Engine Management Systems
John Lahti
John Deere Power Systems, Waterloo, IA, USA
1 Introduction
2 Engine Management System Components
3 Engine Control Strategies
4 Individual Cylinder Models
5 Conclusion
Nomenclature
References
Further Reading
1
1
1
3
13
15
15
16
16
INTRODUCTION
This chapter provides an overview of the engine control
strategies that are commonly used for diesel and spark
ignition engines. Models are now routinely used within the
electronic control unit (ECU) to predict parameters that are
not measured. The models may also be used for calculating
the required actuator positions. These models and their
use in the control structure are described. Strategies are
explained for modeling and controlling the airflow, exhaust
gas recirculation (EGR), variable geometry turbocharger
(VGT) vane position, fuel injection, and spark advance.
Model fidelity is discussed and a new individual cylinder
engine model is introduced.
Engine control strategies for diesel and spark ignition
engines are slightly different because of the different
combustion strategies, but for the most part the engine
models that are used for controlling the engine are the
Encyclopedia of Automotive Engineering, Online © 2014 John Wiley & Sons, Ltd.
This article is © 2014 John Wiley & Sons, Ltd.
DOI: 10.1002/9781118354179.auto068
Also published in the Encyclopedia of Automotive Engineering (print edition)
ISBN: 978-0-470-97402-5
same. The main control differences are in the way the
fuel is delivered, how combustion is initiated, and the
strategy for regulating the air to fuel ratio. With spark
ignition engines, the torque is regulated primarily with
the air throttle, while the fuel is normally delivered at a
rate that results in a stoichiometric mixture in the cylinder
for combustion. Diesel engines regulate torque by directly
controlling the fuel injection mass, with the engine running
lean most of the time. The fuel injection mass may be
limited to prevent smoke when there is insufficient air for
complete combustion. Engine models may be used in the
controller to predict some of the control parameters. The
models of engine flow, throttle flow, EGR, as well as the
turbocharger models are the same for both engine types.
In both applications, EGR is used to reduce emissions of
nitrogen oxides (NOx ). The same models can be used with
each engine type to predict the concentration of air in the
manifolds and in the cylinder.
2
ENGINE MANAGEMENT SYSTEM
COMPONENTS
Engine controls were originally implemented using
mechanical devices such as the carburetor, mechanical
diesel fuel injector, distributor with centrifugal or vacuum
advance, and thermal bimetal actuators. Although these
devices provided acceptable performance in many applications and were relatively inexpensive, they could not
provide the level of control needed to meet the emission
regulations of today. Many of the control functions
performed by these devices are now done electronically
using sensors and actuators. The sensors provide information about the operating condition of the engine while
the actuators are used to regulate its operation. The ECU
2
Engines—Design
Mass airflow sensor
Intake air
Temperature sensor
Turbocharger
speed sensor
Turbine
Compressor
uvgt
VGT vane
postion sensor
mcmp
Barometric
pressure sensor
Tcmp
ECU
Charge
air cooler
mfuel
mcac
Tcac Pcac
uicam
uecam
Crankshaft
position sensor
Intake camshaft
position sensors
Exhaust camshaft
position sensors
mtrb
χaem
Tem
uat
Air throttle
position sensor
mat
Tat
Intake manifold
pressure sensor
Intake
manifold
Intake manifold
temperature sensor
mim χaim
Tim Pim
uegr
miv
χaim
Tim
mev
χaevo
Tev
megr
χaegr
Tegr
Exhaust
manifold
Exhaust manifold
pressure sensor
mem χaem
Tem Pem
Oxygen sensor
megrcin
χaem
EGR valve
position sensor
Tem
EGR
cooler
megrc χaegr
Tegrc Pegrc
Figure 1. Engine components and model parameters.
processes information from the sensors and determines the
desired position for each actuator.
Some of the components that make up the engine control
system are shown in Figure 1. Also shown are model
parameters described later.
2.1
Sensors
Some sensors interpret inputs from the driver of the vehicle.
Examples of these include the accelerator pedal position,
transmission range selector, and brake pedal switch.
Other sensors provide information about the operating
condition of the engine. These include the coolant temperature sensor, intake air temperature sensor, and barometric
pressure sensor. These signals change at a slow rate,
allowing the sampling to occur at a slower rate than other
sensors.
Some sensors provide information about the current
state of the engine and may be used for feed forward and
feedback control. These include the crankshaft position
sensor, which is used for ignition and fuel injection timing
as well as for calculating the engine speed. The camshaft
position sensor along with the crankshaft position sensor
determines where each cylinder is within the engine cycle.
It may also be used to control camshaft phasing if the
engine is equipped with variable valve actuation. The
manifold air pressure sensor and mass airflow (MAF)
sensor are used in the airflow calculations that determine
the amount of fuel to inject and what spark advance is
required. Oxygen sensors in the exhaust system provide
feedback to the engine controller indicating whether the
engine is running rich or lean.
2.2
Actuators
Actuators are devices that regulate operation of the engine.
Examples of actuators include the fuel injector, air throttle,
Encyclopedia of Automotive Engineering, Online © 2014 John Wiley & Sons, Ltd.
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DOI: 10.1002/9781118354179.auto068
Also published in the Encyclopedia of Automotive Engineering (print edition) ISBN: 978-0-470-97402-5
Engine Management Systems
EGR valve, VGT turbine vanes, and ignition system. Actuators that have position control normally have a position
sensor that is used with a feedback controller to maintain
the desired position.
2.3
Controller
One of the factors contributing to widespread use of
electronic engine controls has been emission regulations.
Electronic controls make it possible to more accurately
control the air to fuel ratio, spark advance, fuel injection
timing, and EGR flow rate. Electronic controls can also
improve performance, drivability, fuel economy, and
integration with other vehicle systems.
Figure 1 shows some of the common sensors and actuators on an engine. The air throttle, EGR valve, and VGT
vane are controlled using actuator commands: uat , uegr , and
uvgt , respectively. The intake and exhaust camshaft phasing
are controlled using commands uicam and uecam . Engines
with electronic fuel injection regulate the fuel rate by controlling the duration of the fuel injector for each cylinder.
3
ENGINE CONTROL STRATEGIES
The block diagram for a typical engine control system is
shown in Figure 2. The actuator controls are shown as
just one block in this figure but the actuator control may
have its own sensor and feedback controller. Proportionalintegral-derivative (PID) controllers are commonly used
for actuator position control. The actuator controller is
within the control loop of the setpoint controller, which
requires special consideration when selecting the controller
gains. The actuator controls need to be fast enough during
transient conditions to prevent the setpoint controller from
making adjustments to the actuator setpoint because the
actuator position and the corresponding engine response
have not yet been achieved. To prevent dynamic interactions between these control loops the actuator control
should ideally be more than 10 times faster than the
setpoint control. A factor as low as 5 may be acceptable
in certain cases.
The feed forward calculation shown in Figure 2 is a
calculation of the required actuator position using the
given setpoint command and known system parameters.
Feed forward control allows the system to respond quicker
under transient conditions because the required actuator
position is calculated at each time step with essentially
no lag. The feedback controller is different in that it is
designed to remove control system error over a period with
a certain time constant. Using the combination of feed
forward and feedback control allows the system to respond
quickly to changes in the setpoint command while still
having the ability to correct for system changes or errors
in the feed forward calculation. When the feed forward
calculation is done correctly, the output of the feedback
controller will be small.
The feed forward term can be obtained from tables,
empirical models, or physics-based models. In some cases,
the steady state position for the actuator is determined for
each operating condition and those values are then placed in
tables that are used to determine the feed forward term. This
approach gets the actuator close to the required steady state
position fast but it does not provide compensation for the
system dynamic so the control under transient conditions
is not as good as it could be. Empirical and physicsbased models that more accurately account for the system
dynamics can provide better transient response.
The main difference between empirical models and
physics-based models is that empirical models generally
require engine data for calibration whereas physics-based
models are based mostly on first principles, allowing them
to be calibrated with parameters such as component sizes
and fluid properties.
An example of a physics-based model is the compressible
gas flow equation for an orifice (Equation 1). This equation
is commonly used for modeling airflow through the throttle.
The parameter ψ is a function of the pressure ratio across
Feed forward
calculation
+
Setpoint
command
Error
−
Feedback
controller
+
Actuator
+ setpoint
3
Actuator
(& control)
Actuator
position
Measured
state
Sensor
Figure 2. Engine control using sensor feedback.
Encyclopedia of Automotive Engineering, Online © 2014 John Wiley & Sons, Ltd.
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DOI: 10.1002/9781118354179.auto068
Also published in the Encyclopedia of Automotive Engineering (print edition) ISBN: 978-0-470-97402-5
Engine
state
Engine
4
Engines—Design
1
0.9
0.8
0.7
ψ
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Pout
Pin
Figure 3. Parameter ψ for air throttle compressible gas flow
equation.
the throttle and the ratio of specific heats for the fluid
(Guzzella & Onder, 2010). Within the ECU, the parameter
ψ is typically stored in a table covering a range of pressure
ratios. The table lookup in this case is more efficient in
terms of ECU throughput than the equation for ψ. A plot
of ψ versus pressure ratio is shown for air in Figure 3.
This model considers the throttle opening area, upstream
air properties, and pressure ratio across the throttle. The
effective area (Cd · A) is typically calibrated using data
from a flow bench and a table in the ECU with throttle
position as the input.
Pin
·ψ
(1)
ṁ = Cd · A Rin · Tin
k +1
k −1
2
ψ= k·
, for Pout < Pcr
k +1
1 k −1 2k
k
k
P
Pout
out
· 1−
,
ψ=
·
Pin
k −1
Pin
for Pout ≥ Pcr
k
k −1
2
Pcr =
Pin
k +1
An example of an empirical model is the “speed–
density” calculation for engine airflow using volumetric
efficiency (VE) tables (Equation 2). This is a mean value
model of the engine that does not account for the discrete
events of each cylinder or the delays associated with the
combustion cycle. The model does account for changes
in manifold pressure, manifold temperature, and engine
speed, making it a reasonably good method for predicting
flow to the engine cylinders. This model is discussed in
more detail in Section 3.1.1.
Models such as these can be used in a feed forward
calculation to determine what manifold pressure is required
to achieve the desired airflow to the cylinders or what
throttle position is required to achieve a given airflow
through the throttle.
In some cases, the desired control parameter does not
have a sensor to provide a feedback signal. It may be
impractical to have certain sensors because of cost or
reliability. For example, it is not practical to measure the
flow at the intake valve or to measure the mass fraction of
air within the cylinder. If such parameters are important for
controlling the engine, a model may be used to estimate
these parameters so that the feedback controller can use
them. Such a model is called an observer (Figure 4). The
observer receives the same inputs as the real engine so
dynamically it responds similar to the engine. The states
of the model are compared to the measured states on the
real engine allowing corrections to be made to the model,
reducing the parameter estimation error.
In addition to providing state information to the feedback
controller, information from the observer model and the
model parameters may also be used in the feed forward
calculation.
The following discussion describes how an observer
model can be used to improve the engine airflow estimate
that is used for controlling the air to fuel ratio and setting
the spark advance.
3.1
Engine airflow
A mean value engine model is a model of the engine that
does not consider the effects of individual cylinders. It
assumes the flow through the engine is continuous as it
would be in a gas turbine. When such a model is used
for control purposes, the mass of air, fuel, or exhaust gas
within each cylinder is calculated by evaluating the total
mass going through the engine in one cycle and dividing
by the number of cylinders.
3.1.1 Speed–density–flow
The speed–density model calculates flow to the engine
cylinders using engine speed, the density of the fluid in
the intake manifold, the displacement of the engine, and
the VE (Equation 2). VE is the ratio of the actual flow
to the theoretical flow that would be achieved if flow
Encyclopedia of Automotive Engineering, Online © 2014 John Wiley & Sons, Ltd.
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DOI: 10.1002/9781118354179.auto068
Also published in the Encyclopedia of Automotive Engineering (print edition) ISBN: 978-0-470-97402-5
Engine Management Systems
5
Feed forward
calculation
+
Setpoint
command
Error
−
+
Feedback
controller
+
Actuator
setpoint
Actuator
position
Actuator
(& control)
Engine
state
Engine
Model
correction
Actuator
model
Engine state estimate
+
+
Engine
model
Actuator
position
estimate
Measured
state
Sensor
Observer
controller
Engine
state
estimate
Model
error
+
−
Sensor
model
Measured
state
estimate
Engine observer
Figure 4. Observer-based engine control.
equivalent to the displaced volume of the engine at the
intake manifold fluid density were achieved during each
engine cycle. Sometimes, VE is specified with respect to
the density of air at atmospheric conditions but this method
is seldom used for control purposes. By setting Equation 2
equal to the measured mass flow from an engine test, it
is possible to solve for the VE. The VE is sometimes
calibrated using a table with axes of engine speed and
intake manifold pressure. Turbocharged applications may
require a more complex empirical model to accurately
predict the VE.
ṁiv =
Ne
120
A separate model provides the estimate of mcyc,res . The
residual mass will be affected by engine speed, manifold
pressures, fuel rate, and valve timing.
The speed–density method provides reasonably good
estimates of flow to the cylinder under steady state operation but there are several sources of error under transient
conditions:
1.
· ρim · Vdisp · VE
(2)
This flow estimate includes both air and EGR entering
the cylinder. During operation of the engine, the ECU
calculates the mass entering each cylinder using the intake
manifold fluid density, cylinder displacement, and VE as
shown by Equation 3.
mcyl,in = ρi
Vdisp
ncyl
2.
· VE
(3)
The total mass in the cylinder at the time when the intake
valve closes is equal to the mass that entered through the
intake valve plus the residual mass that remained in the
cylinder from the previous engine cycle (Equation 4).
mcyl,ivc = mcyl,in + mcyl,res
(4)
3.
The mass of residual exhaust gas retained within the
cylinder may change from one cycle to the next, making
the VE under transient conditions different than the
steady state value. When the intake manifold pressure
is increasing the speed–density–flow estimate will be
too low because the residual mass has not yet increased
to the steady state value, which may cause the spark
advance to be set too high resulting in engine knock.
The wave dynamics within the intake manifold will be
changing under transient conditions and the pressure
near the intake valve at the time when the valve closes
may be different than it was during the steady state
condition, resulting in a different VE.
On a port fuel injected engine, the fuel has to be injected
before the intake stroke. The manifold pressure may
change between the time at which the fuel was injected
to the time when the intake valve closes, causing an
error in the air to fuel ratio. The flow estimate will be
too low when the intake manifold pressure is increasing
and it will be too high when the intake manifold pressure is decreasing. The speed–density–flow estimate
will cause the engine to run lean on tip-ins and rich on
Encyclopedia of Automotive Engineering, Online © 2014 John Wiley & Sons, Ltd.
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DOI: 10.1002/9781118354179.auto068
Also published in the Encyclopedia of Automotive Engineering (print edition) ISBN: 978-0-470-97402-5
6
Engines—Design
tip-outs. This flow estimate tends to lag behind the true
flow to the cylinders.
Some of the limitations listed here can be addressed by
adding ad hoc features to the control software that make
corrections under certain conditions. For example, when
a tip-in is detected the spark advance can be reduced by
several degrees to prevent knock. Alternately, to improve
fuel control extra fuel can be added with a tip-in, or
removed with a tip-out. Calibration of these corrections for
all operating conditions can be very time consuming.
The speed–density–flow estimation can be improved by
using predicted manifold pressure instead of a measured
value that may have to be filtered. The method of
using predicted manifold pressure is discussed more in
Section 3.1.3.
3.1.2 Measured mass airflow
A MAF sensor measures flow in the air intake duct between
the air cleaner and the throttle, or before the compressor
on turbocharged engines. Under steady state conditions,
this flow (plus the EGR flow rate) should match the
speed–density–flow estimate. Under conditions where the
intake manifold pressure is changing, the mass contained
within the intake manifold will also be changing. For the
case with no EGR flow, when the intake manifold pressure
is increasing the measured MAF will be higher than the
actual airflow into the cylinders. Likewise, when the intake
manifold pressure is decreasing the measured MAF will
be lower than the actual airflow into the cylinders. These
characteristics are opposite to those of the speed–density
calculation. The measured MAF tends to lead the true
cylinder airflow.
The measured MAF would not provide very good fuel
control under transient conditions if used directly. The
real benefit to using a MAF sensor is that corrections
can be made to the VE, improving the airflow estimate
under steady state conditions. The speed–density model
provides an estimate of flow to the cylinder while the
VE is corrected with the MAF reading. This model-based
approach to cylinder air charge estimation is described more
in the following section.
3.1.3 Model-based cylinder air charge estimation
One way to improve the estimate of air entering the cylinder
is to use a model-based approach. By constructing an
observer model of the engine, it is possible to predict the
rate of change in intake manifold pressure. The rate of
change in manifold pressure can then be used to predict
the pressure in the manifold at the time when the intake
valve closes. The modeled version of the intake manifold
pressure will have less variation than the measured value
and will not require filtering. This approach can overcome
the lag associated with the speed–density–flow estimate
and provide a much more accurate estimate of cylinder air
charge for the fuel injection calculations.
The observer model can also estimate the concentration
of air and exhaust gas within the cylinder, allowing spark
advance and other control parameters to be set for the
expected state of the cylinder. This approach improves
control under transient conditions.
3.2
Exhaust gas recirculation
EGR significantly increases the complexity of the models
needed to predict the mass of air entering the cylinder
and the composition of the mixture within the cylinder.
Modeling airflow, EGR flow, and residual exhaust gas
within the cylinder allows the air per cylinder and exhaust
gas concentration to be calculated. This information can
then be used to deliver the correct amount of fuel and to
set the spark advance.
Diesel engines regulate the exhaust gas concentration
for controlling NOx . Since diesel engines commonly run
lean, the calculation of residual and recirculated exhaust
gas must consider the concentration of excess air retained
in the exhaust gas.
In order to control the mass of air per cylinder and
exhaust gas concentration, an estimate of these parameters
is needed. The next section describes an engine model that
can be used as an observer within the ECU to provide this
information.
3.2.1 Exhaust gas recirculation model
The model described in this section includes airflow,
exhaust flow, and EGR flow. This is a mean value engine
model with lumped parameter manifold models. Lumped
parameter means that the concentration of air and exhaust
gas is assumed to be evenly distributed within each manifold. The pressure and temperature within the manifold is
also assumed to be uniform. Manifold models are based on
the principal of conservation of mass. Manifold pressure
can be calculated using the ideal gas law with manifold
fluid mass and estimated or measured manifold temperature
as inputs.
The equations that follow are for an engine with direct
fuel injection. The equations will be slightly different for
an engine with port fuel injection.
The rate of change in intake manifold mass is equal to
the MAF through the throttle, plus the EGR mass flow,
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DOI: 10.1002/9781118354179.auto068
Also published in the Encyclopedia of Automotive Engineering (print edition) ISBN: 978-0-470-97402-5
Engine Management Systems
7
minus the mass flow entering the engine through the intake
valves (Equation 5).
is a mean value model. In a real engine, these would be
discrete masses for each cylinder event.
dmim
= ṁat + ṁegr − ṁiv
dt
ṁivc = ṁiv + ṁres
(5)
The rate of change in air mass within the intake manifold
is equal to the MAF through the throttle, plus the EGR mass
flow times the mass fraction of air contained in the EGR,
minus the mass flow entering the engine through the intake
valves times the mass fraction of air in the intake manifold
(Equation 6).
dmaim
= ṁat + ṁegr χaegr − ṁiv · χaim
dt
(6)
The mass fraction of air contained in the intake manifold
is equal to the mass of air in the intake manifold divided by
the total mass of air and exhaust gas in the intake manifold
(Equation 7).
χaim =
maim
mim
(7)
The rate of change in exhaust manifold mass is equal
to the mass flow leaving the engine through the exhaust
valves, minus the EGR mass flow, minus the mass flow
through the turbine (Equation 8).
dmem
= ṁev − ṁegr − ṁtrb
dt
dmaem
= ṁev · χaevo − ṁegrcin · χaem − ṁtrb · χaem
dt
(9)
The mass fraction of air contained in the exhaust manifold is equal to the mass of air in the exhaust manifold
divided by the total mass of air and exhaust gas in the
exhaust manifold (Equation 7).
χaem
m
= aem
mem
The exhaust gas residual mass fraction is defined as the
mass of residual exhaust gas divided by the total mass in the
cylinder at the time when the intake valve closes (Equation
12). Engine speed, manifold pressures, fuel rate, and valve
timing all affect the residual mass fraction.
xr =
(10)
The mass flow in the cylinder at the time when the
intake valve closes is equal to the mass flow that enters
the cylinder through the intake valve plus the residual mass
(Equation 11). Mass flow rates are used here because this
mres
miv + mres
(12)
Equation 12 can be rearranged and the residual mass
can be expressed as a flow rate as shown in Equation 13.
Expressing the residual mass as a mass flow allows it to be
used in the mean value model.
xr
ṁres = ṁiv
(13)
1 − xr
The mass flow in the cylinder at the time when the
exhaust valve opens is equal to the mass flow in the cylinder
at the time when the intake valve closes plus the fuel mass
flow rate (Equation 14). Mass flow rates are used here
because this is a mean value model. In a real engine, these
would be discrete masses.
(8)
The rate of change in air mass within the exhaust
manifold is equal to the mass flow leaving the engine
through the exhaust valves times the mass fraction of air
in the exhaust gas when the exhaust valve opens, minus
the mass flow to the EGR cooler times the mass fraction
of air in exhaust manifold, minus the mass flow through
the turbine times the mass fraction of air in the exhaust
manifold (Equation 9).
(11)
ṁevo = ṁivc + ṁfuel
(14)
The mass flow through the exhaust valve is equal to the
mass flow in the cylinder at the time when the exhaust valve
opens minus the residual flow (Equation 15).
ṁev = ṁevo − ṁres
(15)
The MAF in the cylinder at the time when the intake
valve closes is equal to the mass flow through the intake
valve times the mass fraction of air within the intake
manifold, plus the residual mass flow rate times the mass
fraction of air in the cylinder at the time when the exhaust
valve opens (Equation 16).
ṁaivc = ṁiv · χaim + ṁres · χaevo
(16)
The mass fraction of air in the cylinder at the time when
the intake valve closes is equal to the mass of air in the
cylinder at the time when the intake valve closes divided by
the total mass in the cylinder when the intake valve closes
(Equation 17).
Encyclopedia of Automotive Engineering, Online © 2014 John Wiley & Sons, Ltd.
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DOI: 10.1002/9781118354179.auto068
Also published in the Encyclopedia of Automotive Engineering (print edition) ISBN: 978-0-470-97402-5
χaivc =
ṁaivc
ṁivc
(17)
8
Engines—Design
The equations presented up to this point can be shown
in block diagram form as illustrated in Figures 5 and 6.
Figure 5 is a model of the total mass flow through the
engine. Figure 6 is a model of airflow and air concentration.
The orifice equation for throttle airflow was shown in
Equation 1. The speed–density calculation was shown in
Equation 2.
The EGR valve and cooler could be modeled as an
orifice and a volume, or with an empirical model in a
different form. The mass fraction of air in the recirculated
exhaust gas could be modeled using a transport delay
instead of a volume with uniform mixture distribution. The
hardware configuration and desired level of model fidelity
will determine which model is the best for the application.
The mass of air and exhaust gas entering the cylinder
from the intake manifold depends on the pressure in the
manifold and the composition of the mixture within the
intake manifold. Cross coupling exists between the pressure
and concentration terms. To achieve the same mass of
The MAF in the cylinder at the time when the exhaust
valve opens is equal to the MAF in the cylinder at the
time when the intake valve closes minus the fuel mass
flow times the stoichiometric air to fuel ratio (Equation
18). For modeling purposes, the fuel is assumed to react
with a stoichiometric amount of air in the cylinder. This
assumption only applies when the engine is running lean.
If the engine is running rich, there will be no remaining air
in the exhaust gas.
ṁaevo = ṁaivc − ṁfuel · AFRstoich
(18)
The mass fraction of air in the cylinder at the time when
the exhaust valve opens is equal to the mass of air in the
cylinder at the time when the exhaust valve opens divided
by the total mass in the cylinder when the exhaust valve
opens (Equation 19).
ṁaevo
ṁevo
χaevo =
uicam
mat
uecam
(19)
xr
1 − xr
Camshaft
phasing
mim
uat
+
Air
throttle
Pcac
+
1
− s
+
Pim
megr
mres
X
mat
VE
Pim
R imTim
Vim
uvgt
miv
Speed−
density
mem
Pem
Turbo & mtrb
1
RemTem
charge
s
Vem
air cooler
mtrb
m
+
+ + + evo − +
+
+
−
−
mivc
mev
m iv
m fuel
Pim
megrcin
uegr
Pem
EGR
valve &
cooler
megr
Pcac
Figure 5. Engine mass flow model.
mfuel
miv
mat
+ +
maegr
+ −
χaim
1 maim
X
÷
s
mim
AFRstoich
X
maiv maivc −
+ +
+
maiv
÷
mares
megr megrcin
X
χaegr
EGR valve
& cooler
χaem
mev
χaevo
maevo
÷
X
mevo
χaivc
+ − + −
maegrcin
mtrb
X
X
mres
megrcin
megr
Figure 6. Engine air mass concentration model.
Encyclopedia of Automotive Engineering, Online © 2014 John Wiley & Sons, Ltd.
This article is © 2014 John Wiley & Sons, Ltd.
DOI: 10.1002/9781118354179.auto068
Also published in the Encyclopedia of Automotive Engineering (print edition) ISBN: 978-0-470-97402-5
matrb
X
mivc
1 maem
÷
s
mem
χaem
Engine Management Systems
air in the cylinder with a higher concentration of exhaust
gas requires higher intake manifold pressure. In general,
opening the EGR valve, closing the turbocharger vanes
(higher back pressure), or closing the air throttle (lower
intake manifold pressure) will provide more recirculated
exhaust gas to the intake manifold, whereas closing the
EGR valve or opening the air throttle will provide more air
to the intake manifold. Depending on the operating range
of the turbocharger, closing the vanes may increase both
fresh airflow and EGR flow.
Certain actuators are better at providing fast response
under transient conditions while others may be used to
guide the system to an efficient operating point. For
example, the air throttle provides the fastest air response
but in many cases it is desirable to have the throttle opened
all the way to minimize pumping losses. Likewise, the EGR
valve can provide fast response for controlling the EGR rate
but adjusting the VGT vanes also affects the EGR rate and
there will be an optimum setpoint for each actuator under
steady state conditions.
Different manufacturers have different strategies for
controlling these actuators and the details are mostly proprietary. Some research papers have been published on this
topic while additional work is still ongoing to determine the
best approach. PID controls may provide acceptable performance in certain applications where the control response
does not have to be very fast. The controls for these actuators are cross-coupled and very nonlinear, which can limit
the gains used in a PID controller. Some researchers have
proposed methods for decoupling the system, and others
have proposed the use of sliding mode control to better
handle the nonlinear characteristic of the system.
Multivariable control is an option that could provide
very good control but is more difficult to implement. It
uses optimization cost functions to provide a response that
uses all the actuators in a way that can be calibrated to
provide a response that is considered ideal or “optimal.”
The cost functions penalize factors such as excessive
actuator movement, slow response, or control overshoot.
Multivariable control works best with linear systems and
the engine system is very nonlinear. One of the steps to
implementing multivariable control is to create a model
in state variable form, which may require the creation of
several linear operating point models of the system. Another
challenge is the proper handling of system constraints
such as actuator limits, limits on manifold pressure, or
turbocharger speed.
3.3
Fuel injection
On diesel engines, the driver demand torque (or governor
torque) is primarily controlled with fuel. The other engine
9
actuators respond as needed to provide the correct amount
of air and EGR for the mass of fuel that is to be injected into
the cylinder. Diesel engines typically run lean so the mass
of air in the cylinder is not of much concern until operating
at high loads where there may not be sufficient air in the
cylinder to prevent smoke. Under a transient smoke-limited
operating condition, the fuel injection mass may be limited
until the other actuators can make adjustments to provide
sufficient air to the cylinder.
With spark ignition engines, the driver demand torque is
primarily controlled with the air throttle. The fuel injection
quantity depends on the mass of air that is expected to be in
the cylinder. A stoichiometric air to fuel ratio is normally
maintained so that low levels of both hydrocarbons and
NOx can be achieved. In addition, a stoichiometric air to
fuel ratio allows the three-way catalytic converter to be
most efficient at reducing emissions.
The rest of this section focuses on fuel injection controls
for spark ignition engines.
3.3.1 Port fuel injection
Switching from carburetors to throttle body fuel injection
offered the ability to accurately control the amount of fuel
delivered to the engine. The real challenge was calculating
how much fuel was required under transient conditions.
A speed–density type model could predict the airflow to
the engine cylinders with reasonably good accuracy but the
changing intake manifold pressure affected the evaporation
rate of the fuel and the resulting air to fuel ratio for the
mixture entering the cylinders. One solution was to inject
extra fuel with a throttle “tip-in” similar to the accelerator
pump on a carburetor. Likewise, less than the normal
amount of fuel could be injected when a throttle “tipout” was detected. This ad hoc solution was difficult to
calibrate for all operating conditions and did not provide
very accurate control.
Aquino (Aquino, 1981) proposed a “wall-wetting” model
of the intake manifold that accounted for the mass of liquid
fuel within the manifold and the rate at which that fuel
evaporated (Figure 7). By inverting this model, the fuel
injection quantity can be adjusted to compensate for the
liquid fuel accumulation and evaporation that occurs within
the manifold.
The wall-wetting model was initially developed for
throttle body fuel injection systems and then later applied
to engines with port fuel injection. Although each port had
independent fuel films that could be modeled separately it
was common to continue using a single mean value wallwetting model.
The following equations are used to model the wallwetting process. The mass flow of injected fuel entering the
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10
Engines—Design
Fuel injector
Mass flow rates
minj
minj
Intake port
: from injector to cylinder & fuel film
mif
: from injector to fuel film
mic
: from injector to cylinder
mfc
: from fuel film to cylinder
mcyl_fuel : from injector & fuel film to cylinder
m ic
mif
mfc
mf
Fuel film
Calibration parameters
mcyl_fuel
x f : fraction of injected fuel entering fuel film
τ : fuel film time constant
Intake
valve
Figure 7. Port fuel injection wall-wetting model.
film is assumed to enter the cylinder.
fuel film is equal to the mass flow of injected fuel times a
factor xf called the impact factor (Equation 20). The impact
factor is the fraction of injected fuel entering the fuel film.
ṁif = xf · ṁinj
ṁfc =
The mass flow of injected fuel not entering the fuel film
is equal to the mass flow of injected fuel times one minus
the impact factor (Equation 21).
dmf
= ṁif − ṁfc
dt
The fuel film is assumed to evaporate with a time
constant of τ (Equation 22). Fuel evaporating from the fuel
m ic
1 − xf
m cyl_fuel
+
+
mif
xf
dm f
dt
+
−
mf
1
s
m fc
1
τ
Figure 8. Wall-wetting model block diagram.
m cyl_fuel +
m ic
m fc
1
τ
m inj
1
1 − xf
−
mf
1
s
(23)
Figure 8 shows these equations in block diagram form.
This model has the fuel injection mass flow as the input
and the fuel mass flow entering the cylinder as the output.
This model can be inverted as shown in Figure 9 to have
the mass flow entering the cylinder as the input and the
mass of injected fuel as the output. The model in this form
(21)
minj
(22)
The change in mass of the fuel film is equal to the mass
flow entering the film from the injector minus the mass flow
that is evaporating and entering the cylinder (Equation 23).
(20)
ṁic = (1 − xf ) · ṁinj
mf
τ
dm f
dt
+
mif
−
Figure 9. Inverted form of wall-wetting model.
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xf
Engine Management Systems
700
Vo (mV)
can be used in the feed forward calculation to determine the
amount of fuel to inject. This model will cause more fuel
to be injected during a tip-in, when less fuel is evaporating
from the fuel film, and less fuel to be injected during a
tip-out, when more fuel is evaporating from the film.
11
450
200
3.3.2 Gasoline direct injection
The wall-wetting model is not required for engines with
direct fuel injection because all the fuel stays in the cylinder
until combustion. Gasoline direct injection normally occurs
early in the engine cycle before the intake valve closes. This
provides more time for fuel atomization before combustion,
reducing hydrocarbon emissions. In addition, the cooling
effect of the injected fuel allows more air to enter the
cylinder, which allows higher peak torque and power to
be achieved.
3.3.3 Closed loop air to fuel ratio control
To achieve a high level of conversion efficiency with the
catalytic converter the air to fuel ratio has to be controlled
very close to the stoichiometric ratio. Engine to engine
variation, variation in fuels, and purging of the evaporative
emission canister can cause the engine to run rich or
lean of stoichiometry. Closed loop control can be used
to correct for these fueling errors. The closed loop fuel
controller uses an oxygen sensor for feedback (Figure 10).
The oxygen sensor is installed in the exhaust manifold or
exhaust pipe and provides a signal that is related to the
oxygen concentration in the exhaust.
The oxygen sensor is constructed from a ceramic material
called zirconium oxide. The sensor is in the shape of a
thimble that protrudes into the exhaust stream. The inner
and outer surfaces of the sensor are coated with porous
layers of platinum, which act as the electrodes. When
there is a difference in oxygen concentration between the
inner and outer surfaces of the sensor, oxygen ions pass
through the ceramic material with reactions occurring at
the platinum electrodes generating an electric potential that
can be measured as a voltage.
−
Vo
Porous platinum
electrodes
e−
+
ZrO2
Air side reaction:
O2 + 4e− → 2O2−
Figure 10. Oxygen sensor.
Exhaust side reaction:
2O2− → O2 + 4e−
Rich
1
Lean
Air to fuel equivalence ratio (λ)
Figure 11. Oxygen sensor response curve.
The sensor voltage is related to the oxygen partial
pressure at each electrode. The voltage can be approximated
using the Nernst equation:
PO2 ref
R·F
· ln
(24)
Vo =
4F
PO2 exh
where R is the gas constant, T is the temperature, P is
the partial pressure, and F is the Faraday constant. A
typical response curve is shown in Figure 11. As the engine
switches from running lean to rich, the oxygen sensor
voltage increases significantly. The sensor operates as a
switch, indicating whether the engine is currently operating
rich or lean.
The sensor temperature has to be above a certain value
for the reactions to occur at the platinum electrodes, generating the sensor output voltage. The minimum operating
temperature for the sensor is about 300◦ C. Some sensors
use an electric heating element to warm up the sensor so
that it can be used for control sooner after a cold start.
The sensor is normally used with a proportion integral
(PI) controller to adjust the mass of fuel that is injected.
Figure 12 shows two examples: control with just integral
control and control with a PI controller. With integral
control, the fuel injection mass is adjusted up or down
at each fuel injection event depending on the output of
the sensor. When the oxygen sensor indicates that the
engine is running lean, the integrator will increase the fuel
injection mass until the oxygen sensor indicates that the
engine is running rich; then, the fuel injection mass will
start decreasing.
There is a delay between the time when fuel is injected
and the time its effect is detected at the sensor. Part of this
delay is associated with the engine cycle time and part is
due to the transport delay for the exhaust gas to travel from
the exhaust valve to the location of the sensor. The transport
delay causes the air to fuel ratio at the engine to overshoot
the setpoint and affects the period of the rich–lean cycling.
The cycle time can be reduced by using a PI controller.
Since a certain amount of overshoot is expected because
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12
Engines—Design
Integral control
Period
Fuel to air
equivalence
ratio (1/λ)
Equivalence
ratio at
engine
Transport
delay
Equivalence
ratio at
sensor
Oxygen
sensor
voltage
Vo (mV)
700
Rich
1.0
450
Lean
200
Time
Proportional plus integral control
Period
Fuel to air
equivalence
ratio (1/λ)
Equivalence
ratio at
engine
Transport
delay
Equivalence
ratio at
sensor
Oxygen
sensor
voltage
Vo (mV)
700
Rich
1.0
450
Lean
200
Time
Figure 12. Air to fuel ratio control.
of the transport delay, the proportional term can be used to
quickly change the fuel injection mass when a rich-to-lean
or lean-to-rich transition occurs at the sensor. Figure 12
shows a reduction in the period of the rich–lean cycling
with the PI controller.
3.4
Spark advance
Spark advance is normally set to a value that provides
the maximum torque with the minimum amount of spark
advance. This is called the minimum spark advance for best
torque (MBT). Under some conditions with regular grade
fuel the spark advance may have to be set lower to prevent
engine knock. Knock occurs when the combustion mixture
auto-ignites, making a knocking sound rather than burning
as a flame front that propagates from the spark plug to the
edge of the piston. Combustion may start off as a flame
front and then auto-ignite once a certain temperature and
pressure is achieved. Reducing the spark advance lowers
the pressure during combustion, reducing the tendency
to knock. The spark advance for the engine is normally
calibrated using tables that are sometimes called maps. The
base spark advance is normally set to the minimum of the
MBT spark advance and the knock-limited spark advance.
The base spark advance table normally has engine speed
as one axis and some indication of engine load on the
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Engine Management Systems
Engine speed
Exhaust gas
mass fraction
in-cylinder
implemented as an observer in the ECU. There are still
some sources of error that may need to be addressed if
more accurate control is required for advanced combustion strategies such as homogeneous charge compression
ignition (HCCI). These limitations are as follows:
1.
2.
Air mass
in-cylinder
3.
Figure 13. In-cylinder parameter-based spark advance table.
other axis. If only measured parameters are available the
throttle position or intake manifold pressure are sometimes
used as the second axis. If an engine airflow observer is
implemented in the ECU, then the mass of air per cylinder
could be used for the second axis.
The combustion burn rate is affected by the mass fraction
of exhaust gas contained in the cylinder. If an estimate of
exhaust gas mass fraction is available it could be used as a
third table axis as shown in Figure 13.
The use of in-cylinder parameters for setting the spark
advance provides good control under transient conditions
because the advance is set using factors that ultimately
affect the combustion process.
The spark advance may also be adjusted for non-standard
operating conditions such as when the engine is colder or
hotter than normal. These adjustments can be made using
additional tables that adjust the spark advance based on
coolant temperature or the estimated in-cylinder temperature.
Using only actuator positions or sensor measurements as
inputs to spark advance tables would require many tables
to cover all operating conditions and would not provide the
level of transient control that is possible with in-cylinder
estimated parameters.
4
INDIVIDUAL CYLINDER MODELS
As can be seen from what has been described up to
this point, the mean value engine model can provide a
lot of useful information for controlling the engine when
13
The real engine operates in discrete cylinder events
with delays associated with the engine cycle that are
not properly captured by the mean value model. This
can cause errors in the residual cylinder mass and
composition calculations.
The model does not account for the wave dynamics in
the intake manifold that can significantly change the
flow entering the cylinder under transient conditions
from that of the flow predicted by the speed–density
method using VE tables.
Engines with variable valvetrain systems offer a wide
range of valve-opening strategies, making it difficult to
accurately model all possible operating conditions with
VE tables.
These limitations can be overcome by using a higher
fidelity model that includes individual cylinders and by
modeling the wave dynamics of the intake and exhaust
manifolds. Such a model provides more information but
requires more processing capacity from the ECU. This
approach eliminates the need for VE tables.
A project at the University of Wisconsin–Madison
created a real-time combustion and compressible gas flow
model that could be used in an ECU as an observer (Lahti,
2004). The following discussion provides an overview of
that model.
The wave dynamics were modeled using a process called
the method of characteristics. The governing equations
are the continuity equation and the momentum equation.
Through a process or variable transformations the state
of the fluid in the manifold runners can be defined using
parameters called Riemann variables. One Riemann variable defines the right moving characteristic and the other
defines the left moving characteristic. For isentropic flow,
the Riemann variables remain constant as they propagate through the manifold runner. This modeling technique
makes it possible to predict the state of the fluid at the
valve and to predict the flow through the valve when the
cylinder pressure is known. The reader is referred to Benson
(Benson, 1982) for more details on the wave modeling
techniques.
The method of characteristics was originally developed
for solving wave problems on a drafting board. Later it was
implemented as a computer program. Other wave analysis
methods may provide more accuracy but the software
code may not run fast enough to be used in a real-time
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14
Engines—Design
application. This method was found to work well when the
isentropic flow assumption was not violated. If the valve
timing was such that hot cylinder gases entered the intake
runner during part of the intake event, the model would
not accurately represent the wave dynamics at that point. If
such a valve-opening strategy were required, a slightly more
complex model could be implemented to more accurately
model those effects.
An individual cylinder model was developed to calculate
the temperature and pressure in the cylinder throughout the
engine cycle. This information was used with the wave
dynamics model to determine the flow through the valves.
The states of the cylinder were modeled using the first
law of thermodynamics, conservation of mass, and the ideal
gas law. The first law equation for the cylinder is
Q̇cv − Ẇcv + ṁiv · hSi − ṁev · hSe =
d(muS )cv
dt
(25)
This right side of the equation can be rewritten as
dTcyl
d(muS )cv
= (ṁiv − ṁev ) · uS + mcyl · Cv ·
dt
dt
(26)
It is now possible to solve for the rate of temperature
change:
dTcyl
dt
Q̇comb + Q̇wall − Ẇcv + ṁiv · hSi
−ṁev · hSe − (ṁiv − ṁev ) · uS
=
mcyl · Cv
(27)
The temperature at each time step is calculated as
Tcyl (t + t) = Tcyl (t) +
dTcyl (t)
dt
mcyl (t + t) = mcyl (t) + (ṁiv − ṁev ) · t
Pcyl (t + t) =
mcyl (t + t) · Rcyl (t + t) · Tcyl (t + t)
Vcyl (t + t)
(30)
This model was evaluated using a single cylinder spark
ignition research engine. Figure 14 shows the measured
and estimated cylinder pressures through one engine cycle.
During this test, the model was running in real time using
a dSPACE rapid prototype control system. The measured
and estimated cylinder pressures were nearly the same
throughout the cycle. Similar results were obtained for
different combinations of valve timing, valve lift, airflow,
and engine speed.
The combustion heat release was modeled using a mathematical function called a Weibe function. Weibe functions
are commonly used to model the mass fraction of fuel that
has burned as a function of crank angle. The calibration
parameters for the Weibe function were stored in tables
log10[cylinder pressure (kPa)]
3.2
3
2.8
Estimated
2.4
Measured
2
1.8
1.6
0
0.1
0.2
0.3
(29)
The pressure at the new time step is calculated using the
ideal gas law:
3.4
2.2
(28)
The cylinder mass is updated using the mass flow rates
at the valves
3.6
2.6
t
0.4
0.5
0.6
0.7
Normalized volume displaced
Figure 14. Real-time individual cylinder model data.
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0.8
0.9
1
Engine Management Systems
of the form shown in Figure 13 to be consistent with the
strategy used for the spark timing. More complex models
could be implemented to define the heat release for applications using premixed, partially premixed, or multiple direct
inject combustion strategies.
With the individual cylinder models, each cylinder event
is a transient event. The cylinder pressures and temperatures
are continually changing. There is intermittent flow through
the valves, and the mass within the cylinder keeps changing.
This is much different than the mean value model where
the flow is continuous and the engine cycles are assumed
to occur with no delay.
One of the challenges to implementing HCCI in a
production application is controlling the process under
transient conditions. Current engine control strategies using
mean value models are not able to provide information
about the state of the engine with sufficient accuracy to
control the process. The individual cylinder models offer
an alternative that accurately represents many of the factors
that affect when combustion begins. Information from the
models could be used for controlling the trapped residual
mass and EGR flow as a way of regulating the HCCI
process.
A patent for the engine control technology described
in this section is held by the University of Wisconsin
Alumni Research Foundation (WARF) at the University of
Wisconsin–Madison (Lahti & Moskwa, 2006).
5 CONCLUSION
In many cases, the engine parameters that need to be
controlled are difficult or impractical to measure. It may
be possible to model the important parameters using the
actuator and sensor information that is available. Such a
model is called an observer. There are several advantages
to using observers: they provide the desired state feedback
information without adding sensors, the modeled response
does not require filtering like a sensed parameter, the model
information can be used for feed forward calculations to
provide better control response, and the observer can be
used for diagnostics to detect changes in engine operation.
The mean value engine model may provide sufficient
information for controlling the engine in some applications. As with any model, assumptions are made and those
assumptions can be a source of error under certain conditions. The mean value model assumes continuous flow
through the engine with no delays. This assumption may
be acceptable for some applications but not for others.
The level of model fidelity for an application may vary
depending on the requirements. Increasing model fidelity
has many control advantages but the model must be capable
15
of running in real time within the ECU, which has limited
processing capacity. As processor capacity increases, in
the future it may be possible to implement higher fidelity
models such as the individual cylinder model, and models
of the manifold wave dynamics. These higher fidelity
models allow better control under transient conditions,
which may resolve some of the implementation problems
associated with alternative combustion strategies.
NOMENCLATURE
The variables listed below are used in the equations that
follow.
t
ρ im
τ
χ aegr
χ aem
χ aevo
χ aim
χ aivc
ψ
A
AFRstoich
Cd
Cp
Cv
ECU
EGR
H
Hs
k
maem
maim
mcac
mcyc
mcyl,in
mcyl,ivc
mcyl,res
megrc
mem
mf
mim
ṁ
ṁaevo
ṁaivc
controller time step
intake manifold fluid density
wall wetting time constant
mass fraction of air in EGR
mass fraction of air in exhaust manifold
mass fraction of air when exhaust valve
opens
mass fraction of air in intake manifold
mass fraction of air when intake valve closes
compressible gas flow parameter
orifice area
stoichiometric air to fuel ratio
discharge coefficient
specific heat at constant pressure
specific heat at constant volume
engine control unit
exhaust gas recirculation
enthalpy
sensible enthalpy
ratio of specific heats
mass of air in exhaust manifold
mass of air in intake manifold
mass in charge air cooler
mass in cylinder
mass that entered the cylinder from intake
valve
mass in cylinder when intake valve closes
residual mass in cylinder
mass in EGR cooler
mass in exhaust manifold
wall-wetting model fuel film mass
mass in intake manifold
mass flow through orifice
mass flow of air (mean value model) when
exhaust valve opens
mass flow of air (mean value model) when
intake valve closes
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16
Engines—Design
ṁat
ṁegr
ṁegrcin
ṁev
ṁevo
ṁfc
ṁfuel
ṁic
ṁif
ṁinj
ṁiv
ṁivc
ṁres
ṁtrb
MAF
ncyl
Ne
NOx
Pcac
Pcyl
Pcr
Pegrc
Pem
PI
PID
Pim
Pin
Pout
Q̇comb
Q̇cv
Q̇wall
R
Rin
T
Tcac
Tcyl
Tegrc
Tem
Tim
Tin
U
uat
uegr
uecam
uicam
uvgt
US
Vcyl
Vdisp
VE
mass airflow through throttle
mass flow of EGR
mass flow into the EGR cooler
mass flow through exhaust valve
mass flow when the exhaust valve opens
mass flow of fuel from film to cylinder
mass flow of fuel to engine
mass flow of injected fuel entering cylinder
mass flow of injected fuel entering fuel film
mass flow of injected fuel
mass flow through intake valve
mass flow when intake valve closes
mass flow of residual mass in cylinder
mass flow to turbine or exhaust pipe
mass airflow
number of cylinders
engine speed (rpm)
nitrogen oxides
pressure in charge air cooler
pressure in cylinder
critical pressure
pressure in EGR cooler
pressure in exhaust manifold
proportional-integral controller
proportional-integral-derivative controller
pressure in intake manifold
orifice inlet pressure
orifice outlet pressure
combustion heat release rate
control volume heat transfer rate
rate of heat transfer to the cylinder walls
gas constant
gas constant of flow entering orifice
time
temperature in charge air cooler
temperature in cylinder
temperature in EGR cooler
temperature in exhaust manifold
temperature in intake manifold
temperature of flow entering orifice
internal energy
actuator command for air throttle position
actuator command for EGR valve position
actuator command for exhaust camshaft
position
actuator command for intake camshaft
position
actuator command for VGT vane position
sensible energy
volume of cylinder
engine displacement
volumetric efficiency
VGT
Ẇcv
Xf
Xr
variable geometry turbocharger
rate of work done by the control volume
mass fraction of injected fuel entering fuel
film
exhaust gas residual mass fraction
REFERENCES
Aquino, C.F. (1981) Transient A/F control characteristics of the 5
liter central fuel injection engine. SAE 810494.
Benson, R.S. (1982) The Thermodynamics and Gas Dynamics of
Internal-Combustion Engines, vol. 1, Clarendon Press, Oxford.
Guzzella, L. and Onder, C.H. (2010) Introduction to Modeling
and Control of Internal Combustion Engine Systems, 2nd edn,
Springer, Heidelberg.
Lahti, J.L. (2004) Engine control using real time combustion and
compressible gas flow models. PhD dissertation. University of
Wisconsin–Madison.
Lahti, J.L. and Moskwa, J.J. (2006) Internal Combustion Engine
Control System. United States Patent and Trademark Office,
Patent No. 7,275,426 B2, March 31.
FURTHER READING
Heywood, J.B. (1988) Internal Combustion Engine Fundamentals,
McGraw-Hill, Inc., New York.
Heywood, J.B., Higgins, J.M., Watts, P.A., and Tabaczynski, R.J.
(1979) Development and use of a cycle simulation to predict SI
engine efficiency and NOx emissions. SAE 790291.
Iwadare, M., Ueno, M., and Adachi, S. (2009) Multi-variable airpath management for a clean diesel engine using model predictive
control. SAE 2009-01-0733.
Jante, A. (1960) The Wiebe Combustion Law (Das WiebeBrenngesetz, ein Forschritt in der Thermodynamik der Kreisprozess von Verbrennungsmotoren), Kraftfahrzeugtchnik, vol. 9,
pp. 340–346.
Lahti, J.L. and Moskwa, J.J. (2005) Engine Control Using Estimated Parameters from a Real Time Model of an Engine with
Variable Valve Actuation. Proceedings of the ASME International
Mechanical Engineering Congress and Exposition, IMECE200581362, Orlando.
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Encyclopedia of Automotive Engineering, Online © 2014 John Wiley & Sons, Ltd.
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DOI: 10.1002/9781118354179.auto068
Also published in the Encyclopedia of Automotive Engineering (print edition) ISBN: 978-0-470-97402-5