref =4.5 bar in the case)
to below IMEPref. Once the transition is initiated, the engine parameters are controlled in different
ways. IETC is controlled by the LQ tracking control; FDI is controlled in different modes, the
learning and transient modes, according to the different engine operating conditions; all other
parameters are controlled by the pre-scheduled open loop control.
In Figure 5.5, the learning mode of the FDI control is represented by the dashed lines and
the solid lines represent the transient mode. For both control modes, FDI is adjusted every engine
cycle for each cylinder. The transient mode is used for engine operations with fast load variations,
such as the engine tip-out and tip-in operations. In this mode, the learned feedforward term FFF
reduces the cylinder-to-cylinder IMEP variance, and the feedback term FFB helps with the drive
load tracking. To run the learning mode, the engine load is required to be relatively stable and
fairly close to the specified reference. Accordingly, this mode can only be operated during the
vehicle cruise operational condition or during the engine calibration process. Note that in the
learning mode, FDI is not only used as control output but also stored to the nonvolatile memory of
the controller as the feedforward term FFF for next learning iteration or the transient mode control.

5.4 IMEP Regulation for DI Fuel Quantity Control

In this section the DI fuel quantity is used as a direct control arm to regulate the IMEP of
each engine cylinder.

98

5.4.1

Sensitivity analysis of engine IMEP

As discussed in Section 5.2.2, the engine control variables TIVC and θSOHCCI have
response delays due to actuator dynamics, and after the engine reference parameters Πlift, θINTM
and θEXTM are adjusted at the end of cycle 2. It takes a few engine cycles for them to reach the
desired levels corresponding to the HCCI combustion mode, see Figure 5.3. Under such transient
conditions, if the engine were forced to switch to the HCCI combustion mode the engine IMEP
could not be maintained with cycle-by-cycle fuel control FDI. Also the increased cooling effect
caused by the increment of FDI reduces the charge temperature and leads to degraded HCCI
combustions.

Figure 5.6: IMEP sensitivity with FDI input for the SI-HCCI hybrid combustion mode

99

To solve this issue, the engine sparks are maintained during cycles 3 to 5, and the engine
operates in the SI-HCCI hybrid combustion mode during these cycles as shown in Figure 5.4. For
the hybrid combustion mode the engine IMEP is highly correlated to FDI with the lean gas-fuel
mixture, as illustrated in Figure 5.6. Accordingly it is possible to control the engine IMEP of each
cylinder by regulating FDI of the corresponding cylinder.
5.4.2

DI fuel quantity control for learning mode

When the DI fuel control FDI switches to the learning mode, FDI is regulated through the
following equation,
FDI (i  1)  FFF (i )  FILC (i )
 FFF (i )  K ILC  IMEPref  IMEP (i ) 



(5.1)

where the iterative learning control parameter FILC is calculated by a P-type (proportional) self
learning algorithm as described in [93] and [94], and the iterative learning gain KILC is derived
from the IMEP sensitivity (shown in Figure 5.6) satisfying
K ILC 

FDI
IMEP

(5.2)

Note that in this case the stability of the iterative learning is guaranteed. The feedforward term FFF
is the learned control variable from the last step that is stored in the memory of the controller. After
each learning FFF is updated as
FFF (i  1)  FDI (i  1)
5.4.3

(5.3)

DI fuel quantity control for transient mode

When FDI control switches to the transient mode, the iterative learning control is

100

deactivated and the feedback control is activated, as illustrated in Figure 5.5; FDI is controlled by
the combination of the feedforward and feedback controls. It is represented by
FDI  FFF  FFB

(5.4)

where the feedforward term FFF is the same learned control variable as in (5.1); The feedback
term FFB is the output of a PI (proportional and integral) controller.

5.5 Air-to-Fuel Ratio Control

In the last section, the FDI controller is used to control the individual cylinder IMEP. To
maintain the controllability of the fuel control, lean gas-fuel mixture is required during the mode
transition. However, the combustion could become unstable if the mixture becomes extreme lean
since the engine spark might not be able to ignite the extremely lean gas mixture during the
transitional cycles. For this study the desired normalize air-to-fuel ratio is set between λmin (0.97)
and λmax (1.3). In the earlier work presented in [25], a throttle pre-opening approach was proposed
to prevent rich combustions at cycle 3, but it leads to very lean combustions at the following
engine cycles. In this section, an LQ optimal control strategy is developed to achieve the air-to-fuel
ratio target.
5.5.1

Tracking reference of engine MAP

As discussed above, the normalized air-to-fuel ratio needs to be maintained within the
optimal range (λmin < λ < λmax) during the SI to HCCI combustion mode transition. This control
target is difficult to be achieved through the air-to-fuel ratio feedback control due to transportation
delay and short mode transition period. It is proposed to use the LQ tracking approach to regulate
the air-to-fuel mixture to the desired level. To implement this control strategy, the optimal
101

operational range of λ is translated into the operational range of MAP shown in Figure 5.7, where
the upper boundary is corresponding to λmax and lower boundary is corresponding to λmin. an
engine MAP tracking reference shown in Figure 5.7 was generated for the engine Map to stay
within the target range. The reference signal is represented by


Z SI


k  k1
z (k )   Z SI  ( Z  Z SI )
k2  k1


k  k1
 Z  ( Z HCCI  Z )
k2  k1


if

kS  k  k1

if

k1  k  k2

if

k2  k  k E

(5.5)

where k is the sampling index; kS and kE indicate the beginning and ending indices of the mode
transition and they were set to 600 and 900, respectively as shown in Figure 5.7; k1 and k2 are
switch timings and they equal 670 and 720, respectively.

1.1

SI

SI to HCCI mode transition

HCCI

MAP (bar)

1
0.9
0.8
0.7

upper limit, max =1.3

0.6

lower limit, min =0.97
MAP reference z(k)

0.5

600
kS

670 720
k1

k2

780

840

900

Time (ms)

kE

960 1020 1080 1140

Figure 5.7: The target MAP operational range and MAP tracking reference

102

5.5.2

Control oriented MAP model

To develop the proposed LQ tracking control strategy, a control oriented engine MAP
model is required to represent the relationship between the control input (IETC) and the system
output (MAP). The simplified dynamics is represented by a second order dynamics due to the gas
filling dynamics (first order) of the engine intake manifold and the first order response delay of the
engine throttle, assuming that the rotational momentum of the throttle plate is small enough to be
ignored. The governing equation of gas filling dynamics is represented by

V N
RT C  r 2 Pamb
dMAP
TPS
  d e MAP   amb D
dt
120Vm
Vm 2 RTamb

(5.6)

The dynamics of the throttle response is approximated by
dTPS
k
c
  ETC TPS  ETC I ETC
dt
bETC
bETC

(5.7)

Equations (5.6) and (5.7) can be combined, discretized and represented by the following discrete
state space model
x(k  1)  Ax(k )  Bu (k )
y (k )
 Cx(k )  Du (k )

(5.8)

where
 x   MAP 
u  I ETC ; x   1   
;
 x2   TPS 

y  MAP

(5.9)

are the system input, state and output, respectively. The system matrices are
  (k )V N
d e T
1 
120Vm
A


0


C  1 0 ;

 (k ) RTambCD r 2 Pamb
Vm 2 RTamb
k
1  ETC T
bETC

103


0
T 


; B  k


 ETC T 

 bETC





D0

(5.10)

where ΔT is the sample period. State space model (5.8) is linear time-variant since the volumetric
efficiency η and multiplier φ in equations (5.6) and (5.10) are functions of the tracking reference
z(k). Moreover, the sampling time ΔT in (5.10) equals 1 millisecond, and sample time index k is the
same as that from equation (5.5).
5.5.3

LQ optimal controller synthesis

Based on the control oriented engine MAP model, a finite horizon LQ optimal tracking
controller was designed to follow the reference z(k). More specifically, the control objective is to
minimize the tracking error e(k) defined in (5.11) with the feasible control effort IETC or the
feasible throttle control current. The tracking error e(k) is defined as

e(k )  y (k )  z (k )  Cx(k )  z (k )

(5.11)

and the restriction on IETC is -5A < IETC < 5A. To satisfy the objective, the cost function of the LQ
optimal tracking control is defined as
J



1
[Cx(k f )  z (k f )]T F [Cx(k f )  z (k f )]
2
k  k 1



f
1

2 k k
0

[Cx(k )  z(k )]T Q[Cx(k )  z(k )]  uT (k ) Ru(k )

(5.12)

where F and Q are positive semi-definite and R is positive definite. For the control design, F and Q
were selected as constant matrices and R is a function of sample step k (see Figure 5.10) used to
tradeoff between the tracking performance and the control effort.
1 0  8
 4 0  7
F 
 10 , Q   0 0  10 , R  R(k )
0 0



(5.13)

Based on the cost function the corresponding Hamiltonian is as follows
1
1
H  [Cx(k )  z (k )]T Q[Cx(k )  z (k )]  uT (k ) Ru (k )  pT (k  1)  Ax(k )  Bu (k ) 
2
2

104

(5.14)

According to [89], the required conditions for the extremum in terms of the Hamiltonian are
represented as
H
*

p (k  1)
H
*

x (k )

 x* (k  1)  x* (k  1)  Ax* (k )  Bu* (k )

 p* (k ) 
H
*

u (k )

p* (k )  AT p* (k  1)  C T QCx* (k )  C T Qz (k )

 0  0  BT p* (k  1)  Ru* (k )

(5.15)

(5.16)

(5.17)

Note that the superscript “*” denotes the optimal trajectories of the corresponding vectors. The
augmented system of (5.15) and (5.16) becomes
 x* (k  1)   A


 p* (k )  C T QC

 

 BR 1BT   x* (k )   0 


 z (k )
  p* (k  1)   C T Q 
A





(5.18)

Based upon (5.17) the optimal control is in the form of
u* (k )   R 1BT  P( k ) x* ( k )  g (k ) 



(5.19)

Note that matrix P(k) can be computed by solving the difference Riccati equation backwards
P (k )  AT P(k  1)[ I  EP(k  1)]1 A  C T QC

(5.20)

with the terminal condition
P (k f )  C T FC

(5.21)

and vector g(k) can be computed by solving the vector difference equation





g (k )  AT I  [ P 1 (k  1)  E ]1 E g (k  1)  C T Qz (k )

(5.22)

with the terminal condition
g (k f )  C T Fz (k f )

105

(5.23)

The optimal control in (5.19) can be written into the following form
u* (k )   LFB (k ) x* (k )  LFF (k ) g (k  1)

(5.24)

where the feedforward gain LFF is computed by
LFF (k )  [ R  BT P(k  1) B]1 BT

(5.25)

and the feedback gain LFB is computed by
LFB (k )  [ R  BT P(k  1) B]1 BT P(k  1) A

(5.26)

Note that equation (5.24) is the offline representation of the LQ optimal tracking control
*

since the state x used in the feedback control is computed exactly from the closed-loop system
(5.8) as
x* (k  1)  [ A  BLFB (k )]x* (k )  BLFF (k ) g (k  1)

(5.27)

However, when the control is implemented in the HIL simulation environment or the actual engine
control system, the feedback signals are replaced by the physical signals measured by the on-board
engine sensors. In these cases the LQ controller is represented by the online form as
u (k )   LFB ( k ) x(k )  LFF (k ) g (k  1)

(5.28)

where x represents the sampled states. Note that both of the states, MAP and ϕTPS can be measured
in the HIL simulator or in the engine system.

5.6 HIL Simulation Results and Analysis

The multistep combustion mode transition control strategy is composed of the DI fuel
quantity control and LQ optimal MAP tracking control with the SI-HCCI hybrid combustions
during the mode transition. In this section, HIL simulation results are presented.

106

5.6.1

SI-HCCI hybrid combustion mode

As mentioned in Section 5.3, the engine is operated in the SI-HCCI hybrid combustion
mode at cycles 3 to 5 (see Figure 5.4) in the multistep mode transition strategy. To disclose the
significance of using this hybrid combustion mode, the key engine variables, such as TIVC, xHCCI,
and IMEP, are analyzed and plotted in Figure 5.8, for the cases with and without the SI-HCCI

TIVC ( K)

hybrid combustion mode.

450
400

x HCCI

350
1

700

800

900

1000

1100 1200

1300 1400
cylinder #1
cylinder #2
cylinder #3
cylinder #4

0.5
0
5

IMEP (bar)

600

600

700

800

900

1000 1100

1200

1300 1400

Time (ms)

4
3
2

w/o SI-HCCI hybrid
with SI-HCCI hybrid
600

700

800

900 1000 1100 1200
Time (ms)

1300 1400

Figure 5.8: Combustion performances with and without SI-HCCI hybrid combustions

As shown in Figure 5.8, temperature at intake valve closing TIVC has response delay with
or without the hybrid combustion mode due to the dynamics of the valvetrain system and the NVO
107

operation. Under such thermodynamic condition, if the engine was forced into the HCCI
combustion mode, start of combustion timing would be greatly retarded, causing large IMEP
fluctuations. The large fluctuation of IMEP cannot be improved through combustion control due to
the lack of available control variables in HCCI mode as discussed in Section 5.4.1. However by
using the hybrid combustion mode, percentage of HCCI combustion xHCCI is gradually increased
as TIVC approaches the desired temperature. Also note that due to the LQ optimal tracking of the
desired air-to-fuel ratio, the engine IMEP can be regulated by controlling FDI. As a result, smooth
IMEP can be achieved during the mode transition. Note that for the simulation results in Figure 5.8,
the proposed air-to-fuel ratio and DI fuel quantity controls are used during the mode transition with
the hybrid combustions.
Therefore, using the SI-HCCI hybrid combustions during the mode transition is a key
control technique for the smooth combustion mode transition.
5.6.2

Air-to-fuel ratio control

The developed LQ optimal MAP tracking control was implemented in the prototype engine
controller and validated through the HIL engine simulations. The simulated control input IETC, the
system states MAP and ϕTPS, and λ are plotted in Figure 5.9. For comparison purpose, the
simulated responses of these variables with open loop control are also shown in Figure 5.9, in
which IETC is set to the target level before the adjustment of Πlift (happens at 720 ms), as a result,
the engine throttle is gradually opened to the wide open throttle (WOT) position and the MAP is
increased before the valve lift switch. The increased MAP ensures enough fresh charge to each
cylinder when the valve lift switches the low position. However the step IETC control leads to a

108

rapid increment of the engine MAP or excessive fresh air charge, leading to extreme air-to-fuel
ratio λ in the following engine cycles.

6
IETC (A)

4
2
0
-2

 TPS (%)

100 600

750

900

1050

1200

1350

1500

1650

50

0

w/o LQ
w/ LQ
600

750

900

1050

1200

1350

1500

1650

MAP (bar)

1
0.8

max
min

0.6

z(k)

1.5 600

750

900

1050

1200

1350

1500 1650
cylinder #1
cylinder #2
cylinder #3
cylinder #4

750

900

1050

1200

1350

1500

1.4



1.3
1.2
1.1
1
600

1650

Time (ms)
Figure 5.9: Engine performances with and without MAP tracking control
109

Using the proposed LQ MAP tracking control strategy, throttle current IETC is regulated in
a non-monotonic increasing pattern. Note that to maintain IETC in the feasible range (-5A < IETC <
5A) the weighting matrix R in the cost function (5.12) is adjusted as illustrated in Figure 5.10. The
same pattern can also be found for ϕTPS with a small phase lag. As a result, the engine MAP tracks
the reference trace z(k) after the intake valve lift Πlift switches to the low lift, and λ of each cylinder
is successfully maintained within the desired range. Therefore, with the help of the LQ optimal
control, the in-cylinder air-to-fuel ratio is maintained within the desired range, leading to stable
combustions.

1.5

R

1

0.5

0
600

660

720
780
Sampling index k, time (ms)

840

900

Figure 5.10: Adjustment of weighting matrix R in cost function (5.12)

Slight oscillations in the MAP responses are found with both control approaches, which are
due to the flow dynamics of the engine air-handling system. It is almost impossible to eliminate
them due to the slow throttle actuator dynamics. However, the MAP oscillation associated with the
LQ optimal control is within the desired MAP range.

110

DI fuel quantity control with iterative learning mode

(ms)

2.1
2
1.9
1.8
1

(ms)

2

3

4

5

6

7

1

2

3

4

5

6

7

1

2

3

4

5

6

7

1

2.1

2

3

4

5

6

1

2

3
4
5
Learning iteration, i

6

2
1.9
1.8

(ms)

2.1
2
1.9
1.8

(ms)

2.1
2
1.9
1.8
2.1
(ms)

FDI of cycle 5

FDI of cycle 4

FDI of cycle 3

FDI of cycle 2

FDI of cycle 1

5.6.3

2
1.9

7
cylinder #1
cylinder #2
cylinder #3
cylinder #4

1.8
0

7

Figure 5.11: Correction of DI fuel quantity after iterative learning

111

8

When the air-to-fuel ratio is maintained within the desired range, the iterative learning of
FDI was conducted in the learning mode. Figure 5.11 shows that FDI of each cylinder converges

after a few iterations of learning. FDI in cycle 2 was adjusted most significantly due to the large
variation of the engine MAP. The first engine cycle (cycle 3) after the intake/exhaust valve lift
switch demonstrated the largest improvement, leading to significant correction of FDI. The
cylinder-to-cylinder adjustment of FDI after iterative learning compensates for the intake charge
variations, and leads to smooth IMEP of individual cylinder as shown in Figure 5.12. Therefore, it
can be concluded that smooth SI to HCCI combustion mode transition is achievable through the
iterative learning control of the DI fuel quantity.
In Figure 5.12, without ILC the slight IMEP oscillations as discussed in Section 5.2 can be
observed for TIVC and θSOHCCI, however, the oscillations disappears after the ILC was applied.
These oscillations indicate unstable combustions and are due to the cycle-to-cycle residual gas
dynamics of HCCI combustions (including the SI-HCCI hybrid combustions), which has been
discussed in great details in [34] and [36]. Due to the residual gas dynamics, retarded (or advanced)
θSOHCCI of current engine cycle leads to advanced (or retarded) θSOHCCI for the next engine

cycle. As a result, combustion oscillations occur. During the combustion mode transition, the
impact of adjusting Πlift to the individual in-cylinder combustion is quite different. Cylinder 1
experiences the most significant impact since it is during the exhaust stroke when it happens. Both
residual gas quantity and fresh charge quantity were affected. Therefore the IMEP fluctuations of
cylinder 1 are dominated as shown in Figure 5.12. By using the ILC of DI fuel quantity, θSOHCCI
was regulated to the appropriate timing as well as the IMEP was regulated to the control reference.

112

Accordingly the oscillations of TIVC and θSOHCCI were suppressed, and combustion stability
during the mode transition was improved by the iterative learning control.
As a result of suppressing the oscillations of TIVC and θSOHCCI, engine knock index was
also reduced during the combustion mode transition, see Figure 5.13. Note that dP/dθ is a good

TIVC ( k)

indicator of engine knock [62].

450
400

(deg ACTDC)
IMEP (bar)

SOHCCI

350

600

700

800

900

1000 1100

1200

40
20

1300 1400
cylinder #1
cylinder #2
cylinder #3
cylinder #4

0
5

4

3

w/o ILC
w/ ILC
600

700

800

900 1000 1100
Time (ms)

1200

1300 1400

Figure 5.12: Combustion performances with and without ILC

113

knock index (bar/deg)

3.5
3
2.5
2
1.5
w/o ILC
with ILC

1
0.5

600

700

800

900

1000

1100 1200

1300 1400

Time (ms)
Figure 5.13: Engine knock index (dP/dθ) with and without ILC

Engine torque performance comparison

50
40
Torque (N.m)

5.6.4

30
one-step mode transition
multistep w/o hybrid mode
multistep w/o LQ, w/o ILC
multistep w/ LQ, w/ ILC

20
10
600

700

800

900

1000 1100

1200

1300 1400

Time (ms)
Figure 5.14: Engine torque performances of different control strategies

114

Table 5.2: Engine performance comparisons for different control strategies
IMEP error

Max dP/dθ

(%)

(bar/deg)

Torque error
(%)

One-step mode transition

51.6

N/A

81.8

Multistep w/o hybrid mode

26.9

N/A

43.1

Multistep w/o LQ, w/o ILC

7.1

3.13

11.2

Multistep w/ LQ, w/ ILC

1.6

2.82

2.2

In-cylinder pressure of
multistep trnasiton (bar)

In-cylinder pressure of
one-step transition (bar)

cyl 1
40

SI

cyl 2

cyl 3

cyl 4

HCCI

30
20
10
0
40

SI 600

700
800
SI to HCCI mode transition

900
HCCI

1000

900

1000

30
20
10
0

600

700

800
Time (ms)

Figure 5.15: In-cylinder gas pressure profiles during SI to HCCI combustion mode transition

115

Engine torque responses during the combustion mode transitions using the different
control strategies are plotted in Figure 5.14. Their statistics are listed in Table 5.2 for comparison.
The largest engine torque fluctuation is produced by the one-step approach. The fluctuation of
engine torque is reduced when multistep strategy is used. It is further improved as the SI-HCCI
hybrid combustion mode is implemented. At last, smooth combustion mode transition is realized
in multi-steps when both the air-to-fuel ratio (LQ control) and the DI fuel quantity (ILC) controls
are used. The combined control of the LQ tracking and ILC DI fueling with SI-HCCI hybrid
combustions leads to the lowest torque fluctuations (2.2%) when the engine operational conditions
transit from the steady state SI mode to the HCCI mode. The in-cylinder gas pressure profiles are
plotted in Figure 5.15. One can see significant improvement of combustion quality during the
transitional cycles.
5.6.5

Engine performance during the throttle tip out operation

In order to study the mode transition under the transient operation, an HIL simulation was
conducted to simulate the engine throttle tip out operation, where the engine was initially operated
in the SI mode. As a step input was applied to the acceleration pedal, the pedal position decreased
from 40% to 15%. As a result, the engine IMEP reduced from 8.1 to 4 bar, which crosses the
combustion mode transition threshold of 4.5 bar. Accordingly the combustion mode transition was
triggered. Two mode transition strategies were simulated. Both of them were multistep strategies
with the hybrid combustions. One was with the air-to-fuel ratio control (LQ) and the DI fuel
quantity control, the other was not. Note that the DI fuel quantity control was switched to the
transient mode during the engine tip out operation, and the feedforward term FFF used in the
transient mode control was learned by the ILC. The transient responses of engine variables are
plotted in Figure 5.16.

116

40

50
20

00
MAP (bar)

1

500
500

1000
1,000

1500
1,500

2000
2,000

2500
2,500

3000
3,000

0
4000

3500
3,500

0.8
w/o LQ, w/o ILC
w/ LQ, w/ ILC

0.6
500

1,000

1,500

2,000

2,500

3,000

3,500

500

1,000

1,500

2,000

2,500

3,000

3,500
cylinder #1
cylinder #2
cylinder #3
cylinder #4

500

1000

1500

2000

2500

3000

3500



1.4
1.2
1

IMEP (bar)

8
7
6
5
4
0

Time (ms)
Figure 5.16: Engine responses during Tip out operation

117

4000

 acc (%)

 TPS (%)

100

In Figure 5.16 after the step input to the acceleration pedal, both ϕTPS and MAP are
decreased at first, and then increased due to the combustion mode transition. Slightly rich
combustions can be observed during the early stage of the tip out operation since the throttle
opening is decreased in the SI mode. Once the mode transition is started, the in-cylinder gas-fuel
mixture becomes lean for both strategies. However, with air-to-fuel ratio LQ MAP tracking control
λ is maintained within the desired range throughout the engine tip out operation. Furthermore, with

the proposed DI fuel quantity control smooth IMEP responses were achieved for all cylinders
comparing with those without the iterative fuel control. Similar improvement in engine torque
output can also be found in Figure 5.17.
Based on the simulation results shown in Figure 5.16 and Figure 5.17, it can be concluded
that the proposed LQ optimal MAP tracking control is capable of maintaining the air-to-fuel ratio
during engine transient operations, and the iterative DI fuel quantity control is also effective in
transient mode.

one-step mode transition
multistep w/o LQ, w/o ILC
multistep w/ LQ, w/ ILC

Engine torque (N.m)

100
80
60
40
20
0

0

500

1000

1500

2000 2500
Time (ms)

3000

3500

Figure 5.17: Engine torque response during tip out operation

118

4000

5.7 Conclusions

The combustion mode transition between the SI and HCCI combustions is challenging but
necessary to implement the promising HCCI combustion technology to production SI engines. As
demonstrated in this chapter, smooth combustion mode transition can be realized in a
multi-cylinder gasoline engine equipped with the dual-lift VVT valvetrain system. The mode
transition was accomplished within multiple engine cycles with the help of the LQ MAP tracking
control and the ILC of DI fuel quantity. Based on the HIL simulation results presented in this
chapter, the LQ control tracks the engine MAP to the desired target with small oscillations; and the
normalized air-to-fuel ratio is maintained within the desired range. As a result, the individual
cylinder IMEP can be regulated through adjusting the corresponding DI fuel quantity. With the
help of the ILC DI fuel control, the cylinder-to-cylinder variations of the engine IMEP can be
reduced significantly and tracks the control reference. Furthermore, the ILC is able to compensate
the influence of the cycle-to-cycle residual gas dynamics, and accordingly reduces the fluctuations
of the engine knock index during the mode transition. In addition, combining the learned
feedforward control with the PI feedback control, smooth SI to HCCI combustion mode transition
can also be realized during transient engine operations.

119

CHAPTER 6
CONCLUSIONS AND FUTURE WORK

6.1 Conclusions

To model IC engine behaviors for the purpose of real time control strategy development
and validation, this dissertation investigates an engine modeling approach that combines
time-based and crank-based modeling methods. The engine air-handling system is modeled in
time-based by “so-called” mean-value models, and engine combustion process is modeled as
functions of the engine crank angle. This modeling approach was first applied to a dual-stage
turbocharged SI engine and satisfactory HIL simulation results were obtained. As a result, this
approach was used to model the HCCI capable SI engine. The developed SI-HCCI hybrid
combustion model of the HCCI capable SI engine is capable of simulating the SI, HCCI and
SI-HCCI hybrid combustion modes. The entire HCCI capable SI engine model was calibrated and
validated with the corresponding one-dimensional GT-Power model. Afterward, it was
implemented into the HIL simulation environment. Based on the HIL simulation results the
following conclusions are drawn.


The mixed time-based and crank-based engine models are capable of real-time HIL
simulation



The developed engine models are effective in simulating both continuous and discrete
engine dynamics in the HIL simulation environment



The SI-HCCI hybrid combustion model is appropriate for the control strategy development
of the combustion mode transition, since it models the SI, HCCI and SI-HCCI hybrid
120

combustion modes seamlessly.
The control strategy development for the SI to HCCI combustion mode transition is the
other research concentration of this dissertation. It was developed based upon the developed HCCI
capable SI engine model. The developed control strategy was a multistep mode transition control
strategy. The SI-HCCI hybrid combustion mode was implemented in the combustion mode
transition to bridge the gap between the SI and HCCI combustion modes. The LQ optimal MAP
tracking control was applied in the multistep control strategy to optimize the engine air-to-fuel
ratio. DI fuel quantity of each cylinder was optimized by the iterative learning control. The entire
control strategy was validated in the HIL simulation environment. The following are the
conclusions:


Smooth SI to HCCI combustion mode transitions are realized for both steady state and
transient operating conditions using the proposed multistep control strategy



The SI-HCCI hybrid combustion mode plays an important role in the multistep combustion
mode transition control strategy



Smooth SI to HCCI combustion mode transition is achievable for an HCCI capable SI
engine equipped with dual-stage valve lift and electrical VVT systems

6.2 Recommendations for Future Work

The engine models presented in this dissertation are in the quasi-steady state. The
calculations of in-cylinder gas mass, mass flow rate across intake/exhaust valve, heat exchange,
etc., are mainly based on governing equations of mass and energy conservations, whereas the gas
flow dynamics (momentum conservation) is ignored. However, the intake gas flow dynamics
affects the homogeneity of the in-cylinder gas-fuel mixture seriously, hence, it affects the HCCI

121

combustion. Combining the gas flow dynamics model with the existing combustion model
described in Chapter 3 could improve the modeling accuracy for the HCCI combustion and
combustion mode transition.
In addition, the SI-HCCI hybrid combustion mode has one additional control variable,
spark timing that affects the start of the HCCI (SOHCCI) combustion time and the HCCI
combustion percentage (xHCCI) in the hybrid combustion mode as demonstrated in HIL
simulations. It is recommended to use this control variable to extend the HCCI combustion to
higher engine load.
With the successful demonstration of smooth combustion mode transition from the SI to
HCCI modes using the multistep control strategy developed in Chapter 5, the logical next step is to
extend the control strategy to the mode transition from the HCCI to SI combustion. Note that this is
not a simple reversed process since the mode transition from the HCCI to SI combustion has quite
different dynamics, comparing to the transition from SI to HCCI.
Finally, the most important future work is to use engine test data to validate the developed
engine models and demonstrate the proposed control strategy in the engine dynamometer tests.

122

BIBLIOGRAPHY

123

BIBLIOGRAPHY
[1]

X. Yang and G. G. Zhu, “A Mixed Mean Value and Crank-based Model of a Dual-Stage
Turbocharged SI Engine for Hardware-In-the-Loop Simulation”, Proceedings of 2010
American Control Conference, Baltimore, MD, 2010.

[2]

G. Colin, Y. Chamaillard, and B. Bellicaud, “Robust Control for the Air Path of a
Downsized Engine,” Proceedings of the Institution of Mechanical Engineers, Part D:
Journal of Automobile Engineering July, 2011 vol. 225 no. 7 930-943.

[3]

A. Lefebvre and S. Guilain, “Modeling and Measurement of the Transient Response of a
Turbocharged SI Engine,” SAE Technical Paper, 2005-01-0691.

[4]

Byungchan Lee, Dual-Stage Boosting Systems: Modeling of Configurations, Matching and
Boost Control Options, PhD thesis, University of Michigan, 2009.

[5]

A. Chasse, “Double Stage Turbocharger Control Strategies Development,” SAE Technical
Paper, 2008-01-0988, 2008.

[6]

S. Saulnier and S. Guiliain, “Computational Study of Diesel Engine Downsizing Using
Two-stage Turbocharging,” SAE Technical Paper, 2004-01-0929, 2004.

[7]

S. Kim, T. Wakisaka, and Y. Aoyagi, “A Numerical Study of the Effects of Boost Pressure
and Exhaust Gas Recirculation Ratio on the Combustion Process and Exhaust Emissions in
a Diesel Engine,” International Journal of Engine Research, 2007 8: 147.

[8]

Y. Duchaussoy, A. Lefebvre and R. Bonetto, “Dilution Interest on Turbocharged SI Engine
Combustion,” SAE Technical Paper, 2003-01-0629.

[9]

W. Chatlatanagulchai, K. Yaovaja, S. Rhienprayoon, and K. Wannatong, “Fuzzy Knock
Control of Diesel-Dual-Fuel Engine,” SAE International, 2011-01-0690.

[10] I. Haskara, G. Zhu, C. Daniels, and J. Winkelman, “Closed Loop Maximum Dilution Limit
Control using In-Cylinder Ionization Signal,” SAE Technical Paper, 2005-01-3751, SAE
Powertrain and Fluid Systems Conference & Exhibition, San Antonio, Texas, USA.
[11] G. G. Zhu, I. Haskara, and J. Winkelman, “MBT Timing Detection and its Closed-Loop
Control Using In-Cylinder Ionization Signal,” SAE Technical Paper, 2004-01-2976, SAE
Powertrain and Fluid Systems Conference, Tampa, Florida, USA.
[12] G. G. Zhu, C. Daniels, and J. Winkelman, “MBT Timing Detection and Its Closed-Loop
Control Using In-Cylinder Pressure Signal,” SAE Technical Paper, 2003-01-3266, SAE
Powertrain and Fluid Systems Conference & Exhibition, Pittsburgh, Pennsylvania, USA.
[13] C. F. Daniels, G. G. Zhu, and J. Winkelman, (2003) “Inaudible Knock and Partial Burn
Detection Using In-Cylinder Ionization Signal,” SAE Technical Paper, 2003-01-3149.

124

[14] F. Zhao, T. Asmus, D. Assanis, J.E. Dec, J.A. Eng, and P.M. Najt, Homogeneous Charge
Compression Ignition (HCCI) Engines Key Research and Development Issues. 2003,
Warrendale, Pennsylvania: Society of Automotive Engineers.
[15] R. M. Wagner, K. D. Edwards, et al, “Hybrid SI-HCCI Combustion Modes for Low
Emissions in Stationary Power Applications,” 3rd Annual Advanced Stationary
Reciprocating Engines Meeting Argonne National Laboratory, Argonne, IL June 28-30,
2006.
[16] H. Zhao, J. Li, T. Ma, and N. Ladommatos, “Performance and Analysis of a 4-Stroke
Multi-Cylinder Gasoline Engine with CAI Combustion,” SAE International, 2002-01-0420,
2002.
[17] C. J. Chiang and A. G. Stefanopoulou, “Stability Analysis in Homogeneous Charge
Compression Ignition (HCCI) Engines With High Dilution,” IEEE Transactions on Control
System Technology, Vol. 15, No. 2, March 2007.
[18] J. S. Souder, J. H. Mack, J. K. Hedrick, and R. W. Dibble, “Microphones and Knock
Sensors for Feedback Control of HCCI Engines,” Proceedings of ICEF’04 2004 ASME
Internal Combustion Engine Division Long Beach, California, USA, October 24-27, 2004.
[19] M. Hillion, J. Chauvin, O. Grondin, and N. Petit, “Active Combustion Control of Diesel
HCCI Engine: Combustion Timing,” SAE Technical Paper, 2008-01-0984.
[20] U.S. Department of Energy Energy, Efficiency and Renewable Energy Office of
Transportation Technologies, Homogeneous Charge Compression Ignition (HCCI)
Technology, A Report to the U.S. Congress, April 2001.
[21] X. Lu, Y. Hou, L. Zu, and Z. Huang, “Experimental Study on the Auto-Ignition and
Combustion Characteristics in the Homogeneous Charge Compression Ignition (HCCI)
Combustion Operation with Ethanol/n-Heptane Blend Fuels by Port Injection,” Fuel, 85
(2006) 2622–2631.
[22] S. C. Kong, R. D. Reitz, “Application of Detailed Chemistry and CFD for Predicting Direct
Injection HCCI Engine Combustion and Emission,” Proceedings of the Combustion
Institute, Volume 29, 2002/pp. 663–669.
[23] Sloane, Thompson Milton, Tsai, Ping-ho, Method of operating HCCI engines at low speed
and low load, United States Patent 6662785.
[24] Halim G. Santoso, Managing Transient Behaviors of a Dual Mode Spark Ignition /
Controlled Auto Ignition Engine with a Variable Valve Timing System, PhD thesis,
Massachusetts Institute of Technology, 2000.
[25] X. Yang and G. Zhu, “SI and HCCI Combustion Mode Transition Control of A
Multi-Cylinder HCCI Capable SI Engine Via Iterative Learning,” Proceedings of the 4th
Annual Dynamic Systems and Control Conference, Westin Arlington Gateway, Arlington,
VA, USA. Oct 31 - Nov 2, 2011.
125

[26] S. S. Nathan, J. M. Mallikarjuna, A. Ramesh, “Effects of charge temperature and exhaust
gas re-circulation on combustion and emission characteristics of an acetylene fuelled HCCI
engine,” Fuel, 89 (2010) 515–521
[27] Z. Ren, G. Zhu, “Modeling and Control of an Electric Variable Valve Timing System for SI
and HCCI Combustion Mode Transition,” Proceedings of 2011 American Control
Conference, San Francisco, California, USA, 2011.
[28] N Kalian1, H Zhao1, and J Qiao, “Investigation of transition between spark ignition and
controlled auto-ignition combustion in a V6 direct-injection engine with cam profile
switching,” Proc. IMechE Vol. 222 Part D: J. Automobile Engineering, IMechE 2008.
[29] G. Haraldsson, P. Tunestal, B. Johansson, and J. Hyvönen, “HCCI Closed-Loop
Combustion Control Using Fast Thermal Management,” SAE Technical Paper,
2004-01-0943.
[30] G. M, Shaver, M. J. Roelle1, P. A. Caton1, N. B. Kaahaaina1, et al, “A Physics-Based
Approach to the Control of Homogeneous Charge Compression Ignition Engines with
Variable Valve Actuation,” International Journal of Engine Research, 2005 6: 361.
[31] G. M. Shaver, Physics-Based Modeling and Control of Residual-Affected HCCI Engines
Using Variable Valve Actuation, PhD thesis, Stanford University, September, 2005.
[32] G. M. Shaver, J. C. Gerdes and M. J. Roelle, “Physics-Based Modeling and Control of
Residual-Affected HCCI Engines,” Journal of Dynamic Systems, Measurement, and
Control, Volume 131, Issue 2, 021002, February 2009.
[33] N. Ravi, H. H. Liao, A. F. Jungkunz, and J. C. Gerdes, “Modeling and Control of Exhaust
Recompression HCCI Using Split Injection,” Proceedings of 2010 American Control
Conference, Baltimore, MD, 2010.
[34] N. Ravi, M. J. Roelle, A. F. Jungkunz, J. C. Gerdes, “Model-Based Control of HCCI
Engines Using Exhaust Recompression,” IEEE Transactions on Control Systems
Technology, Published by: IEEE Control Systems Society, Volume 18, Issue 6, pp 1289 1302, Nov. 2010.
[35] N. J. Killingsworth, S. M. Aceves, et al, “HCCI Engine Combustion-Timing Control:
Optimizing Gains and Fuel Consumption Via Extremum Seeking,” IEEE Transactions on
Control Systems Technology, Vol. 17, No. 6, November 2009, pp. 1350-1361.
[36] J. Kang, C. Chang, and T. Kuo, “Sufficient Condition on Valve Timing for Robust Load
Transients in HCCI Engines,” SAE International, 2010-01-1243
[37] Jason Scott Souder, Closed-Loop Control of a Multi-Cylinder HCCI Engine, PhD thesis,
University of California, Berkeley, 2004.

126

[38] G. M. Shaver, M. J. Roelle and J. C. Gerdes, “Modeling cycle-to-cycle dynamics and mode
transition in HCCI engines with variable valve actuation,” Control Engineering Practice,
Volume14 (2006) 213–222.
[39] Y. Zhang, H. Xie, et al, “Study of SI-HCCI-SI Transition on a Port Fuel Injection Engine
Equipped with 4VVAS”, SAE Paper 2007-01-0199.
[40] M. J. Roelle, G. M. Shaver, and J. C. Gerdes, “Tackling the Transition: A Multi-Mode
Combustion Model of SI and HCCI for Mode Transition Control,” Proceedings of IMECE
2004 International Mechanical Engineering Conference and Exposition, Anaheim,
California, USA, November 13-19, 2004.
[41] G. Tian, Z. Wang, Q. Ge, J. Wang, and S. Shuai, “Mode Switch of SI-HCCI Combustion on
a GDI Engine,” SAE International, 2007-01-0195.
[42] H. Wu, M. Kraft, et al, “Experimental Investigation of a Control Method for SI-HCCI-SI
Transition in a Multi-Cylinder Gasoline Engine,” SAE International, 2010-01-1245.
[43] Zhang, Y., H. Xie, N. Zhou, T. Chen, and H. Zhao, “Study of SI-HCCI-SI Transition on a
Port Fuel Injection Engine Equipped with 4VVAS,” SAE International, 2007-01-0199.
[44] A. Cairns and H. Blaxhill, “The Effects of Two-Stage Cam Profile Switching and External
EGR on SI-CAI Combustion Transitions,” SAE International, 2007-01-0187.
[45] X. Yang, G. G. Zhu and Z. X. Sun, “A Control Oriented SI and HCCI Hybrid Combustion
Model for Internal Combustion Engines”, Proceedings of 2010 ASME Dynamic Systems
and Control Conference, Cambridge, MA, 2010.
[46] J. H. Park, S. Han, and W. H. Kwon, “LQ Tracking Controls with Fixed Terminal States
and Their Application to Receding Horizon Controls,” Systems & Control Letters, Volume
57, Issue 9, Pages 772-777. September 2008.
[47] T. N. Trajkov, H. Koppe, and U. Gabbert, “Active Vibration Control Using Optimal LQ
Tracking System with Additional Dynamics,” International Journal of Control, Vol. 78, No.
15, October 2005, 1182-1197.
[48] M. S. Meridjet and N. Debbache, “Control Motor Using State Space Discrete Time Optimal
Tracking Controller,” Journal of Theoretical and Applied Information Technology.
[49] K. Kinosita, T. Sogo, and N. Adachi, “Iterative Learning Control Using Adjoin Systems
and Stable Inversion,” Asian Journal of Control, Vol. 4, No. 1, pp. 60-67, March 2002.
[50] Abdelhamid Tayebi, “Adaptive Iterative Learning Control for Robot Manipulators,”
Automatica, 40 (2004) 1195 – 1203. Available online at www.sciencedirect.com.
[51] M. Heertjes and T. Tsoc, “Nonlinear Iterative Learning Control with Applications to
Lithographic Machinery,” Control Engineering Practice, 15 (2007) 1545–1555. Available
online at www.sciencedirect.com.

127

[52] K. Lamberg, P. Walterman, “Using HIL Simulation to Test Mechatronic Components in
Automotive Engineering,” 2nd Congress on Mechatronics in Automobile, Munich, Nov.
2000.
[53] Andy Beaumont, “Hardware in the Loop (HIL) for Engine Control Strategy Development,”
3rd Biennial dSPACE USA User Conference, Plymouth, MI, 21-23 June 2004.
[54] M. Jung, R. G. Ford, “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.
[55] D. J. Rausen, et al, “A mean value model for control of homogeneous charge compression
ignition (HCCI) engines,” ASME Journal of Dynamics, Measurement, and Control, Vol.
127, September, 2005, pp. 355-362.
[56] N. Killingsworth, S. Aceves, D. Flowers, and M. Krstic, “A Simple HCCI Engine Model
for Control,” IEEE International Conference on Control Applications, Munich, Germany,
October 4, 2006 through October 6, 2006.
[57] M. Shahbakhti, C. R. Koch, “Control Oriented Modeling of Combustion Phasing for an
HCCI Engine,” American Control Conference, July 9-13, 2007, New York, NY, USA.
[58] M. Canova, R. Garcin, M. M. Shawn, Y. Guezennec, and G. Rizzoni, “A Control - Oriented
Model of Combustion Process in a HCCI Diesel Engine,” 2005 American Control
Conference, June 8-10, 2005, Portland, OR, USA.
[59] G. G. Zhu, I. Haskara, and J. Winkelman, “Closed-Loop Ignition Timing Control for SI
Engines Using Ionization Current Feedback,” IEEE Transaction on Control System
Technology, VOL. 15, NO. 3, MAY 2007.
[60] J. Bengtsson, P. Strandh, R. Johansson, P. Tunest, and B. Johansson, “Closed-Loop
Combustion Control of Homogeneous Charge Compression Ignition (HCCI) Engine
Dynamics,” International Journal of Adaptive Control and Signal Processing, 18: 167–179
2004.
[61] F. Willems, E. Doosje, F. Engels, and X. Seykens, “Cylinder Pressure-Based Control in
Heavy-Duty EGR Diesel Engines Using a Virtual Heat Release and Emission Sensor,” SAE
International, 2010-01-0564.
[62] M. M. Andreae, W. K. Cheng, T. Kenney, and J. Yang, “On HCCI engine Knock,” SAE
International, 2007-01-1858, 2007.
[63] Aceves, S.M., D.L. Flowers, R.W. Dibble, and A. Babajimopoulos, Overview of Modeling
Techniques and their Application to HCCI/CAI Engines, in HCCI and CAI Engines for the
Automotive Industry, H. Zhao, Editor. 2007, Woodhead Publishing: Cambridge.

128

[64] O. Colin, A. P. Cruz, and S. Jay, “Detailed Chemistry-Based Auto-Ignition Model Including
Low Temperature Phenomena Applied to 3-D Engine Calculations,” Proceedings of the
Combustion Institute 30 (2005) 2649–2656.
[65] P.M. Diaz, D. Prasad, and S. M. Raman, “A CFD Investigation of Emissions Formation in
HCCI Engines, Including Detailed NOx Chemistry,” IETECH Journal of Mechanical
Design, Vol: 1, No: 1, 056 – 061, 2007.
[66] Gamma Technology, “Engine Performance Application Manual,” GT-Suite version 7.0,
Sep. 2009. Available: http://www.gtisoft.com/.
[67] W. Chatlatanagulchai, K. Yaovaja, S. Rhienprayoon, and K. Wannatong, “Fuzzy Knock
Control of Diesel-Dual-Fuel Engine,” SAE International, 2011-01-0690.
[68] G. G. Zhu, D. Hung and H. Schock, et al, “Combustion characteristics of a single-cylinder
spark ignition gasoline and ethanol dual-fuelled engine,” Proceedings of the Institution of
Mechanical Engineers, Part D: Journal of Automobile Engineering, Volume 224, Number 3
/ 2010, pp 387-403.
[69] L.Guzzella and C.H.Onder, Introduction to Modeling and Control of Internal Combustion
Engine Systems, Springer, Inc., 2004.
[70] A. Y. Karnik, J. H. Buckland, J. S. Freudenberg, “Electronic Throttle and Wastegate
Control for Turbocharged Gasoline Engines,” American Control Conference, pp.
4434-4439, 2005.
[71] K. L. Hoag, R. J. Primus, Fundamentals of Diesel Engine Performance, Cummins Engine
Company, Inc., 1992.
[72] M. Locatelli, C. H. Onder, and H. P. Geering, “An Easily Tunable Wall-Wetting Model for
PFI Engines,” SAE Technical Paper 2004-01-1461.
[73] J. B. Heywood, Internal Combustion Engine Fundamentals, McGraw-Hill, Inc., 1988.
[74] J. Chang, O. Guralp, “New Heat Transfer Correlation for an HCCI Engine Derived from
Measurements of Instantaneous Surface Heat Flux,” SAE 2004-01-2996.
[75] Lars Eriksson, “Spark Advance Modeling and Control,” PhD Dissertation, Linkoping
University, Linkoping, Sweden, 1999.
[76] J. Etheridge, S. Mosbach and M. Kraft, “A Fast Detailed-Chemistry Modeling Approach
for Simulating the SI-HCCI Transition,” SAE International, 2010-01-1241.
[77] Andreas Vressner, Studies on the Load Range of an HCCI Engine using In-Cylinder
Pressure, Ion Current and Optical Diagnostics, PhD thesis, Lund University, Sweden.
November, 2007.

129

[78] Zigler Bradley Thomas, An experimental investigation of the ignition properties of low
temperature combustion in an optical engine, PhD thesis, University of Michigan, 2008.
[79] X. Yang and G. Zhu, “A Two-Zone Control Oriented SI-HCCI Hybrid Combustion Model
for the HIL Engine Simulation,” Proceedings of 2011 American Control Conference, San
Francisco, California, USA, 2011.
[80] M. Canova and S. M. Mohler, Y. Guezennec, and G. Rizzoni, “Mean Value Modeling and
Analysis of HCCI Diesel Engines with External Mixture Formation,” Journal of Dynamics,
Measurement, and Control, Vol. 131, January, 2009.
[81] M. Hillion, J. Chauvin, and N. Petit, “Controlling the Start of Combustion on an HCCI
Diesel Engine,” American Control Conference, June 11 – 13, 2008.
[82] M. McCuen, Z. Sun, and G. Zhu, “Control-oriented mixing model for homogeneous charge
compression ignition engine,” Proceedings of 2010 American Control Conference,
Baltimore, MD, June 2010
[83] N. Ravi, H. H. Liao and A. F. Jungkunz, “Modeling and control of exhaust recompression
HCCI using split injection,” Proceedings of 2010 American Control Conference, Baltimore,
MD, 2010
[84] Y. A. Cengel and M. A. Boles, Thermodynamics: An Engineering Approach, 5th edition,
McGraw-Hill, 2006.
[85] A. Babajimopoulos and D. N. Assanis, “An Approach for Modeling the Effects of Gas
Exchange Processes on HCCI Combustion and Its Application in Evaluating Variable Valve
Timing Control Strategies,” SAE International, 2002-01-2829.
[86] A. Ghazimirsaied, M. Shahbakhti, C. R. Koch, “HCCI Engine Combustion Phasing
Prediction Using a Symbolic-Statistics Approach,” Journal of Engineering for Gas
Turbines and Power, Vol. 132 / 082805-1, August, 2010.
[87] A. Ghazimirsaied1, M. Shahbakhti, A. Audet, and C. R. Koch, “HCCI Engine Cyclic
Variation Characterization Using Both Chaotic and Statistical Approach,” Proceedings of
Combustion Institute-Canadian Section, Spring Technical Meeting. University of Toronto,
Ontario. May 12-14, 2008.
[88] J. Ma, G. G. Zhu, and H. Schock, “Adaptive Control of a Pneumatic Valve Actuator for an
Internal Combustion Engine,” IEEE Transactions on Control Systems Technology, Volume:
19 Issue: 4, pages: 730 - 743. July, 2011.
[89] D. Naidu, Optimal Control Systems, pp. 232-239. ISBN: 0849308925. Published by CRC
Press. August 2002.
[90] K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control, ISBN-13:
978-0134565675, Published by Prentice Hall, August, 1995.

130

[91] Jian-Xin Xu and Ying Tan, Linear and Nonlinear Iterative Learning Control, ISBN
3540401733, published by Springer, 2003.
[92] Y. Chen, K. L. Moore, J. Yu, and T. Zhang, “Iterative learning control and repetitive control
in hard disk drive industry—A tutorial,” International Journal of Adapt Control Signal
Processing, August, 2007.
[93] P. R. Ouyang, B. A. Petz and F. F. Xi, “Iterative Learning Control with Switching Gain
Feedback for Nonlinear Systems,” Journal of Computational and Nonlinear Dynamics, Vol.
6. January 2011.
[94] Adam James Heinzen, Iterative Learning Control of a Fully Flexible Valve Actuation
System for Non-throttled Engine Load Control, MS Thesis, University OF Minnesota, May,
2011.

131