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SAE TECHNICAL
PAPER SERIES 1999-01-0857

Air/Fuel Ratio Control Using Upstream Models

in the Intake System
Yoshishige Ohyama
Hitachi, Ltd.

Reprinted From: Electronic Engine Controls 1999: Neural Networks,

Diagnostic and Electronic Hardware, and Controls
(SP-1419)

International Congress and Exposition

Detroit, Michigan
March 1-4, 1999

400 Commonwealth Drive, Warrendale, PA 15096-0001 U.S.A. Tel: (724) 776-4841 Fax: (724) 776-5760
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1999-01-0857

Air/Fuel Ratio Control Using Upstream Models

in the Intake System
Yoshishige Ohyama
Hitachi, Ltd.

Copyright © 1999 Society of Automotive Engineers, Inc.

ABSTRACT transient conditions. Many calculation methods have

been presented to compensate for the air mass change
Generalized models of the air/fuel ratio control using esti- [3-14]. A/F control strategies for conventional spark igni-
mated air mass in the cylinder were presented to obtain tion engines with the hot wire air flow meter and three-
highly accurate control during transient conditions in high way catalytic converter in which A/F is stoichiometric,
supercharged direct injection systems with a complex air have already been investigated [4-13]. But, general meth-
induction system. The air mass change was estimated by ods adaptable to lean burn spark ignited engines, such
using upstream models which estimated the pressure of as direct injection stratified charge, high supercharged
the intake manifold by introducing the output of the air spark ignited engines, and high supercharged compres-
flow meter and the differential of the output into aerody- sion ignited engines with integrated interactive drivetrain
namic equations of the intake system. The air mass into control systems in which A/F varies under a wide range,
the cylinders was estimated at the beginning of the intake have not yet been examined completely.
stroke under a wide range of driving conditions, without
The aim of this paper is to clarify the control models of A/
compensating for changes in the downstream parame-
F using air flow meters for an engine drivetrain control
ters of the intake system and engine. Therefore, the
system which provides better fuel economy, lower
upstream models required relatively minor calibration
exhaust emissions, and better driveability. Generalized
changes for each engine modification to be able to esti-
models of the air mass estimation during transient condi-
mate the air mass on a cylinder-by-cylinder basis. The
tions of engine speed, throttle opening, charge pressure,
fuel mass could be injected without delay during the
residual gas, and exhaust gas recirculation are investi-
intake stroke, keeping the air-fuel ratio within 1% of the
gated.
target value during transient conditions.
CONTROL SYSTEM
INTRODUCTION
Figure 1 shows an engine control system which is com-
Air/fuel ratio(A/F) characteristics exert a large influence
posed of an upper level controller, a coordinator and a
on exhaust emissions and fuel economy in internal com-
low level controller.
bustion engines [1]. The accuracy of A/F control depends
on the accuracy of the air mass estimation in the cylin-
ders at the beginning of the intake stroke in fuel injection
systems. The air mass is calculated by using the air flow
rate measured by an air flow meter or intake manifold
pressure ( in the case of a speed density method). The
speed density method is influenced by heat transfer from
the cylinder walls to the air, fuel evaporation and valve
overlap [2]. The air flow meter method is suitable for
improving the accuracy. Among the many kinds of air flow
meters such as hot wire, vortex, ultrasonic, and moving
vane, the hot wire air flow meter is most suitable because
of its high accuracy under a wide range of driving condi-
tions.
The air metered by the air flow meter enters the cylinder
through the intake manifold. The air mass in the cylinder
is not equal to the air mass measured by the air flow
meter, due to the air mass change in the manifold during Figure 1. Engine control system
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UPPER LEVEL CONTROLLER – The upper level con- LOW LEVEL CONTROLLER – The lower level controller
troller determines the desired acceleration and the target has to determine the throttle and/or brake commands
torque by using acceleration pedal position for conven- required to track the desired acceleration [15]. The con-
tional operations and without using the position for longi- trol objective is to track torque demands imposed by the
tudinal control of automated vehicles[14]. The energy driver, while minimizing A/F excursions from the target A/
management in the controller chooses the optimum oper- F. Unfortunately, the above strategies may lead to higher
ating point of the auxiliary power unit APU (torque and emissions because the A/F control system may have
speed ) as a function of the reference power ( cf. opti- problems with the transients in the APU speed/torque
mum operating line ) for the series hybrid system. The (fast switch between operating points) [16]. Precise regu-
energy management starts and stops the APU [15]. The lation of A/F is typically achieved through a combination
drive management obtains the drive and brake pedal sig- of feedforward ( fast, based on air flow rate measurement
nals of the driver and generates the reference torque of ) and feedback ( slow, based on feed gas oxygen level)
the traction drives and the brake signal of the mechanical control. However, even if the feedforward term is accu-
brakes. rate, the current A/F controller cannot compensate fully
for these fast transients. This is because fuel injection is
COORDINATOR – It is necessary to coordinate the tar- performed on a closed intake valve (multipoint injection
get torque and the efficiency to improve fuel economy systems), or at the beginning of intake stroke (direct
and exhaust emissions, according to internal factors and injection systems) and thus the fuel computation and
external factors. scheduling must be performed at least 360 deg of the
crankangle rotation before the air change is completed in
Internal factors the cylinder. To overcome this difficulty, an A/F control
has been studied by using intake manifold model [14].
1. Series hybrid systems
Internal factors include the state of the different com- Intake manifold model – Flows through valves in the
ponents in the vehicle and their efficiency and engine intake manifolds and intake valves have been modelled
emission maps for series hybrid system [15]. Electric with the orifice flow equations using the effective flow
power demands by the traction drives (the road passage area through the the valves [14]. Models for the
power) may be provided either by the battery or the evaluation of the air mass rate in a spark ignition engine,
APU. A decision on which component is best suited based on the estimation of the effects of the exhaust gas
has to be based on the efficiency maps of APU and internal recirculation and of the heat exchanges in the
battery[16]. intake system, have been presented [17-18]. The pres-
ence of the external exhaust gas recirculation system
a. Thermostat mode: The APU operates at a con-
and of the purge flow from the canister was investigated.
stant operating point and is turned on and off.
Gas flow rate and pressure estimates have been used in
b. Power-tracking mode: The APU follows the road control and diagnostic algorithms [17-23]. It is necessary
power actually demanded and fixes the operating to estimate the exact air mass in the cylinder. During tran-
point (torque and speed) according to the opti- sients, feedback from the exhaust gas oxygen sensor is
mum operating line. For small power demands or too slow to correct errors in the A/F. Using mass air flow
during regenerative braking the APU is stopped or MAP sensors to estimate air flow rates in the cylinder
or goes into idling [16]. has limitations related to sensor noise and sensor
2. Parallel configurations response time. Ideally, the air and fuel flows into the cyl-
For load leveling the controller forces the engine to inders should be predicted based on movement of the
act at or near its peak point of efficiency at all times. throttle plate and the commanded pulse width of the fuel
The idea is to move the actual operating point as injection by using the intake manifold model.
close to the point of best efficiency for every instant in
time during vehicle operartion. The resulting power Filtering – Periodic motions of the intake valves and the
difference will be taken up or contributed by the elec- intake cycle of the engine produce strong changes in the
tric machine.[16]. air mass flow and pressure waves in the manifold. The air
mass and pressure oscillations also cause perturbations
External factors – External factors are as follows: to the output signals of the pressure and mass flow sen-
sor. The dominant frequency corresponds to the double
(i). the power demands caused by the kind of track; speed. In the case of sensor signals with stochastic and
(ii). the kind of driver; deterministic perturbations, Kalman filter techniques are
(iii). characterisitics of the driving cycle as well as an effective method of sensor signal filtering [17].
weather conditions and uphill or downhill driving; and As the frequency spectra of the pulsations vary with the
(iv). preheating of the electrically heated catalyst [15]. engine speed, the pulsations frequency can only be
assumed constant if the sampling is done at equidistant
crank angles, yielding a constant crank angle increment

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between two samples. Therefore the intake manifold A/F controller – The A/F control systems are based on
model has to be transformed into the crankangle domain, contineous time, or based on crankangle period. The
described the transformation law, from the time domain main dymamics which the A/F controller should compen-
measured in seconds to the crank angle domain mea- sate is the fuel and air dynamics in the intake manifold
sured in degrees. and transport and process delay owing to the event
based nature of the engine. The air dynamics in the
Data fusion – If a manifold pressure sensor and an air intake manifold is highly nonlinear, and has fast tran-
mass sensor are available, data fusion for the estimation sients in normal driving conditions. To keep up with these
of the mass of air in the cylinders can be realized based fast transients, the A/F controller should have a high
on the equation of mass conservation in the manifold. bandwidth. Air flow control has been studied for an elec-
The measurements coming from the pressure and the air tronically controlled throttle. The cylinder air flow could
mass sensor, however, cannot be utilized directly, for the also be regulated by variable intake valve timing and sec-
following reasons: ondary throttle.
(i). the pressure pulsations in the manifold cause strong A discrete event based on the nature of the engine com-
estimation errors; bustion process introduces time-varying delays depend-
(ii). the dynamics of the hot film air mass meter has to be ing on the engine speed, which motivates discretizing the
taken into account; and intake manifold model synchronized with the engine
events. Figure 2 shows the strategies of A/F control. Tar-
(iii). failure of one of the sensors causes the algorithm to
get engine torque is synchronized with injection events
deliver incorrect air mass information.
and engine torque is determined. Fuel mass is calculated
To avoid these problems, the A/F control system incorpo- by using the efficiency and the engine torque and the fuel
rates manifold pressure, air mass flow signal of a hot film injection is activated. In-cylinder air mass is determined
air mass meter and the throttle angle in its observation by the target engine torque or by using the target A/F and
model[6]. the fuel mass. The mass air flow rate through the throttle
is calculated by using the intake manifold model. The
Exhaust gas recycle (EGR) system – The A/F control mass air flow rate into the intake manifold through the
systems include EGR have to consider both EGR and air throttle is a function of the throttle angle, the upstream
flow as independent parameters. In practice the air flow pressure and the downstream pressure. The mass air
rate is set by another control algorithm responsible for flow rate into the cylinder is a function of manifold pres-
load control. Two separate loops controlling respectively sure and engine speed. The estimation of the air flow rate
air flow and A/F are supplemented by a model which pre- is based on estimated manifold pressure, which is
dicts the behavior of the EGR system [19]. The benefits derived from the intake manifold model and the direct
of coordinated variable nozzle geometry turbocharger measurement of the mass air flow rate from the hot-wire
and EGR control for a high speed diesel engine have air flow meter [21]. The throttle is activated to get the tar-
been presented and an EGR control system using pres- get mass air flow rate past the throttle. Figure 3 shows
sures which are estimated by an intake/exhaust system traces of fuel mass and air mass in the cylinder schemat-
model was described [23]. Esimation of the intake and ically. The air flow rate past the throttle Wh during intake
exhaust pressures using the output of the air flow sensor stroke is a function of the air mass A(i-1) and A(i). When
as the main parameter was investigated. EGR limits are A/F is constant, A(i) and A(i-1) are proportional to fuel
typically determined by transient response rather than mass F(i) and F(i-1), respectively. The air flow rate throug
steady state performance [6]. It is necessary to use a the throttle Wh is a function of A(i-1) and F(i). The throttle
model to calculate the air mass in the cylinder. is controlled based on the air flow Wh as described else-
where [24].

Figure 2. A/F control

Figure 3. Traces of fuel mass and air mass (1)

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An advanced crank encoder is employed to reduce the of the intake stroke. Therefore, the air mass estimation is
time required for engine controller synchronization. Once delayed each intake stroke. When the fuel is injected (
the engine and controller are synchronized, the special- shown as F**(k)) before the intake stroke, the air mass
ized cylinder-event-based algorithms are activated. The A** (k) is determined at that time. When the fuel is
fuel injection timing, fuel mass, and spark timing are all injected ( F*** (k)) after the beginning of and during the
controlled on a cylinder-by-cylinder basis [5]. intake stroke, the air mass A*** (k) is determined by the
target engine torque at that time, the throttle must be con-
The feedforward control calculation is made by the
trolled quickly to attain the target in-cylinder air mass
observer based on the estimated throttle trajectory and
untill the end of the intake stroke. The fuel mass F**(k),
on the the estimated mean engine speed through the
F*** (k) is calculated by using A(k). When the fuel is
intake stroke. The fuel calculation must be made one
injected during the conpression stroke, the fuel mass is
segment (180 degrees of a crank-shaft rotation) before
determined by the air mass A(k) and A/F.
the start of the corresponding intake event because the
fuel is injected at the start of the event. The intake mani-
Compensation – In multipoint injection systems, the
fold model is advanced every 45 degrees of a crank-shaft
transportation of fuel injected into the cylinder is delayed
rotation (4 times per segment) and it outputs the esti-
due to fuel impingement on the intake port. Therefore,
mated mass of air in one of the four cylinders one per
the in-cylinder air mass is compensated according to the
segment [13].
transportation delay. The amount of the injected fuel
mass is calculated before the amount of air induced into
Priority – The fuel mass is determined by the engine
the cylinder is controlled. Therefore, there is no time lag
torque, independent of the air mass in Fig. 2. But, such a
between air mass and fuel mass in the system described
strategy has some problems when the air mass is satu-
in Fig. 2.
rated at wide open throttle. The air mass is not enough to
keep A/F stoichiometric when the fuel mass increases. In the direct injection system, free from the effects of fuel
Therefore, the in-cylinder air mass is determined by the films in the intake ports, some form of transient fuel com-
target engine torque, taking maximum air mass attain- pensation is not required to maintain the desired induced
able in the driving conditions into consideration. The fuel A/F.
mass is determined by using the air mass and A/F. The
air mass calculation takes priority over the fuel mass cal- Throttle air flow control – The effective opening area of
culation at full load. The efficiency of the engine is stable the throttle, or opening angle is given to control the air
at full load. The air mass characteristics can be similar to flow past the throttle in Fig.3. But, the air flow is affected
those of a conventional engine at steady state. by the air temperature, and atmospheric pressure. It is
necessary to compensate the error between the refer-
ence air mass determined by the fuel mass and the esti-
mate of the air mass by feedback control strategy which
adjusts the throttle so that the air mass into the cylinder
follows the reference values.

Switching – Air quantity is controlled by the air bypass

valve or electrically controlled throttle valve. Because a
short delay in air quantity control caused by the plenum
chamber volume, is inevitable, switching should be per-
formed under the condition in which the generated torque
of both modes under the same quantity of air is precisely
the same to avoid the shock caused by the torque differ-
ence before and after the switching [10].

INTAKE MANIFOLD MODEL

Figure 4. Traces of fuel and air mass (2)
The air mass in the cylinder can be estimated by using
Figure 4 shows more traces of the fuel mass and air
the air mass map(throttle angle, engine speed) and the
mass. Air mass A* determined by the target engine
time constant map(air mass, engine speed), without
torque is calculated at the beginning of the intake stroke.
using physical models and the air flow meter [24-25]. For
Then, the in-cylinder air mass A is calculated by the
a fixed engine configuration, the volumetric efficiency is a
intake manifold model. Then, the fuel mass is determined
function of at least engine speed, MAP (manifold abso-
by A/F and A. The fuel mass and air mass during the
lute pressure), instantaneous temperature of intake wall,
intake event t(k) are controlled to keep the A/F target
intake valve and manifold air. The transient volumetric
value. The air mass is controlled by the throttle. The in-
efficiency was found to be as much as 10% larger than
cylinder air mass can be calculated based on the throttle
the steadystate value [5]. Therefore, it is necessary to
angle. The target engine torque changes based on con-
measure the air mass directly by using an air flow sensor.
tinuous time. The air mass is determined at the beginning

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The cost of using map-based schemes is in terms of test control system, which would require only relatively minor
bed time. Both diesel and gasoline technologies seem to calibration changes for each engine modification. To con-
be moving towards adding more tables for future engines. trol engine-out A/F during transients accurately, the
This would result in significant increases in complexity engine controller needs reliable predictions or measure-
which might make it harder to get the powertrain into pro- ments of the amount of intake air, and the amount of fuel
duction in time. One new approach which could help con- injected that will go directly in-cylinder as described in
siderably in reducing the dependence on maps is to use Section 2. It is necessary to calculate the air mass which
a physical model as the basis for control. Physical model is inducted into the cylinder each cycle. Only in the
using pressure, air flow and A/F have cost effective tech- steady state operating mode is the mass flow measured
nical solutions [11]. with an air flow meter identical with the air mass charged
into the cylinder [3]. Under transient operating conditions
COMPLEX AIR INTAKE SYSTEM – In the future, more there is a difference between them. The amount of the
complex air induction systems are likely, especially on difference is the air mass which is necessary to charge
premium powertrains. Probable systems include dual- the density of the air volume in the manifold. The mathe-
runner and dual plane actively tuned manifolds, variable matical, downstream model of the intake manifold system
valve timings, and passive or active air inlet duct tuning. based on MAP has been described elsewhere [3].
All of these features complicate the volumetric efficiency
characterization of an engine. In particular, active sys- dpm κRTm
tems are not easy to handle, especially those which can = (Wh − We )
dt Vm
be modulated. A mass air flow sensor is largely unaf- (1)
fected by such factors, unlike a speed density system [6].
pm
In a complex system like that shown in Figure 5, a large We = N × S w × η v ×
RTm
volume in the intake system causes a charge lag and, as (2)
a result, idling instability and fluctuating A/F. Generally,
The global downstream model, a complete physical
the total volume included between the throttle and intake
model based on equations (1) and (2) was then devel-
valves should not be greater than twice the engine dis-
oped, which leads to a correction strategy for transient
placement. For upstream throttling, however, it is difficult
operation of the engine [26]. But, to solve the above
to design the intake system within this limit, and it is
equations, it is necessary to use the volumetric efficiency
especially so when an intercooler is to be provided. If the
which is dependent upon instantaneous cylinder temper-
supercharger is equipped with a clutch, the bypass valve
ature as described above. It is not easy to model the ther-
prevents a large change of air flow by switching of the
modynamic behavior of the cylinder with simple
clutch, bringing about smooth driveability [7]. The EGR
equations.
system also affects the volumetric efficiency charateriza-
tion. In this system, it is necessary to measure the air In this paper, a new upstream model is investigated
mass by using the air flow meter upstream from the throt- which uses equation (3) in place of equation (2).
tle valve, as shown in Fig. 5. Nowadays fully-flexible
intake valve control is considered to be the most promis- l dWh 1
ing improvement measure for SI (spark ignited) engines pm = po − − ξ h Wh Wh
a dt 2 (3)
besides, or in combination with, direct fuel injection [8]. In
these cases, fuel must be injected according to the esti- The MAP pm is calculated using the parameters only
mated air mass as described in Section 2. upstream from and the throttle valve and the air flow
meter related signal, which would require relatively minor
PHYSICAL MODELS – There would be great advan- calibration changes for each engine modification.
tages to developing a generic form of the electric engine

Figure 5. Intake system

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There is one further problem associated with the calcula- noise from vibration and electrical noise. Adding analog
tion of air flow. The above model indicates the air flow or digital filtering to smooth out the noise is possible, but
rate to cylinders at a particular moment in time, but the the response time is slowed, and fueling errors are then
fuel induced with this measured air was injected at some introduced. In this paper, the MAP is computed using
time previously. Fuelling changes will always lag behind equation (3), without using the MAP sensor. The com-
requirements. The throttle clearly moves a finite time puted MAP is available almost instantaneously and is
before changes in manifold pressure occur, so using noise-free enough that the computed MAP may be
throttle movement as an indication of imminent changes extrapolated into the future to estimate the MAP near the
in manifold pressure may be possible, from which an air time of intake valve closing. The computations to esti-
flow anticipation scheme would be possible [12]. mate Wh using the MAP sensor become inaccurate as
the MAP approaches atmospheric pressure. Therefore,
OBSERVER – The air intake process is modeled in this paper the upstream throttle mass air flow meter is
through the upstream model based on equations (1) and used.
(3). The model is calculated by using an observer. The
new family of observers provides the SI engine control UPSTREAM MODEL – Tables 1 and 2 compare the con-
system designer with a variety of robust control systems ventional downstream model and upstream model. The
which can easily be made redundant in order to satisfy upstream model has many advantages compared with
newer engine emissions regulations and diagnosis the downstream model. But it is necessary to take the fol-
requirements. Observers in A/F control act as a lowing into consideration.
smoothers and predictors for the air mass flow. The
1. When the intake manifold pressure decreases below
actual configuration of the observers which can be con-
critical pressure, the air flow is chocked due to sonic
structed on the basis of the differential equations above,
phenomenon. The calculation of MAP with equation
is dependent on the sensor selection. Sensors for the
(3) becomes impossible. The air flow rate versus the
throttle angle and crank shaft speed are obviously neces-
MAP is slightly changed by using a small bypass
sary in any case as well as sensors for the ambient and
valve through the throttle which adds the air flow rate
intake manifold temperatures. Apart from these input
proportional to the manifold depression. By adding
variables the state variables which are to be estimated in
this device, the MAP can be calculated by using the
an observer should correspond to the air mass flow
air flow rate Wh.
related sensors which are used:
2. It is necessary to estimate atmosperic pressure by
(i). MAP sensor; using learning strategies.
(ii). upstream throttle mass air flow sensor; and 3. It is necessary to compensate the loss coefficient of
(iii). port air mass flow sensor. the compressor and the throttle valve, according to
the perturbation of air flow rates because the pres-
The MAP sensor experiences both periodic noise associ-
sure loss is nonlinear to the air flow rate.
ated with filling events for each cylinder, and random

Table 1. Conventional downstream model and new upstream model

Downstream model Upstream model

Air mass flow past throttle Calculated by pressure diffrence across Measured directly by air flow meter
valve Wh throttle valve pm

Manifold pressure pm Measured by MAP sensor Calculated by air mass flow rate

Air mass flow in cylinder We Calculated by using MAP pm and volumetric Calculated by air mass flow rate (a-2)
efficiency η v (a-1)

dpm κ RTm p
= (Wh − We ) We = N × Sw × η v × m
dt Vm RTm
(a-1)
Vm dpm
We = Wh −
pm = po − f (Wh , ξ ) κRTm dt
(a-2)

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Table 2. Comparison between models

Conventional downstream model New upstream model
It is not easy to handle active systems such as It is free from such problems
supercharger, exhaust gas recycle control system,
variable valve timing, etc.
Computed mass flows using modeling of throttle air Mass flows are measured directly by using
mass flow are not accurate due to small pressure airflow meter, there are no systematic errors
difference across throttle plate
It is influenced by volumetric efficiency It is free from the change in volumetric efficiency
characterization
Volumetric efficiency is a function of at least engine It requires only minor calibration changes for
speed, MAP, temperature of intake wall, intake each engine modification
valve and manifold air. It requires map-based
schemes
MAP sensor experiences both periodic noise MAP is computed by using model and noise-free
associated with filling events, and random noise
from vibration

Real time calculation of upstream model – A nonlinear

pm − pm (t − ∆t ) Vm
dynamic model of an intercooled, supercharged spark We = Wh −
ignited engine is developed for the purpose of evaluating ∆t κRTm
(10)
microprocessor-based control strategies. The engine
system is thermodynamically modelled to match engine We can be calculated from the air flow sensor signal Wa ,
data [14]. using equations (4)-(10). The air mass in the cylinder is
calculated by integrating We over an intake stroke.
Air flow rate through the compressor Wc can be calcu-
lated using the equation: The integration of the equations can be accomplished
using a specially designed three-stage, first-order,
Wc = Wa + Wb (4)
Runge-Kutta numerical integration method. While it is
more complex than other more common integration
Wb is calculated using the equation: methods, this method has an extended stability region
which allows a larger sampling period than would ordi-
Wb = f ( pi , po , ξ b ) narily be the case. This is necessary because the small-
(5)
est effective time constant can be below 0.4 ms [6].
Where Wb =0,
Mean value calculation of upstream model – In the case
Wc = Wa (6)
of the real time calculation, it is necessary to calculate at
each time set-up (for example, time step = 1ms). Mean
The pressure of the intercooler pi can be expressed as: value calculation describes the time development of the
most important measurable engine variables (or states)
1 W − Wc (t − ∆t ) lc on time scales a little larger than an engine cycle [7]. The
pi = pai * po − ξ cWc Wc − c
2 ∆t ac perturbation can be obtained approximately by assuming
(7) that the air mass flow through the engine port is a series
The flow rate through the throttle valve Wh can be of overlapping cosine pulses. An algorithm works by inte-
expressed as : grating a signal over an event (and perhaps dividing by
the event time)[6]. The calculation can be made one seg-
pi − pi (t − ∆t ) Vi ment (180 degrees of crank shaft rotation ) before the
Wh = Wc − Wb − corresponding intake-event. The calculation of the air
∆t κRTi flow rate from mean value of the air flow rate measured
(8)
with an air flow meter is described elsewhere[1].
The intake manifold pressure pm can be calculated using
the equation:

1
pm = pi − ξ hWh Wh
2 (9)

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engine port was a series of sine pulses(every 180

degrees of the crank angle). The calculations were down
using the real time and the mean value calculation. The
time step with the real time calculation was 1.0 ms and
that with the mean value calculation was 25 ms( N=1200
rpm).

Table 3. Simulation conditions

Engine 4-cycle, 4-stroke
ab 0.7065 × 10 −3 m 3
ac 1.96 × 10 −3 m 3
a h 0.7065 × 10 −3 m 3
lc 2.0m
N 1200rpm
pai 6.6 − 128 × Wc
Figure 6. Calculation We from Wa po 1.0 × 10 5 Pa
Calculation of air mass – Figure 6 shows the calculation R 287 J kg K
⋅
procedure of the air mass and pressures. When the air −3
flow rate is measured at event (i), the mean value Wa (i),
Sw . × 10 m 3
15
pi(i), Wh(i-1), pm(i-1) and We(i-1) are calculated as Tc 293.0 K
described elsewhere [1]. Therefore, the air mass in the Tm 293.0 K
cylinder We(i-1) is estimated reliably without using the
changed parameters of the engine. When a(i+1) is given, Vi 2.0 × 10 −3 m 3
Wh (i), pi (i+1), pm (i) , and We(i) can be estimated. Then, Vm 2.0 × 10 −3 m 3
pm (i+1) is calculated by using Wh (i) and We(i). After that,
We(i+1) is calculated as follows, without using the volu-
AIR MASS ANTICIPATION DURING THE RAPID
metric efficiency when the intake valve timing is not
THROTTLE VALVE OPENING – Figure 7 shows the
changed.
traces of Wa , (the air flow rate through the air flow meter),
Wam (the mean value of Wa , ), and We (the air mass into
pm (i + 1)
We (i + 1) = We (i ) the cylinder calculated by the real time calculation), Wem
pm (i ) (the air mass into the cylinder estimated by the mean
(11) value calculation), when the throttle valve was opened
The fuel can be injected at the beginning of the intake linearly during the period from 0.3-0.5 s. The level of fluc-
event (i+1) according to the air mass We(i+1) and the tar- tuations in the air mass flow related sensor signal W a is
get A/F. The throttle can be controlled according to a(i+1) very large and manifold filling spikes in the air mass flow
during the intake event (i+1). The air mass flow during the signal Wam are apparent because of the rapid throttle
event (i+1) is given as follows, movement. The main source of disturbances in the sig-
nals is pumping fluctuations. These fluctuations are
a (i + 1) pi (i ) − p m (i + 1) greatest on tip-ins because it is necessary under such
Wh (i + 1) = Wh (i ) conditions to pump large quantities of air into the engine.
a (i ) pi (i ) − p m (i ) We which was calculated by the real time calculation and
(12)
at the end of the intake event is equal to the real air mass
in the cylinder. Wem is advanced by one event ( 180
ANALYSIS
degrees of the crank angle) against We . This indicates
that Wem can be a predictor of We .Therefore the fuel is
SIMULATION CONDITIONS – A 4-cylinder, 4-stroke
injected by using Wem before the beginning of the intake
engine with a total cylinder volume of 1500 cm3 and the
event of We , while keeping the A/F ratio within 1% of the
complex intake system as shown in Fig. 5 were used for
target value. It is seen that the air mass can be estimated
the simulations. Table 3 lists the conditions. The intake
at the beginning of the intake stroke, resulting in fuel
dynamics was simulated by using equations (4)-(10). The
injection without any delay, thus there is precise A/F ratio
time step of the calculation was 0.1 ms. The perturbation
control.
due to pumping of the piston reciprocating motion was
given by assuming that the air mass flow through the

8
 Downloaded from SAE International by Mahindra & Mahindra Ltd. - 127805, Tuesday, June 09, 2020

FUTURE OUTLOOK – The analysis mentioned above

are based on simulation, although some cases have
tested already in mass production engines. Application
examples will be presented after taking the dynamics of
the hot-wire mass air flow sensor into consideration.

SUMMARY

A new A/F ratio control system using physical models

which are used in high supercharged direct injection
stratified charge engines was investigated.
(i). The upstream model uses parameters only upstream
from and the throttle valve and the air flow meter
related signal, which would require relatively minor
calibration changes for each engine modification.
Figure 7. Traces of Wa, Wam, We and Wem
(ii). The real time calculation of the model is executed at
each time step (order of 1ms). The mean value cal-
culation of the model is executed at each time step of
an intake event (25ms at engine speed of 1200 rpm).
(iii). Air mass during the rapid throttle valve opening can
be estimated at the beginning of the intake stroke,
keeping the A/F ratio within 1% of the target value.
(iv). Air mass on a cylinder-by-cylinder basis can be esti-
mated by using the real time calculation. Unbalance
on a cylinder-by-cylinder basis can be identified by
using the mean value calculation.
(v). The upstream model can easily handle active sys-
tems such as supercharger, exhaust gas recycle con-
trol system, variable valve timings, etc.
Figure 8. Traces of We and Wec
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pi (i ) : pressure in the intercooler
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March 1, 1998, Mohican State Park, Loudonville, Ohio, po : atmospheric pressure
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ξ h : loss coefficient of the throttle valve
10