MODELING AND MODE TRANSITION CONTROL OF AN HCCI
CAPABLE SI ENGINE
By
Shupeng Zhang

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Mechanical Engineering - Doctor of Philosophy
2014

ABSTRACT
MODELING AND MODE TRANSITION CONTROL OF AN HCCI CAPABLE SI ENGINE
By
Shupeng Zhang
While the homogeneous charge compression ignition (HCCI) combustion has its advantages
of high thermal efficiency with low emissions, its operational range is limited in both engine
speed and load. To utilize the advantage of the HCCI combustion an HCCI capable SI (spark
ignition) engine is required. One of the key challenges of developing such an engine is to achieve
smooth mode transition between SI and HCCI combustion, where the in-cylinder thermal and
charge mixture properties are quite different due to the distinct combustion characteristics. In this
research, mode transition between SI and HCCI combustion was investigated for an HCCI
capable SI engine equipped with electrical variable valve timing (EVVT) systems, dual-lift
valves and electronic throttle control (ETC) system.
For the purpose of reducing research cost and development duration, one of the most
efficient approaches is to develop and validate the control strategy using an HIL
(hardware-in-the-loop) simulation environment, where the real engine is replaced by a
control-oriented real-time engine model. This dissertation describes a two-zone HCCI
combustion model, where the in-cylinder charge is divided into the well-mixed and unmixed
zones as the result of charge mixing. Simplified fluid dynamics is used to predict the residual gas
fraction before the combustion phase starts, which defines the mass of the unmixed zone, during
real-time simulations. The unmixed zone size not only determines how well the in-cylinder

charge is mixed, which affects the start of HCCI combustion, but also the resulting peak
in-cylinder pressure and temperature during the combustion process. The developed model was
validated in the HIL simulation and experiments.
To achieve smooth combustion mode transition, the throttle position needs to be controlled
accurately with fast response. In this dissertation, an electronic throttle control (ETC) system was
modeled as an LPV (linear parameter varying) system in discrete-time domain, where the
nonlinearities are modeled as varying parameter or compensated through feed-forward control.
Mixed constrained H 2 H  LPV controller was designed to achieve the best performance and
also guarantee the system robustness. Then a model-based mode transition control strategy
between SI and HCCI combustion was developed and experimentally validated for an HCCI
capable SI engine equipped with electrical variable valve timing (EVVT) systems, dual-lift
valves and ETC system. During the mode transition, a manifold air pressure controller was used
to track the desired intake manifold pressure for managing the charge air; and an iterative
learning fuel mass controller, combined with sensitivity-based compensation, was used to
manage the engine torque in terms of net effective mean pressure, an indicator of engine output
torque, at the desired level for smooth mode transition. Experiment results show that the
developed controller is able to achieve smooth combustion mode transition with guaranteed
robustness.

Copyright by
SHUPENG ZHANG
2014

ACKNOWLEDGMENTS

This dissertation would not have been possible without the help of so many people. I would
like to express my sincere appreciation to these who provided me guidance, support,
encouragement, and also brought a lot of fun to my research and life.
I would like to express my deepest gratitude to my advisor, Dr. Guoming Zhu. It is my
fortune and great privilege to do my research work under his continued support and excellent
guidance. His comprehensive knowledge of control theory and automotive application inspired
me to keep on pursuing and enriching my knowledge and experience. His systematic guidance
encouraged me to improve the way of think and exploring. Besides, he also gave me generous
encouragement for my future career and life, which is a lifetime of wealth!
I would like to express my appreciation to my committee members: Dr. Harold Schock, Dr.
Hassan Khalil, and Dr. Jongeun Choi, for their discussions and insight comments during my
dissertation work. Their wonderful graduate courses also provided me valuable knowledge and
firm foundation for my research work, and brought me to the world of engine and control.
I would also like to say thanks to the graduate students and research assistants in the lab,
who helped me set up the engine bench and run the experiments, even day and night: Xuefei
Chen, Jerry Yang, Andrew Huisjen, Ruitao Song, Jie Yang, Tao Zeng, Yifan Men, Tom
Stuecken.
Lastly, I am overly grateful for my parents’ continued support and warm hearted solicitude
that makes me full of courage to strive for the future.

v

TABLE OF CONTENTS

LIST OF TABLES ....................................................................................................................... viii
LIST OF FIGURES ....................................................................................................................... ix
CHAPTER 1 INTRODUCTION .................................................................................................... 1
1.1 Motivation ....................................................................................................................... 1
1.2 Research Work ................................................................................................................ 2
1.2.1 Engine modeling and HIL simulation ...................................................................... 4
1.2.2 Electronic throttle control ........................................................................................ 5
1.2.3 Combustion mode transition .................................................................................... 6
1.3 Dissertation Contributions .............................................................................................. 8
1.4 Dissertation outline ......................................................................................................... 9
CHAPTER 2 CONTROL-ORIENTED CHARGE MIXING AND TWO-ZONE HCCI
COMBUSTION MODELING ...................................................................................................... 10
2.1 Introduction ................................................................................................................... 10
2.2 Engine Description and Modeling Framework ............................................................. 12
2.3 Two-zone Charge Mixing and Combustion Model....................................................... 15
2.3.1 Intake phase ........................................................................................................... 16
2.3.2 Compression phase ................................................................................................ 25
2.3.3 Combustion and expansion phase .......................................................................... 26
2.3.4 Exhaust phase......................................................................................................... 29
2.3.5 NVO phase ............................................................................................................. 30
2.3.6 Throttle and manifold model ................................................................................. 30
2.4 Simulation Results ........................................................................................................ 32
2.5 Conclusions ................................................................................................................... 42
CHAPTER 3 LPV MODELING AND MIXED CONSTRAINED H2/H∞ CONTROL OF AN
ELECTRONIC THROTTLE ........................................................................................................ 44
3.1 Introduction ................................................................................................................... 44
3.2 System Modeling .......................................................................................................... 47
3.2.1 Electronic throttle modeling .................................................................................. 49
3.2.2 Discrete-time LPV model ...................................................................................... 51
3.2.3 LPV uncertainty model .......................................................................................... 53
3.2.4 Set-point control..................................................................................................... 54
3.2.5 Reduced order observer ......................................................................................... 55
3.3 LPV Control Design ..................................................................................................... 55

vi

3.3.1 Augmented LPV system ........................................................................................ 55
3.3.2 Mixed constrained H2/H∞ control synthesis ......................................................... 58
3.4 Weighting Matrices Tuning........................................................................................... 65
3.5 Experimental Validation................................................................................................ 67
3.6 Conclusions ................................................................................................................... 76
CHAPTER 4 MODEL-BASED CONTROL FOR MODE TRANSITION BETWEEN SI AND
HCCI COMBUSTION.................................................................................................................. 77
4.1 Introduction ................................................................................................................... 77
4.2 Mode Transition Control Problem ................................................................................ 79
4.2.1 Engine configuration .............................................................................................. 79
4.2.2 EVVT and NVO .................................................................................................... 80
4.2.3 Hybrid combustion mode ....................................................................................... 82
4.2.4 Split injection ......................................................................................................... 86
4.2.5 Control problem ..................................................................................................... 87
4.2.6 Control framework ................................................................................................. 91
4.3 Engine Combustion Modeling ...................................................................................... 92
4.3.1 Polytropic process .................................................................................................. 93
4.3.2 Charge mixing........................................................................................................ 94
4.3.3 Combustion process ............................................................................................... 94
4.4 Manifold Pressure Control ............................................................................................ 96
4.5 Fuel and NMEP Control ............................................................................................... 97
4.5.1 Iterative learning control ........................................................................................ 98
4.5.2 Sensitivity-based compensator............................................................................. 100
4.6 HIL Simulation Validation .......................................................................................... 104
4.7 Experimental Validation.............................................................................................. 108
4.8 Hybrid Combustion Mode Observation .......................................................................117
4.9 Conclusions ................................................................................................................. 121
CHAPTER 5 CONCLUSIONS .................................................................................................. 122
5.1 Conclusions ................................................................................................................. 122
5.2 Recommendations for Future work ............................................................................ 123
BIBLIOGRAPHY ....................................................................................................................... 126

vii

LIST OF TABLES

Table 2. 1: Engine Specifications.................................................................................................. 33
Table 2. 2: Calibration Parameters ................................................................................................ 33
Table 2. 3: Simulation Results Comparison .................................................................................. 37
Table 3. 1: Electronic throttle parameters..................................................................................... 51
Table 3. 2: Weighting matrices tuning .......................................................................................... 66
Table 3. 3: Controller Performance Comparison .......................................................................... 73
Table 4. 1: Engine Specifications................................................................................................. 80

viii

LIST OF FIGURES
Figure 1. 1: Two-zone model architecture ...................................................................................... 2
Figure 1. 2: HCCI capable SI engine .............................................................................................. 3
Figure 1. 3: Mode transition cases .................................................................................................. 7
Figure 2. 1: Two-zone model architecture .................................................................................... 13
Figure 2. 2: Two-zone charge mixing and HCCI combustion model ........................................... 14
Figure 2. 3: Two-zone charge mixing and HCCI combustion model ........................................... 15
Figure 2. 4: Charge mixing process .............................................................................................. 21
Figure 2. 5: A simplified charge mixing model ............................................................................ 22
Figure 2. 6: HCCI combustion mass fraction burnt and heat release rate .................................... 28
Figure 2. 7: HIL simulation environment ..................................................................................... 32
Figure 2. 8: GT-Power engine model diagram ............................................................................. 34
Figure 2. 9: In-cylinder pressure comparison. .............................................................................. 34
Figure 2. 10: In-cylinder temperature comparison. ...................................................................... 35
Figure 2. 11: In-cylinder pressure during the gas exchange process. ........................................... 36
Figure 2. 12: In-cylinder temperature during the gas exchange process. ..................................... 36
Figure 2. 13: Mass flow rate comparison. .................................................................................... 37
Figure 2. 14: Size change of each zone. ....................................................................................... 38
Figure 2. 15: Temperature of each zone. ...................................................................................... 39
Figure 2. 16: In-cylinder pressure of two-zone and one-zone models.......................................... 40

ix

Figure 2. 17: In-cylinder temperature of two-zone and one-zone models. ................................... 40
Figure 2. 18: IMEP and SOC of two-zone model and GT-Power model. .................................... 41
Figure 2. 19: Experimental comparison of In-cylinder pressure and MFB. ................................. 42
Figure 3. 1: An electronic throttle system .................................................................................... 48
Figure 3. 2: Nonlinear property of return spring .......................................................................... 48
Figure 3. 3: Approximation of sign function ................................................................................ 51
Figure 3. 4: Closed loop system block diagram............................................................................ 56
Figure 3. 5: Parameter space polytope .......................................................................................... 58
Figure 3. 6: Simulation results ...................................................................................................... 66
Figure 3. 7: Relationship between input constraint and performance .......................................... 67
Figure 3. 8: Test bench setup ........................................................................................................ 68
Figure 3. 9: Large opening case - rising ....................................................................................... 69
Figure 3. 10: Large opening case - falling .................................................................................... 69
Figure 3. 11: Crossing limp-home case ........................................................................................ 70
Figure 3. 12: Small opening case .................................................................................................. 71
Figure 3. 13: Comparison with fixed gain PID controller ............................................................ 72
Figure 3. 14: Comparison with sliding mode controller ............................................................... 73
Figure 3. 15: Battery voltage drop case ........................................................................................ 75
Figure 3. 16: Battery voltage recovery case ................................................................................. 75
Figure 4. 1: Engine setup.............................................................................................................. 80
Figure 4. 2: Combustion performance with different pilot injection timing ................................ 81

x

Figure 4. 3: EVVT action and in-cylinder recompression ............................................................ 82
Figure 4. 4: Three types of combustion modes ............................................................................. 83
Figure 4. 5: An unsuccessful mode transition without hybrid mode combustion ........................ 85
Figure 4. 6: In-cylinder pressure w/ and w/o assisted spark during mode transition ................... 85
Figure 4. 7: Effects of pilot injection timing on the combustion performance ............................. 87
Figure 4. 8: Split injection strategy............................................................................................... 87
Figure 4. 9: Combustion mode transition strategy from SI to HCCI ............................................ 89
Figure 4. 10: Combustion performance during mode transition ................................................... 90
Figure 4. 11: Combustion mode transition strategy from HCCI to SI .......................................... 91
Figure 4. 12: Mode transition control diagram ............................................................................. 92
Figure 4. 13: Combustion events .................................................................................................. 93
Figure 4. 14: Intake manifold pressure during mode transition .................................................. 104
Figure 4. 15: Iterative learning of fuel mass ............................................................................... 105
Figure 4. 16: Resulted NMEP under iterative learning control .................................................. 106
Figure 4. 17: Low MAP case validation ..................................................................................... 107
Figure 4. 18: High MAP case validation .................................................................................... 108
Figure 4. 19: Manifold pressure tracking.................................................................................... 109
Figure 4. 20: Iterative learning w/o sensitivity compensation .....................................................110
Figure 4. 21: Iterative learning with sensitivity compensation ....................................................110
Figure 4. 22: Iterative learning of injected fuel mass .................................................................. 111
Figure 4. 23: Fuel mass learning in the 6th cycle .........................................................................112

xi

Figure 4. 24: Comparison with fixed gain PID controller ...........................................................113
Figure 4. 25: Mode transition from SI to HCCI at 1500rpm with 5.0 bar NMEP .......................113
Figure 4. 26: Mode transition from HCCI to SI in 2000rpm, 4.5bar ...........................................114
Figure 4. 27: Mode transition from HCCI to SI in 1500rpm, 5.0 bar ..........................................115
Figure 4. 28: Successful mode transition from SI to HCCI in 2000rpm, 4.5 bar ........................116
Figure 4. 29: Combustion mode transition between SI and HCCI ..............................................117
Figure 4. 30: Mode transition from SI to HCCI in 2000rpm, 4.5 bar ..........................................119
Figure 4. 31: Mode transition from HCCI to SI in 2000rpm, 4.5 bar ..........................................119
Figure 4. 32: Mode transition from SI to HCCI in 1500rpm, 5.0 bar ......................................... 120
Figure 4. 33: Mode transition from HCCI to SI in 1500rpm, 5.0 bar ......................................... 120

xii

CHAPTER 1
INTRODUCTION

1.1 Motivation
Homogeneous charge compression ignition (HCCI) combustion has been widely
investigated in past decades, and demonstrated the potential of providing higher fuel thermal
efficiency and lower emissions than those of the conventional spark ignition (SI) combustion.
The un-throttled HCCI combustion significantly reduces the pumping loss, and the lean HCCI
combustion results in relatively low in-cylinder flame temperature and has the advantage of
reducing the level of NOx emissions [1]-[5].
However, the operational range of the HCCI combustion is limited by knock (determined by
the rate of in-cylinder pressure rise) at high load, and by combustion instability (partial burn or
misfire) at low load as shown in Figure 1.1. Although the HCCI operational range could be
enlarged to a certain extent as reported in [6] and [7], it will be able to cover the entire engine
operational range. Therefore, it is important to have an HCCI capable SI engine that is able to
operate at both SI and HCCI combustion modes under different operational conditions to take the
advantages of both combustion modes; and smooth combustion mode transition is essential for
the HCCI capable SI engine. Achieving smooth mode transition between the SI and HCCI
combustion is challenging due to the significant thermal and charge mixture differences between
1

the HCCI and SI combustion. HCCI combustion requires un-throttled operation to reduce
pumping loss, while the SI combustion operates in a throttled mode with relatively low manifold
pressure, especially around the combustion mode transition region. Besides, in order to trigger
the auto-ignition, HCCI combustion requires relatively high in-cylinder temperature at intake
valve closing (IVC). The most common approach is to use the negative valve overlap (NVO) to
trap high fraction of the hot residual gas from the previous cycle, where a variable timing
valve-train is utilized. Then during the combustion mode transition, combustion control
parameters such as fuel mass, air-to-fuel ratio, and EGR rate have to be well managed to achieve
smooth combustion mode transition.
9
8

NMEP (bar)

7

SI

6
5
4

HCCI

3
2
1
500

1000

1500

2000
2500
3000
Engine speed (rpm)

3500

4000

Figure 1. 1: Two-zone model architecture
1.2

Research Work
To realize stable HCCI combustion on an HCCI capable SI engine has many challenges,

and this dissertation focuses on the smooth mode transition between SI and HCCI combustion.
The engine been studied in this dissertation is a 2.0L four-cylinder engine equipped with
electronic throttle, two-step valve lift and variable timing valve-train system. The engine is
2

capable of SI and HCCI combustion. Figure 1.2 shows the top-view of the engine with actuators.
During the mode transition, these actuators have to be controlled separately. Firstly, the
electronic throttle control (ETC) guarantees the throttle position acting between small opening
(SI mode) and wide opening (HCCI mode) for the combustion modes requirement. Secondly, the
electrical variable valve timing (EVVT) system achieves negative valve overlap (NVO) in HCCI
mode to trap certain portion of residual gas to initiate auto-ignition by advancing the exhaust
cam and retarding the intake cam in the few transition cycles. Thirdly, due to the different
combustion characteristics of SI and HCCI modes, injected fuel mass and ignition timing have to
be adjusted cycle by cycle during the mode transition, to achieve constant NMEP (net mean
effective pressure, related to engine output torque). Normally the EVVT system has much less
nonlinearities and external disturbances than ETC system, and an existing OCC (output
covariance constraint) controller [8] was used to accurately regulate the intake and exhaust valve
timings. This dissertation focuses on the electronic throttle control and NMEP control.

Figure 1. 2: HCCI capable SI engine

3

1.2.1 Engine modeling and HIL simulation
Nowadays for the purpose of reducing research cost and development duration, one of the
most efficient approaches is to develop and validate the control strategy using an HIL
(hardware-in-the-loop) simulation environment, where the real engine is replaced by a
control-oriented real-time engine model.
To accurately control the HCCI combustion process, a precise charge mixing and
combustion model is a necessity. Especially during the combustion mode transition, where the
hybrid combustion mode most likely to occur, accurate auto-ignition timing prediction is
essential for NMEP control. Widely used high fidelity engine models, such as GT-Power and
WAVE, provide fairly accurate engine charge mixing and combustion simulations. However,
they can only be used for off-line simulations and cannot be used for model-based control, where
real-time HIL simulations are required. The mean-value models are simple and can run fast
enough for real-time application; however, it can’t provide detailed combustion information such
as in-cylinder pressure and temperature, which are essential for control design and validation,
especially for combustion feedback.
In this dissertation a control-oriented charge mixing and two-zone HCCI model was
developed, based on thermodynamics and fluid dynamics, and it provides instantaneous
in-cylinder pressure and temperature information for control purpose. By dividing the in-cylinder
into mixed zone and unmixed zone, it provides a more accurate auto-ignition timing prediction,
which is essential for hybrid mode combustion and mode transition control.
The HIL simulation is a powerful tool for control development. In this dissertation, the
4

dSPACE engine simulation system was used as the HIL simulator that runs the proposed engine
model and communicates with the controller; that is, it provides various engine output signals
based upon the control signals provided by the engine controller at different engine operational
conditions. All the control strategies developed in this dissertation were validated in HIL
simulation before experimental validation.
1.2.2 Electronic throttle control
Accurate control of electronic throttle motion is required in combustion mode transition to
achieve desired air-to-fuel level. Around the mode transition region, where the engine load is
usually low, the SI combustion is operated with relatively low manifold pressure and small
throttle opening; while the HCCI combustion operates in an un-throttle mode with widely
opened throttle. Hence, during the few transition engine cycles, the electronic throttle needs to be
opened (from SI to HCCI) or closed (from HCCI to SI) in a relatively short duration.
Furthermore, the transient response of throttle plate highly affects the manifold filling dynamics,
and thereby affects the air-to-fuel ratio and combustion performance.
However, it is challenging to control the throttle plate accurately due to its nonlinearity
caused by high nonlinear limp-home (LH) spring. The success of mode transition highly depends
on whether the throttle plate can cross the LH position smoothly. Moreover, the intake air flow
brings external disturbance to the electronic throttle system; especially when valve lifts change
during mode transition, large additional torque caused by the pressure wave is applied to the
throttle plate. In this dissertation an LPV gain-scheduling controller was designed to achieve the
best performance, and also guarantee the robustness due to the external disturbance.
5

1.2.3 Combustion mode transition
It is fairly challenging to achieve smooth mode transition between the SI and HCCI
combustion due to the significant thermal and charge mixture differences between the HCCI and
SI combustion. Around the mode transition region, the SI combustion requires to be operated in
a throttled mode with relatively low manifold pressure, while the HCCI combustion operates in
an un-throttle mode to reduce pumping loss; furthermore, SI combustion operates with
stoichiometric air-to-fuel ratio and PVO (positive valve overlap) which implies relatively low
trapped residual gas ratio, while HCCI requires lean combustion and large amount of trapped
residual gas. Therefore, it is essential to develop control strategies during the transition cycles to
guarantee the smooth combustion mode transition between steady SI mode and HCCI mode
without engine torque fluctuations.
Combustion mode transition has been widely investigated in recent years. Successful mode
transition between SI and HCCI combustion within one engine cycle was reported by utilizing
camless valve-train system including electromagnetic [9][10] and electro hydraulic [11] ones.
However, camless valve-train system is difficult for commercial production due to its high cost,
system complexity, and relatively lower reliability. In [12] an experimental investigation on
SI-HCCI-SI mode transition using hydraulic two-stage profile camshafts with VVT (variable
valve timing) system was performed, where the valve timing, one-step throttle opening timing,
and fuel mass were optimized. However, considerable engine torque fluctuation during the
combustion mode transition was observed. In [13] a state feedback controller was designed based
on a state-space model obtained from system identification, fuel mass and NVO were used as the
6

control inputs to track the desired IMEP and combustion phasing. This model-based controller
reduces torque fluctuation over the traditional PI (proportional and integral) controller, but
engine torque output still varies unexpectedly, especially at the beginning of the mode transition.
Figure 1.3 shows three combustion mode transition cases from SI to HCCI at 1500rpm and
5.0 bar NMEP, including successful mode transition, unsuccessful mode transition and failed
transition. For unsuccessful mode transition, significant NMEP can be observed which was
possibly due to the inappropriate fuel mass or ignition timing. For failed mode transition, misfire
or incomplete burning led to large drop of NMEP during the mode transition, and that might be
caused by the ultra-lean combustion which was resulted from the inappropriate throttle opening.

40
30

4

20
10

3
-4

-2

0

6

8

10

12

14

0
16

60

5

40

4

20

3
-4

-2

0

2

4

6

8

10

12

14

Failed mode transition

6

NMEP (bar)

4

Unsuccessful mode transition

6

NMEP (bar)

2

0
16

60

5

50

4

40

3

30

2

20

1

10

0
-4

-2

0

2

4

6

8

10

12

Figure 1. 3: Mode transition cases

7

14

0
16

In-cylinder pressure (bar)

NMEP (bar)

50
5

In-cylinder pressure (bar)

60

Mode transition

In-cylinder pressure (bar)

Successful mode transition
6

In this dissertation, based on the actuator (ETC and EVVT) setup, a model-based control
strategy was developed to achieve smooth mode transition between SI and HCCI combustion.
This control strategy includes manifold pressure tracking control, iterative learning fuel mass
control and sensitivity-based fuel mass compensator for improved robustness. The model-based
controller was validated in HIL simulation first, with the developed two-zone control-oriented
engine model, and then validated experimentally.
1.3

Dissertation Contributions
The dissertation has the following major contributions:



A control-oriented charge mixing and two-zone HCCI combustion model was developed, which
is able to predict the combustion timing with improved accuracy over the existing one-zone
model. The improved flow dynamic modeling also guarantees the fidelity of the HIL simulations
during the combustion mode transition. The model can be also used for other control
developments, such as HCCI combustion control in future work.



An LPV gain-scheduling control strategy for electronic throttle control dealing with the high
system nonlinearity and external disturbance was developed and validated. This control approach
can be also applied to other mechatronics or powertrain systems.



The proposed control strategy to achieve smooth combustion mode transition is based upon
manifold pressure control and fuel mass management. The iterative learning approach provided
an efficient way for a wide operational range calibration, and the sensitivity-based feed-forward
compensation can deal with certain type of cycle-by-cycle variation. The experimental results
show that the maximum absolute variation during the model transition is compatible with that for
8

steady SI and HCCI combustion.
1.4

Dissertation outline
The material presented in this thesis is organized into three chapters. In chapter 2, a

two-zone charge mixing and HCCI combustion model is proposed, and was implemented into
the HIL simulation environment. The simulation results were compared with GT-Power
simulation results and experimental data. It provides a simulation platform for developing the
real-time mode transition control strategy. In chapter 3, a discrete-time gain-scheduling mixed
constrained H 2 H  controller is designed for an electronic throttle system, which can be
controlled accurately and also robust to external disturbance during the combustion mode
transition. In chapter 4, a model-based control strategy for combustion mode transition between
SI and HCCI is proposed, and smooth transition was achieved both in HIL simulation end
experimentally. Chapter 5 provides conclusions and future work.

9

CHAPTER 2
CONTROL-ORIENTED CHARGE MIXING AND TWO-ZONE HCCI
COMBUSTION MODELING

2.1

Introduction
One challenge for the HCCI combustion control is to predict the start of combustion

precisely. Moreover, HCCI combustion mode can only operate in a certain range of engine
conditions and is limited at high engine load due to knock and low load due to misfire. Several
approaches have been demonstrated to achieve auto-ignition combustion for an SI engine, such
as intake charge heating, increasing the compression ratio, exhaust gas recirculation, and residual
gas trapping that is achieved by negative valve overlap (NVO) [5], along with corresponding
control strategies. Nowadays for the purpose of reducing research cost and shortening the
development duration, one of the most efficient approaches is to develop and validate the control
strategy using an HIL (hardware-in-the-loop) simulation environment, where the real engine is
replaced by a control-oriented real-time engine model.
To accurately control the HCCI combustion process, a precise charge mixing and
combustion model is a necessity.

Widely used high fidelity engine models, such as GT-Power

and WAVE, provide fairly accurate engine charge mixing and combustion models. However,
they can only be used for off-line simulations and cannot be used for model-based control, where
10

real-time HIL simulations are required. Multi-zone models based on chemical kinetics, that
divide the cylinder into adiabatic core zones and thermal boundary layers, are capable of
simulating more realistic HCCI combustion phenomena [14][15]. Unfortunately, these models
are not fast enough for real-time simulations. The mean-value single-zone method was used in
[16] to model the averaged chemical kinetics and thermodynamic properties and a
control-oriented modeling approach was used for multi-mode HCCI engine in [17].
In [18] a control-oriented one-zone HCCI combustion model was constructed based on the
assumption that the in-cylinder fuel, air, and residual gas charges are uniformly premixed at the
intake valve closing (IVC). However, during the engine intake process, some of the residual gas
is not mixed with the fresh intake gas, which remains at certain position of the cylinder. This
unmixed portion is so-called unmixed residual gas fraction. Ignoring the unmixed residual gas
fraction will result in modeling errors for the peak in-cylinder pressure and temperature since the
unmixed residual gas may have a quite different temperature compared with the well mixed zone.
Also the volume and air-to-fuel ratio (AFR) of the mixed zone will be affected by the unmixed
portion in the cylinder. During the gas exchange process described in [5], a first order transfer
function was used to approximate the in-cylinder pressure, which led to large errors compared
with the actual pressure. In [19] and [20] a two-zone HCCI model were established taking into
consideration of unmixed zone during combustion phase. Reference [19] developed a two-zone
model based on thermochemistry and chemical kinetics, which ensures better combustion results,
but the charge mixing process is not modeled. As a result, the size of the unmixed zone cannot be
determined in real-time. In [20] the unmixed zone was assumed to remain at the bottom of the
11

cylinder with a columnar intake flow jet, and the mass transfer rate from unmixed zone to mixed
zone is proportional to the kinetic energy of the intake flow, which denoted that the charge
mixing only occurs during the intake phase; however, this simplified model ignored the turbulent
phenomenon caused by both of the bifurcated intake flow shear and high speed moving piston,
which would last for the entire intake phase and compression phase.
In this article, to make the real-time simulation possible, mass fraction burned Wiebe
function, along with energy conservation principle, was used to model the combustion process to
guarantee the accuracy of thermodynamics characteristics such as in-cylinder pressure and
temperature. One dimensional flow dynamics equations are used to model the detailed gas
exchange dynamic process. During the intake phase, the in-cylinder charge is divided into two
zones, mixed and unmixed zones, and modeled based upon the turbulent flow analysis approach.
This chapter is organized as follows.

In section II the engine description and modeling

framework are discussed. In section III detailed modeling approach is described for each
combustion phase and simulation results are compared with GT-Power simulation results and
experimental data in section IV. Section V addresses the conclusions.
2.2

Engine Description and Modeling Framework
The engine used for the modeling work is a 2.0L four-cylinder equipped with two-step

valve lift and electrical cam phaser. The engine is capable of SI and HCCI combustion.

Figure

2.1 shows the architecture of the entire engine model. Compared with the one-zone model in [18],
it has the similar overall framework. The engine model receives inputs from the engine controller,
including spark signal, injection signal, throttle signal, etc. The outputs of the engine model
12

include mean-value based crank shaft speed, exhaust pressure, crank based in-cylinder pressure,
temperature, etc. Also, the engine crank, cam and gate signals are generated to synchronize with
engine control unit for HIL simulations. The engine model consists of five subsystem models:
combustion model, throttle and manifold model, EGR (exhaust gas recirculation) model,
piston/crank dynamics and dyno model. Crank-based combustion related variables are updated
every crank degree; and mean-value engine variables, including throttle, manifold model, crank
and dynamometer models are updated with a fixed sample time at 1ms.
Spark timing

Piston and Crank
Dynamics

Dyno

Fuel pulse

.
.
.

Cam
Gate

Throttle position
Valve timing

Crank

EGR
Combustion

Pressure
Temperature

Throttle &
Manifold

.
.
.

Figure 2. 1: Two-zone model architecture
However, one challenge for the HCCI combustion control is to predict the start of
combustion precisely. Moreover, HCCI combustion mode can only operate in a certain range of
engine conditions and is limited at high engine load due to knock and low load due to misfire.
Several approaches have been demonstrated to achieve auto-ignition combustion for an SI engine,
such as intake charge heating, increasing the compression ratio, exhaust gas recirculation, and
residual gas trapping that is achieved by negative valve overlap (NVO) [5], along with
corresponding control strategies. Nowadays for the purpose of reducing research cost and
shortening the development duration, one of the most efficient approaches is to develop and
validate the control strategy using an HIL (hardware-in-the-loop) simulation environment, where
13

the real engine is replaced by a control-oriented real-time engine model.
For the charge mixing process, the in-cylinder charge mixture is divided into two zones,
mixed and unmixed, before the combustion starts. In order to predict the size of the unmixed
zone, it is essential to model the flow dynamics during the entire intake process. A compressible
flow dynamics method is used to predict the flow rate in real-time. When combined with
turbulent diffusion analysis, the transfer rate between the two zones can finally be obtained.
During the intake phase, due to the NVO recompression occurred before the intake phase, the
in-cylinder pressure is usually higher than the intake manifold pressure at the start of the intake
phase. Therefore, at the beginning of the intake process, the trapped in-cylinder gas flows from
cylinder to manifold and then flow back to the cylinder. This intake process is considered in the
model.

Figure 2. 2: Two-zone charge mixing and HCCI combustion model
Figure 2.2 shows a diagram of the two-zone mixing process over an entire engine cycle.

14

The unmixed zone is assumed to be located in the inner part of the cylinder, and its size is
shrinking due to the gas diffusion to the mixed zone. Once auto-ignition occurs, it is assumed
that the mass of unmixed zone does not change and a polytropic compression is assumed. When
combustion ends, the two-zone assumption is not essential to in-cylinder analysis, hence it is
assumed that the in-cylinder residual gas distributes homogeneously. Since the calculated
temperature and volume of the unmixed zone can be updated each crank degree under this
assumption, it is easy to analyze the combustion process in the mixed zone. In this article, it is
also assumed that there is no heat exchange between the two zones, but the mixed zone
exchanges heat with the cylinder wall.
2.3

Two-zone Charge Mixing and Combustion Model
The thermodynamic characteristics of the in-cylinder gas, such as in-cylinder pressure and

temperature, are of great interest in the SI and HCCI combustion modeling research. This is
especially important at certain critical combustion phases such as the IVC (intake valve closing).

Figure 2. 3: Two-zone charge mixing and HCCI combustion model
Figure 2.3 shows five key combustion phases of an HCCI combustion process within one
15

engine cycle. They are: intake valve closing; start of HCCI combustion (SOC); exhaust valve
opening (EVO); exhaust valve closing (EVC); and intake valve opening (IVO). For each
combustion phase, the in-cylinder combustion variables, such as pressure and temperature are
modeled using thermodynamic governing partial differential equations that are discretized every
crank degree and solved analytically. For the HCCI combustion process, Wiebe based mass
fraction burned (MFB) function, calibrated using experimental data, was used to approximate the
complicated chemical reaction process to make the real-time simulation possible with required
simulation accuracy; for the gas exchange process, the discretized governing equations (2.6) and
(2.8) were solved iteratively, along with 1-D flow dynamics equations, with the guaranteed
convergence for in-cylinder thermodynamics characteristics. In the rest of this section, crank
resolved model of each combustion phase are presented.
2.3.1 Intake phase
During this phase, the fresh charge enters the cylinder and mixes gradually with the residual
gas. As a result, the total mass of the unmixed zone reduces. The goal is to predict the size of the
unmixed zone at IVC; hence, it is essential to model the flow dynamics during the entire intake
phase. Calculation of the intake flow rate is based on the one-dimensional compressible flow
equations [21]:
a) When the flow is not choked ( PT P0  2   1

  1

),
12

 1   
CD Av P0  PT   2   PT 

1   

mv 
  
RT0  P0     1   P0 
 



1

16

(2.1)

b) When the flow is choked ( PT P0   2   1

  1

C AP
 2 
mv  D v 0  1 2 

RT0
  1 

),

 1 2 1

(2.2)

where CD is the discharge coefficient and experimentally determined, P0 and T0 are the
upstream stagnation pressure and temperature, PT is the downstream pressure, Av is the intake
valve reference area, and  is the specific heat ratio.
For an HCCI combustion engine with the NVO strategy, most often, the in-cylinder
pressure is higher than the intake manifold pressure at the IVO due to the residual gas
recompression and early exhaust valve closing. Hence, a certain portion of the residual gas will
escape into the manifold after IVO. This is called backflow. In order to simplify the modeling
process, the entire intake phase is divided into three stages under certain assumptions:
Firstly, right after the IVO, the trapped residual gas flows out of the cylinder through the
intake valve. In this case, P0 and T0 in (2.1) and (2.2) are in-cylinder pressure and temperature,
respectively, PT is the manifold pressure, and m is treated as a negative value in the model for
calculation convenience. During this stage, as the in-cylinder total mass is decreasing while the
cylinder volume is increasing, the in-cylinder pressure and temperature both drop significantly.
Secondly, once the in-cylinder pressure becomes lower than the intake manifold pressure,
the flow direction reverses. It is assumed that the escaped residual gas in the first stage was not
mixed with the fresh charge in the manifold. Since the GT-Power and CFD (computational fluid
dynamics) simulation results show that the back flow occurred during the first stage will be
charged back into the cylinder completely. Therefore, this assumption will not lead to large

17

modeling error at the end of the charge mixing process. For equations (2.1) and (2.2), in this case,

P0 is the manifold pressure, PT is the in-cylinder pressure, and T0 is the residual gas
temperature reduced by a factor governed by heat transfer and expansion.
Finally, after all the escaped residual gas flows back into the cylinder, the actual fresh
charge process begins. During this stage, P0 and T0 are the intake manifold pressure and
temperature, respectively, and PT is the in-cylinder pressure. This stage has the longest duration
among the three stages. Mixing occurs in this stage.
The calculation of in-cylinder pressure and temperature is based upon the first law of
thermodynamics. Since there is only one-direction flow path at one time due to the NVO
operation, the energy conservation equation can be written as
d  mu 
 Qw  W  mh
dt

(2.3)

where W is the rate of the transferred work, which equals pV . Qw is the total heat-transfer
rate to the cylinder walls, which can be obtained using the Woschni correlation model [22][23]:

Qw   Ac hc T  Tw  Ne

(2.4)

where Ac is the contact area between gas and cylinder wall, Tw is average temperature of
cylinder wall, N e is the engine speed, and hc is the instantaneous convection coefficient that
can be calculated by

hc   B

0.2

0.8

P T

0.55



Vd Tr
 P  Pmot 
C1S p  C2
prVr



0.8

(2.5)

where B is the bore; P is the in-cylinder pressure; S p is the mean piston speed; Vd is the
displaced volume; Tr, pr, and Vr are the in-cylinder temperature, pressure and volume at some
18

reference state, such as intake valve closing; and Pmot is the motored in-cylinder pressure at the
current crank position.  , C1 and C2 are the scaling factors used as model calibration parameters.
To simplify calculation, it is assumed that hc is constant within the calculation step but variable
step-by-step.
In the developed model equation (2.3) is discretized and solved analytically. Note that Cp
and Cv do change as a function of temperature and species. However, within one computational
step (one crank degree) the variations of Cp and Cv are fairly small. To simplify calculation, it is
assumed that Cp and Cv are constant within the calculation step but variable step-by-step. It is
also assumed that the pressures in mixed and unmixed zones are identical. Then the in-cylinder
temperature can be determined at every crank degree by the following equation
T (i ) 

Qw  P(i 1 ) V (i )  V (i 1 )  mtC pT0  m(i 1 )CvT (i 1 )

 m(i 1 )  mt  Cv

(2.6)

where  is crank angle; T0 is the intake flow temperature; t is the time interval for each
crank degree; and Qw is the heat transfer to the cylinder wall during the time interval, which can
be obtained by

Qw  Qw i 1  t

(2.7)

based on the assumption that the heat transfer rate remains unchanged within one calculation
step.
Since the mixture can be considered as an ideal gas, in-cylinder pressure can be obtained by

P(i ) 

m(i ) RT (i )
V (i )

(2.8)

Equations (2.1) and (2.2) are discretized at each crank step and solved numerically, where
19

the solution is obtained using iterative approach for a given step, along with (2.6) and (2.8).
In-cylinder pressure, temperature and intake flow rate are updated at each iteration. During the
third phase of the process, the residual gas mixes with the fresh charge gradually in a fairly
complicated dynamic process. The main task of the modeling work is to describe the mass
transfer rate from the unmixed zone to the mixed zone using a simple approach, which is
solvable in real-time for HIL simulations.
Due to the high intake flow velocity and piston motion, there is significant in-cylinder
turbulent motion, combined with tumble and swirl. The flow field changes significantly as
manifold shape, combustion chamber geometry and valve timing vary. CFD models were widely
used to provide the relatively accurate estimation of in-cylinder gas motion [24][25]. Figure 4
shows a side view of a simulated charge mixing process with NVO. The entire process can be
considered as a turbulent diffusion process. Figure 2.4 (a) shows that at the beginning of the third
stage, as discussed previously, the fresh charge comes in, and bifurcates into two jets; the right
jet flows along the cylinder wall towards the piston, and the left jet flows along the cylinder head
and past the exhaust valve. As the valve lift increases, additional incoming fresh charge leads to
faster in-cylinder flow velocity and turbulent intensity, and forms two main vortices: the left-top
vortex caused by the shear between the left jet and cylinder wall, and the right-bottom vortex
caused by the interaction between the right jet and piston, as shown in Figure 2.4 (b). The mass
transfer from residual gas to well-mixed gas, resulting from the species gradient between fresh
charge and residual gas, is augmented by this in-cylinder turbulence. Once the intake valve is
about to close and the piston is approaching to BDC (bottom dead center), the in-cylinder
20

average flow velocity drops, but turbulence keeps the process going albeit at a decreasing rate, as
shown in Figure 2.4 (c). When the piston moves up towards the TDC (top dead center), it pushes
the residual gas to the upper location of the cylinder, and a newly formed vortex is conducive to
charge mixing, as shown in Figure 2.4 (d).

Figure 2. 4: Charge mixing process
Based on the CFD simulation results [24][25], although different valve timing strategies
will lead to different flow fields and residual gas shapes, the shape of the unmixed zone formed
by the residual gas is similar. In most of the cases, the residual gas is surrounded by the mixed
charge due to continuous shear flow. Hence a simplified model is proposed in Figure 5.

21

Figure 2. 5: A simplified charge mixing model
It is assumed that during the charge mixing process the unmixed zone (formed by residual
gas) remains in the center of the cylinder, and the shape is assumed to be spherical. The fresh
charge surrounds the unmixed zone with velocity tangent to the sphere and mixes with the
residual gas gradually, which forms the mixed zone. The mass transport from the unmixed zone
to mixed zone is caused by gas diffusion, which consists of both molecular diffusion and
turbulent diffusion. Since the turbulent diffusion rate is much higher than that of molecular
diffusion, the latter is ignored. Under this assumption Fick's first law of diffusion will be applied
[26]:
jt   Dt

d
dr

(2.9)

where jt is the turbulent mass flux of the residual gas;  is the density of the residual gas; Dt
is the turbulent diffusivity and the last term describes the mass fraction of the residual gas
distribution in the mixed zone in the radius direction. This mass flux denotes the mass flow rate

22

from unmixed zone to mixed zone per unit interaction area per unit time. To simplify the
problem, it is assumed that at any time the residual gas in the mixed zone has a constant
distribution gradient, hence the last term can be rewritten as 0 l , where 0 is the
concentration of residual gas at the interaction surface and l is the thickness of mixed zone.
The relationship between turbulent diffusivity and turbulent viscosity leads to the following
equation that can be used to solve Dt :

Sct 

t
Dt

(2.10)

Here, Sct is a dimensionless constant known as the turbulent Schmidt number. The
turbulent viscosity can be obtained by:

 t  c1 v l

(2.11)

where v is the average velocity in the mixed zone, which is approximated by mean value of
intake flow velocity and piston velocity; l is the thickness of the mixed zone, the same as in
residual gas distribution gradient calculation; and c1 is a constant to be calibrated. Finally the
mass transfer rate can be expressed as

mtr i    i  c1v i  0c2 A i  Sct

(2.12)

where A is the surface area of the unmixed zone, which can be easily calculated under the
“sphere” assumption; and c2 is a calibration constant due to the assumptions made. Notice that
at the beginning of the charge mixing process, the amount of the incoming fresh charge is not
enough to surround the residual gas, and in this case A should be the surface area of the mixed
zone and calculated by assuming that the thickness of the mixed zone is identical to the intake

23

valve lift.
Notice that during the entire intake phase temperature gradient exists between two zones,
resulting in heat transfer from the unmixed zone to the mixed zone. Hence a polytropic process
can be approximated in the unmixed zone, and the polytropic exponent n was calibrated as a
function of temperature to match the GT-Power simulation results over a wide engine operation
range. Then the temperature in both zones can be obtained sequentially, assuming that the
pressures of the mixed and unmixed zones are identical:

T (i )unmixed

T (i )mixed 

 P( IVO ) 
 T ( IVO )  

 P(i ) 

n 1 n

m(i )T (i )  munmixed (i )T (i )unmixed
mmixed (i )

(2.13)

(2.14)

The volume of both zones can be determined by ideal gas law.
Since the developed model is capable of SI and HCCI combustion modes, the modeling
methodology described above can be also used for the positive valve overlap (PVO) case.
Similar analysis can be used during the intake valve opening and exhaust valve closing; however,
during the valve overlap stage, complicated in-cylinder mixing process exists. Due to the strong
in-cylinder motion (combination of turbulence and tumble) after intake valve opening, it is
assumed that intake fresh charge will not get out through the exhaust valve, that is, there is no
fresh charge flow into the exhaust port. This assumption is due to the fact that under most engine
operational conditions there is no fresh charge escaped through the exhaust valve. Hence the
intake charge mixing process and residual gas exhaust process can be calculated separately. Note
that in some case the backflow phenomenon does exist, including flow from cylinder to intake
24

manifold, and flow from exhaust manifold to cylinder. Similar criteria and method can be
applied to this case as in the first two stages mentioned above.
2.3.2 Compression phase
Since at the end of compression phase the in-cylinder temperature might be very high, the
heat transfer effect cannot be neglected to achieve an accurate prediction of the start of HCCI
combustion. Based on energy conservation, temperatures of both mixed and unmixed zones can
be calculated separately:
T (i )unmixed 

T (i )mixed 

munmixed (i 1 )CvTunmixed (i 1 )  P i 1  V i   mtr (i )tC pT (i )unmixed

 munmixed (i1 )  mtr (i )t  Cv

Qmixed  P i 1  Vˆ i   mmixed (i 1 )CvTmixed (i 1 )  mtr (i )tC pT (i )unmixed

 mmixed (i 1 )  mtr (i )t  Cv

(2.15)

(2.16)

where
V i   Vunmixed i   Vunmixed i 1  , Vˆ i   Vmixed i   Vmixed i 1 

Note that Qmixed is heat transfer to the cylinder walls from the mixed zone; and mtr is the
mass transfer rate from unmixed zone to mixed zone that can be obtained by (2.12). Heat transfer
between mixed zone and unmixed zone is neglected here. Then, the average in-cylinder
temperature can be obtained by

T (i ) 

mmixed T (i )mixed  munmixed T (i )unmixed
mIVC

(2.17)

The compression phase ends when the HCCI combustion starts. A commonly used criterion
for the start of combustion (SOC) timing is the Arrhenius integral [27][28], that depends on the
oxygen and fuel concentration, which is described as

25

ARI  

i

 IVC

Ap O2   Fuel  e
a

b

c



Ea
RTmixed  

d

(2.18)

where Ea is the activation energy for the auto ignition reaction and is chosen to be a
constant; and A is a scaling factor related to fuel composition. Since for NVO strategy EGR rate
has a strong effect on ignition delay [29], A is also a function of EGR, and a lookup table can be
used to calibrate A.
The SOC crank position is defined as the crank angle for 1% fuel burned under HCCI
combustion. During this phase, the Arrhenius integral continues its integration. As the
in-cylinder temperature and pressure increase gradually due to compression, the Arrhenius
integral increases as well. Once the ARI reaches criteria of the SOC (ARI ≥ 1), it shows that the
HCCI combustion phase starts. At this moment, the temperature of mixed zone will be recorded
as T ( SOC ) and volume of unmixed zone as Vunmixed (SOC ) to be used for calculation in the next
phase.
2.3.3 Combustion and expansion phase
In the HCCI combustion phase, the following two assumptions are made:
1) There is no mass exchange between the mixed (burned) and the unmixed zones due to the
weak in-cylinder gas motion during the combustion phase (near TDC).
2) There is no heat transfer between the two zones but each zone has heat transfer to the
cylinder wall.
Under the two assumptions, thermodynamic activity in both zones can be solved separately.
In order to simplify the coupled equations, in-cylinder pressure in the last crank degree is used to

26

calculate the volume of the current unmixed zone.
1

 P( SOC ) 
Vunmixed (i )  Vunmixed ( SOC ) 

 P(i 1 ) 

(2.19)

In the mixed zone, the fuel MFB is modeled based upon the Wiebe MFB function and
associated heat release rate function. Experimental results show that the heat release rate curve
for HCCI combustion varies significantly and is heavily dependent on the fuel types and engine
operational conditions. Typically the combustion process can be divided into two stages,
cool-flame reactions and main combustion [30][31]. Under certain lean combustion cases,
especially with very high EGR rate (combined with both NVO trapped residual mass and
external EGR), or highly diluted mixture case (high N2 concentration or low fuel concentration),
the main HCCI combustion stage can be further divided into two stages: fast reaction (heat
release) rate stage and slow reaction rate stage [32][33], as shown in Figure 2.6. In order to
develop a generic combustion model that can be applied to all types of four-stroke SI and CI
engines, a generalized formula for MFB curve, that covers most possible combustion processes,
is modeled by a combination of three functions

x     x1     x2    1      x3  

(2.20)

and each of these three functions is modeled by the Wiebe function [21] with
(   0,   0,  +  1 )

xi    1  e

  0 i 
 ai 

 i 

mi 1

, i  1, 2,3

(2.21)

where coefficients ai , mi , factors  ,  , and predicted burn duration i are calibration

27

parameters of engine speed and load, and coolant temperature;  0i represents the start of
combustion for the stage i ; and 01   SOC is given by the Arrhenius criterion in (18). All these
parameters were calibrated within certain engine operation condition range and lookup tables
were used as functions of engine speed and air-to-fuel ratio. For the combustion with relatively
low EGR rate and not extremely lean combustion the third combustion stage does not exist and

   can be set to one; and for gasoline type fuels combustion where the cool-flame reaction is
not evident  can be set to one and  to zero

Figure 2. 6: HCCI combustion mass fraction burnt and heat release rate
The energy conservation equation applied to the mixed zone has the form
mmixed

du
dV
dx
p
 Qw   HCCI m fuel QLHV
d
d
d

(22)

where the combustion efficiency  HCCI is a calibration parameter used to match the simulated
IMEP (indicated mean effective pressure) provided by GT-Power model, and QLHV is the low
heating value of the fuel. Considering the time interval for each crank degree is fairly small, the
temperature calculation was simplified into two steps shown in (2.23) to make real-time
28

simulation possible. They are a polytropic volume change process without heat exchange and a
heat exchange process without volume change, where in the numerical simulations parameter n
is equal to . Then the temperature, pressure and volume of mixed zone can be solved by

 V ( ) 
Tmixed (i )  Tmixed (i 1 )   mixed i 1 
 Vmixed (i ) 

n 1

P(i )  P(i 1 ) 



 HCCI m fuel QLHV  x(i )  x(i 1 )  Q(i )
mmixed Cv

Vmixed (i 1 ) Tmixed (i )

Vmixed (i ) Tmixed (i 1 )

(2.23)

(2.24)

and

Vmixed (i )  V (i )  Vunmixed (i )

(2.25)

Temperature in the unmixed zone can be obtained by (2.15).
After the HCCI combustion phase, the two-zone analysis is no longer essential for
in-cylinder combustion behavior, and the two zones are assumed to be well mixed
instantaneously. The in-cylinder average temperature can be obtained by (2.13) with the initial
condition:

T (e ) 

mmixed T (e )  munmixed Tunmixed (e )
mIVC

(2.26)

where the index e denotes the crank position when combustion terminates.
2.3.4 Exhaust phase
The exhaust process is similar to the intake phase. Equations (2.1), (2.2), (2.6) and (2.7) are
used for calculating the exhaust flow rate, in-cylinder temperature and pressure. Note that during
this phase the in-cylinder pressure is higher than the exhaust manifold pressure in most of time,
however, the situation can be reversed. Therefore, the backflow occurring is also considered. At

29

the exhaust valve closed (EVC), the trapped mass can be calculated by

mEVC 

PEVCVEVC
RTEVC

(2.27)

2.3.5 NVO phase
The NVO phase is called as engine recompression. During this phase the trapped
in-cylinder gas is polytropically compressed or expanded in a closed system with heat transfer to
the cylinder wall, so (2.28) and (2.8) are used to calculate both temperature and pressure with

m(i ) replaced by mEVC in (2.8).
 V i 1  
T i   T i 1   

 V i  

n 1

(2.28)

2.3.6 Throttle and manifold model
Throttle and intake manifold models provide the manifold pressure required for intake flow
rate calculation in real-time. The fresh air flow rate through the throttle plate can be calculated
using the one-dimensional compressible flow equation similar to the one used to solve intake
valve case:
mt 

Cd At P0 2    1
RT0

  pr 

(2.29)

where Cd is the discharge coefficient; P0 and T0 are the atmosphere pressure and
temperature; At is the throttle reference area; and pr  pman p0 where pman denotes the
manifold pressure. The function  is given by

30




  pr   






 1


2

 2   1
, if pr  

  1 

pr  pr

  1   2 



 2     1 

 1
 1



(2.30)

 2   1
, if pr  

  1 

Considering the throttle geometry, At can be approximated by
At 


4

D 2 1  cos    0 

(2.31)

where D is the diameter of the throttle plate, and  0 is the closed throttle angle.
Actual flow dynamics and thermodynamics in the manifold are quite complicated. In order
to simplify the problem, a uniform condition assumption for the manifold is made, which
assumes that there is no pressure gradient or temperature gradient in spatial distribution. By
choosing the entire manifold as the control volume and applying the mass conservation, the mass
change in the manifold is the difference between inlet mass flow (combined with air mass flow
past the throttle and external EGR flow) and outlet mass flow (flow enter the cylinder through
the valves). Then the equation for manifold mass change rate can be expressed as

mman  mt  mEGR  mv

(2.32)

Applying the ideal gas law in the manifold volume V , the pressure differential equation
can be written as
pman 

mman RTman
V

(2.33)

Neglect the different gas thermodynamic properties between fresh air and EGR, the
difference equation for manifold temperature is

[Tman (i )mman (i )  Tman (i 1 )mman (i 1 )]Cv ,man 
T0 mt i  Cv 0  TEGR mEGR i  Cv , EGR  Tman (i 1 )mv (i )Cv ,man  t

31

(2.34)

where t is the time interval for each crank degree. Then equations (2.32) and (2.33) can be
discretized, along with (2.29) and (34), pman and Tman can be solved online iteratively, which
is similar to solving equations (2.1) – (2.8).
2.4

Simulation Results
The two-zone HCCI combustion model was validated in the HIL simulation environment

(see Figure 2.7 for the HIL system architecture). On top of the figure a host computer is used for
running the Opal-RT based engine controller; the lower host computer is used for running the
dSPACE based real-time engine simulator which was introduced in this paper. The two host
computers can communicate with each other to get all the data updated each crank angel to
achieve the real-time simulation. An oscilloscope can be applied to display the simulation
results.

Figure 2. 7: HIL simulation environment

32

Table 2. 1: Engine Specifications
Parameter

Model value

bore/stroke/con-rod length
compression ratio
intake valve opening duration
exhaust valve opening duration
Intake/exhaust valve lifts

86mm/86mm/143.6mm
9.8:1
148 crank degree
148 crank degree
5mm

The engine parameters are given in Table 2.1, and Table 2.2 shows the model calibration
parameters and how they are calibrated.
Table 2. 2: Calibration Parameters
Parameter
CD

，C1 , C2
c1 ,c2

n
A, a, b, c
，

Equations
(1), (2), (29)
(5)
(11), (12)
(13),
(23),
(28)
(18)
(20)

Calibration method
GT-Power
GT-Power
Experiment
GT-Power
Experiment
Experiment

The two-zone model was validated for the engine operation at 2000 rpm with various loads.
The simulation results at 4.2 bar IMEP are presented below. The associated valve timing for
EVO, EVC, IVO and IVC are 156, 304, 382, and 530 after TDC (top dead center). A
four-cylinder GT-Power model is also developed and used to provide baseline simulation results,
and Figure 2.8 shows the architecture of the model. For the purpose of validation, the proposed
two-zone charge mixing and combustion model was compared with the one-zone model in [13],
along with the improved one-zone model where the gas exchange flow dynamics was included
but with the assumption of homogeneous mixing during the entire gas exchange process.

33

Figure 2. 8: GT-Power engine model diagram
Figures 2.9 and 2.10 show the in-cylinder pressures and temperatures over an engine cycle.
Note that the two-zone charge mixing model can provide an accurate simulation results that
match with GT-Power simulation results quite well.
40

GT-Power model
Two-zone model

In-cylinder pressure (bar)

35
30
25
20
15
10
5
0

-100

0

100
200
300
Crank position (deg)

400

Figure 2. 9: In-cylinder pressure comparison.
34

500

In-cylinder temperature (K)

2000

GT-Power model
Two-zone model

1500

1000

500

0

-100

0

100
200
300
Crank position (deg)

400

500

Figure 2. 10: In-cylinder temperature comparison.
Figures 2.11 and 2.12 show the in-cylinder pressures and temperatures during the gas
exchange process. Compared with one-zone model without fluid dynamics, two-zone charge
mixing model shows a significant improvement, and the simulated pressure and temperature
responses match with these provided by GT-Power simulations quite well. On the other hand, the
in-cylinder pressure of one-zone model has a large error with respect to GT-Power simulation,
especially at the beginning of valve opening, but at the end of the intake process it converges to
the accurate value due to the effect of the first-order approximation; the in-cylinder temperature
of one-zone model has significant error during the entire gas exchange process since it was
obtained based upon the in-cylinder pressure, assuming an isentropic process at each time
interval. Moreover, at IVC the temperature does not converge to a reasonable value, leading to
inaccurate trapped mass calculation and SOC prediction.

35

In-cylinder pressure (bar)

10

GT-Power model
Two-zone model
One-zone model

8

6

4

2

0

200

250

300
350
400
Crank position (deg)

450

500

Figure 2. 11: In-cylinder pressure during the gas exchange process.

GT-Power model
One-zone model
Two-zone model

In-cylinder temperature (K)

1400
1200
1000
800
600
400
200

250

300
350
400
Crank position (deg)

450

500

Figure 2. 12: In-cylinder temperature during the gas exchange process.
Table 2.3 compares the simulation results between two-zone and one-zone models under the
same engine operation condition, where GT-Power simulation results are used as the baseline.
Since the temperature obtained in one-zone model is always higher than the unmixed zone
temperature in two-zone model, the SOC prediction is much earlier than that of the two-zone
model. The IMEP is also higher due to the error in intake phase and combustion phase.
36

Table 2. 3: Simulation Results Comparison
Model
GT-Power
Two-zone model
One-zone model (w/ flow dynamics)
One-zone model (w/o flow dynamics)

Fuel
(mg)
13.2
13.2
13.2
13.2

SOC

IMEP

2
2
4
8

4.2
4.22
4.23
4.36

In Figure 2.13 both of the simulated exhaust and intake flow rates obtained from the
two-zone model were compared with these of GT-Power simulations. Again they matched quite
well; on the other hand, the simulation result of one-zone model is not shown here since a first
order transfer function was used to approximate the in-cylinder pressure, the flow rate
calculation is trivial. This indicates the benefit of the proposed charge mixing model. Note that
the error between GT-Power and two-zone model responses are due to the un-modeled pressure
wave in both of the intake and exhaust manifolds; and this dynamics is fairly difficult to model
using a simplified modeling approach for real-time simulations. However, the proposed charge
mixing model does provide good charge flow estimation without pressure wave.

GT-Power model
Two-zone model

Mass flow rate (kg/s)

0.1

0.05

0

-0.05
100

150

200

250
300
350
400
Crank position (deg)

450

Figure 2. 13: Mass flow rate comparison.

37

500

Figure 2.14 shows the charge mixing process during the intake phase. At the beginning of
intake valve open, the total in-cylinder trapped mass is reducing due to the backflow in the first
stage; afterward, the backflow is sucked back to the cylinder and the trapped mass returns to the
level before IVO. Then the third stage begins, fresh charge flows into the cylinder, which causes
the mixed zone expanding and unmixed zone shrinking. At first the mass transfer rate is
relatively slow since the unmixed zone is not been surrounded by the fresh charge thoroughly;
then the transfer rate increases due to the increased intake flow and piston movement; and after
IVC, the unmixed zone continues shrinking tardily, which indicates the effect of piston
movement on mass diffusion is relatively weaker than that of the intake flow.
0.4
Mixed-zone mass
Unmixed-zone mass
Total trapped mass

0.35
0.3

Mass (g)

0.25

stage 1 stage 2

stage 3

0.2
0.15
0.1

SOC

IVC

IVO

0.05
0
-0.05

350

400

450

500
550
600
Crank position (deg)

650

700

Figure 2. 14: Size change of each zone.
Figure 2.15 shows the in-cylinder average temperature, along with temperature in both of
mixed zone and unmixed zone. Obviously, before combustion starts, since the unmixed zone
consists of residual gas, its temperature is higher than that of the mixed zone; hence the average
in-cylinder temperature is a little higher than that of the mixed zone, since the mixed zone

38

occupies most portion of the cylinder volume. After combustion, the temperature in the mixed
zone rises significantly, but there is no combustion occurs in the unmixed zone, which results in
higher temperature in the mixed zone than the average temperature.
1000
500

Average temperature
Unmixed-zone temperature
Mixed-zone temperature

Temperature (K)

0
2500
2000
1500
1000
500
0

-150

-100
-50
0
Crank position (deg)

50

Figure 2. 15: Temperature of each zone.
Figure 2.16 compares in-cylinder pressure of the two-zone model with that of the improved
one-zone model during compression and combustion phases. This improved one-zone model
contains the flow dynamics during the gas exchange phase. Since the in-cylinder pressure is
assumed to be uniformly distributed at any time, the averaged in-cylinder pressure of the
two-zone model is much closed to these of the improved one-zone model. It can be seen that in
the two-zone model the prediction of the SOC in the two-zone model is later than the one-zone
model, and also the peak in-cylinder pressure is lower. This is due to the difference in estimated
in-cylinder temperatures since the one-zone model uses the averaged temperature of two zones to
estimate the SOC while the two-zone model uses the mixed zone temperature that is lower than
the unmixed zone. It can be seen in Figure 2.17 that the Arrhenius integral increases slower for
39

the two-zone model than that for the one-zone model.

In-cylinder pressure (bar)

40

One-zone model
Two-zone model

30
20
10

Error (bar)

0
6
4
2
0
-2

-80

-60

-40

-20
0
20
Crank position

40

60

80

-80

-60

-40

-20

40

60

80

0

20

Figure 2. 16: In-cylinder pressure of two-zone and one-zone models.

Figure 2. 17: In-cylinder temperature of two-zone and one-zone models.
To validate the charge mixing two-zone model over an operating range, additional
simulations were conducted with nine different load conditions at 2000 rpm, where the injected
fuel mass varies between 13.2 mg and 10.8 mg; exhaust valve timing EVO and EVC at 156 and
304, respectively; and intake valve timing IVO and IVC at 382 and 530, respectively. Figure
40

18 compares the IMEP and SOC of the two-zone model with those of GT-Power model, and
shows that two-zone model has good agreement with GT-Power model.
The two-zone HCCI combustion model was then validated using experimental data. The
engine was equipped with intake air heater and without external EGR, and the engine parameters
are listed in Table 1. The associated valve timing for EVO, EVC, IVO and IVC are 146, 294,
392, and 540 after TDC, respectively. Intake air temperature is 330K. Figure 2.19 shows the
in-cylinder pressure and MFB of the two-zone model and experimental results during
combustion phase. Note that the MFB was calibrated based upon the two-piece Wiebe function
(a special case of the three-piece one) using experimental data. The parameters in equations (2.20)
and (2.21) are:   0.79 ,   0.21 , a1  a2  0.61 , 02  6 , m1  2 , m2  1.5 , 1  8 , and

2  22 . It shows that the two-zone model matches experimental result fairly well during

5

15

4

10

SOC, two-zone model

IMEP, two-zone model

combustion process.

3

2

1

0
0

1

2

3

4

5

0

-5

-10
-10

5

IMEP, GT-Power

-5

0

5

10

15

SOC, GT-Power

Figure 2. 18: IMEP and SOC of two-zone model and GT-Power model.

41

In-cylinder pressure (bar)

40
Experiment
Two-zone model
30

20

10

0

-80

-60

-40

-80

-60

-40

-20

0

20

40

60

80

40

60

80

MFB

1
0.5
0

-20
0
20
Crank position (deg)

Figure 2. 19: Experimental comparison of In-cylinder pressure and MFB.
In summary, the charge mixing two-zone model is capable of achieving much more
accurate simulation results than that of the one-zone model due to utilizing the fluid dynamics
analysis. The two-zone charge mixing and combustion model provides the simulation results that
are comparable with these of GT-Power model and experimental results.
2.5

Conclusions
A two-zone charge mixing and HCCI (homogeneous charge compression ignition)

combustion model is proposed in this chapter based upon the simplified fluid dynamics. The
developed model was implemented into the hardware-in-the-loop simulation environment for
model validation. The simulation results of the proposed model match with the GT-Power
simulation and experimental data well, and it is also demonstrated that the discretized fluid
dynamics approach provides a satisfactory simulation results compared with GT-Power model.
This indicates that it is feasible to develop a real-time control-oriented engine model that
provides comparable simulation results to these provided by high fidelity model such as
42

GT-Power. The simulation results also show that the unmixed zone plays an important role in
predicting the start of combustion, in-cylinder pressure and temperature during the combustion
process. It is believed that the two-zone charge mixing and HCCI combustion model provides an
improved simulation platform for developing the real-time HCCI control strategy.

43

CHAPTER 3
LPV MODELING AND MIXED CONSTRAINED H2/H∞ CONTROL OF
AN ELECTRONIC THROTTLE

3.1

Introduction
Electronic throttle replaces the mechanical link between the vehicle acceleration pedal and

engine intake throttle valve plate by accurately regulating the throttle plate position using either a
DC motor or step motor [34] for internal combustion (IC) engines. This process is called
electronic throttle control (ETC). The traditional engine throttle is mechanically connected to the
vehicle acceleration pedal and the engine charge air quantity is controlled by the throttle plate
position directly. The engine fuel quantity tracks the charge air to provide the desired air-to-fuel
ratio, which is critical for engine emission regulation. The advantage of using the ETC for IC
engines is that the engine charge air and fuel can be regulated simultaneously, providing accurate
air-fuel-ratio control, especially under the transient engine operations. The ETC is also a key
enabler for torque based engine control [35], where the acceleration pedal provides the desired
torque and the engine control system determines the desired engine charge air and fuel to meet
the torque requirement. The torque based control is especially important for hybrid powertrains
([36] and [37]), where the IC engine, electric machine(s) and generator(s) are managed by their
torque outputs or loads. In recent years, as the HCCI (homogeneously charge compression
44

ignition) combustion is widely studied, the ETC also plays an important role in the mode
transition control between SI (spark ignition) and HCCI combustion, where the accurate transient
response of the ETC is essential for precise management of cycle-by-cycle charge air, thereby
guaranteeing the stable hybrid mode combustion and smooth engine torque output [38].
A conventional electric throttle consists of a DC (or step) motor, a set of speed reduction
gears, a throttle plate, and a limp-home (LH) spring set that keeps the valve plate at its default
position. The electronic throttle system is highly nonlinear due to the LH spring set, the
rotational static and dynamic friction; the vehicle battery voltage fluctuation due to the vehicle
electrical load variation introduces another degree of variation; in addition, the torque load
introduced by the intake air flow [39] brings additional external disturbance to the electronic
throttle system. In this paper, these nonlinearities and variations are modeled as the measurable
LPV (linear parameter varying) parameters.
Proportional-integral-derivative (PID) control is widely used in powertrain control systems
due to its simplicity ([40] and [41]), and is capable of achieving good performance in large
throttle opening case. However, the high nonlinearities of the ETC prevent the PID control from
achieving the desired performance under certain operation conditions, especially with small
opening near the limp-home position. The other commonly used approach for the electronic
throttle control is sliding mode control, where the nonlinearities of friction and spring forces are
considered as the parameter uncertainty and bounded external disturbance, respectively
([42]-[44]); however, the robust performance cannot be guaranteed, and sometimes the fast
response is achieved with high magnitude of steady state control “chattering”. In [45], a
45

nonlinear feed-forward and feedback controller based on flatness was designed; however,
parameter variations, especially the battery voltage variation, were not considered, leading to a
relatively poor performance under these operational conditions. In [46] a linear position regulator
was designed based upon the identified linear dynamics part of the system, and adaptive control
was applied for the nonlinear time-varying friction and preload torque compensator. To meet the
requirement of optimizing the control system performance over a certain operating range, and
improve the accuracy of linearization of nonlinear system, LPV method was widely used in
control of mechatronic systems [47]-[49] and in ETC system [49][50] in recent years. In [49] a
gain-scheduling PID controller was designed to optimize the performance at each fixed operating
point; and the stability of the closed-loop system was validated using LPV techniques by
transforming the parametric closed-loop system into the LPV form. However, the closed loop
performance is not guaranteed under parameter variations. In [50] a physics-based LPV throttle
model was established to convert the highly nonlinear system into an LPV system, and an H2
static output feedback control was designed to guarantee the system performance; however, due
to the lack of robustness small modeling error could affect the system stability when a high gain
controller was used to improve throttle performance. This motivates the application of the mixed
constrained H 2 / H  LPV gain-scheduling control technique to ETC problem in this paper.
The nonlinear electronic throttle system was modeled as an LPV system in this paper,
where the friction torque and battery voltage are the varying parameters; and the disturbance
torque, induced by the air flow and other sources, was modeled as an exogenous input. A virtual
state was introduced to integrate the tracking error for set-point control to achieve zero
46

steady-state error. A feed-forward control was also used to compensate the preload spring torque
designed for the limp-home operation. A mixed constrained H 2 / H  LPV gain-scheduling
controller was designed based upon the developed LPV model utilizing the LMI (linear matrix
equality) convex optimization scheme, where the H 2 performance was optimized under a loose
H  constraint used to guarantee the robust stability of the closed-loop system under modeling

uncertainties. A hard constraint, in terms of H 2 bound, is also used to guarantee that the control
does not exceed its hardware limit.

All weighting matrices were well-tuned during the control

design and simulation validation process until the satisfactory performance was achieved. The
finalized LPV controller was experimentally validated on a test bench.
This chapter is organized as follows. Section II presents a discrete-time electric throttle
model that is linearized into the desired LPV form; and Sections III and IV describe the LMI
based convex optimization design for the LPV ETC system and weighting matrices tuning
process through simulation, respectively. The associated experimental validation results are
shown in Section V. The last section adds some conclusions.
3.2

System Modeling
An electronic throttle system can be described by the schematic diagram shown below in

Figure 3.1. A DC motor is driven by a controlled voltage Va , which is powered by the battery.
Note that Va  Vbu is often regulated by a PWM (pulse width modulated) duty cycle signal u ,
where the duty cycle is the output of the electronic throttle controller and Vb is the battery
voltage. An H-bridge drive module is used to make it possible to apply the voltage in both
directions, or equivalently, the duty cycle control signal is between -1 and 1. R and L denote
47

the resistance and inductance of the DC motor, respectively. The motor is connected to the
throttle plate shaft by a set of gears, and a pair of return springs that keeps the throttle plate
resting at the default position to enable the limp-home operation when the control input is zero.

Figure 3. 1: An electronic throttle system
Figure 3.2 shows the nonlinear characteristic of the return spring. The magnitude of spring
torque at limp-home position  0 is Ts , and the spring torque at  0 could take any value
between Ts and Ts . Since the developed model in this paper is linear, the parameter denoting
the throttle angle position discussed later is the position relative to  0 .

Figure 3. 2: Nonlinear property of return spring

48

3.2.1 Electronic throttle modeling
The electronic throttle (a mechatronic system) dynamics can be expressed using the
following differential equations

Va  iR  L

di
 Em ,
dt

J

d 2
 Tm  Ts  T f  Td
dt 2

(3.1)

where Va , i, L, and R are the motor voltage, current, inductance and resistance, respectively;

Em  Km is the motor back EMF (electro-magnetic field) voltage, K m is the back EMF
coefficient associated with throttle plate angular velocity; J and  are motor throttle assembly
inertia and throttle angle; and Tm , Ts , T f and Td represent the motor output torque, nonlinear
spring torque, friction torque and other exogenous input torque such as the disturbance torque
due to the unbalanced force, caused by the charge air flow, applied on the throttle plate.
Since the inductance L is relatively small for a DC motor, the inductance dynamics can be
ignored and the motor current can be approximated by setting L  0 . That is

i



1
Va  K m
R



(3.1)

and the motor output torque satisfies

Tm  K ai 



Ka
Va  K m
R



(3.2)

where K a is the motor torque coefficient associated with the torque at the throttle plate.
Finally the throttle system dynamics can be described by the following nonlinear
differential equation.

J 





 

Ka
Vbu  K m  K s  Ts sgn    K B  T f sgn   Td
R
49

(3.3)

where K B and K s represent the viscous friction and spring stiffness coefficients; Ts and T f
represent the spring preload torque used to hold the throttle at the limp-home position and
Coulomb friction torque, respectively. Note that Ts  K s  Ts sgn   and Tf  K B +Tf sgn( ).
Differential equation (3.4) can be represented by the following continuous-time state space
model





x  Ax  Bu    , , y  Cx

(3.4)

where
 0
A   Ks

 J


 0 
, B  
 , x   x1     ,
1  Ka Km
K
V

 x   
 a b
 
 KB 
 2  
J R
 JR 
 
1

0


  , = 1
  Ts sgn    T f sgn   Td
 J







 




 , C  1 0



(3.5a)

(3.6b)

Since the system is of high nonlinearity due to term  , it has quite different dynamic
behaviors (or transfer functions) under different operational conditions. Furthermore, system
parameters are coupled in state space matrices; and it is almost impossible to use the
experimental throttle step and sinusoid response data to determine all system parameters.
Experiments were designed to isolate the throttle system parameters so that the system
parameters can be determined by experiments. The spring preload torque and stiffness were
obtained by measuring the torque at different stationary points; the Coulomb friction was
obtained approximately by moving the throttle plate from the same initial position to opposite
directions through electronic control; and the system inertia and viscous friction were obtained
together by releasing the throttle plate freely from different holding positions, recording
50

correspondent responses, and conducting the simulation studies to find the best match for inertia
and viscous friction. The obtained system parameters are shown in Table 3.1.
Table 3. 1: Electronic throttle parameters
Parameter

Value Parameter

R

2.07

J

Value
0.0035

Ka

0.487

Km

0.4889

KB

0.005

Ks

0.0914

Tf

0.089

Ts

0.3193

3.2.2 Discrete-time LPV model
To design an LPV gain-scheduling controller, the nonlinear system (3.6) needs to be
converted into an LPV one. The entries in matrix  were treated in different ways.
Firstly, the spring preload torque Ts sgn( ) can be compensated by a control signal u0 ( )
as function of 

where

u0 

RTs
sgn  
K aVb

(3.6)

Figure 3. 3: Approximation of sign function
Secondly, as shown in Figure 3.3, T f sgn( ) is approximated by

 

T f sgn  

Tf



   1  T f ,

51

(3.7)

where

Tf



is treated as a term containing varying parameter  1 which is defined below

 T f /  ,

   min

T f /  min ,

else

1  

T f is an uncertain input used to model the error caused by approximation of the sign function.
Note that  max in Figure 3.3 can be experimentally determined by operating the ETC at the full
motor torque and  min is chosen to be small enough to reduce approximation error.
Finally, Td , along with uncertainty T f , forms the system exogenous input w , where

w

1
 Tf  Td 
J

(3.8)

Since the battery voltage varies during operations, Vb can be expressed as

Vb  Vb 1   2 

(3.9)

where  2 is the second varying parameter that is measurable. The following equation defines
the ranges of  1 and  2 .

 1  t   0.0046, 32 ,  2  t    0.417, 0.167

(3.10)

Then the continuous-time state space model can be converted into the following LPV
system

x   Ac +A  1  x  Bc1 1   2  u  Bc 2 w
y  Cc x

(3.11)

where the system matrices in (3.5) can be expressed as a sum of nominal state space matrices Ac ,

Bc1 , Bc 2 , Cc , and varying parameter depended matrices A  1 and Bc1 2 .
There are two approaches to design a discrete-time controller required for microprocessor
based control implementation for a continuous-time plant. One is to design a continuous-time

52

controller and then discretize it and the other is to discretize the plant and design a discrete-time
controller directly. Note that both approaches lead to certain errors when the controller is
implemented in a microprocessor. For this application, the second approach was selected due to
the easy implementation of the designed discrete-time controller and the availability of
discrete-time LPV synthesis method. With the selected small sampling period (1ms) it is
believed that the required accuracy can be achieved for the discrete-time LPV system. The first
order approximation described in [51] was used as follows:

AP

 e Acts  e Acts A  1ts , CP

BPw

 e

Acts

Bc 2ts ,

BP

 Cc ,

 e Acts Bc1 1   2  ts

(3.12)

where ts, equal to 1ms, is the sampling period of the discrete-time system. For convenience,  1
and  2 are assumed to lie in the compact structure   diag  1 ,  2  , and

   diag  1 ,  2  : 0.000115   1  0.8, 0.417   2  0.167

(3.13)

The resulting discrete-time state-space LPV system is in the following form of

xP  k  1  AP   xP  k   BP   u  k   BPw w  k 
yP  k 
 CP xP  k 

(3.14)

3.2.3 LPV uncertainty model
The existence of modeling errors, due to part-to-part production deviations or circumstance
changes (such as temperature and aging), cannot be neglected. For the purpose of enhancing the
robustness of the ETC system, modeling uncertainties should be considered. Note that the state
matrices in the LPV system (3.12) can be expressed as

1 
 0
 0 
Ac  A  1  
, Bc1 1   2   


 A21   A22  
 B2  

53

(3.15)

and let 1 denote the uncertainty on inertia J and  2 denote the uncertainty corresponding to
the friction (including Coulomb and viscous friction), then the continuous-time state matrices of
the LPV system with uncertainties are in the form of

0
1


A    
,
A

1


A

1


1









21
1
22
1
2


0


B    

 B2  1  1  

(3.16)

Based on the LFT (linear fractional transformation) technique [54] with the first-order
approximation, extra inputs and outputs can be appropriately defined to “pull out” the
uncertainty parameters. Choosing z1  x1 , z 2  z 4  x2 , z3  u and w , respectively, and
discretizing the system using the same first order approximation method as in (3.13) results in a
discrete-time system in the LFT form:

 xP  k  1  AP   xP  k   BP   u  k   BP   w  k 

 z  k 
 w  k 
where w   w1 , w 2 , w3 , w 4  ,
T

z   z1 , z 2 , z3 , z 4 

T

(3.17)

and   diag 1 , 1 , 1 ,  2  . The
T

detailed procedure of LFT is omitted here.
3.2.4 Set-point control
In order to achieve zero steady-state regulation error, a third state was added to the electric
throttle model in the discrete-time form：

xI  k  1  xI  k   ts r  k   ts x1  k 

(3.18)

where r denotes the reference signal. Since the throttle position can be measured directly, xI
can be obtained by integrating the tracking error online, and it is available for the state feedback.

54

3.2.5 Reduced order observer
Since the angular velocity, the second state (x2), cannot be measured directly, an observer is
required for output feedback control. A reduced order observer below was designed based upon
the method described in [55] to estimate x2:
xO  k  1   AP 22  k   LAP12  k   xO  k   BP 2  k  u  k 
  AP 21  k   LAP11  k   LAP 22  k   L2 AP12  k   x1  k 

(3.19)

xˆ2  k   xO  k   Lx1  k 

where APij is the (i,j)th element of system matrix Ap in (3.13). Let

AO1  k  :  AP 22  k   LAP12  k  
AO 2  k  :  AP 21  k   LAP11  k   LAP 22  k   L2 AP12  k  

and the reduced observer can be rewritten as

xO  k  1  AO1  k  xO  k   AO 2  k  x1  k   BP 2  k  u  k 

(3.20)

The observer gain was chosen by pole placement to guarantee that the estimation converges
faster than the system response.
3.3

LPV Control Design

3.3.1 Augmented LPV system
0 shows the closed-loop discrete-time system architecture, where plant P is the resulting

discrete-time state space model described in (15) and (18) with the third state x3  xI added for
the set-point control; K is the closed-loop LPV controller to be designed.

The control input of

the system is a summation of feedback control u (from LPV controller K) and the feed-forward
control u0 (used to compensate the spring preload torque). Since u0 can be obtained directly by

55

(3.7) with known (measured) battery voltage, and will only change sign when crossing the
limp-home position, it will be ignored during the closed-loop control design process and
compensated with a feed-forward control.

For the LPV control design, since the system is

linear, the reference signal can be set to zero for control design. System nominal performance is
addressed by minimizing the weighted H 2 norm of outputs (tracking error z1 and integral of
tracking error z2 ), subject to control input H 2 constraint, to have the balanced performance
between small tracking error and fast response. This problem is a deterministic ICC (input
covariance constraint) problem defined in [53], where LMI convex optimization approach can be
used. Weighting functions We and WI are selected as design constants and were tuned during the
control design and experimental validation process for the best performance possible.

Figure 3. 4: Closed loop system block diagram
Robust stability is considered by investigating the LFT structure with extra inputs and
outputs shown in the upper part of Figure 3.4. Since H  controllers is capable of providing
robust stability margins that H 2 controllers cannot [54], a predetermined bound on the H 

56

norm of the closed-loop transfer function from input w to output z was imposed.
Finally, the augmented discrete-time LPV systems  2 ( ) and   ( ) can be constructed:

 2 ( ) :

 x  k  1   A   Bw   Bu   

 
  x k  
0
D2  

 u k     0
w  k 

 z  k    C1
0
0 

 
  u  k  
0
0  
 y  k    C2

(3.21a)

  ( ) :

 x  k  1   A   B   Bu    x  k  

 


Dw
Du   w  k 
 z  k     C
 y  k    C2
0
0   u  k  

(3.22b)

where x  k    xTp  k  xIT  k  xOT  k  
T

4

, the performance output z  k    z1  k  z2  k  
T

measurement for control y  k    yP  k  , yI  k  , yD  k  
T

3

2

and the

. Note that u denotes control inputs

subject to certain constraints. For this application with single input,
to one and u  u . w and output z are defined in (18).

D2 is a scalar that was set

The state space matrices are

0
0 

 BP   
 BPw   
 AP  
0
0 





A   
, Bw     0  , Bu     0  ,
 ts
0 
0 1
 BP 2   
 0 


A

A

0
0




O1
 O2

 1 0 0 0 
 We 0 0 0 
C1

, C2   L 0 0 1  , D2  1,

 0 0 WI 0 
 0 0 1 0 
1 0 0 
0 
0 1 0 
0 
 B   


 .
B     P
,
C

,
D

0,
D


w
u

0 0 0
1 
 0 


 
0 1 0 
0 

(3.22)

In the next subsection, the varying parameter compact set  will be expressed in a
polytope structure, where the vertices of the polytope and the time-varying parameter rate of
change will be defined. The system model will be put into a form applicable for the LMI convex

57

optimization.
3.3.2 Mixed constrained H 2 H  control synthesis
For the augmented system (3.22), the goal is to design a static output feedback LPV
gain-scheduling controller, u  k   K   y  k  , that minimizes the upper bound of the H 2
norm from w  k  to z  k  over any trajectories of   k   for closed-loop LPV system  2
subject to the constraint on the H 2 norm from w  k  to u  k  , and at the same time, H 
norm constraint  from w to z for closed-loop LPV system   to guarantee the robust
stability against the uncertain constraint 



  1 .

Figure 3. 5: Parameter space polytope
The state space model (22) was converted into a discrete-time polytopic time-varying
system by expressing state space matrices containing varying parameters ( A   and B   ) at
the vertices of the parameter space polytope, as shown in Figure 3.5. Any system inside the
polytope is represented by a convex combination of the vertex systems as weighted by the vector

  k  of the barycentric coordinates, and formula for computing the barycentric coordinates is
available in [56]. The discrete-time polytopic time-varying system is given by

58

 x  k  1   A    k   Bw    k   Bu    k   
  x k  

 
u
k
0
0


D




2
2 : 
w  k 



 z k  
C1
0
0
 u k  

 


0
0
 y  k    C2


(3.23a)

 x k  
 x  k  1   A    k   B    k   Bu    k    

 : 
  w  k  

Dw
Du
  u k 
 z  k    C
  

(3.24b)

where the system matrices

B    k   

44

A  k  

44

,

Bw    k   

41

Bu    k   

,

41

and

belong to the following polytope


  A, Bw , Bu , B    k   :









A, Bw , Bu , B    k     i  k   Ai , Bw,i , Bu ,i , B,i i ,   k    
i 1




N

(3.24)

where Ai , Bw,i , Bu ,i and B ,i are vertices of the polytope with N  4 in this case, and   k 
is a vector in the barycentric coordinates which belongs to the unit simplex


   



,N


N

N

:   i  1,  i  0, i  1,
i 1

(3.25)

The rate of variation of   k  can be defined as

i  k   i 1  k   i  k  , i  1,

,N

(3.26a)

which is bounded by

b  i  k   b, i  1,

,N

(3.27b)

where b   0,1 . In this paper, b was selected to be 0.1 to cover the worst operational condition.
Note that the uncertainty domain, where the vector
be modeled by the compact set

59

   k  ,   k 
i

T



2N

assumes values, can


b   

N


i 1

2N

 f j
:   co  g 1 ,..., g M  , g j   j  , f j 
h 

N

, hj 

N

,
(3.27)


fi j  1 with fi j  0, i  1,..., N ,  hi j  0, j  1,..., M 
i 1

N

Then using   k    M ,
 f j
 k 
j  j
j 1  h 
M

   k  , i  k     
T

(3.28)

Before introducing the mixed H 2 H  LPV control problem, the constrained H 2 and

H  LPV control problems are to be discussed, respectively. Note that the LMIs of the standard
H 2 LPV for discrete-time systems was introduced in Theorem 9 of [57]; and the LMI conditions
for the constrained H 2 problem (also called the input covariance constraint problem) were
given for discrete-time LTI systems in [53]. Theorem 1 below provides the LMIs for the
constrained H 2 LPV systems. Note that the input covariance constraint matrix U is now part
of the LMIs stated in equations (3.32) and (3.33). The proof of Theorem 1 is provided in
Appendix.
Theorem 1. Consider system  2 , given U , if there exists, for i = 1, ... , N, matrices Gi 
and Zi 

14

, and symmetric positive-definite matrices P2,i 

44

and Wi 

44

44

such that

the following LMIs hold

  N  fi j  hi j  P2,i
 i 1
 G T AT  Z T B T
j u, j
 j j
T

Bw, j


*
G j  G Tj   i 1 fi j P2,i
N

0

for j = 1, ... , M;

60

*

*   j  0

I


(3.29)

  N  fi j  fi l  hi j  hil  P2,i
i 1

T T
G j Al  GlT ATj  Z Tj BuT,l  ZlT BuT, j

BwT , j  BwT ,l


*
 22, jl
0

*

*    jl  0

2I 


(3.30)

where
22, jl  G j  G Tj  Gl  GlT  i 1  fi j  fi l  P2,i
N

for j = 1, ... , M-1, and l = j+1, ... , M;
 N fi jU
 i 1
 Z T DT
 i 2,i


  j 0
N
T
j
Gi  Gi   i 1 fi P2,i 
*

(3.31)

for j= 1, ... , M;
 N  fi j  fi l U
 i 1
 ZiT D2,T j  Z Tj D2,Ti

* 
   jl  0
 22, jl 

(3.32)

where
 22, jl  G j  G Tj  Gl  GlT  i 1  fi j  fi l  P2,i
N

for j = 1, ... , M-1, and l = j+1, ... , M;
Wi  C1P2,iC1T  0, i  1,

,N ,

(3.33)

with
N

N

i 1

i 1

G j   fi j Gi , Z j   fi j Zi
then the state feedback controller
1
K    k    Zˆ    k   Gˆ    k  

where

61

(3.34)

N

N

i 1

i 1

Gˆ    k     i  k Gi , Zˆ    k     i  k Zi

(3.35)

stabilizes system  2 with a guaranteed H 2 performance  given by

2 

min

P ,i , P2,i Gi , Zi ,Wi

max trace Wi   trace  C1P2C1T 

(3.36)

i

and also satisfies the input constraint

U  D2 KP2 K T D2T  D2 KP2 K T D2T  U

(3.37)
□

Proof of Theorem 1: LMIs (3.30) and (3.31) follow Theorem 9 of [57]. Define

Acl  k   A  k   Bu  k  K  k  , and let P2  k  denote the closed-loop controllability Gramian,
then

P  k  satisfies

P2  k  1  Acl  k  P2  k  Acl  k   Bw  k  Bw  k  , P2  0   0
T

T

Since equations (3.30) and (3.31) imply that

P2  k  1  Acl  k  P2  k  Acl  k   Bw  k  Bw  k 
T

T

there exists a matrice M  k   M  k   0 such that
T

P2  k  1  Acl  k  P2  k  Acl  k   Bw  k  Bw  k   M  k 
T

T

Consequently, P2  k   P2  k  for all k  0 . Then for any   k    M , multiply (3.32) by  2j
and sum for

j  1,..., M and multiply (3.33) by  j l and sum for j  1,..., M  1 and

l  j  1,..., M . Adding the two resulting expressions to obtain

62

   j 1  2j  j   j 1

M 1

M


U

T
 Z    D2T




M
l  j 1

 j l  jl
*

G     G      j 1  j
M

T


U

T
T
 Z    k   D2



N
i 1

f i j P2,i









0
T
G    k    G    k    P2    k   
*

Multiply  by I  D2 K    k   on the left and by its transpose on the right yielding
U  D2 K    k   P2    k   K    k   D2T  0  U  D2 KP2 K T D2T  D2 KP2 K T D2T  U
T

Similarly, from (3.34) it can be shown that

Wi  C1P2,iC1T  C1P2C1T , for all i  1,

,N

Therefore,

2 

min

P ,i , P2,i Gi , Zi ,Wi

max trace Wi   trace  C1P2C1T  .
i

□
Note that equations (3.30) and (3.31) address the stability issue; equations (3.32) and (3.33)
apply the input constraint to the system; and equation (3.34) gives the condition corresponding to

H 2 performance.
For the

H  LPV control problem, consider system   . Based on Theorem 8 of [57], if

there exists, for i = 1, ... , N, symmetric positive-definite matrices P,i 

33

such that the

following LMIs hold

  N  fi j  hi j  P ,i
 i 1
 G T AT  Z T B T
j
j
j u, j

T

B , j

0


*

*

G j  G Tj   i 1 f i j P ,i

*

0

I

C , j G j  Du , j Z j

Dw, j

N

63

*

*  0

j
*

 I 

(3.38)

for j = 1, ... , M, and

  N  fi j  fi l  hi j  hil  P ,i
 i 1

21, jl

T
B , j  BT ,l


0


*

*

22, jl

*

0

2 I

42, jl

Dw, j  Dw,l

* 

* 
   jl  0
* 
2 I 

(3.39)

for j = 1, ... , M-1, and l = j+1, ... , M , where

21, jl  G Tj AlT  GlT ATj  Z Tj BuT,l  Z lT BuT, j
22, jl  G j  G Tj  Gl  GlT   i 1  fi j  fi l  P,i
N

42, jl  C, j Gl  C,l G j  Du , j Z l  Du ,l Z j
then the static output feedback controller K    k   given by (35) also stabilizes the system 

  with a guaranteed H  performance from w to z bounded by  .
Mixed constrained H 2 H  LPV control design problem:
For both systems  2 and   find an optimal LPV (gain-scheduling) controller, defined
in (3.36), that minimizes the H 2 performance  , defined in (3.37), with the given input
(control) covariance bound U for system  2 and H  norm bound  for system  
subject to the LMI conditions (3.30)-(3.34) and (3.38)-(3.39).
□
The LMI convex optimization approach can be used to solve the above LPV
gain-scheduling control problem. That is also reported in [58]-[60].
The resulting closed-loop system with the LPV optimal control is robustly stable for





  1 , where  is the system modeling uncertainty defined in (3.18); and assuming   0

the system H 2 performance defined in (3.37) is minimized with satisfactory constraint on the

64

control covariance defined in (3.38).
Note that the maximum singular value of U in (3.36) provides an upper bound for the
control covariance matrix of the closed-loop system, which can be interpreted as an upper bound
of the system l2 to l gain from w to control input u, that is,
u

2


sup uT (t )u(t )   (U )  w 2

2

t 0

due to the system l2 to l gain; see [52], where  () denotes the maximum singular valve.
Therefore, the l norm of control signal u(t) is bounded by  (U )

1

2

for any l2 disturbance

input w with its norm less than or equal to 1, which provides a method of designing LPV
controllers with hard constraints on control inputs by selecting a proper U .
3.4

Weighting Matrices Tuning
All weighting matrices were tuned during the control design and simulation validation

phase. We and WI, defined in Figure 3.4, are weighting matrices corresponding to performance
outputs z1 and z2 ，which are tracking error and integral of tracking error, respectively. Under
an l2 bounded exogenous input w assumption with its l2 norm bounded by 1, the l norm of
outputs z1 and z2 are bounded by the diagonal elements of Wi defined in (3.37) due to the
system l2 to l gain. Tuning We and WI leads to changing the penalty levels of the peak values
of tracking error and error integral (their l gains), which could result in different tracking
performance, such as overshoot, rise time and settling time, etc. Table II shows a sequence of
controllers with different weighting matrices. Controllers 1 to 3 were designed to find a balance
between We and WI for achieving fast response without overshoot; controllers 4 to 6 were the
results of relaxing the control constraint to obtain high control gain, leading to fast response. The
65

constraint  on the system H  norm, defined in (3.39) and (3.40) is 250. Note that controllers
were also designed with the same weighting matrices and the H  norm bound as these used for
controller 6 but with more relaxed control constraint U , however the closed-loop system
response was similar to that of controller 6. This is mainly due to the fact that as the control gain
reaches certain point, the H  norm constraint becomes active, which prevents the control gain
from increasing, and the result is illustrated at the end of this section. As a result, controller 6
shows the most satisfactory performance and was experimentally validated later on.
Table 3. 2: Weighting matrices tuning
We
2.5
2.5
2.5
2.5
2.5
2.5

Controller
1
2
3
4
5
6

WI
2.0
1.0
0.6
0.7
0.8
0.8

U

2
2
2
5
10
25

Throttle angle (deg)

100
80
Reference
Controller 1
Controller 2
Controller 3
Controller 4
Controller 5
Controller 6

60
40
20
0

0

0.2

0.4
Time (s)

0.6

0.8

Figure 3. 6: Simulation results
Figure 3.7 shows the relationship between the input constraint U and the achieved H 2
performance  , where  is the minimum value given by (3.35) corresponding to the maximum

66

achievable performance under each given input constraint U . An H 2 control without
considering H  performance bound  (   ) is also plotted for comparison. As the input
constraint increases (physically larger control effort), improved H 2 performance can be
achieved. Note that when the input constraint is small, the performance curve of H 2 control and
mixed control overlaps each other; this is because within this range, the H  norm constraint is
not active. On the other hand, when input constraint is large, the resulting controller have
relatively high control gain, which makes the system robust stability sensitive to the uncertainties.
Therefore, the H  bound  becomes active which prevents the LPV control from improving
its H 2 performance. In fact, the performance could become worse in practice due to unmodeled
uncertainty. This demonstrates that the mixed constrained H 2 H  is able to provide a good
balance between the robust stability and performance.

2

H2 control
Mixed H2/Hinf control

1.8

1.6

ν

H∞ bound activated

1.4

1.2

1

0

10

20

U

30

40

50

Figure 3. 7: Relationship between input constraint and performance
3.5

Experimental Validation
The finalized controller was then implemented into the MSU Opal-RT based prototype

controller with a sampling time ts = 1ms. The controller provides both PWM signal reference and

67

sign control signals to an H-bridge driver used to control the electronic throttle DC motor, see
Figure 3.8 for the test bench setup.

Figure 3. 8: Test bench setup
Firstly, three typical cases were investigated: large opening, crossing limp-home, and small
opening operations, and the corresponding responses are shown in Figure 3.9 to 3.12. In general,
to guarantee the vehicle’s acceleration performance with reduced time delay between
acceleration pedal position and throttle position, the settling time of the ETC system should be as
short as possible. For example, during the SI and HCCI mode transition, it requires that the
throttle plate opens from a small angle to widely-open within a few engine cycles, which is less
than 0.2 second; furthermore, in order to control the charge air precisely, the throttle
displacement needs to track a desired trajectory. Figure 3.9 and 10 show that for both opening
and closing against a small angle and a large angle, the settling timing of the ETC system is
within 0.1 second, which shows satisfactory performance. Simulation results are also plotted in
Figure 3.9 and 10 for comparison purpose, and show a good match with the experimental results;

68

the tiny differences at the beginning and the end of the tracking could be due to unmodeled static

Throttle angle (deg)

friction and state estimation error.
80
60
Reference
Experiment
Simulation

40
20
0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

100
Experiment
Simulation

u (%)

50
0
-50
0

0.1

0.2

0.3

0.4
0.5
Time (s)

0.6

0.7

0.8

Throttle angle (deg)

Figure 3. 9: Large opening case - rising
80

Reference
Experiment
Simulation

60
40
20
0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

100
Experiment
Simulation

u (%)

50
0
-50
-100
0

0.1

0.2

0.3

0.4
0.5
Time (s)

0.6

0.7

0.8

Figure 3. 10: Large opening case - falling
Figure 3.11 shows the system responses in case of crossing limp-home. Due to the effect of
dual return springs, when the throttle plate crosses the LH position during the opening or closing
operation, the DC motor has to overcome the preload torque in either direction, respectively.
Thus any conventional linear controller without feed-forward control compensation (such as
69

fixed gain PID controller) will stop at the LH position for a while, leading to extended settling
time. However, since a parameter-dependent feed-forward control u0 was designed in the
proposed control strategy to compensate the preload torque, the experiment result shows clearly
that the throttle plate could cross the LH position fairly smoothly in both opening and closing
cases; see Figure 3.11. An averaged tracking trajectory of 25 repeated cycles was also plotted in
Figure 3.11 to reduce the sensor noise effect in the large scale.

Throttle angle (s)

12
10

LH

8

Reference

6

Single tracking

4
2

Average tracking
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Throttle angle (s)

12
Reference

10

Single tracking

LH

8

Average tracking

6
4
2
1.2

1.3

1.4

1.5

1.6
1.7
Time (s)

1.8

1.9

2

Figure 3. 11: Crossing limp-home case
When the throttle plate opens with a small angle, the engine is operated under a fairly low
load. Manifold pressure is quite sensitive to the throttle angle within this operation range. Since
the throttle position highly affects the engine combustion property, it is essential to control the
throttle plate position accurately with fast response. Figure 3.12 shows a good performance with
a small tracking angle between 4°and 6°, the 2% settling time is about 0.15s with no
overshoot. The overlay of the single tracking trajectory under the 25-cycle averaged tracking also
demonstrates that the response is repeatable. In the following paragraphs the proposed LPV

70

Throttle angle (deg)

Throttle angle (deg)

controller is compared with some commonly used controllers.
7
6
Reference

5

Single tracking

4
3

Average tracking
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

7
Reference
Single tracking
Average tracking

6
5
4
3
1.2

1.3

1.4

1.5

1.6
1.7
Time (s)

1.8

1.9

2

Figure 3. 12: Small opening case
Figure 3.13 compares the LPV controller with a well-tuned (fast response with no overshoot
in a wide operation range) fixed gain PID controller. Note that the same reduced-order observer
defined in (21) was used to estimate x2 (  ) and used for derivative control in the PID controller
to have a fair comparison. This PID controller is able to achieve quite similar performance as the
LPV controller for the large opening case; however, for the small opening case it shows its
weakness and its settling time is twice longer than that of the LPV controller. As shown in
Figure 3.13, at the beginning of the rising period, these two controllers act almost the same;
while approaching the target position, the response of the PID controller slows down
significantly. The main reason is that Coulomb friction becomes significant under small angular
velocity. The fixed gain PID controller cannot compensate this variation while the LPV
controller takes the friction into consideration (modeled as a velocity dependent parameter) and
the control gain is adjusted as a function of velocity.

71

Throttle angle (deg)

7
6
5

Reference
LPV controller

4
3

Fixed gain PID controller
0

0.1

0.2

0.3

0.4
0.5
Time (s)

0.6

0.7

0.8

Figure 3. 13: Comparison with fixed gain PID controller
The other widely used control strategy is sliding mode control [42]-[43].

Here an

anti-chattering type of sliding mode controller with integral control was used for comparison as
follows.

u

1 
 s 
A21 x1  A22 x2  0e1  1e2  r     s at   

B2 
  

(41)

where the sliding surface is s  0e0  1e1  e2 with e0   e1dt , e1  x1  r , and e2  x2  r ; the
sub-index (i,j) is associated with the (i,j) element of matrix A or B in 3.6(a); and  is the upper
bound of the nonlinear term. Note that the saturation function was used to replace the sign
function sgn( s) to reduce steady state chattering. Since there is a trade-off between
convergence speed and the chattering phenomenon, a sequence of sliding mode controllers with
different parameters were tested, as listed in Table III. The performance was also compared
based upon the integral of the absolute tracking error between 4°and 6°; the last column of the
table shows the maximal chattering magnitude of control signal u at steady state, due to the
chattering phenomenon and sensor noise. It can be seen that the sliding mode control is capable
of achieving better performance than the proposed LPV controller (sliding mode controller 2),
but the control signal chatters severely at the steady state, which wastes a lot of control energy
and could damage the mechanical system quickly; on the other hand, if the control is “soft” with
72

a small chattering (sliding mode controller 4), the tracking response becomes really slow.
Table 3. 3: Controller Performance Comparison
Controller

λ1

β

ε

 e dt

max u

Sliding mode controller 1
Sliding mode controller 2
Sliding mode controller 3
Sliding mode controller 4
Sliding mode controller 5
LPV controller

50
50
100
50
50

1000
2000
1000
1000
1000

2
2
2
3
1

0.082
0.048
0.054
0.174
0.061
0.052

0.25
0.8
0.5
0.15
0.65
0.25

Sliding mode controller 1 provides the best balance between control energy and
performance, thus it was selected to compare with the LPV controller in Figure 3.14. In order to
observe the control signal, single tracking data was plotted instead of average data. It is obvious
that with the similar control chattering magnitude, sliding mode controller provides slower

Throttle angle (deg)

tracking response than that of the LPV controller.
7
6
Reference

5

LPV controller

4
3

Sliding mode controller
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

100

u (%)

LPV controller
50

Sliding mode controller

0
-50

0

0.1

0.2

0.3

0.4
0.5
Time (s)

0.6

0.7

0.8

Figure 3. 14: Comparison with sliding mode controller
Finally, the robust performance of the throttle operation under battery voltage disturbance
was studied. It is assumed that a stabilized throttle position is interrupted with a sudden vehicle

73

battery voltage change. For instance, this could happen during the engine crank start-up process.
The performance of the LPV controller is compared with that of fixed gain PID controller with
and without the feed-forward parameter dependent control u0 in (7). Both battery voltage
dropping and recovery cases were studied. Figure 3.15 shows the system responses when the
battery voltage drops from 13V down to 7V within 10ms and remains at that level; the tracking
error of the PID control without u0 is about 1.5 degrees and it recovers within 0.8 second, while
the fluctuation of throttle position is about 0.2 degree under PID control with u0 , and about 0.1
degree under LPV control. Figure 3.16 shows the case when the battery voltage recovers to its
normal level. The tracking error of the PID control without u0 is about 2.4 degrees and it
recovers within 0.6 second, while the fluctuation of throttle position is about 0.4 degree under
PID control with u0 , and about 0.1 degree under LPV control. Firstly, these results show the
essential effect of the battery voltage depended u0 in compensating the spring preload torque
under any battery voltage condition. For the PID control without u0 , when the battery voltage
changes, motor torque driven by the PID closed loop control cannot provide equivalent torque to
compensate the spring preload torque, leading to a sudden tracking deviation which requires the
integral term of the PID controller to compensate it gradually. This could be observed from the
plot of control u, which changes immediately as battery voltage changes in the LPV controller,
while it changes gradually for the PID controller. Secondly, due to the system modeling
uncertainty u0 might not fully compensate the preload torque; it could be seen that under the
same u0 , the response of the LPV controller is still more robust than that of the PID controller.
The reason is that LPV gain-scheduling controller adjusts its control gains as a function of the
74

battery voltage since battery voltage is one of the varying parameters. In this case, the control
gains increase as the battery voltage drops. Combining both effects, the LPV controller provides

Battery voltage (V) Throttle angle (deg)

the best performance.

10
PID w/o u0
PID w/ u0
LPV controller

9
8
0

0.2

0.4

0.6

0.8

1

0

0.2

0.4

0.6

0.8

1

15
10
5

u (%)

40
PID w/o u0
PID w/ u0
LPV controller

20
0

0

0.2

0.4

0.6

0.8

1

Time (s)

Battery voltage (V) Throttle angle (deg)

Figure 3. 15: Battery voltage drop case
13
PID w/o u0
PID w/ u0
LPV controller

12
11
10
0

0.2

0.4

0.6

0.8

1

0.2

0.4

0.6

0.8

1

15
10
5

0

u (%)

40
PID w/o u0
PID w/ u0
LPV controller

20
0

0

0.2

0.4

0.6

0.8

Time (s)

Figure 3. 16: Battery voltage recovery case
75

1

3.6

Conclusions
In this chapter a discrete-time gain-scheduling mixed constrained H 2 H  controller was

designed for an electronic throttle system based upon the LMI (linear matrix inequality) convex
optimization scheme. To enable model-based control gain tuning, a sequence of the LPV
controllers were designed with control effort from low to high by varying the H 2 constrain on
control input and the designed controllers were evaluated through both simulation studies and
experiment validation. The controller associated with the best performance was chosen for
experimental validation and used for performance comparison with the conventional fixed gain
PID (proportional-integral-derivative) and sliding mode controllers. The experimental results
show significant tracking performance improvement of the LPV controller over the PID one,
where the 2% settling time was reduced from 0.3 second (PID) down to 0.15 second (LPV). The
LPV control also demonstrated superior performance under battery voltage variation with
throttle plat held constant under 7 volts battery voltage step change.

76

CHAPTER 4
MODEL-BASED CONTROL FOR MODE TRANSITION BETWEEN SI
AND HCCI COMBUSTION

4.1

Introduction
Due to the significant thermal and charge mixture differences between the HCCI and SI

combustion, it is fairly challenging to achieve smooth mode transition between the SI and HCCI
combustion. Note that the un-throttled HCCI combustion reduces pumping loss with relatively
high in-cylinder temperature at intake valve closing (IVC) required by auto-ignition of HCCI
combustion; while the SI combustion requires to be operated in a throttled mode with relatively
low manifold pressure and temperature, especially around the combustion mode transition region.
In [12] an experimental investigation on SI-HCCI-SI mode transition using hydraulic two-stage
profile camshafts was performed, where the valve timing, one-step throttle opening timing, and
fuel mass were optimized. However, considerable engine torque fluctuation during the
combustion mode transition was observed. In [13] a state feedback controller was designed based
on a state-space model obtained from system identification, fuel mass and negative valve overlap
(NVO) were used as the control inputs to track the desired IMEP and combustion phasing. This
model-based controller reduces torque fluctuation over the traditional PI (proportional and
integral) controller, but engine torque output still varies unexpectedly, especially at the beginning
of the mode transition. In [66] a control-oriented combustion model was linearized around the
77

steady-state SI and HCCI operational conditions, and a controller, composed of state-feedback
and model-based feed-forward components, was used to control the fuel injection timing to track
the desired combustion phasing without considering the hybrid mode combustion that starts with
SI and ends with HCCI combustion. In [67] a model-based linear quadratic tracking strategy was
used to track a desired manifold pressure to guarantee a reasonable air-to-fuel ratio and the fuel
mass was controlled by using the iterative learning to maintain the torque at the desired level and
the proposed control strategy was validated only in HIL (hardware-in-the-loop) simulations.
Since the engine MAP was controlled based on the linearized intake dynamic model, which
could lead to significant transition-by-transition variations. This could adversely affect the
combustion stability during the mode transition.
In this chapter a model-based control strategy was developed to achieve smooth SI-HCCI
combustion mode transition. The control strategy mainly consists of three parts: open-loop
scheduled control, manifold pressure control for regulating charge air and fuel mass control for
managing engine output torque. The valve lift, valve timing and spark timing are open-loop
scheduled. By considering the filling dynamics of the intake manifold, a feed-forward control for
the predetermined desired cycle-by-cycle throttle position was developed and an LPV
closed-loop throttle position control strategy [50] was implemented to track the desired MAP
(manifold air pressure) profile during the combustion mode transition. For the NMEP (net mean
effective pressure) control, iterative learning approach was used to obtain the fuel mass at each
transition cycle to maintain the engine NMEP at the desired level under any transition point;
sensitivity-based feed-forward control was designed to compensate the potential NMEP
78

fluctuation due to the transition-by-transition variation (such as MAP variation). The developed
control strategy was validated in a single-cylinder HCCI capable SI engine at four different
transitional engine operational conditions.
This chapter is organized as follows. Section 4.2 describes the combustion mode transition
control problem and provides a general control framework; based on the engine model described
in Sections 4.3, manifold pressure control, fuel and NMEP control were presented in Sections 4.4
and 4.5, respectively. The associated experimental validation results are provided in Section 4.6.
The last section adds some conclusions.
4.2

Mode Transition Control Problem

4.2.1 Engine configuration
As shown in Figure 4.1, the HCCI capable SI engine used for developing and validating the
combustion mode transition strategy is a single cylinder engine equipped with EVVT systems for
both intake and exhaust camshafts, dual-lift valve-train, and electronic throttle control (ETC)
system. The LPV control strategy was used for precise and fast throttle position control [50]; and
an OCC (output covariance constraint) controller [8] was used to accurately regulate the intake
and exhaust valve timings. The intake air is heated by engine coolant through a heat exchange to
around 350 K before entering the intake manifold to stabilize the HCCI combustion and extend
the lean combustion limit. The engine was equipped with the in-cylinder pressure sensor to make
it possible to calculate combustion characteristics such as NMEP and CA50 (crank position
where 50% trapped fuel is burned). Table 4.1 lists the engine specifications.

79

Figure 4. 1: Engine setup
Table 4. 1: Engine Specifications
Parameter
bore/stroke/con-rod length
compression ratio
Intake air temperature
Intake/exhaust valve lifts-high
intake valve opening duration-high
exhaust valve opening duration-high
Intake/exhaust valve lifts-low
intake valve opening duration-low
exhaust valve opening duration-low

Model value
86mm/86mm/151mm
12.7:1
350K
8.8 mm
252 crank degree
252 crank degree
4.4 mm
148 crank degree
148 crank degree

4.2.2 EVVT and NVO
SI and HCCI combustion requires quite different in-cylinder thermo-condition and charge
mixture property. For instance, the engine is normally operated under mediate or low load when
the mode transition is required between SI and HCCI combustion; see Figure 1.1. For example,
during the mode transition from SI to HCCI combustion, before the transition the intake
manifold pressure is relatively low due to throttled SI combustion and the engine is operated

80

under stoichiometric air-to-fuel ratio (AFR) required by the aftertreatment system; and after the
transition the HCCI combustion is normally operated under a widely opened throttle with a
relatively lean AFR and high exhaust-gas-recirculation (EGR), where the NVO is also utilized to
trap a desired amount of the hot residual gas to manage the in-cylinder temperature at IVC,
leading to high percentage of EGR. Managing the thermal-condition and charge-mixture
property during the mode transition is the key for a smooth mode transition.
Figure 4.2 shows the cam profile with EVVT and dual-lift valve system. The dark solid
curves show the cam profile in high valve lift, the dark dashed curves show the cam profile in
low valve lift at the original position, and the grey solid curves show the phased cam profile in
low valve lift for the required HCCI combustion. Both camshafts are able to phase 80 in crank
angle.
9
8

Exhaust valve

Intake valve

7

Valve lift (mm)

Lift switch
6

Phasing

Phasing

5
4
3
2
1
0
100

150

200

250

300
350
400
Crank angle (deg)

450

500

550

600

Figure 4. 2: Combustion performance with different pilot injection timing
One of the advantages of the EVVT system is that its operational performance is
81

independent of engine operating conditions such as engine oil temperature and pressure [8].
Hence with the fixed control system and driven actuator, the cycle-by-cycle performance of the
EVVT can be easily determined, which is essential for EGR estimation, MAP and air-to-fuel
ratio control strategy development. Figure 4.3 shows the in-cylinder pressure trace during the
recompression phase (due to the NVO) under different cam phases of the EVVT at 2000 rpm. It
took eight cycles for the cams to phase to the desired position for the HCCI combustion from its
default SI location, and the internal EGR rate kept increasing which is reflected by the
recompression pressure peaks.

In-cylinder pressure
Exhaust valve lift
Intake valve lift

10

8

6
8
4

nsit
iona
l cy

6

cle

7
5

2

4

0

2
100

150

200

250

300

350
400
Crank angle (deg)

450

Tra

3
1
500

550

Figure 4. 3: EVVT action and in-cylinder recompression
4.2.3 Hybrid combustion mode
Theoretically, the HCCI combustion is initiated by auto-ignition; while the SI combustion is
spark ignited without auto-ignition during the entire combustion process. However, there exists

82

another type of combustion that is a combination of SI and HCCI combustion, called hybrid
combustion. Under this combustion mode, the combustion is initiated by the spark in the SI
combustion mode and when the gas-mixture in the unburned zone satisfies the condition for
auto-ignition, the HCCI combustion continuous in the unburned zone. This can be illustrated by
the mass fraction burned (MFB) curve shown in Figure 4.4. Ignited by the spark, the hybrid
combustion starts in the SI mode with a relatively slow heat release rate (see the solid curve
between two circles); once the thermo condition of the auto-ignition in the unburned zone is
satisfied, the combustion continues in HCCI mode with a relatively fast heat release rate (see the
solid curve after the second circle). Hence the hybrid combustion mode is also called spark
assisted HCCI combustion.

Mass fraction burned

1
0.8

SI combustion mode
HCCI combustion mode
Hybrid combustion mode

0.6

Start of HCCI
0.4
0.2

Spark ignition
0
-60

-40

-20

0
20
Crank angle (deg)

40

60

Figure 4. 4: Three types of combustion modes
The spark assisted HCCI combustion has been demonstrated to be able to improve the
stability of HCCI combustion [69][70] and to expand the HCCI combustion operation limit to
low load or high load [71][72]. Also it was used in the SI-HCCI combustion mode transition for
achieving improved performance [71][73]. For the proposed mode transition strategy in this

83

study, the hybrid combustion is essential to the success of achieving smooth mode transition
since the NVO level and manifold pressure are changing gradually between SI and HCCI
conditions due to the slow EVVT response time.
Figure 4.5 shows an unsuccessful combustion mode transition from SI to HCCI at 2000 rpm
without utilizing the hybrid combustion mode under relatively slow EVVT actuation. From the
3th cycle, as the trapped residual gas increasing while the cam phasing starts, the spark timing
was retarded and set to TDC at and after the 5th cycle. Large drop of NMEP can be observed
from cycles 4 to 7, along with large variations of CA50. By inspecting the in-cylinder pressure
over these cycles during combustion transition shown in the left hand side of Figure 4.6, it can be
observed that without the spark assistance, cycle 5 is under an ultra-late burning (see CA50 in
Figure 4.5); and cycle 6 is almost misfired with very low NMEP (see Figure 4.5) due to the lean
and high in-cylinder residual gas percentage. As a result, the unburned mixture along with the
pilot injected fuel (to be discussed in the next subsection) resulted in an unexpected combustion
during the NVO phase of cycle 6, leading to an extreme high pressure peak around 24 bar shown
in Figure 4.5. This unexpected combustion during the NVO heats up the charge mixture at IVC
of cycle 7, and triggered an ultra-early auto-ignition in cycle 7 with CA50 located at 25 BTDC
with relatively low NMEP; see Figure 4.5. By utilizing the spark assisted hybrid combustion
mode, the combustion performance can be significantly improved as shown in the right hand side
of Figure 4.6. From the in-cylinder pressure traces it can be seen that the combustion starts with
low heat release rate and switches to the HCCI combustion, which leads to the small bump for
cycles 5 and 6; and the auto-ignition locations kept advancing from cycles 5 to 7 as the residual
84

gas percentage increases due to the graduate increment of the NVO by cam phasing. By
scheduling the spark timing carefully, the combustion timing, represented by CA50, can be
maintained properly to achieve a smooth combustion mode transition.
6

60

NMEP (bar)

5

NMEP

4

40

3
In-cylinder pressure
2

20

In-cylinder pressure (bar)

Mode transition

1
0
-3

-2

-1

0

1

2

3

4

5

6

7

8

9

0
10 11 12

Crank angle (deg)

60
Spark timing
CA50

40
20
0
-20
-40
-60
-3

-2

-1

0

1

2

3 4 5 6
Engine cycle

7

8

9

10 11 12

Figure 4. 5: An unsuccessful mode transition without hybrid mode combustion
w/o hybrid mode combustion

w/ hybrid mode combustion

60

40

4th cycle
5th cycle
6th cycle
7th cycle

50

In-cylinder pressure (bar)

In-cylinder pressure (bar)

50

60

30
20
10
0
-40

40

4th cycle
5th cycle
6th cycle
7th cycle

30
20
10

-20

0
20
Crank angle (deg)

0
-40

40

-20

0
20
Crank angle (deg)

40

Figure 4. 6: In-cylinder pressure w/ and w/o assisted spark during mode transition

85

4.2.4 Split injection
Split injection is also widely used in the HCCI combustion [74][75]. By injecting certain
amount of fuel into the hot residual gas during NVO phase, the reformed fuel stabilizes the
auto-ignition and combustion timing for the HCCI combustion, especially at low load.
Experimental results show that during the hybrid combustion cycles, pilot injection during the
recompression is able to stabilize the HCCI combustion especially when the trapped residual gas
is not high enough to initiate the auto-ignition.
To optimize the split injection strategy, a set of experiments of steady-state HCCI
combustion with different pilot injection timings were conducted under different operational
conditions. Figure 4.7 shows the experimental results for the engine operated at 2000 rpm with
fuel mass of 13.8 mg, where 20% of the total fuel was injected during pilot injection and the pilot
injection timing was varied from 320 to 360 ATDC (after top dead center). Note that the
injection timing is defined as the end of injection pulse. It can be seen that there is a strong
correlation between the pilot injection timing and CA50 (or NMEP). For this operational
condition, 345 ATDC was chosen as the pilot injection timing for the highest NMEP and lowest
COV (coefficient of variation). Figure 4.8 shows the corresponding fuel injection strategy, where
the pilot injection is set to be 345 ATDC with 20% of the total fuel mass and main injection is
set to be at 420 ATDC with 80% of the total fuel. Note that on the plot both of the injection
pulse widths include 1 ms pre-charge period for the injector to reduce injection-to-injection
variation and no fuel is injected during that period.

86

4.54

5
12

4.5

4.48

4

4.46

3.5

4.44

3

4.42

2.5
320
330
340
350
360
Pilot injection timing (CAD)

CA50

NMEP (bar)

4.5

4.4

14

COV

4.52

5.5
NMEP
COV

10

8

2

6

320
330
340
350
360
Pilot injection timing (CAD)

Figure 4. 7: Effects of pilot injection timing on the combustion performance
14
In-cylinder pressure
Pilot injection
Main injection

In-cylinder pressure (bar)

12
10
8
6
4
2
0
280

300

320

340

360
380
400
Crank angle (deg)

420

440

460

Figure 4. 8: Split injection strategy
4.2.5 Control problem
By combining the EVVT, split injection, and electronic throttle control using the hybrid
combustion during the mode transition, the control strategy to achieve a smooth mode transition
can be developed. Figure 4.9 shows the mode transition strategy for the SI to HCCI combustion
mode transition when the engine is operated at 2000 rpm with 4.5 bar NMEP. Both of the intake
and exhaust valves are switched from high lift to low lift at the beginning of mode transition. The
intake valve was retarded by 63 crank degrees while the exhaust valve was advanced by 80 crank

87

degrees from the SI to HCCI combustion mode within 8 engine cycles. While the change of
valve lift would result in a sudden change of in-cylinder temperature due to reduced effective
compression ratio at the cycle from high to low lift, the spark timing was advanced significantly
at the first transitional cycle to avoid the late combustion due to the reduced in-cylinder
temperature caused by the declined effective compression ratio at the beginning of the transition.
Starting with the 3rd cycle the single fuel injection was split into pilot and main injections to
prepare for the following hybrid combustion; from the 6th cycle as the percentage of the HCCI
combustion kept increasing in the hybrid combustion mode, the spark timing was retarded
gradually to maintain the proper combustion timing; and finally at and after the 9th cycle the
spark timing is remained at TDC (top dead center) for the stable HCCI combustion mode, which
is used as a precaution in case of misfire. The throttle is opened step-by-step to follow the
desired incremental MAP trajectory to maintain the normalized AFR between 1.0 and 1.2 such
that the spark can reliably initiate the SI combustion for stable hybrid combustion. Figure 4.10
shows the in-cylinder pressure and AFR during a smooth mode transition using the proposed
control strategy based upon the HIL simulation results. The AFR increases from stoichiometric
SI combustion to lean (AFR=1.2) steady HCCI combustion mode gradually.

It can be seen that

as the MAP and AFR increase, the peak in-cylinder pressure increases gradually due to the
increased rate of heat release in the SI-HCCI hybrid and HCCI combustion, and at the same time,
the engine NMEP remained unchanged. As the exhaust valves gradually advances and intake
valve gradually retards, the magnitude of pressure peaks during NVO phase also increases,
which is indicated by the small peaks between the large in-cylinder pressure peaks in Figure 4.10
88

during the mode transition and HCCI combustion periods. For other transitional points, since the
EVVT motion is independent of engine operational condition, the time-based valve opening
trace is fixed, and the cycle-based spark timing and throttle opening could be determined
similarly. Taking the transition at 1100 rpm as an example, the EVVT is able to complete the
required cam phase adjustment within approximately 6 engine cycles, and the spark timing
should start being retarded gradually from the 4th cycle, and the step-opening of throttle should
be accelerated to ensure that the throttle is widely opened by the 5th cycle.

SI mode

400

300

Mode transition

HCCI mode
IVO

Lift shift

200

EVO
350
-4 -3 -2 -1

0

1

2

3

4

5

6

7

8

100
9 10 11 12 13 14 15 16

0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16

EVO (ATDC)

IVO (ATDC)

450

-10
-20
-30
-4 -3 -2 -1

100

0.95
0.9
0.85
0.8
0.75
0.7
0.65
-4 -3 -2 -1

50

MAP

0

1

2

3

4

5 6 7 8
Engine cycle

0
9 10 11 12 13 14 15 16

Throttle angle (deg)

MAP (bar)

Spark timing

0

Figure 4. 9: Combustion mode transition strategy from SI to HCCI

89

6

60

Mode transition

SI mode

HCCI mode
40

4

20

NMEP (bar)

5

3
-4 -3

-2 -1

0

1

2

3

4

5

6

7

8

9

In-cylinder pressure (bar)

NMEP
In-cylinder pressure

0
10 11 12 13 14 15 16

0.9

1.1

0.8

1.05

λ
MAP

1
-4 -3

-2 -1

0

1

2

3

4

5

6

7

8

9

0.7

MAP (bar)

λ

1
1.15

0.6

10 11 12 13 14 15 16

Figure 4. 10: Combustion performance during mode transition
For the case of combustion mode transition from HCCI to SI combustion, it is quite similar
by reversing the order of all control sequences for the SI to HCCI mode transition. As shown in 0,
the intake valve is advanced by 63 crank degrees while the exhaust valve is retarded by 80 crank
degrees to transit to the steady SI operational condition. The MAP is required to follow a
reversed control sequence shown in 0. However, it will take a few engine cycles for the MAP to
reduce down to the desired level since the fresh air trapped in the manifold needs to be consumed
by the intake process in a few engine cycles, hence, the MAP reduces at a slower rate than that in
the case shown in 0. As a result, the throttle was closed immediately for the HCCI to SI mode
transition, instead of a graduate step down operation. Consequently, between cycles 6 and 8, due
to the relatively lean in-cylinder mixture, the spark timing needs to be further advanced to keep
the combustion at the desired level.

90

Mode transition

HCCI mode
400

350
-4

300

SI mode
Lift shift

EVO

200

IVO
-2

0

2

4

6

8

10

12

14

100
16

-2

0

2

4

6

8

10

12

14

16

EVO (ATDC)

IVO (ATDC)

450

-20
-30

MAP (bar)

-4

100

0.95
0.9
0.85
0.8
0.75
0.7
0.65
-4

MAP

-2

0

2

4

6

50

8

10

12

14

0
16

Throttle angle (deg)

Spark timing

0
-10

Figure 4. 11: Combustion mode transition strategy from HCCI to SI
4.2.6 Control framework
Figure 4.12 shows the architecture of the proposed model-based controller for combustion
mode transition. The open-loop feed-forward control parameters are scheduled for spark timing,
valve lift, intake and exhaust valve timings, the initial fuel mass of the iterative learning, and the
reference throttle position to track the target MAP (see Section 4.4). The NMEP is controlled by
regulating the fuel mass through iterative learning, and the sensitivity-based feed-forward
controller adjusts the fuel mass to compensate the possible NMEP fluctuation by utilizing the
measurement of CA50 of the last engine cycle and the MAP of current cycle; see Section 4.5.
Note that is normally calculated based upon the measured in-cylinder pressure. During engine
calibration process or steady-state operational condition, the iterative learning is turned on; and
after the learning process converges, it could be turned off and the sensitivity-based
compensation will continue for improved robustness. Note that the iterative learning gain cam

91

also be remained on with relatively small learning gain to make the control to be robust to engine
aging and engine-to-engine variations.

 ST
 lift

NMEP(i )

 IN
 EX

Engine



Throttle

Scheduled TPS
Open-loop
Control

PMAP

CA50




TPS

PMAP
Intake
Manifold

Sensitivity-based
Feed-forward
 m fuel
Controller

CA50

m fuel


NMEP

Memory

NMEP(i  1)
Iterative learning
m fuel (i  1)

m fuel (i )

Figure 4. 12: Mode transition control diagram
4.3

Engine Combustion Modeling
In order to investigate the impact of intake charge action and fuel mass injected to the

engine combustion characteristics, engine thermodynamics equations are derived for different
combustion phases over the entire engine cycle. Figure 4.13 shows the definition of the engine
cycle and its associated combustion events, where SOC, EOC, EVO, EVC, IVO, and IVC denote
start of combustion, end of combustion, exhaust valve opening, exhaust valve closing, intake
valve opening, and intake valve closing, respectively.

92

Cycle k

In-cylinder pressure

Cycle k-1

IVC

SOC EOC

EVO

EVC

IVO

Figure 4. 13: Combustion events
EVO was used as the dividing point between cycles k-1 and k, and the calculation of
in-cylinder thermodynamics characteristics of cycle k was based on the measured in-cylinder
pressure at cycle k-1 and current intake manifold pressure at IVC of cycle k. Since the fuel
injection timing was set to 300 degrees before TDC, which is close to IVO. All the parameters
required for feed-forward fuel control shall be made available about 30 crank angle before fuel
injection timing so that the engine control has enough time to schedule the fuel injection pulse;
and the MAP at TDC before IVO was use instead of the MAP at IVO due to the assumption that
the MAP at TDC and IVO is closed to each other. Modeled in-cylinder thermodynamics for
different combustion phases is presented below.
4.3.1

Polytropic process
Polytropic process is assumed during the exhaust period (from exhaust valve opening to

intake valve opening), compression, and expansion phases. Under the configuration of valve lifts
and EVVT strategy, NVO starts from the second transition cycle once the valves have been
shifted to the low lift. For polytropic process, the in-cylinder temperature at crank angle  is

93

given by

V 
T  Te  e 
 V 

n 1

(4.1)

where the index e denotes the event of EVO, EVC, IVC, or EOC when  locates within the
exhaust, NVO, compression or expansion phase, respectively.
4.3.2 Charge mixing
During the intake phase, the residual gas and intake fresh charge can be considered
separately. Firstly, the in-cylinder pressure at IVC is approximated to be equal to the intake
manifold pressure, then the volume of the residual gas and the fresh charge can be obtained
sequentially at IVC as follows:
 P k  
Vres  k   VEVC  k   EVC

 PMAP  k  

1/n

(4.2)

 P k  
Vair  k   VIVC  k   VEVC  k   EVC

 PMAP  k  

1/n

(4.3)

By the ideal gas law, the masses of the fresh charge and the average in-cylinder temperature
are

mair  k  
TIVC  k  

PMAP  k Vair  k 
RTMAT
PMAP  k VIVC  k 

 mres  k  1  mair  k   m fuel  k   R

(4.4)

(4.5)

respectively.
4.3.3 Combustion process
Three combustion modes are investigated; and they are SI combustion mode applies for

94

transition cycles 1 to 5, SI-HCCI hybrid combustion mode for cycles 6 to 8, and HCCI
combustion mode for cycles 9, 10, and beyond. Note that the in-cylinder temperature calculation
can be simplified to be a sum of a polytropic volume change process and a heat release process
[76]. In the SI mode, during the combustion process,

 V k  
T  k   TIVC  k   IVC

 V 

n 1



QLHV m fuel  k  x  
mCv

(4.6)

where m  mres  k   mair  k   m fuel  k  is the total in-cylinder mass,  is the combustion
efficiency, QLHV is the low heating value of the fuel, and x   is the MFB (mass fraction
burned) which can modeled by the Wiebe function. Note that MFB can also be calculated based
upon the in-cylinder pressure [77].
In the HCCI combustion mode, since the combustion duration is much shorter than that in
the SI mode, a constant volume heat release process can be assumed. Therefore, at the EOC

 V k  
TEOC  k   TIVC  k   IVC

 V 

n 1



QLHV m fuel  k 
mCv

(4.7)

For the SI-HCCI hybrid combustion mode, Arrhenius integral [79] is used to determine the
start of HCCI (SOHCCI) combustion:
 SOC



IVC

Ea

A  RT  
e
d  1
Ne

(4.8)

and the MFB is calculated before SOHCCI, which is represented by xSI   . Consequently, at
the switching point

 V k  
TSI  HCCI  k   TIVC  k   IVC

 V 

n 1



QLHV m fuel xSI  
mCv

(4.9)

and at the EOC the in-cylinder temperature has the same expression as (4.7). The in-cylinder
95

pressure is obtained by ideal gas law for all of these three cases.
4.4

Manifold Pressure Control
Since the manifold filling dynamics is much slower than that of the electronic throttle, and

pressure wave exists in the intake manifold due to the periodic engine intake valve events, a
step-by-step manifold pressure feed-forward control strategy was developed. By using the ETC
system in [50], for each engine cycle within the transition cycles, the throttle was set to a target
position to achieve required manifold pressure, and the transient behavior of the throttle position
was ignored due to its fast response time, which simplifies the calculation.
For the lean combustion circumstance, the fresh air prepared for combustion in cycle k
consists of the newly charged air in (4.4) (cycle k) and also the unburned air in the residual gas
from cycle k-1. Hence the normalized air-to-fuel ratio in cycle k is obtained by

 k  

mair  k   mair  k  1   k   1
14.6m fuel  k 

(4.10)

The fuel mass m fuel  k  is expected to lie inside the range of fuel mass in steady SI mode
and in steady HCCI mode. Based on a predetermined sequence of   k  , and controlled valve
timing, required MAP can be obtained by Equations (4.3), (4.4), and (4.10).
Then consider the filling dynamics equation of the intake manifold

PMAP  k   PMAP  k  1 

RTMAT
min  k  1  mout  k  1 
Vman 

(4.11)

where TMAT , Vman , min , and mout denote the manifold temperature, manifold volume, intake
air mass through the throttle to the manifold, and the air mass going to the cylinder from the

96

intake manifold, respectively. Note that mout is easy to obtain by the scheduled nominal target
and min can be obtained by the compressible flow equation below
min  

During

each

engine

Cd  r 2 P0 2    1

cycle,

RT0

the

averaged

  PMAP 

manifold

(4.12)
pressure

PMAP

(where

PMAP   PMAP  k  1  PMAP  k   2 ) is used as an approximation of PMAP in Equation (4.2),
therefore the target throttle position   k  can be obtained that is also related to the engine
speed.
4.5

Fuel and NMEP Control
The NMEP is defined as engine effective work done per unit volume over an engine cycle

and it can be calculated the following integral
NMEP   pdV

(4.13)

Since the in-cylinder pressure can be expressed as a function of the injected fuel mass, the
intake manifold pressure, and the blowdown temperature at EVC from previous modeling
analysis, the engine NMEP can also be written as
NMEP  k   f  m fuel  k  , PMAP  k  , TEVC  k  

(4.14)

The control target is to maintain NMEP at the desired level by regulating the fuel mass for
each transition cycle during the transition. In engine calibration process while repetitive
operations are available, iterative learning control (ILC) [67][78] is an efficient approach to
improve good tracking performance (fixed trajectory in this case) with simple control structure.

97

4.5.1 Iterative learning control
1） P-type iterative learning control
As the fuel mass m fuel is the only control input, the nonlinear equation (14) can be partially
linearized to obtain a simple state space for control purpose:
x  k  1  f  x  k    B  k  u  k 
y k   x k 

(4.15)

where the x(k )  NMEP  k  is the state, and B is the fuel sensitivity function which will be
illustrated in the following subsection.
A P-type ([81] -[83]) ILC was used with a form of

u  i +1, k   u  i, k   K  yd  y  i, k  

(4.16)

where indexes i and k represent mode transition event number and engine cycle number for the
given transition event, respectively; K is the proportional iterative learning gain; and yd is the
desired NMEP output. The system is stable if the learning gain satisfies that
1 K  B k   1

(4.17)

which implies that

K  2 B  k   2 m fuel  k  NMEP  k 

(4.18)

2） Robustness analysis
If the condition in (4.17) holds, the tracking error converges to zero as the iteration steps go
to infinity assuming there are no external disturbances or measurement errors. However, in real
engine applications, engine cycle-by-cycle variation can’t be neglected. For mode transition, this
cycle-by-cycle variation is mainly due to two reasons. One is that the engine combustion is

98

heavily dependent on in-cylinder turbulence for SI and HCCI combustion and the in-cylinder
turbulence varies cycle-by-cycle; and the other is that the MAP tracking error and trapped
mixture property variations caused by the previous combustion event.
Considering the following system with disturbance

x  k  1  f ( x  k )  B  k  u  k     k 
y k   x k 

(4.19)

and the disturbance

  k   1  k   2  k 

(4.20)

is combined by 1 , defined as NMEP perturbation due to cycle-to-cycle variations of the
turbulence charge-mixing, and  2 , defined as NMEP perturbation due to the trapped mixture
property variations of the previous engine cycle. Note that 1 is difficult to be compensated due
to its random nature and  2 can be compensated by the sensitivity-based feed-forward control
illustrated in the following subsection. It can also be shown that with bounded disturbance 1 ,
the convergence of system in (4.19) is guaranteed by the ILC law in (4.16) with a output tracking
error bound in the form of
limsup  yi  f1  K   1 f 2  K 
i 

(4.21)

where f1  K  and f 2  K  are functions of the learning gain K. More details are provided in
[83]. Note that there is a tradeoff between the rate of convergence and the ILC robustness. That
is, the high learning gain could result fast learning convergence with large steady-state error;
while low learning gain leads to small steady-state tracking error but with slow learning
convergence.

99

4.5.2 Sensitivity-based compensator
1） Sensitivity analysis
Let S m , S P , and ST represent the NMEP sensitivities with respect to fuel mass, MAP, and
exhaust temperature at EVC and they can be expressed as follows.

Sm  k  
SP  k  
ST  k  

NMEP  k 
f

m fuel  k 
m fuel  k 

(4.22)
m fuel  k ,TEVC  k 1, PMAP  k 

NMEP  k 
f

PMAP  k 
PMAP  k  m

(4.23)
fuel  k ,TEVC  k 1, PMAP  k 

NMEP  k 
f

TEVC  k  1 TEVC  k  1 m

(4.24)
fuel

 k ,TEVC  k 1, PMAP  k 

where m fuel  k  , TEVC  k  1 and PMAP  k  denote the nominal values for fuel mass, MAP, and
exhaust temperature at EVC under the current operational condition, and the same notation will
be used in the following sections. Therefore, the first order approximation of (4.14) is

 NMEP  k    m fuel  k  Sm  k    PMAP  k  SP  k    TEVC  k  1 ST  k 

(4.25)

Since the sensitivity-based feed-forward control target is to eliminate the NMEP fluctuation,
by setting  NMEP  k   0 the fuel mass correction can be obtained by

 m fuel  k   

1

 PMAP  k  S P  k    TEVC  k  1 ST  k  
Sm  k  

(4.26)

The sensitivity functions Sm  k  , S P  k  and ST  k  is derived in the following
subsections.
2） Sensitivity of fuel mass
The small deviation of the in-cylinder pressure and temperature during the compression
phase caused by the evaporation of mfuel is ignored in this derivation. Then for the SI
100

combustion case, during the combustion phase

mRTIVC  k   VIVC  k  
P  k  


V
 V 

QLHV m fuel  k  x  

n 1



(4.27)

CvV

And as a result, assuming that the MFB does not change due to small variation of the fuel
mass, the instantaneous in-cylinder pressure deviation is
P  k   P  k  

QLHV  m fuel  k  x  

(4.28)

CvV

Note that the NMEP variation due to fueling mass based upon the MAP deviation is
relatively small; hence the integral of pressure-to-volume within this period was omitted. During
the combustion phase it can be expressed as



EOC

SOC

 P  k   P  k   dV  
SOC

EOC

QLHV  m fuel  k  x  
CvV

  m fuel  k  

EOC

SOC

 QLHV x  
CvV

dV
(4.29)

dV

And during the expansion,



EVO

EOC

 P  k   P  k   dV  
EOC

EVO

QLHV  m fuel  k   VEOC  k  



CvV

  m fuel  k  

EVO

EOC

n

 dV


V

QLHV  VEOC  k  

CvV 

n

(4.30)

 dV


V

Since all the parameters containing in the integrals of Equations (4.29) and (4.30) are
available for offline calculation, the sensitivity function of fuel can be finally obtained as
follows.

Sm  k   

EOC

SOC

QLHV x  
CvV

dV  

EVO

EOC

101

QLHV  VEOC  k  

CvV 

V

n

 dV


(4.31)

The derivation of Sm  k  in the HCCI mode and SI-HCCI hybrid mode is similar, thus
omitted here.
3） Sensitivity of intake manifold pressure
The change of intake manifold pressure results in variations of air charge mass, the
in-cylinder temperature and air-to-fuel ratio. This consequently affects the engine NMEP. Under
lean combustion operational condition with high percentage of residual gas, CA50 deviation,
caused by air-to-fuel ratio change, is the dominant factor for NMEP fluctuations. Experimental
results also reveals the strong relationship between CA50 and MAP deviations that can be
expressed by
1250   k  -1 e
1.5

 CA50  k    PMAP  k 

50   k -1

2.5

(4.32)

PMAP  k 

and the effect of CA50 deviation to NMEP can also be approximated by






 NMEP  k   0.2  1  0.0085  CA50  k  



2 0.6


 1 NMEP  k 


(4.33)

see similar approximation in [84].
Finally the sensitivity function of the intake manifold pressure S P  k  can be calculated by
combining Equations (4.32) and (4.33).
In the HCCI combustion mode, since the throttle is widely opened, the manifold pressure
would remain unchanged and S P  k  is set to be zero.
4） Sensitivity of in-cylinder temperature
In the hybrid combustion mode, change of in-cylinder temperature affects the auto-ignition
timing, which is the major factor of the NMEP deviation. The in-cylinder temperature of cycle k
102

is mainly affected by the trapped residual gas temperature from the previous cycle (k-1); the
compensated fuel mass mfuel also leads to temperature variation. While the in-cylinder
temperature is not measurable, CA50 can be used as a replacement measurer. Due to the page
limitation, only the final calculation results are shown in this subsection. The in-cylinder
temperature variation at EVC can be obtained by
TEVC  k   TEVC  k  



QLHV

n 1
CvVEVO
 k  1

 m  k  1 V  k  1
CA50
 fuel

n2



m

fuel

 k  1 VCA50  k  1

n2



(4.34)

Then the deviation of in-cylinder pressure at IVC is in the form of

TIVC  k   TIVC  k 
  TEVC

PMAP  k VIVC  k 
m  k  1 R

: g  k   TEVC

 n 1 n
1 n  n
 1
PMAP
 k  PEVC
 k  1 



nTMAT
 TEVC


(4.35)

The deviation of auto-ignition timing with respect to the deviation of TIVC is provided in
[80] through first order approximation approach. The complete sensitivity function is
EVO mRg  V
 VIVC  k  
IVC  k  

 dV  SOC


V  V 
 V 
n

ST  k   

SOC

IVC

  PEOC  k   PSOH  k  

lg  k  E A
e
2
RTIVC
k 



EA

RTSOH  k 

n 1

dV
1-n



SOH

IVC

 V   RT A k 
d

 e
 VIVC  k  
E

(4.36)

where the index SOH denotes the crank position associated with the start of auto-ignition (HCCI
mode) during the hybrid combustion cycles, and l  V  |SOH .
In the SI combustion mode, the effect of in-cylinder temperature of cycle k-1 to the
combustion of cycle k is minimum, and hence,

ST  k  is set to zero.

103

4.6

HIL Simulation Validation
The proposed controller was first validated in HIL simulation environment as described in

chapter 2 and Figure 2.7. The developed two-zone combustion engine model was used to replace
the new engine, which is running in the dSPACE based host computer. Firstly, Figure 4.14
shows the throttle response and intake manifold pressure trajectory during mode transition, and
the actual MAP signal matches the target MAP very well. Instantaneous MAP waves could also

Throttle angle (deg)

be observed in the figure, which is mainly due to the periodic manifold filling dynamics.
100

50

0

Manifold pressure (bar)

1.1

5

10

15

20

1
0.9
0.8
0.7
Actual MAP
Target MAP

0.6
0.5

5

10
Engine cycle

15

20

Figure 4. 14: Intake manifold pressure during mode transition
Secondly, the iterative learning control of fuel and NMEP was validated at 2000 rpm from
SI to HCCI. Figure 4.15 shows the learned fuel mass for each transitional cycle at different
learning iterations, and Figure 4.16 shows the resulted NMEP during transition. The initial fuel
mass for the first three single injection cycles was set to be the same as that under steady SI
combustion, and for the latter five engine cycles dual injection pulse widths were set to be
identical to that under steady HCCI combustion. For the first mode transition, as the fuel mass is
104

relatively low during the last five transitional cycles, large drop of NMEP could be observed (see
red curve in Figure 4.16). By the iterative learning, fuel mass was increased significantly for
these five cycles (see yellow curve in Figure 4.15) at the 2nd learning iteration, and as a result,
the NMEP level was also improved (see yellow curve in Figure 4.16). Then after 5 learning
iterations, the fuel mass for each transitional cycle converged, and shows a continuous decrease
from cycle 1 to cycle 8, due to the reducing pumping loss and increasing fuel economy. The
NMEP fluctuation was maintained within 0.094 bar, which demonstrated a smooth combustion
mode transition has been achieved.

18
1st learning
2nd learning
3rd learning
4th learning
5th learning
6th learning

17

Fuel (mg)

16

15

14

13

12
1

2

3

4
5
Transitional cycle

6

7

Figure 4. 15: Iterative learning of fuel mass

105

8

6.5
1st learning
2nd learning
3rd learning
4th learning
5th learning
6th learning

6
5.5

NMEP (bar)

5
4.5
4
3.5
3
2.5

1

2

3

4
5
Transitional cycle

6

7

8

Figure 4. 16: Resulted NMEP under iterative learning control
Thirdly, in order to validate the proposed sensitivity-based feed-forward control strategy,
the engine MAP dynamics were disturbed by an error introduced on the throttle opening during
the transition. First a lower MAP case (that throttle opening is below the desired level) was
simulated, and the result was shown in Figure 4.17. Note that filtered MAP traces were plotted to
provide a clean vision of the MAP deviation. Under open-loop nominal controller, it can be seen
that the NMEP fluctuation is more than 7% during mode transition under very small MAP
deviations. However, with sensitivity-based feed-forward controller, a correction of the fuel
injection quantity was realized to compensate for the possible deviation of NMEP, which reduces
the transient NMEP fluctuation down to 0.5%. The other observation is that under open-loop
control, a higher NMEP was shown for cycles 9 to 10, and a lower NMEP was shown for cycles
11 to 12. The reason is that for the hybrid combustion mode, a higher in-cylinder temperature
will result in an increased HCCI combustion percentage and a reduced SI combustion percentage,
106

which could increase the combustion efficiency; and however in the pure HCCI combustion
mode, the early combustion phase could lead to reduced thermal efficiency.

MAP (bar)

1
0.9
0.8
Reference
Tracking

0.7
0.6
2

4

6

8

10

12

14

16

18

20

NMEP (bar)

4.6
4.4
4.2
w/o feed-forward control
w/ feed-forward control

4
3.8

Fuel mass (g)

2

4

6

8

10

12

0.016

14

16

18

20

w/o feed-forward control
w/ feed-forward control

0.014
0.012

Fuel correction (g)

2

4

6

8

4

6

8

10

12

14

16

18

20

10
12
Engine cycle

14

16

18

20

-4

x 10
6
4
2
0
-2

2

Figure 4. 17: Low MAP case validation
Figure 4.18 shows a high MAP case. It is clear that under the open-loop control, there was a
sharp drop of the NMEP during the transition. The main reason is that the high MAP leads to
high in-cylinder pressure during the compression phase, which could increase the pumping loss;
while on the other hand the unchanged fuel injection mass would not provide additional work to
compensate that loss. Under sensitivity-based feed-forward control, the fuel injection mass
compensation leads to much smooth transient NMEP. From Figure 4.18, the NMEP fluctuation
was reduced from around 14% down to 0.5%.

107

MAP (bar)

1

Reference
Tracking

0.8
0.6
2

4

6

8

10

12

14

16

18

20

12

14

16

18

20

NMEP (bar)

4.5

4
w/o feed-forward control
w/ feed-forward control
3.5
2

4

6

8

10

Fuel mass (g)

0.02
w/o feed-forward control
w/ feed-forward control
0.015

Fuel correction (g)

0.01

2
-4
x 10

4

6

8

4

6

8

10

12

14

16

18

20

10
12
Engine cycle

14

16

18

20

10
5
0
2

Figure 4. 18: High MAP case validation
4.7

Experimental Validation
The finalized controller shown in Figure 4.12 was then implemented into the MSU Opal-RT

based prototype engine controller, and tests were conducted on an HCCI capable SI engine
described in Section II. The instantaneous engine performance parameters were measured (such
as valve timing, manifold pressure, and in-cylinder pressure) and calculated (such as NMEP,
CA50) by Opal-RT engine controller in real-time.
Firstly, the mode transition from SI to HCCI was studied at 2000 rpm with 4.5 bar NMEP.
Figure 4.19 shows the manifold pressure tracking results for a sequence of 10 mode transition
cases. It can be seen that the manifold pressure follows the desired trajectory very well, the
maximum tracking error (mostly occurs between
108

the 5th and 7th cycles) is about 0.03 bar (5%),

and the maximum resulting air-to-fuel ratio tracking error is also about 0.05 (5%). This error is

Manifold pressure (bar)

small enough for the sensitivity based control to compensate the resulting deviation.
1
0.9
0.8

0.03bar

0.7
1

2

3

4

5

6

7

8

λ

1.2
0.05

1.1
1
1

2

3

4
5
6
Transitional cycle

7

8

Figure 4. 19: Manifold pressure tracking
Figure 4.20 shows the iterative learning results without sensitivity-based fuel compensation,
and the learning gain was selected as follows

K  Sm  k   NMEP  k  m fuel  k 
Similar to the simulation validation, the initial fuel mass for the first three single injection
cycles was set to be the same as that under steady SI combustion, and for the latter five engine
cycles dual injection pulse widths were set to be identical to that under steady HCCI combustion.
It could be seen that at the first learning iteration the deviation of NMEP is fairly large,
especially around 4th to 5th cycles, where the charge mixture is relatively lean with a large
percentage of residual gas existing. With the selected learning gain, the NMEP error reduced
very fast but remained within a range of about 0.5 bar thereafter.

109

5

NMEP (bar)

4.5

Cycle 1
Cycle 2
Cycle 3
Cycle 4
Cycle 5
Cycle 6
Cycle 7
Cycle 8
Target

4

3.5

3
1

2

3
Learning iteration

4

5

Figure 4. 20: Iterative learning w/o sensitivity compensation
Figure 4.21 shows a much better learning performance with the sensitivity compensation
under the same operational condition, and with the learning gain chosen to be K  Sm  k  / 2 .

4.8
4.6

NMEP (bar)

4.4
4.2
Cycle 1
Cycle 2
Cycle 3
Cycle 4
Cycle 5
Cycle 6
Cycle 7
Cycle 8
Target

4
3.8
3.6
3.4
3.2
3
2.8

1

2

3
Learning iteration

4

5

Figure 4. 21: Iterative learning with sensitivity compensation
The engine NMEP of all the transition cycles converges to the target in a little bit slower
pace, but remains within a smaller error window around 0.1 bar. Note that there are still NMEP
fluctuations during the transition especially for cycles 4 and 5, where the fuel sensitivity is far
110

away from the linear range; however, the learning still shows a good convergence at the end.
From Figure 4.22 it can be observed that during the learning iterations, for each learning
iteration the updated fuel mass reduces for the first three cycles and increases for the next five
cycles. After five learning iterations, the resulted fuel mass continuously reduces from the first
cycle to the last cycle. The reason is that as the throttle is opened, the pumping loss is gradually
reduced, leading to improved fuel economy. That is, less fuel is required to remain the same
NMEP.

1 st le a rning

14
13
12
11
10
2 nd le a rning

14
13
12
11
10

Fuel (mg)

3 rd le a rning

14
13
12
11
10
4 th le a rning

14
13
12
11
10
5 th le a rning

14
13
12
11
10
1

2

3

4
5
6
Transition cycle

7

8

Figure 4. 22: Iterative learning of injected fuel mass
Taking the fuel mass learning process for the 6th cycle as an example, Figure 4.23 shows the
111

uniform fuel mass convergence, where the total fuel is modified by the sensitivity-based
compensation to reduce possible cycle-by-cycle variation, and learning error due to system
uncertainty as well.
12.5

Fuel (mg)

12

Nominal fuel
Total fuel

11.5
11
10.5
10
0.4

Fuel (mg)

Fuel compensation
0.2
0
1

2

3
4
Learning iteration

5

Figure 4. 23: Fuel mass learning in the 6th cycle
Once the iterative learning is converged, the fuel quantity can be fixed or the learning gain
can be reduced significantly. Figure 4.24 shows a continuous 10 transitions under the fixed
learned fuel strategy with or without sensitivity-based compensation. Due to the cycle-by-cycle
variations caused by uncontrolled flow characteristics, certain NMEP fluctuation is expected for
both cases; however, the maximum error reduced greatly from 0.424 bar to 0.171 bar
when the sensitivity-based compensation control was turned on. Significant improvement was
achieved especially for those cycles at the middle of transition, where the cycle-by-cycle
variation is dominated by the fluctuation of manifold pressure, which results combustion phase
shifting.

112

5
4.8

0.342 bar

NMEP (bar)

4.6
4.4
4.2

0.848 bar

4
3.8
3.6
3.4
1

2

3

4
5
Transitional cycle

6

7

8

Figure 4. 24: Comparison with fixed gain PID controller

NMEP (bar)

6
5
4
3
2

1

2

3
4
Learning iteration

5

6

Fuel (mg)

15
13
11
6

5

9
1

4
2
3
4
Tra nsitio
nal cy cle 5

3

2
6

1

g
nin
ar
e
L

n
tio
ra
ti e

Figure 4. 25: Mode transition from SI to HCCI at 1500rpm with 5.0 bar NMEP
113

In Figure 4.25 to Figure 4.27 other combustion mode transition cases were studied at
different engine operational conditions, including transition from SI to HCCI at 1500 rpm with
5.0 bar NMEP, transition from HCCI to SI at 2000 rpm with 4.5 bar NMEP and at 1500 rpm
with 5.0 bar NMEP. Due to the figure size limitation, legend was omitted in these figures but
they are the same as those in Figure 4.20 and Figure 4.21. Good convergences are shown for all
of these cases within 5 to 6 learning iterations.

NMEP (bar)

5.5
5
4.5
4
3.5

1

1.5

2

2.5
3
3.5
Learning iteration

4

4.5

5

13
12

Fuel (mg)

11
10
13
12
11
10
Le 5
arn 4
ing 3
it e 2
ra t
ion 1

1

2

7
6
5
4
le
c
y
c
3
ional
Tra nsit

8

Figure 4. 26: Mode transition from HCCI to SI in 2000rpm, 4.5bar
Note that 6 engine cycles are needed for the transition from SI to HCCI at 1500 rpm. The
initial fuel mass was set to the level for the steady SI mode for the first two cycles and HCCI

114

mode for the last four cycles. Similar performance could be observed as in 2000 rpm; NMEP
dropped at middle cycles in the first iteration, and after the iterative learning converges, the total
learned fuel mass shows a continuous decreasing from transition cycles 1 to 6.
For combustion mode transition from HCCI to SI, as the actions of all the actuators and the
initial fuel mass are set opposite to the case of transition from SI and HCCI, NMEP was dropped
from cycles 1 to 5 as the pumping loss increased, and was increased suddenly at cycle 6 as fuel
mass in steady state SI was set. After 5 learning iterations, a continuous increasing fuel mass

NMEP (bar)

from cycle 1 to 8 was obtained as expect.

5
4.5
4
1

1.5

2

2.5
3
3.5
Learning iteration

4

4.5

5

14

Fuel (mg)

12
10
14
12
10
1

4
2

3
Tra nsition 4
5
al cy cle

3

6

ing
rn
a
Le

2
7

1

5 n
tio
ra
it e

Figure 4. 27: Mode transition from HCCI to SI in 1500rpm, 5.0 bar

115

For the case of 1500 rpm, the other initial fuel condition was tried: fuel mass in steady
HCCI mode was set to all the transition cycles. No sudden “jump” of NMEP appeared in the first
learning iteration anymore, and after 5 iterations, the learning converges and similar result was
obtained as in 2000 rpm.
6

60
Mode transition

NMEP (bar)

4

40

3
2

20

In-cylinder pressure (bar)

5

1
0
0
-4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Engine cycle

Figure 4. 28: Successful mode transition from SI to HCCI in 2000rpm, 4.5 bar
A successful mode transition from SI to HCCI combustion at 2000 rpm with 4.5 bar NMEP
is represented by the in-cylinder pressure and the corresponding NMEP in Figure 4.28. During
the combustion mode transition, the in-cylinder pressure trace shows a similar tendency as in
Figure 4.10, and there was no significant late combustion or early auto-ignition. Note that
significant combustion phase shifting could lead to large NMEP fluctuations. The smooth mode
transition can be observed clearly from a continuously combustion mode transition between SI
and HCCI as shown in Figure 4.29, where four mode transitions were completed within 300
engine cycles. The maximum absolute NMEP fluctuation during mode transition is about 5%.

116

Note that at this operational condition the maximum absolute cycle-by-cycle variation for the SI
combustion is 3.5% and for the HCCI combustion is 4%. This indicates that the absolute NMEP
fluctuation during the mode transition is compatible with these of steady SI and HCCI
combustion. Furthermore, the maximum rate of the in-cylinder pressure rise during these
transitional cycles is between these of SI combustion at about 1 bar/degree and HCCI
combustion at about 4.5 bar/degree. This shows that smooth mode transition using the well
regulated hybrid combustion mode was achieved by the control strategy without misfire or
knock.

HCCI

5 NMEP

SI

HCCI

60

SI

40

4

20

CA50

3

0

2
1

Max. pressure rise (bar/deg)

SI

CA50

NMEP (bar)

6

-20
0

50

100

150

200

250

-40
300

0

50

100

150
Cycle

200

250

300

8
6
4
2
0

Figure 4. 29: Combustion mode transition between SI and HCCI
4.8

Hybrid Combustion Mode Observation
Then for all

of these mode transition conditions, the experimental mass fraction burned

(MFB) curves of the transitional cycles are shown in Figure 4.30 to Figure 4.33, where the red
dots denote the auto-ignition (start of HCCI combustion in the unburned zone) location for the

117

hybrid combustion mode. From Figure 30 it can be observed that during the mode transition
from the SI to HCCI combustion, the hybrid combustion starts at the 4th cycle when the split
injection begins and it lasted for four cycles. The percentage of HCCI combustion gradually
increases over the four hybrid combustion cycles. While for the case of mode transition from
HCCI to SI combustion shown in Figure 4.31, the hybrid combustion lasted for five cycles, and
the percentage of the HCCI combustion gradually decreases over the five hybrid combustion
cycles. Note that it is not guaranteed that the mode transition always follows this pattern since
the cycle-by-cycle variations, intake air temperature perturbation, and manifold pressure tracking
error could affect the auto-ignition timing and even the start of the hybrid combustion cycle. To
further investigate the spark timing in Figure 4.11 it can be seen that, in transitional cycles 6 and
7, the spark timing was heavily advanced; however the start of combustion, indicated by the
CA10 locations of these two cycles were close to other transitional cycles; see Figure 4.31. The
long ignition delay is caused by the reduced in-cylinder temperature due to the reduced effective
compression ratio at beginning of transition and relatively low in-cylinder mixture temperature at
IVC. This demonstrated the spark timing control is effective to maintain a reasonable CA50 for
the hybrid combustion during the mode transition.

118

1

0.8

MFB

0.6

0.4

0.2

0
1

2

3
4
5
Tra nsit
6
ional cy
cle

7

8

30
10 20
-10 0
g)
e
(d
-20
-30
a ngle
Crank

40

50

Figure 4. 30: Mode transition from SI to HCCI in 2000rpm, 4.5 bar

1

0.8

MFB

0.6

0.4

0.2

0
1

2

3
4
Tra nsition 5
6
al cy cle

7

8

40
20 30
0 10 (de g)
-10
le
-20
k a ng
-40 -30
Cr an

50

Figure 4. 31: Mode transition from HCCI to SI in 2000rpm, 4.5 bar

119

1

0.8

MFB

0.6

0.4

0.2

0
1

2

3
4
Tra nsit
5
ional cy
cle

6

7

30
10 20 e g)
(d
-10 0
le
g
n
a
-20
-30
Crank

40

50

Figure 4. 32: Mode transition from SI to HCCI in 1500rpm, 5.0 bar

1

0.8

MFB

0.6

0.4

0.2

0
1

2

3
Tra nsit4
ional c5y
cle 6

7

30 40
10 20 e g)
0
(d
-10
le
g
n
a
-30 -20
Crank

50

Figure 4. 33: Mode transition from HCCI to SI in 1500rpm, 5.0 bar
In the case of mode transition at 1500 rpm, hybrid combustion happened one cycle before
the split injection for the SI to HCCI transition and after the split injection for the HCCI to SI
transition; see Figure 4.32 and Figure 4.33. We believe that the engine thermal condition under
low valve lift at this operational condition makes the auto-ignition easier than the other
operational conditions.
120

4.9

Conclusions
A model-based control strategy for spark-ignition (SI) and homogeneously charge

compression ignition (HCCI) combustion mode transition is proposed in this chapter that
consists of manifold pressure control, iterative learning of NMEP (net mean effective pressure)
control and sensitivity-based fuel compensator. The NMEP sensitivity of injected fuel quantity
was derived based upon the control-oriented combustion model. Experiment results showed that
the proposed MAP and iterative learning controller are able to achieve smooth mode transition
between SI and HCCI combustion at a range of operational conditions, and the robustness under
cycle-by-cycle variation has been greatly enhanced by utilizing the sensitivity-based
feed-forward fuel compensator. The NMEP, an indication of engine output torque, fluctuation
during the combustion mode transition was kept within 3%.

121

CHAPTER 5
CONCLUSIONS

5.1

Conclusions
In this dissertation, mode transition control between SI and HCCI combustion was

investigated, which is one of the key challenges of realizing HCCI combustion on an HCCI
capable SI engine. Firstly, for the purpose of control strategy development and validation, a
control-oriented HCCI combustion engine model was developed for real-time HIL simulations.
Secondly, an LPV gain-scheduling controller for the electronic throttle was designed for accurate
throttle position control required by the combustion mode transition. Finally, a model-based
mode transition controller between SI and HCCI combustion was developed, and smooth mode
transition was demonstrated by both of the simulation and experimental validation. Based on the
research results presented in Chapters 2, 3 , and 4 the following conclusions can be drawn.


The developed control-oriented charge mixing and two-zone HCCI combustion model has
shown significant improvement on combustion timing prediction and in-cylinder flow behavior
than the existing one-zone model. This model is accurate enough to replace a real engine so that
the proposed control strategy can be developed and validated through HIL simulations.



The proposed LPV gain-scheduling control strategy for electronic throttle control has shown
great improvement compared with conventional controllers in dealing with the high system
122

nonlinearity and external disturbance, and guarantees that the throttle plate position can be
controlled accurately during mode transition with fast reposnse. The modeling and control design
process also provides a novel approach for other mechatronics application.


Smooth combustion mode transition was achieved by controlling the manifold pressure to track a
reference trajectory that guarantees the air-to-fuel ratio to be within a reasonable range and by
using the iterative learning method to regulate the NMEP

during the transition.

The

sensitivity-based feed-forward control is able to compensate the NMEP fluctuations due to
combustion cycle-by-cycle variations and the mode transition robustness was greatly improved.
5.2

Recommendations for Future work
In this dissertation, the combustion process modeling was based on MFB (mass fraction

burnt) trace approximated by multiple Wiebe functions. The advantage of this approach is its
simplicity, especially with low calculation requirement for real-time simulations. However, for a
large operational range, calibrating the engine becomes complicated. And for the HCCI
combustion, different operational conditions, such as air-to-fuel ratio and residual gas fraction,
could lead to quite different combustion characteristics; a simple Wiebe function may not
approximate the combustion process accurately. To improve this part of model, the alternative
approach is chemical reaction-based modeling. By considering the chemical reactions of a few
major molecules in the fuel, the real-time simulation requirement might be also satisfied.
In addition, controlling the HCCI combustion process is another important topic. Due to the
cycle-to-cycle residual gas dynamics, auto-ignition timing is also relatively difficult to control.
However, to consider the effect of combustion indecs (such as CA50, burn duration, etc.) of
123

current cycle to the next cycle, the complicated nonlinear system might be simplified into an
LPV system, and certain control strategies could be applied for the combustion control problem.

124

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125

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