Yanmar 3 jh25a marine diesel engine service repair manual
IITBMastersReport
1. Control of Injection Timing in
Port Fuel-Injected Gasoline Engines
Dissertation submitted in partial fullfilment
of the requirements for the degrees of
B.Tech in Mechanical Engineering
and
M.Tech in Computer Aided Design and Automation
by
Pranav Rajendra Shah
(Roll 03D01010)
under the supervision of
Prof. Shashikanth Suryanarayanan
Department of Mechanical Engineering
Indian Institute of Technology Bombay
July 2008
2. Abstract
This thesis focuses on studying response of wall-wetting dynamics observed
in port-fuel injected gasoline engines to changes in fuel injection timing. In
particular, it investigates the manner in which real time changes in fuel injec-
tion timing influence the quantity of fuel that evaporates from the deposited
wall-film in the intake port. An advancement in injection timing is shown
to cause greater amount of fuel to enter the cylinder in the transient state
though with no change in the steady state. A mathematical model captur-
ing this observed phenomenon is derived and utilized to build a controller
to achieve tighter control of air-fuel ratio(AFR) in the transient state. Ex-
periments are also conducted to confirm the efficacy of the proposed control
action.
8. List of Symbols
α Throttle position
γ Specific heat ratio of air
λ Air-fuel ratio
κ Injected-fuel impingement fraction
µ Dynamic viscosity of air
ρa Density of air
ρf Density of fuel
ω Engine crank-shaft speed
CAs Fuel vapor concentration at droplet surface
CD Droplet drag coefficient
DAB Diffusivity of gasoline
M Molecular weight of gasoline
R Universal gas constant
Sc Schmidt number
¯Sh Sherwood number
T Engine cycle time
Tatm Atmospheric air temperature
Ts Droplet surface temperature
Vman Volume of manifold
cd Throttle discharge coefficient
vi
9. hfg Specific enthalpy of gasoline
˙mcylinder Air mass flow rate into cylinder
˙mevp Mass rate of fuel-film evaporation
mf Mass of fuel-film
˙minj Mass rate of fuel injection
mman Mass of air in manifold
mpul Fuel injected per injection
˙mthrottle Air mass flow rate from throttle
pAs Vapor pressure at droplet surface
pman Average manifold pressure
sW Distance from injector to opposite wall
tinj Timing of fuel injection
tIV O Intake valve opening time
vii
10. List of Abbreviations
AFR Air-Fuel Ratio
EFI Electronic Fuel Injection
EOT Engine Oil Temperature
FID Fuel Injection Duration
FIT Fuel Injection Timing
MAP Manifold Air Pressure
MAT Manifold Air Temperature
PFI Port Fuel Injection
TDC Top Dead Center
viii
11. Acknowledgments
First and foremost, I would like to sincerely thank my advisor, Professor
Shashikanth Suryanarayanan, for his immense support and guidance right
through my undergraduate and graduate days at IIT. I greatly appreciate
his openness to whatever I wanted to express as well as the freedom that he
provided me to pursue research of my interest. A guide and a mentor like
him will always be hard to find.
I am also grateful to Pushkaraj Panse for all that I have learned from
him. His patience and mentoring were very vital for my understanding of
various aspects of the project. I am proud to have a person like him as a
very good friend of mine.
I thank all my friends at IIT - wingmates and mates from the mechanical
department - for all the fun that we had together and which has helped me
make my stay at IIT a memorable one.
Finally, I am deeply thankful to my parents and my family for always
being very supportive of whatever I wanted to pursue. Little could have
been achieved without their blessings and love.
ix
12. Chapter 1
Introduction
Gasoline engines today are fitted with three-way catalytic converters in the
exhaust pipe to curb tailpipe emissions. The efficiency of these catalytic con-
verters to curb hydrocarbon(HC), nitrogen oxide(NOx) and carbon monox-
ide(CO) emissions depends critically on the air-fuel ratio(AFR) of the mix-
ture undergoing combustion in the cylinder. In order to meet emission reg-
ulations set by governing bodies, most larger gasoline engines(greater than
500 cc) today are fitted with electronic fuel injection(EFI) systems for fuel
delivery rather than carburetors. This is because EFI systems help with
better metering of the injected fuel as well as better atomization of fuel into
droplets, both of which play an important role in achieving good performance
of the engine.
A fuel injection system delivers finely atomized droplets by allowing pres-
surized fuel to flow through a nozzle with fine orifices. The opening of the
nozzle is usually controlled by using an electronically actuated solenoid valve.
The time for which the nozzle is kept open decides the amount of fuel deliv-
ered per injection event. The work for this thesis is carried out on an engine
based on port-fuel injection(PFI) architecture(figure 1.1). In these engines
1
13. Figure 1.1: Port-fuel injection engine architecture
fuel is sprayed into the intake manifold which then forms a combustible mix-
ture with incoming air. Specifically, we study the influence of injection tim-
ing on engine performance in port-fuel injected, four stroke, single cylinder
gasoline engines.
1.1 Problem Addressed
The engine cycle can be looked upon as made up of a number of discrete
events synchronized with opening of the intake valve. The important deci-
sions to be made every cycle with fuel injected engines are the amount of
fuel to be injected and the timing of fuel injection with respect to top dead
center(TDC) of the intake stroke. We define fuel injection timing(FIT) as the
crank angle in degrees before the top dead center of intake stroke at which
injection happens(figure 1.2).
2
14. Figure 1.2: Fuel injection advance diagram
The usual methodology to achieve AFR control is to make appropriate
changes in amount of fuel quantity injected based on accurate air-flow esti-
mation schemes[2][7][8]. Injection timing is known to influence size of fuel
droplets entering the cylinder[12] and hence plays an important role in deter-
mining hydrocarbon(HC) emissions[20]. Injection timing is also important
from the point of view of drivability as it is believed to affect the torque
response by influencing air-fuel mixture formation in the intake-port[13].
Further, a commonly suggested heuristic while implementing AFR control
systems is to fix injection timing such that the end of fuel injection occurs
at the opening of the intake valve[7]. This heuristic helps minimize the error
between the sensed quantity of air flow at the time of injection and the ac-
tual air flow when intake valves open and thereby help achieve tighter air-fuel
ratio control.
3
15. Figure 1.3: AFR variation for change in FIT
In this thesis we investigate the influence of real-time changes in injection
timing on quantity of fuel entering the cylinder per cycle and thus on AFR
control. As far we know all studies previously made to study influence of
injection timing consider it as a fixed parameter. It is shown in this thesis
that changes in fuel injection timing have a significant influence on AFR
transients(figure 1.3). It is this conclusion that is exploited to achieve tighter
AFR control by controlling fuel injection timing in real-time.
1.2 Contributions of the thesis
Methodologies to control AFR by appropriately adjusting opening-closing
time of the injector is a well researched topic in the power-train control
research community. The work in this thesis will help put forth the view
that injection timing can act as an additional degree of freedom to achieve
4
16. AFR control. This claim is also intended to fuel further similar studies for
multi-cylinder and larger engines.
The more immediate contribution of this thesis is toward commercial en-
gine management system developers. With the goal of automobile manufac-
turers set to meet increasingly stricter emissions norms along with improved
fuel economy and drivability, the work in this thesis will help build better
AFR controllers for engines.
1.3 Outline of the thesis
The structure of the thesis is as follows. Chapter 2 briefly describes engine
and control preliminaries needed to understand the remainder of the thesis
while chapter 3 describes the experimental facilities used to carry out in-
vestigation for this thesis. Since injection timing is conjectured to play a
role through aperiodic excitation of the wall-wetting dynamics, chapter 4
describes a detailed model for this dynamics by separately considering the
phenomenon of droplet and wall-film evaporation. Chapter 5 presents the
investigation made to study influence of injection timing. This chapter also
describes a methodology to use it as a control input for AFR control while
chapter 6 gives a summary of the thesis, list important conclusions as well
as outlines direction for possible future work.
5
17. Chapter 2
Preliminaries
Internal combustion engines today are fitted with a number of sensors and
actuators for diagnosis and control. The need for these elements necessitates
out of the requirement to obtain improved performance from vehicular sys-
tems. This chapter focuses on few preliminaries related to engines and their
control which will aid understanding of rest of the thesis. Section 2.1 covers
basic material on internal combustion engines while section 2.2 covers mate-
rial on basic control theory. Section 3 details out the experimental facility
that was used for conducting experiments related to work in this thesis.
2.1 Internal Combustion Engines
The purpose of internal combustion engines is the production of mechanical
power through the release of chemical energy contained in the fuel. This
energy is released by burning fuel inside the engine. The majority of the
internal combustion engines are of reciprocating nature and operate on what
is known as the four-stroke cycle. In particular we would be looking at four-
stroke, port fuel-injected, spark ignited gasoline engines.
6
18. Figure 2.1: Four stroke engine operating cycle [5]
Engine Operating Cycle
Four-stroke internal combustion(IC) engines require each cylinder to undergo
four strokes for completion of the engine cycle as shown in figure (2.1). The
four strokes, which comprise the engine operating cycle, are described below:
• An intake stroke which starts with the piston at top center (TC) and
ends with the piston at the bottom center (BC) and which draws fresh
mixture into the cylinder. To increase the air-fuel mass inducted, the
inlet valve opens shortly before the stroke starts and closes after it ends.
• A compression stroke where both valves are closed and the mixture
inside the cylinder is compressed. Towards the end of the compression
stroke, combustion is initiated by sparking the in-cylinder mixture with
a spark plug.
• A power stroke which starts with the piston at the TC and ends at BC
7
19. as the high temperature, high pressure gases push the piston down and
force the crank to rotate. The crank in turn causes the road wheel to
rotate which makes the vehicle move.
• An exhaust stroke where the remaining burned gases in the cylinder are
driven out. As the piston approaches the TC the inlet valve opens and
just after the TC the exhaust valve closes and the cycle starts again.
Fuel Injection
Carburetors have been used extensively in commercial throttle operated gaso-
line vehicles for mixing of air and fuel in the intake manifold. A suction
created by flowing air in the intake manifold draws fuel from the fuel tank
into the intake manifold and forms air-fuel mixture. However, they do not
provide accurate fuel metering and good atomization of the incoming fuel.
Fuel injection using electronic fuel injectors is an increasingly common
alternative to carburetors. In electronic fuel injectors, pressurized fuel is
passed through very fine orifices which cause atomization of injected fuel.
Amount of fuel to be injected is decided by the opening and closing time of
the solenoid valve in these injectors (see[9]). This control over the amount
and timing of fuel injection helps with accurate metering of the fuel entering
the manifold as well as better air-fuel mixture preparation, both of which
have an influence on performance of the engine.
Engine Emissions
The exhaust gases of gasoline engines contain mixture of nitric oxide (NO)
and small amounts of nitrogen dioxide (NO2) and nitrous oxide (N2O) which
are collectively called NOx, un-burnt or partially burned hydrocarbons (HC)
8
20. Figure 2.2: Time-trace of TVS Victor GLX following Indian Drive Cycle
and carbon dioxide (CO), in addition to the predominant gases carbon diox-
ide (CO2) and water vapour(H2O).
Regulatory bodies have been setup around the world to set and implement
emission regulation laws in-order to curb current vehicular emissions. A
vehicle emission test consists of driving the vehicle through a velocity versus
time profile that the vehicle is required to go through within certain limits.
The Indian drive cycle(IDC) is as shown in the figure (2.2). The total mass
emission of each pollutant over the drive cycle is measured and in order for
the vehicle to be certified for usage by the regulatory authorities, these values
must be below the allowed limits of emissions.
Emission norms are getting stricter with time and hence mechanisms to
curb emissions are gaining increased importance.
9
21. Figure 2.3: Conversion efficiency of three-way catalytic converter [17]
Three-way Catalytic Converter
Engine out pollutants of spark-ignited gasoline engines greatly exceed levels
mandated by most regulatory authorities. These requirements can only be
satisfied if appropriate exhaust gas after-treatment systems are used. The
three-way catalytic (TWC) is one common after-treatment system used which
facilitates the conversion of three pollutant species, namely, NOx, CO and
HC present in the exhaust gas into less harmful water, carbon dioxide and
nitrogen. Most catalytic converters consist of noble metals platinum, palla-
dium and rhodium. It is these metals that dictate the conversion efficiency of
the converter. The conversion efficiency is high only if the air-to-fuel ratio by
mass (AFR) of the in-cylinder mixture is kept in a narrow band around the
stoichiometric value of 14.6 (figure 2.3) during operating conditions of the
engine (figure 2.3). Thus air-fuel ratio excursions are to be strongly avoided
10
22. and this requirement necessitates accurate metering and control of the in-
jected fuel. This is one of the vital reason for wide-spread replacement of
carburetors by electronic fuel injectors.
2.2 Control Preliminaries
This section gives brief introduction to the basic concepts and ideas in linear
control theory. For detailed discussion one may refer to [3][11].
Linear Time Invariant(LTI) Systems
Definition 2.2.1. A system L is a map from one set of signals u(t), called
as inputs to another set of signals y(t), called as outputs. Such maps are
often denoted as L : u → y
Definition 2.2.2. A map L : u → y is called linear if for every u1(t), u2(t)
and α, β ∈ ,
L(αu1(t) + βu2(t)) = αL(u1(t)) + βL(u2(t))
Definition 2.2.3. A system L is said to be time-invariant if for every τ > 0,
L(u(t)) = y(t) =⇒ L(u(t − τ)) = y(t − τ)
The class of linear, time-invariant systems are expressed mathematically
using linear, constant coefficient, ordinary differential equations of the form
yn
(t) + an−1yn−1
(t) + · · · + a0y(t) = bmum
(t) + bm−1um−1
(t) + · · · + b0u(t)
with u(t), y(t) as input, output signal respectively. All coefficients ai’s and
bi’s here are real. The above representation of LTI systems is in the time
11
23. domain. An equivalent representation of the system in the Laplace domain
can be expressed as
L : u → y :=
Y (s)
U(s)
=
bmsm
+ bm−1sm−1
+ · · · + b0
sn + an−1sn−1 + · · · + a0
A convenient representation for linear, time-invariant systems with multiple
inputs(say,p) and outputs(say,q) in time domain is in the state-space form
expressed as
˙x(t) = Ax(t) + Bu(t) (2.1)
y(t) = Cx(t) + Du(t) (2.2)
where x(t) ∈ n
is the state vector, u(t) ∈ p
is the input vector to the
system, y(t) ∈ q
is the output vector of the system, A ∈ n×n
is the
state matrix, B ∈ n×p
is the input matrix, C ∈ q×n
is the output matrix
and D ∈ q×p
is the feedforward matrix. The state x(t) of the system is a
collection of variables that help predict future response of the system.
The state-space representation in the Laplace domain is of the form
X(s) = (sI − A)−1
BU(s)
Y (s) = (C(sI − A)−1
B + D)U(s)
where U(s), X(s) and Y(s) are Laplace transforms of u(t), x(t) and y(t)
respectively.
Linearization of Non-linear Systems
Non-linear systems of the form
˙x(t) = h(x(t), u(t))
12
24. y(t) = f(x(t), u(t))
may be approximated around an operating point under the assumption that
output deviation is small when the input perturbations are small. Suppose
that for some constant input vector uo, the state of the system is x0 i.e.
h(x0, u0) = 0
Now for a small deviation in the state from x0 to x0 + ∆x(t) due to a small
perturbation ∆u(t) in the input, we can write
∆ ˙x(t) = h(x0 + ∆x(t), u0 + ∆u(t))
≈ h(x0, u0) +
∂h
∂x
|x0,u0 ∆x(t) +
∂h
∂u
|x0,u0 ∆u(t) · · · (Taylor series)
= A∆x(t) + B∆u(t)
where, A := ∂h
∂x
|x0,u0 and B := ∂h
∂u
|x0,u0 are called Jacobians. The above is a
linear state-space approximation of the non-linear system. A similar linear
approximation can be obtained for y(t) = f(x(t), u(t))
Controllability and Observability of Systems
Definition 2.2.1. The system
˙x(t) = Ax(t) + Bu(t)
is said to be completely controllable if for x(0)=0 and any given state x1,
there exists a finite time t1 and a piecewise continuous input u(t), 0 ≤ t ≤ t1
such that x(t1) = x1.
Qualitatively, the above definition implies that if the system is completely
controllable then it is possible to drive the system from any initial value to
any specified final value in a finite time.
13
25. Theorem 2.2.1. The system
˙x(t) = Ax(t) + Bu(t)
is completely controllable if and only if the n × np matrix
M = [B, AB, · · · , An−1
B]
has rank n.
The above matrix M is called the controllability matrix.
Definition 2.2.2. The system
˙x(t) = Ax(t) + Bu(t) (2.3)
y(t) = Cx(t) + Du(t) (2.4)
is completely observable if there exists t1 > 0 such that knowledge of u(t) and
y(t) for all t, 0 ≤ t ≤ t1 is sufficient to determine x(0).
Once x(0) is known, equation 2.1 can then be used along with known
input u(t) to determine x(t) for all t, 0 ≤ t ≤ t1. Control inputs are usually
decided upon the basis of outputs available. If the available outputs do not
convey complete information on the state vector, which along with inputs
govern the future response of the system, then it may not be possible to
achieve desired control performance. Thus, both complete controllability
along with observability is important to get good control performance.
Theorem 2.2.2. The system
˙x(t) = Ax(t) + Bu(t) (2.5)
y(t) = Cx(t) + Du(t) (2.6)
14
26. is completely observable if and only if the qn × n matrix
S =
C
CA
CA2
...
CAn−1
has rank n.
State Feedback and LQR control
The state variable x(t) along with the input signal u(t) decide the future
response of the system. Thus, in order to regulate the response of the system,
it is important to adjust the input signal in accordance with the value of the
state variable. A commonly used linear control strategy is of the form
u(t) = −Kx(t)
Equation 2.1 then turns into
˙x(t) = (A − BK)x(t) (2.7)
The eigenvalues of the matrix A − BK govern response of the system. In
order for the system to be stable, it is required that all eigenvalues of A−BK
have negative real parts i.e.
(λ) < 0 where λ is an eigenvalue of A − BK
The value of the gain matrix K is chosen such that desired performance
specifications in terms of response of the system are met.
A commonly used methodology to specify the desired performance is in
the form of a cost function of the form
J =
∞
t=0
(xT
Qx + uT
Ru)dt (2.8)
15
27. which needs to be minimized by proper choice of the gain matrix K. The
first term in the above criteria represents the cost incurred when the system
response is away from the desired value (i.e. x = 0) while the second term
represents the cost incurred in using the actuator (higher is the actuation
effort higher is the cost). The key quantities in this criteria that a designer is
required to choose based on the performance specifications are the matrices
Q and R both of which have to be positive definite. They represent the
relative weightage given to the two cost criteria. Arriving at the right values
for the matrices Q and R based on the performance specifications is usually
an iterative process.
The gain matrix K that minimizes the integral 2.8 for the system 2.1 is
given by
K = −R−1
BT
P
where P is given by the Ricatti equation
AT
P + PA − PBR−1
BT
P + Q = 0
2.3 Control Systems for Internal Combustion
Engines
This section looks at the important control problems of relevance in internal
combustion(IC) engines. In particular, control problems in port fuel-injected,
spark-ignited gasoline engines are discussed.
Input-Output view of IC engine
An engine can be viewed as a map from input variables like throttle angle,
fuel injection amount, fuel injection timing, spark timing and load torque to
16
28. Figure 2.4: Input-Output view of Engine
output variables like engine torque, engine speed and engine out emissions
(figure 2.4). The engine control problem is to decide on a strategy to control
the input variables of the engine in a manner such that desired performance
of the engine is obtained in terms of the output variables. However, not all
input variables may be available for control, e.g. like the throttle angle which
is used by the driver to express torque demand or the load torque which the
engine experiences due to external forces. All inputs which cannot be used
as control inputs as classified as disturbances.
The following sections discuss some important engine control problems.
Air-Fuel Ratio(AFR) Control
Port fuel-injected gasoline engines are fitted with three-way catalytic con-
verters to reduce emissions(section 2.1). In-order for these converters to do
17
29. well, the in-cylinder AFR needs to be kept in a narrow band around stoi-
chiometric value. Over the years various feed-forward and feedback schemes
have been proposed and devised for AFR control in gasoline engines.
• Feed-forward schemes depend on precise estimates of incoming air mass
flow rate. These estimates are made by means of engine maps developed
by performing a large number of controlled experiments under steady
state operating conditions. Based on an estimate of mass flow rate of
air from these maps, the controller issues command to the fuel injector
in real-time so that appropriate quantity of fuel is injected to keep
AFR at the desired value. However, these maps developed at steady
state operation cannot help overcome air-fuel ratio excursions during
engine transients. Also, performance of these feed-forward schemes
gets affected by external uncertainties like variations in atmospheric
conditions, fuel quality variations, engine aging, etc.
• Feedback schemes rely on measurement of air-fuel ratio made by an
oxygen sensor placed in the exhaust pipe. These measurements help the
controller decide on the correction to be made to the quantity of fuel
injected to keep the AFR at the desired value. Feedback systems are
much more robust in performance than feed-forward systems as they are
not as prone to uncertainties as the feed-forward systems are. However,
the sensor measurement process of air-fuel ratio is based on diffusion
and includes delay of the order of tens of milliseconds. In addition,
there exists a delay of the order of few hundreds of milliseconds due to
the time taken by the air-fuel mixture at the intake to reach the sensor
placed in the exhaust. These delays limit the maximum achievable
bandwidth (speed of response) of the feedback system.
18
30. Figure 2.5: Engine feedback system architecture
In practice, a combination of both schemes is used. The feed-forward sys-
tem helps achieve faster response while the feedback system helps achieve
robustness to disturbances and uncertainties.
In-order to obtain improved performance during transients, detailed dy-
namic control oriented modeling of the engine air-flow dynamics, fuel sup-
ply dynamics, air-fuel mixture formation dynamics, exhaust gas dynamics,
etc becomes necessary. Some of these issues have been covered in previous
projects on engine management design at IIT Bombay [6][14]. This project
looks at fuel supply dynamics and assesses the role of injection timing in it.
19
31. Ignition Control
For other inputs held constant, the brake torque of the engine varies with
the spark timing or spark advance. At each operating condition of the en-
gine, there exists a spark advance which maximizes the brake torque called
as Maximum brake torque (MBT) timing. With maximum brake torque a
higher fuel economy can be achieved. However, it may not always be possible
to operate the engine at MBT due to tendencies of knocking and also increase
in NOx production at MBT. Thus spark timing is controlled in a manner
such that maximum brake torque is obtained without engine knocking as
well as keeping NOx emissions under a desired value. Various feedback and
feed-forward control schemes exist for spark timing control. One such control
scheme has been implemented by [6].
20
32. Chapter 3
Experimental Setup and
Operation
An engine is a system whose performance depends on multiple variables. A
systematic study to understand behavior of the engine would require un-
derstanding the influence of a variable on engine performance with other
engine variables held fixed. Carrying out such controlled experiments re-
quires accurate monitoring and control of the engine through sophisticated
instrumentation. A state of the art facility to work on small engines (100-
300 cc) exists at the engine management systems(EMS) laboratory at IIT
Bombay, the details of which are given in this chapter.
3.1 Sensing and Actuation Architecture
The engine used to carry out investigations for this thesis is a single cylinder,
four-stroke, small-sized gasoline engine of the type which is commonly found
in motorcycles in India. The details of the engine are put in table 3.1a(page
27). This engine has been fitted with a number of sensors and actuators for
21
33. Figure 3.1: Schematic of engine fitted with sensors and actuators
its monitoring and control(figure 3.1), the details of which given below.
Actuators
The engine is fitted with an electronically controlled, solenoid actuated fuel
injector which is excited using a pulse train like one shown in figure 3.2. The
opening of the injector allows pressurized fuel to enter the intake manifold. A
higher voltage is applied across the injector for a time duration for which it is
desired to be open and we call this duration as fuel injection duration(FID).
An electric spark plug is used to initiate combustion of the air-fuel mixture
in the cylinder. A voltage greater than breakdown voltage of air is applied
across its terminals when combustion of the mixture is desired to be initiated.
22
34. Figure 3.2: Typical fuel injection pulse (Electronic)
Sensors
An universal exhaust gas oxygen sensor(UEGO) is fitted in the exhaust
tailpipe of the engine to monitor air-fuel ratio by mass(AFR) of the mix-
ture that had entered the cylinder for combustion in the just finished cycle.
The engine is also fitted with a manifold air pressure and temperature sensor
to monitor state of air moving into the cylinder while a thermocouple is used
to monitor engine oil temperature(EOT).
A sensor in the form of an inductive pickup is used to obtain position of
the crank shaft once every rotation. Detailed specifications for sensors and
actuators used are put in table 3.1b.
The important decisions to be made during engine operation are the
amount and timing of fuel injection and timing of the sparking event. In
addition to current engine state perceived using various sensors, an elec-
tronic hardware is usually employed to perform computations in order to
23
35. Figure 3.3: Schematic of engine with a computational element
arrive at these decisions. Architecture of such a system is shown in fig-
ure 3.3. dSpace R DS1104 rapid prototyping card was used as the electronic
hardware device for all experiments. This has the provision to accept ana-
log/digital signals from various sensors as well as give actuator command
signals. Programming of the control algorithm is carried out in MATLAB-
SIMULINK R and the developed program is then transferred onto the proto-
typing hardware for real-time operation.
3.2 Controlled operation of the engine
The mass of air inducted per cycle by the engine at steady state is a function
of engine speed(ω), throttle position(α) and manifold air temperature(MAT)
(see [7]). Thus, holding these variables constant helps ensure that the mean
mass flow rate of air into the engine is held at a steady value.
24
36. Figure 3.4: Engine fitted with transient dynamometer
(EMS Lab, IIT Bombay)
Engine speed(ω) is held at a steady value using a high bandwidth tran-
sient dynamometer coupled to the engine crank-shaft(figure 3.4). The tran-
sient dynamomter achieves this by appropriately applying load torque to
the engine crank-shaft. For engine operation at 3000 rpm, the transient
dynamometer helps hold the speed within a band of ±1.5%.
Manifold air-temperature(MAT) is held with an accuracy of ±0.5 ◦
C using
an external air-blower while a stepper motor attached to the engine throttle
helps hold the throttle at a fixed opening. It is found that such controlled
operation of the engine helps hold the mean mass flow rate of air with an
accuracy of ±2.0% about the nominal value.
With the mass flow rate of air held reasonably fixed, changes in AFR can
be attributed to changes in fuel mass inducted into the cylinder. AFR is thus
used as a measure of amount of fuel entering into the cylinder under such
25
37. controlled operation. Further, it is assumed that the mass of fuel delivered
through the fuel injector is proportional to the opening time of the injector
and hence for all experiments FID is taken as a measure of the amount of fuel
injected into the manifold. During AFR transients the mass of fuel injected
into the manifold is different from the mass of fuel that enters the cylinder
because of the wall-wetting phenomenon(chapter 4).
In this thesis change in injection timing is conjectured to influence re-
sponse of the wall-wetting phenomenon. We therefore describe a physics
based model for this phenomenon so that influence of injection timing can
be better understood. This is the subject of the next chapter.
26
38. No. of cylinders one
Cylinder Volume 125 cc
Max Power(at 7250 rpm) 7.16 kW
Max Torque(at 5000 rpm) 9.3 Nm
Compression Ratio 9.2 : 1
Intake Valve Opens (5% of maximum) 17 ◦
before intake TDC
Intake Valve Closes (5% of maximum) 210 ◦
after intake TDC
(a) Engine Specifications
Part Specifications
UEGO Response time = 25 ms
Pressure transducer Response time = 1 ms; Range-(0-3 bar abs)
Fuel Injector Used in Honda CBR 600RR motorcycle
(b) Sensor and Actuator Specifications
Motor Make Bosch Rexroth
Motor Type 3-Phase Synchronous Servo
Motor
Peak Power 39 kW
Peak Torque 231 Nm
Max Speed 2800 rpm
Speed Control rise time 5 ms
Torque Control rise time 0.6 ms
(c) Transient Dynamometer Specification
Table 3.1: Experimental setup details
27
39. Chapter 4
Wall-Wetting phenomenon
In port-fuel injected engines not all of the injected fuel enters the cylinder
for combustion but a significant fraction gets accumulated onto the intake
pipe walls and intake valves in the form of a liquid film (figure 4.1). This
accumulated fuel film evaporates over time and enters the cylinder for com-
bustion only in subsequent engine cycles. This phenomenon is described as
the wall-wetting phenomenon.
In this thesis fuel injection timing is shown to influence the quantity
of the wall-film that evaporates over an engine cycle. Thus, in order to
understand the influence of injection timing better it is important to gain
greater insight into the wall-wetting phenomenon. This is accomplished in
this chapter by considering a simplistic model for this phenomenon(section
4.1), parameters of which are then determined by considering the phenomena
of droplet(section 4.2) and wall-film evaporation(section 4.3).
28
40. 4.1 Aquino Model
The accumulated wall-film mass experiences convective evaporation due to
flow of air in the intake pipe from the throttle side (figure 4.1). The evap-
Figure 4.1: Wall-film deposition
oration of this accumulated fuel film is considered to be proportional to the
area and hence to the mass of the wall-film itself(mf )[1]. Thus, it is modeled
as
˙mevp =
mf
τ
(4.1)
The parameter τ is the evaporation time constant which is expected to be
dependent on the engine operating conditions. Assuming κ as the fraction
of the injected fuel that hits the intake pipe walls, applying mass balance to
the wall-film gives,
˙mf = κ ˙minj − ˙mevp
⇒ ˙mf = κ ˙minj −
mf
τ
29
41. ⇒ τ ˙mf + mf = κτ ˙minj (4.2)
where ˙minj is the mass rate of fuel injection. Equation 4.2 governs how the
fuel-film mass and hence the rate of evaporation of it varies with the rate of
fuel injection. It may be noted that at a steady rate of fuel injection into the
engine i.e. when ˙minj = constant, the wall-film film mass settles to a steady
value. This implies that rate of evaporation of mass-film and therefore the
mass of fuel entering the cylinder also reaches a steady value.
Let ∆ ˙minj be deviation in the rate of fuel injection from a steady value
and let ∆mf be corresponding deviation in the mass of the wall-film. Then
from equation (4.2), we have
τ∆ ˙mf + ∆mf = κτ∆ ˙minj
Putting the above equation in Laplace domain gives,
∆mf (s)
∆minj(s)
=
κτs
τs + 1
From equation (4.1) we have,
∆mevp(s)
∆minj(s)
=
κ
τs + 1
Since any deviations in AFR at steady state operation of the engine can
be attributed to deviations in the mass of fuel entering the cylinder while
deviations in fuel mass injected are proportional to deviations in fuel injection
duration(FID)(section 3.2), we have
∆λ
∆FID
=
−c1
τs + 1
(4.3)
where c1 > 0 is a parameter which is experimentally determined. The nega-
tive sign in numerator indicates that an increase in FID causes a decrease in
AFR.
30
42. Figure 4.2: Wall-wetting dynamics
(ω = 3000 rpm, pman = 0.80 bar, MAT= 65 ◦
C)
Figure (4.2) demonstrates the wall-wetting dynamics when a step change
in FID is given to the engine. The model fits the observation well for c1 = 10.0
ms−1
and τ = 0.3 s
The parameters κ and τ signify the impingement fraction and the evapo-
ration time constant of the deposited fuel film respectively. These parameters
vary based on engine operating variables and the conventional approach has
been to identify them experimentally at a few operating conditions of the en-
gine and interpolate for other operating conditions. However, this approach
is very time-consuming and would be not very efficient at meeting future
stricter emission standards. Moreover, a physics based understanding would
provide greater insight into the dynamics and its dependence on engine vari-
ables than one based on extensive experimentation. This chapter proposes
one such model for wall-wetting dynamics considering the phenomena of
31
43. droplet evaporation and wall-film evaporation.
Section 4.2 proposes a model for evaporation of a fuel droplet once it
is injected into the intake pipe while section 4.3 proposes an accumulated
wall-film evaporation model.
4.2 Droplet evaporation
With port-fuel injected engines, pressurized fuel is injected into the intake
pipe through fine orifices of the injector. This causes fuel to be injected in the
form of a fine spray of droplets. It is assumed that all droplets are spherical
in shape and having the same diameter. In addition, since the fuel injection
pressure is usually much higher (∼ 4-5 times) compared to the pressure in
the manifold, the speed of the injected droplet is assumed to be far greater
than the speed of air flowing in the intake pipe.
4.2.1 Motion of a droplet
A droplet injected at high speed into the intake pipe is expected to experience
high drag force during its travel in the surrounding air. A measure of this
drag force is given by coefficient of drag defined as [19]:
CD :=
FD
1
2
ρaAVD
2
The drag coefficient for a spherical object has been found to be[19]:
CD = 0.4 +
24
ReD
+
4
√
ReD
Applying Newton’s law to the droplet gives,
dVD
dt
= −
1
2mD
ρaAVD
2
CD
f1(D,VD)
(4.4)
32
44. The initial value for the velocity of the droplet VDo can be obtained by
applying Bernoulli’s principle across the injector. Thus,
VDo =
2
ρf
(pf − pman) (4.5)
Equation (4.4) is a nonlinear differential equation in velocity of the droplet
(VD) and also involving droplet diameter(D). Solution to this equation would
give variation of speed of droplet with time as it travels through intake pipe
after injection. The droplets would travel until either they hit the intake pipe
walls or the intake valves open, whichever occurs earlier. It is assumed that
when the intake valve opens, all airborne droplets would be drawn directly
into the combustion chamber.
However, the droplet diameter changes with time as in travels in air due
to fuel evaporation from the surface. This is discussed in the next section.
4.2.2 Convective mass transfer
During travel of fuel droplets in the intake pipe, in addition to the drag
experienced by them, vaporization of fuel also occurs from the surface. This
vaporization causes the droplet diameter to decrease continuously and the
vaporized fuel diffuses into the surrounding air contributing to the air-fuel
mixture for combustion.
The convective mass transfer rate of species A from a surface maintained
at species molar concentration of CAs and with a fluid of species molar con-
centration CA∞ flowing over it will depend not only on the differences in
the concentrations but also on the tendency of gasoline vapor to diffuse into
surrounding medium of air. This tendency of diffusion is captured by the
convective mass transfer coefficient hm. The molar rate of evaporation can
33
45. thus be expressed as:
NA = hm(CAs − CA∞ ) (4.6)
where NA is in kmol/s.m2
. For a spherical droplet of diameter D, molar
mass transfer rate from the surface is given by:
NA := −
d(m/As)
dt
= −
ρf
6M
dD
dt
(4.7)
The molecules of the fuel droplet at the surface, due to their intrinsic
kinetic energy, have a tendency to escape and form a layer of vaporized fuel
around the droplet. At the same time, the gaseous vapor has a tendency to
condense back onto the droplet. An equilibrium between liquid and gaseous
phase is reached at a particular partial pressure of the vaporized fuel based on
the temperature of the droplet. This partial pressure at a given temperature
Ts of the droplet is given by the Clausius-Clayperon equation as[18]:
pAs = pref exp
hfgM
R
1
Tref
−
1
Ts
(4.8)
where hfg is the enthalpy of vaporisation of gasoline and Tref is the boiling
temperature of gasoline at reference pressure pref . It is assumed in this
analysis that the temperature of the droplet does not change during its travel
in the intake pipe. Thus, molar concentration of fuel vapor at the surface,
given as:
CAs =
pAs
RTs
depends only on the temperature of the droplet, assuming ideal gas behavior
of gasoline vapor.
Several empirical relations exist expressing the convective mass transfer
coefficient from a spherical droplet as a function of physical properties of the
droplet and the surrounding medium. One widely used empirical relationship
34
46. given for freely falling droplets by Ranz and Marshal[16] is:
ShD :=
hmD
DAB
= 2 + 0.6 Re
1/2
D Sc1/3
(4.9)
where Sc is the Schmidt number defined as Sc := ν
DAB
. The first term
represents natural convective mass transfer while the second term is for forced
transfer. DAB is a property of the binary mixture called as binary diffusion
coefficient. It is a measure of ease of diffusion of gasoline vapor into a gaseous
mixture of air and gasoline. Using kinetic theory of gases, it has been deduced
that DAB ∝ T3/2
p−1
where T and p are temperature and pressure of the
complete mixture respectively[18]. Physically, this can be justified as an
increase in temperature causes an increase in kinetic energy of the vapor
molecules and hence is expected to increase the tendency for diffusion while
an increase in pressure would increase the opposition to motion and hence
decrease diffusion.
Putting equations (4.7) and (4.9) in equation (4.6) gives:
−
ρf
6M
dD
dt
= 2 + 0.6Re
1/2
D Sc1/3 DAB
D
(CAs − CA∞ )
⇒
dD
dt
=
−6MDAB (CAs − CA∞ )
ρf
2 + 0.6Re
1/2
D Sc1/3
D
The first factor in this nonlinear ordinary differential equation is a constant
for one operating condition of the engine while the second factor is a func-
tion of droplet diameter(D) and velocity of droplet(VD) through Reynolds
number. Substituting for the Reynolds number in terms of D and VD, the
equation can be written as:
dD
dt
=
−L 2 + Λ
√
VDD
D
f2(D,VD)
where, (4.10)
35
47. L :=
6MDAB (CAs − CA∞ )
ρf
Λ := 0.6
ρa
µ
Sc1/3
L and Λ are constants at a given operating condition of the engine. The so-
lution to this equation, at a given operating condition, will give the variation
of droplet diameter during its motion in the intake pipe.
4.2.3 Coupled differential equation analysis
Equations (4.4) and (4.10) are coupled differential equations which are to
be solved simultaneously to get variation of droplet diameter and distance
traveled by the droplet as a function of time during its flight. The droplets are
assumed to remain airborne until either they hit the intake walls or intake
valve opens when all droplets are assumed to be drawn into the cylinder,
whichever occurs earlier. Thus equations are solved until time t = ξ where
ξ = min(tw, tivo − tinj). The time the droplet takes after injection to hit the
walls (tw) is obtained by solving the equation:
sw =
tw
0
VD dt (4.11)
where sw is shortest distance of the wall across the injector.
A sample solution of these equations has been plotted for two different
initial droplet diameters. Data for the engine operating conditions was ob-
tained from measurements made on the engine. The data used for simulation
has been tabulated in table 4.1.
From figure 4.3a, it is observed that a droplet of initial diameter 150µm
takes around 4 ms to cover a distance of swall = 6.08 cm and reach the
wall on the opposite side. During this travel towards the opposite end the
droplet can lose at most around 14% of its total mass through evaporation.
Now, if injection of fuel happens less than 4 ms before intake valve opening
then most of the injected fuel would enter the cylinder under the assumption
36
48. ω 2500 rpm
pman 0.70 bar
MAT 56 ◦
C
sw(manifold geometry) 6.08 cm
(a) Engine parameters
Tboil (1atm) 126 ◦
C
hfg(octane) 300 kJ/kg [18]
M 112.2 kg/kmol
ρf 746.6 kg/m3
(b) Fuel properties
µair (T = 56 ◦
C) 2 × 10−5
Ns/m2
[10]
Sc 1.5 [15]
(c) Air-Gasoline mixture properties
pinj 4 bar
Do(simulation) 50 & 150 µm
(d) Fuel injection properties
Table 4.1: Simulation Parameters
that when intake valve opens all airborne fuel droplets are sucked into the
cylinder. However, less than 14% of the fuel mass would be in vapor form
and other would be in liquid droplet form which are known to produce excess
hydrocarbons[20]. On the other hand, if fuel is injected more than 4 ms before
intake valve opening then only 14% of injected mass enters the cylinder, all
of which is in vapor form, and the remanining fuel forms a wall film in the
intake pipe.
Contrastingly, it is found that for initial droplet diameter of 50µm,
injected droplets never reach the opposite wall but always remain airborne
(figure 4.3b). Hence most of the fuel is expected to enter the cylinder on
intake valve opening. However, based on injection timing, there would be
varying proportion of fuel in droplets and vapor form entering the cylinder.
Similar computations can be done at each operating condition of the engine
pman, ω, MAT and for a given injection timing to predict the fraction of
37
49. (a) Initial Droplet Dia = 150µm (b) Initial Droplet Dia = 50µm
Figure 4.3: Droplet evaporation with time
injected fuel entering the cylinder. This would be the parameter κ in the
wall wetting dynamics model described at the beginning of the chapter.
4.3 Port-Wall Film Evaporation
The injected droplets which hit the intake pipe wall form a layer of fuel along
the length of the intake pipe. This fuel evaporates with time and mixes with
the incoming air to form the air-fuel mixture for combustion. The rate of
evaporation of the film will depend on the flow rate of air in the intake pipe
and a methodology to estimate it is proposed in section 4.3.1. Section 4.3.2
then proposes a model for predicting the rate of evaporation of wall film.
4.3.1 Estimation of air velocity
An engine cycle is composed of a number of discrete events. One impor-
tant discrete event that plays a role in the intake air dynamics is the open-
38
50. Figure 4.4: Intracycle manifold pressure variation
ing/closing event of the intake valve. This is reflected in the way in the way
manifold pressure varies over an engine cycle called as intra-cycle variation.
A sample plot of intra-cycle manifold pressure over an engine cycle is shown
in the figure 4.4. The manifold pressure rises during the period when intake
valve is closed due to filling of the manifold with air from the throttle side
and it falls when intake valve is open due to the air drawn into the cylin-
der causing the manifold to empty. This emptying-filling phenomena can be
modeled as follows:
Considering the manifold as a control volume, mass conservation equation
at any instant of time can be written as(figure 4.5):
dmman
dt
= ˙mthrottle − ˙mcylinder (4.12)
The intake pipe of the engine is usually modeled as a converging-diverging
39
51. Figure 4.5: Intake pipe air-flow
nozzle with the throat occurring at the location of throttle plate[7][4]. It is
assumed that the flow in the intake pipe is isentropic and frictionless. Using
compressible fluid flow theory, the mass flow of air through the throttle can
then be expressed as[7]:
˙mthrottle = cd · Athrottle ·
patm
√
RTatm
· Ψ(
patm
pman
) (4.13)
Ψ
patm
pman
=
γ 2
γ+1
γ+1/γ−1
if pman ≤ pcr
pman
patm
1/γ
· 2γ
γ−1
· 1 − pman
patm
γ−1
γ
if pman ≥ pcr
(4.14)
(4.15)
and where
pcr =
2
γ + 1
γ
γ−1
patm
is the critical pressure where the flow reaches sonic conditions at the throttle
section. At patm = 1 bar, pcr turns out to be 0.528. The manifold pressure,
for most operating conditions, remains above this critical value and hence
it is assumed for this analysis that flow never chokes at the throttle. When
the intake valve is closed, no air flows into the cylinder and hence the second
40
52. term on the right of equation 4.12 can be dropped. Hence equation becomes:
dmman
dt
= ˙mthrottle (4.16)
Assuming ideal gas behavior of air we have:
dmman
dt
=
VmanMa
RTman
dpman
dt
(4.17)
Using equations 4.13, 4.16 & 4.17 we get:
dpman
dt
= K ·
IV O
IV C
pman
patm
1/γ
· 1 −
pman
patm
γ−1
γ
dt (4.18)
where the parameter K varies largely with the throttle position(Athrottle) as:
K :=
cdAthrottlepatm
√
RTatm
2γ
γ − 1
MaVman
RTatm
patm (4.19)
The solution to this equation predicts the variation of manifold pressure
with time when the intake valve is closed. The value of the parameter K is
chosen such that the mean square error is minimized between the predicted
and actual value measured using a manifold air pressure sensor. A sample
calibration plot is as shown in figure 4.6.
The value of parameter K obtained by such a calibration is a measure of
throttle opening of the engine. This value can then be used in equation 4.13
to get:
˙mthrottle =
cdAthrottlepatm
√
RTatm
2γ
γ − 1
pman
patm
1/γ
1 −
pman
patm
γ−1
γ
(4.20)
(4.21)
= K ·
MaVman
RTman
patm
pman
patm
1/γ
1 −
pman
patm
γ−1
γ
(4.22)
The average flow rate of air can then be obtained as:
˙mavg =
K · MaVman
RTman
patm cycle
pman
patm
1/γ
1 − pman
patm
γ−1
γ
dt
tcycle
(4.23)
41
53. Figure 4.6: Model calibration based on observed manifold pressure
Once K is known, above equation can be integrated using measurements
made by a manifold pressure and temperature sensor to get the average air
mass flow rate. An estimate of velocity of air (Va) flowing in the intake
pipe can thus be obtained through real-time implementation of the above
methodology.
4.3.2 Film evaporation
The fuel film in the intake pipe is modeled as a liquid surface A exposed to
an air-stream flowing with a velocity Va over it. The analysis for wall film
evaporation is on similar lines as that for droplet evaporation. The rate of
evaporation from the film surface is expressed :
NA = hm(CAs − CA∞ )
42
54. ⇒
˙mevp
MAwf
= hm(CAs )assuming CA∞ = 0
⇒ ˙mevp = MAwf hmCA
⇒ ˙mevp = M
mf
tf ρf
hmCA (4.24)
The factor CA∞ is assumed 0 because incoming air is assumed to contain
hardly any gasoline vapors. The concentration (CA) is obtained using wall
film temperature(Tw) in a manner similar to that used for droplet evapo-
ration. The convective mass transfer coefficient (hm) is obtained using the
widely used empirical relation given below[10]:
ShF :=
hmDpipe
DAB
= 1 + 0.023 Re0.83
pipe Sc0.44
The estimate of velocity of air at a given operating point obtained using
methodology of Section 4.3.1 is used to obtain Reynolds number in the above
equation.
Comparing equations 4.24 and 4.1, we get:
τ =
tf ρf
MhmCA
(4.25)
The wall film thickness (tf ) and convective mass transfer coefficient (hm) are
different at different operating conditions of the engine. Hence the wall-film
dynamics is expected to change at different operating conditions. Further,
since wall-film evaporation is dependent of mass of the wall-film, the output
of the droplet evaporation model in terms of fraction κ is used as an input
to solve wall-film evaporation model.
To summarize, models for estimating fraction of injected fuel that evapo-
rates and rate of evaporation of wall-film have been proposed in sections 4.2
and 4.3. These models when put together can be used to estimate the mass
of fuel entering the cylinder per cycle. However, before these models can be
43
55. validated and used, it is important to determine how parameters of the model
are sensitive to operating conditions so that measurements can be made with
appropriate accuracy. This is the done in the next section.
4.4 Model sensitivity analysis
The equation governing evolution of the droplet in the evaporation model
proposed in section 4.2 is:
dD
dt
=
−L 2 + Λ
√
VDD
D
f(D,VD)
where,
L :=
6MDAB (CAs − CA∞ )
ρf
The parameters DAB, CAs and Sc depend on temperature of the droplet and
thus we determine sensitivity of the model to droplet temperature estimates.
Now, as discussed previously, we have
DAB ∝ T3/2
p−1
and
CAs =
pAs
RTs
where,
pAs = pref exp
hfgM
R
1
Tboil
−
1
Ts
Thus for a ∆TD change in temperature of the droplet ,assuming other
conditions remains the same, we have:
∆DAB
DAB
=
3
2
∆TD
TD
and (4.26)
∆CA
CA
=
hfgM
R
∆TD
T2
D
−
∆TD
TD
(4.27)
Thus ∆L
L
can be written as:
∆L
L
=
3
2
∆TD
TD
+
hfgM
R
∆TD
T2
D
−
∆TD
TD
(4.28)
44
56. Using the above equation it is found that a 6% in change in TD at TD =
330 K gives a 76% change in L for parameter values stated in table 4.1. Hence
evolution of the droplet is very sensitive to the temperature of the droplet
and an accurate estimation of it is desired. This high sensitivity is due to
exponential dependence of CA on droplet temperature. This exponential
factor also makes the solution very sensitive to errors in values of enthalpy
(hfg) and molecular weight(M) of gasoline. Hence accurate composition of
gasoline used is also desired.
4.5 Summary
This chapter discusses a model to capture wall-wetting phenomenon observed
in port-fuel injected engines. The phenomenon has been modeled by first
considering evaporation of fuel droplets once fuel is injected. The output
result of this model is then used as an input for the wall-film evaporation
model and both these models together help determine the quantity of fuel
that enters the cylinder. The predictions of these models for droplet and
wall-film evaporation have been shown to be very sensitive to droplet and
wall-film temperature as well as to the physical properties of fuel and hence
accurate determination of these quantities is critical to validation. Further,
the model for wall-film evaporation depends on the thickness of the fuel
film deposited in the intake port and a measurement for this is necessary to
validate the model.
The influence of injection timing on engine behavior is shown to depend
on the parameters of the wall-wetting model in the next chapter and thus a
methodology to accurately estimate these parameters becomes important in
order to use injection timing as a control input.
45
57. Chapter 5
Influence of injection timing
The engine cycle is composed of a number of discrete events which occur
periodically. Fuel injection is one such discrete event which usually occurs
once every cycle. We define fuel injection timing(FIT) as the crank angle in
degrees before the top dead center of intake stroke at which injection happens
(figure 5.1). Advancement in injection timing is considered as an increase in
Figure 5.1: Injection timing diagram
46
58. injection timing as measured from TDC of intake stroke while retardation is
considered as a decrease in injection timing.
This chapter describes the experimental observation made on air-fuel ratio
when FIT is changed in real-time(section 5.1). A mathematical model is
derived to describe the observed phenomenon ans subsequently the model
is used for synthesis of a controller to achieve tighter control of AFR. The
efficacy of the control action has been verified experimentally.
5.1 Experiments - Change in FIT
5.1.1 Measured quantities
Figure 5.2: Fuel flow dynamics study using AFR
A dynamic relationship exists between the amount of fuel injected into
the manifold and the amount of fuel entering the cylinder because of the
wall-wetting phenomenon. In order to understand and validate any proposal
47
59. describing this dynamics it is important to have measures of both these
quantities.
An input-output view of the air and fuel flow dynamics is shown in figure
5.2. The mass of air inducted is a function of the throttle position(α), engine
speed(ω) and manifold air temperature(MAT)[7]. The throttle position is
held at a fixed position using a stepper motor while the engine speed is held
steady using the transient dynamometer. An external air blower helps hold
MAT with sufficient accuracy. All this helps ensure a steady flow rate of air
into the engine. AFR signal is then used as to monitor changes in fuel flow
into the cylinder.
Further, we assume that the amount of fuel injected into the manifold
is directly proportional to the opening time of the injector. Thus for all
experiments, fuel injection duration(FID) is taken as a measure of fuel that
is injected into the manifold every injection event.
5.1.2 Experimental Observation
Figure 5.3 shows the response of AFR to a step advance and a step re-
tardation in injection timing with the engine held at a steady state. This
experiment was conducted at an engine speed of 3000 rpm and MAT of 65 ◦
C.
FID was fixed at a particular value to ensure that same amount of fuel was
injected every injection event.
As observed from figure 5.3, an advancement in injection timing from
100 to 300 degrees causes an initial sharp fall in AFR from 14.6 to 13.3
though the steady state AFR remains the same. It is thus concluded that an
advancement in injection timing by 200 degrees causes close to 9% change
in quantity of fuel that enters the cylinder initially. However, the steady
state value of amount of fuel entering the cylinder remains the same before
48
60. Figure 5.3: AFR variation with FIT
(ω = 3000 rpm, pm = 0.80 bar, MAT = 65 ◦
C)
and after the change in timing is made. A similar conclusion is drawn for a
retardation in injection timing.
A phenomenological explanation for this observation is given in the next
section while a mathematical model capturing this phenomenon is proposed
and validated in sections 5.2 and 5.3. This observed phenomenon is then
exploited for tighter control of AFR in the transient state in section5.4.
5.2 Phenomenological explanation
The wall-wetting dynamics in port-fuel injected engines gets excited every
time fuel injection happens in its intake port. Every fuel injection event leads
to deposition of a fraction of the injected fuel onto the intake port walls which
49
61. Figure 5.4: Wall-film evaporation and FIT diagram (∆FIT = 0)
then evaporates and enters the cylinder for combustion in subsequent cycles.
A widely used model describing this evaporation process, as discussed in
section 4.1, is expressed mathematically as [1]:
˙mevp =
mf
τ
(5.1)
The wall-wetting dynamics thus turns into the following(section 4.2):
˙mf = k ˙minj − ˙mevp
⇒ τ ˙mf + mf = kτ ˙minj (5.2)
Periodic excitation(once every engine cycle) of this dynamics simulating
engine running conditions at 3000 rpm gives the following plot (figure 5.4).
This plot gives variation of wall-film mass(mf ) with time. From equation
5.1 it may be noted that the shaded area in the above figure is a measure of
the amount of fuel that enters the cylinder per cycle for combustion through
wall-film evaporation.
50
62. Figure 5.5 shows the response of wall-wetting dynamics to an advance-
ment in injection timing. It may be noted that a change in injection timing
causes a change in the time interval between a pair of injection pulses(see
the injection pulse below).
Figure 5.5: Wall-film evaporation and FIT diagram(∆FIT = 200 ◦
)
As observed from this figure, an advancement in injection timing causes
an aperiodic deposition of fuel on the intake walls. This leads to an increased
amount of fuel entering the cylinder for few subsequent cycles through greater
evaporation. However, the steady state value of fuel amount entering the
cylinder remains unchanged. Further, it is observed that a change in FIT
causes a sharp initial change in amount of fuel that enters the cylinder. It
is this observed phenomenon that provides the motivation to use FIT as a
control input to achiever tighter transient AFR control.
We propose a mathematical model in the next section capturing this
phenomenon which is later used for systematic controller development to
51
63. control AFR using both FID and FIT.
5.3 Modeling influence of injection timing
5.3.1 Analytical Formulation
Combining the wall-film dynamics model (5.2) with the evaporation model
(5.1) we get,
τ ¨mevp + ˙mevp = κ ˙minj
Expressing it as a transfer function gives,
Mevp(s)
Minj(s)
=
κ
τs + 1
(5.3)
where Mevp(s) and Minj(s) are the Laplace transforms of the signals mevp(t)
and minj(t) respectively. We now compare the mass of wall-film that evap-
orates when an advance in injection timing is made with the case when no
advance in timing is made. This will help us get an analytical formulation of
the excess mass of fuel that evaporates and enters the cylinder for combustion
for an injection timing advance.
A typical fuel mass flow-rate pulse train ( ˙minj signal) is shown in figure
(5.6). The area under each injection pulse numerically equals the mass of
fuel that is injected into the engine per cycle(mpul). Assuming each injection
pulse to be an impulse of area equal to mpul, the Laplace transform for the
injection pulse train with advance can be written as,
sMinj(s) = mpul + mpule−s(T−∆FIT)
+ mpule−s(2T−∆FIT)
+ · · · (5.4)
From equation 5.3 we get,
Mevp(s) =
κ
s(τs + 1)
sMinj(s) = (
1
s
−
τ
τs + 1
)κsMinj(s) (5.5)
52
64. Figure 5.6: Fuel mass flow-rate signal
Combining equations 5.4 and 5.3, we get
Mevp(s) = mpul
κ
s
(1 + e−s(T−∆FIT)
+ e−s(2T−∆FIT)
+ · · ·
− mpul
κτ
τs + 1
(1 + e−s(T−∆FIT)
+ e−s(2T−∆FIT)
+ · · ·)
The inverse Laplace transform to fetch the output signal in time domain
gives
mevp(t) = mpulκ[u(t − 0) + u(t − (T − ∆FIT)) + · · ·]
− mpulκe−t/τ
[1 + e−∆FIT/τ
(eT/τ
+ · · ·)]
where u(t−Γ) is the unit step at t = Γ (figure 5.7). Thus, wall-film evaporated
after n-injection pulses is,
mevp(nT)|with advance = mpulκ(n + 1)
53
65. Figure 5.7: Unit step signal (Γ = 2sec)
− mpulκe−nT/τ
[1 + e−∆FIT/τ
(eT/τ
+ · · ·)]
= mpulκ(n + 1)
− mpulκ[e−nT/τ
+ e−∆FIT/τ 1 − e−nT/τ
1 − e−T/τ
]
This gives the mass of wall-film that evaporates after n-injection pulses when
an injection timing advance of ∆FIT is given.
In order to obtain mass of wall-film that evaporates after n-injection
pulses without any advance in injection timing, we simply set ∆FIT = 0
in the above equation. Thus we get,
mevp(nT)|no advance = mpulκ(n + 1)
− mpulκ(e−nT/τ
+
1 − e−nT/τ
1 − e−T/τ
) (5.6)
Thus the extra mass of wall-film that evaporates when an advance in injection
timing is given is expressed as:
∆mevp(nT) = mevp(nT)|with advance − mEV P (nT)|no advance
= mpulκ(1 − e−∆FIT/τ
)
1 − e−nT/τ
1 − e−T/τ
(5.7)
54
66. Figure 5.8: Prediction of the analytical formulation
(∆FIT = 200 degrees, κ = 0.8, τ = 0.3, mpul = 0.3mg, T = 40 ms)
For sufficiently large n, the above equation can be turned into a continuous
time equation by putting nT ≈ t which gives
∆mevp(t) = mpulκ
(1 − e−∆FIT/τ
)
(1 − e−T/τ )
(1 − e−t/τ
)
⇒ ∆ ˙mevp(t) = mpul
κ
τ
(1 − e−∆FIT/τ
)
(1 − e−T/τ )
e−t/τ
evolves with time
(5.8)
The above equation gives the manner in which the excess wall-film mass
evaporates with time when a step change in injection timing is made. The
response of this equation for ∆FIT = 200 degrees is shown in figure 5.8.
5.3.2 Model Validation
As seen from figure 5.8, response of the analytical formulation to a change
in injection timing consists of an impulsive part(derivative action) and a
decay part similar to one observed for first order systems. This provides the
55
67. Figure 5.9: FIT model - fitting on observation
(ω = 3000 rpm, pm = 0. bar, MAT = 65 ◦
C)
motivation to capture influence of injection timing using the following linear
model expressed in transfer function domain as:
∆λ(s)
∆FIT(s)
=
−c2s
τs + 1
(5.9)
The evaporation constant τ is determined experimentally by fitting the
wall-wetting dynamics model on actual response of AFR to changes in FID
(section 4.1). Fitting of the model on experimental observation made at
engine operating conditions of ω = 3000 rpm, pm = 0.80 bar, MAT = 65 ◦
C
gives τ = 0.3.
Figure (5.9) shows how prediction of the model(equation 5.9) for influence
of injection timing compares with the observation. The parameter c2 was
found to be 2.05 × 10−3
s/crank deg.
Looking at the above equation as well as the observed response of air-fuel
56
68. Figure 5.10: Comparison - AFR response with and without FIT change
(ω = 3000 rpm, pm = 0. bar, MAT = 65 ◦
C)
ratio to changes in injection timing, it can be seen that though injection
timing cannot influence the steady state value of AFR, the rate of change of
∆FIT term on the input side can produce sharp changes in AFR when finite
changes in injection timing are made due to its derivative action. This opens
up the possibility to obtain tighter control in AFR by using injection timing
as a control input in conjunction with quantity of fuel delivered. This is the
focus of the next section.
5.4 Controller development
The speed of response of AFR to changes in fuel quantity injected is limited
by the wall-wetting dynamics. This speed of response can be significantly
57
69. Figure 5.11: MIMO control - feedback architecture
enhanced if appropriate changes in FIT are made in conjunction with FID.
The plots (figure 5.10) compare the experimentally observed performance of
system using both FID and FIT as inputs vis-a-vis one using only FID as an
input. It is clearly seen that faster AFR response is obtained through the
use of both inputs.
In order to achieve tight AFR control, an appropriate strategy has to be
decided upon to control the two available inputs. The approach we adopt
uses an AFR sensor in feedback to decide upon the inputs FID and FIT.
This particular system architecture is demonstrated in figure (5.11).
In-order to build a linear feedback controller, we express the two input
one output system in state space form as discussed in section 2.2.
58
70. 5.4.1 State Space Model of the plant
The influence of fuel injection duration and injection timing on AFR are
captured through the following linear models (equations 4.3 and 5.9):
∆λ(s)
∆FID(s)
=
−c1
τs + 1
&
∆λ(s)
∆FIT(s)
=
−c2s
τs + 1
On putting them together we obtain,
∆λ(s) =
−c1
τs + 1
∆FID(s) +
−c2s
τs + 1
∆FIT(s) (5.10)
which on little manipulation gives,
∆λ(s) =
−c2
τ
∆FIT(s) +
1
τs + 1
[−c1∆FID(s) +
c2
τ
∆FIT(s)]
X(s)
(5.11)
Thus in the time domain,
∆λ(t) =
−c2
τ
∆FIT(t) + x(t) (5.12)
where x(t) is an intermediate variable given by
τ ˙x + x = −c1∆FID(t) +
−c2
τ
∆FIT(t) (5.13)
Putting equations (5.13) and (5.12) in matrix form gives,
˙x =
−1
τ
x + −c1
τ
c2
τ2
∆FID(t)
∆FIT(t)
(5.14)
∆λ(t) = x + 0 −c2
τ
∆FID(t)
∆FIT(t)
(5.15)
The above is the state space representation of the engine system. We
have a two-input, one-output system with one intermediate state. The state
59
71. x here represents the mass of the fuel film(mf ) on the walls of the intake
pipe. Comparing with the standard state-space form in section 2.2, we see
that in this case
A =
−1
τ
B = −c1
τ
c2
τ2
C = 1
D = 0 −c2
τ
Thus the controllability and observability matrices are
M = [B] = −c1
τ
c2
τ2
S = [C] = 1
Both these matrices have rank = 1 except for c1 = c2 = 0 and hence the
system is completely controllable and observable (section 2.2).
5.4.2 Feedback Controller
We employ state feedback to regulate output of the system around a desired
value. On substituting
∆FID(t)
∆FIT(t)
= −
k1
k2
x (5.16)
into equation 5.14, we get
˙x = (
−1
τ
+
c1k1
τ
−
c2k2
τ2
)
β
x (5.17)
In-order for the feedback system to be stable, we require that β < 0. Further,
β governs the speed of response of the system. A larger magnitude for β gives
faster convergence of x to 0 and hence faster response of the system.
We compare the following two scenarios:
60
72. • FIT is not used as control input i.e. k1 = 0, k2 = 0
• Both FID and FIT are used as control inputs i.e. k1 = 0, k2 = 0
While comparing it is ensured that the AFR response for the two cases is
kept as close to each other as possible and then comparison is made between
the amount of input effort needed to achieve that response in either case.
Responses are kept similar by choosing the same value for β in both the
cases.
Figure 5.12a shows the response of the system using only FID as a control
input for k1 = −0.1 as well the actuator effort in terms of change in FID
(∆FID) required to achieve that response. In this case β turns out to be
−6.67.
With k1 and k2 both non-zero, it is seen that infinite combinations of
them can give β equal to −6.67. Thus, we impose additional constraint in
terms of the amount of control inputs that can be used in order to determine
the gain values. We express this constraint in the form of an LQR integral
to be minimized (section 2.2) with Q and R matrices as follows:
Q = 95.92
R =
3840 0
0 0.0058
The specific choice made for the matrices Q and R is explained in Appendix
A. The gain values obtained for these performance matrices by solving the
Ricatti equation are k1 = −0.0565, k2 = 51. Figure 5.12b shows the system
response along with the actuation effort for this case.
Since the state ’x’ of the system, which is the mass of the wall deposited in
the intake pipe, is a quantity not measurable usually, we employ an observer
to estimate the state which is then used for feedback. The value of the
61
73. observer gain is chosen such that estimated state converges to the actual by
an order of magnitude times faster than the performance desired out of the
feedback system.
5.4.3 Results and Discussion
It is observed from figures (5.12a) and (5.12b) that in order to achieve same
level of system performance in terms of AFR response, the maximum FID
actuation input required in the case where both inputs are utilized is close
to 0.04 ms compared with the case with only FID as the input where it is 0.1
ms. Thus, considerably lower actuation effort is required(lower by 60%) to
achieve the same level of system performace when both inputs are utilized.
Expressed in other terms, utilizing the same amount of actuator, a faster
response of the system can be obtained with the use of both FID and FIT
as inputs and thus tighter air-fuel ratio control is achievable.
62
74. (a) Only FID as input
(b) Both FID and FIT as input
Figure 5.12: AFR response and actuation effort
63
75. Chapter 6
Conclusion
This chapter provides a summary of work presented in this thesis as well as
outlines possible problems for future work.
6.1 Summary and Conclusion
The focus of this thesis has been on investigating influence that dynamic
changes in injection timing has on the quantity of fuel that evaporates from
wall-film and hence on mass of fuel entering the cylinder per cycle. The
investigation has been carried out by conducting experiments on a single-
cylinder, port-fuel injected small-sized gasoline engine. This study gains
importance with the underlying objective of achieving tighter air-fuel ratio
control to reduce engine-out emissions.
Through the work for this thesis, it has been found that changes in injec-
tion timing cause a sharp change in quantity of fuel that enters the cylinder
for a few cycles, though the steady state value remains the same before and
after the change(section 5.1). This occurs because a change in injection tim-
ing causes a change in mass of wall-film that evaporates over an engine cycle
64
76. for few subsequent cycles.
It is this observed phenomenon that opens up the possibility to use injec-
tion timing as a control input to influence mass of fuel entering the cylinder
and subsequently achiever tighter AFR control. This has been demonstrated
in section 5.4.
6.2 Outline for future work
The work for this thesis was carried out on a single cylinder, port-fuel in-
jected, small-sized(125 cc) gasoline engine. It would be interesting to note
if an observation similar to one made in this thesis regarding influence of
injection timing can be made in multi-cylinder engines, particularly on ones
based on multi-point port-fuel injection(MPFI) architecture.
Also while carrying out work for this thesis, it was always ensured that fuel
was injected into the intake port in the time interval when intake valve was
closed. An investigation can be carried out to compare influence of injection
timing with injection done when intake valve is open to that made when
intake valve is closed and understand the possible reasons for the difference,
if any.
Another possible extension for this work could be a study to determine the
correlation between the wall-wetting phenomenon and influence of injection
timing on AFR at different operating conditions of engine, particularly at
different wall-film temperatures. An experimental validation of the wall-
wetting dynamics model proposed in chapter 4 would be of substantial help
while carrying out this study.
65
77. Appendix A
LQR Controller Design
The choice of the gain values for a controller required to meet LQR criteria
is arrived at by solving the Ricatti equation for appropriate choice of the
matrices Q and R(section 2.2). The specific choice of matrices Q and R is
made on the basis of performance desired of the feedback system.
In this thesis, we compare the following two control strategies for AFR
performance:
• FIT is not used as control input i.e. k1 = 0, k2 = 0
• Both FID and FIT are used as control inputs i.e. k1 = 0, k2 = 0
While comparing performances in the two cases, it is ensured that AFR re-
sponse for both cases is kept as close to each other as possible and comparison
is then made between the amount of input effort needed to achieve that re-
sponse. Responses are kept similar by choosing the same value for β in both
cases(section 5.4.2).
We set the following performance criteria to be achieved in both of the
above cases:
66
78. Figure A.1: System Response - Only FID as input
• AFR response for a unit initial displacement settles to within the 10%
band of its steady state value in a time period of less than 0.2 seconds
Mathematically, the specifications can be stated as
x(t) = 1.0 when t = 0,
x(t) < 0.1 for t > 0.2,
(A.1)
where x(t) is the state representing the mass of the wall-film. Figure 5.12a
shows system response when only FID is used as the control input. Specif-
ically, the gain values used are k1 = and k2 = 0.0 and the value of the
parameter β turns out to be -6.67.
For the case with both FID and FIT as control inputs, infinite combi-
nations of the gain values, k1 and k2, yield the same β value. Additional
constraints are thus imposed in the form of maximum limits on input signals
67
79. u1(t) and u2(t). We set the following limits:
|u1(t)| < 0.05 for all t > 0 and
|u2(t)| < 50 for all t > 0
Assuming a linear system, the free response of the state ’x(t)’ for a unit
initial deviation is of the form
x(t) = e−λt
for all t > 0
where λ is chosen such that the set performance specifications are met. Here
we choose λ = 12.0
Thus,
∞
t=0
x2
(t)dt =
∞
t=0
e−24t
dt = 0.0417 (A.2)
Since for a state-feedback controller u(t) = −Kx(t) we assume
u1(t) = 0.05e−12t
& u2(t) = 50e−12t
The coefficients 0.05 and 50 help satisfy the performance requirements in
terms of bounds on input signals. Thus
∞
t=0
u2
1dt = 1.042 ∗ 10−4
&
∞
t=0
u2
2dt = 104.2
(A.3)
The LQR criteria can thus be expressed in the form:
J =
∞
t=0
q
x2
(t)
0.0417
xT Qx
+ (r
u2
1
1.042 ∗ 10−4
+ (1 − r)
u2
2
104.2
)
uT Ru
dt where
q ≥ 0 and 0 ≤ r ≤ 1 (A.4)
68
80. Figure A.2: System Response - FID and FIT as inputs
Coefficient q decides which of the two criteria, accurate state regulation or
minimization of input effort, is given additional weightage while coefficient r
determines weightage for performance among the two inputs.
Trial and error to meet performance similar to that shown in figure A.1
leads to q = 4.0 and r = 0.5 and corresponding controller gain values ob-
tained by solving the Ricatti eqaution are k1 = −0.0565 and k2 = 51.76. The
system performance for these gain values is shown in figure A.2.
The Q and R matrices thus turn out to be:
Q =
4
0.0417
= 95.92 &
R =
r
1.042∗10−4 0
0 1−r
104.2
=
3840 0
0 0.0058
69
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