8/9/2019 Beltrami 2003

1/6

AFR control in SI engine w ith neural prediction of cylinder air mass

C. Beltrami', Y. Chamaillard , G. Millerioux', P.

Higelin**

nd G. Bloch'

Centre de Recherche en Automatique de Nancy (CRAN, UM R CN RS 7039)

ESSTIN, 2 rue Jean Lamour, 545 19 Vandoeuvre les Nancy Cedex, France.

gerard.bloch@esstin.uhp-nancy.fr

..

Laboratoire d e Mecanique etd'Energitique (LME,

EA 1206)

ESEM, 8 rue Leonard de Vinci, 45072 Orleans Cedex 2, France.

yann.chamaillard@univ-orleans.fr

Abstract

Accurate Air-Fuel Ratio (AFR) control in a spark-

ignition engine is

a

critical point to satisfy pollutant

emission legislation. Using

a

three-way catalytic

converter with an electronic fuel injection, today's most

effective solution, requires the regulation of the cylinder

AFR in a narrow band around the stoichiometric

conditions during both steady and transient engine

operation to be efficient.

AFR control depends essentially on prediction of the air

mass to be admitted. In this paper, the building of an air

mass predictive neural network is described and its

performances are evaluated. Using this predictor in

addition with transient fuel film compensation for AFR

control allows to drastically reduce the AFR excursions

during fast transients.

Keywords

air-fuel ratio, event-based control, prediction, neural

network.

1. Introduction

In today 's spark ignition engines, three-way catalysts are

used to reduce the exhaust emission of the three main

pollutants that are: unburned hydrocarbons (HC), carbon

monoxide (CO) and nitrogen oxides (NOx). The

optimization of the three-way catalyst efficiency requires

the cylinder Air-Fuel Ratio (AFR) to be kept in

a

narrow

band which corresponds to the stoichiometric conditions

[6].

igure 1 describes the catalytic conversion efficiency

for the three main pollutants versus the in-cylinder

mixture AFR. Even a small deviation from

stoichiometric conditions can result in

a

dramatic

degradation o f the conversion efficiency.

A modern engine control unit , as the ones commonly

installed on new vehicles, handles this AFR regulation

task very well under steady state conditions [4]. It

provides the injection controller with a prediction

of

the

air mass to be admitted in the cylinder and uses a

0-7803-7896-2/03/ 17.00

2003

EEE

Universal Exhaust Gas Oxygen (UEGO) sensor in the

exhaust flow for the AFR measurement to allow a

possible bias to be corrected by feedback.

The control problem becomes more difficult in transient

phases because of the m ore d ifficult prediction of the air

mass, the fuel flow dynamics and the inherent delay in

the feedback system. This results in AFR excursions

during fast transients, and so increased pollutant

emissions. A lot of work has been perform ed in the topic

of air mass prediction [9] [ I l l [I61 and fuel film

dynamics [ I ] [3]

[7]

to improve A FR control.

Air-Fuel Ratio

AFR)

FIG.

1:

Catalytic converter efficiency

Th e AFR is defined as the ratio between the air mass and

the fuel mass admitted into the cylinder. These variables

are not accessible for measurement but depend

essentially (though dynamic systems) on throttle angle

and injection duration.

In

a

first part, a description of the two sub-systems, fuel

and air dynamics, involved in the AFR determination is

provided to understand the process. The AFR control

method is then detailed and

the

air mass prediction issue

developed. Finally, a solution using a neural air mass

predictor, with a physical model based structure, in

addition to transient fuel film compensation, is proposed

and evaluated.

1404

Proceedings

01

the American Control Conference

Denver,

Colorado June

46 2003

mailto:gerard.bloch@esstin.uhp-nancy.frmailto:yann.chamaillard@univ-orleans.frmailto:yann.chamaillard@univ-orleans.frmailto:gerard.bloch@esstin.uhp-nancy.fr

8/9/2019 Beltrami 2003

2/6

2. Engine model

The

simulations are performed on a non-linear fuel-

injected, mean-value and event-based model.

Computation is performed at each,T op Dead Center. The

engine m odel includes the engine (fuel flow dynamics,

air

mass

flow dynamics, combustion and delays inherent

to four-stroke engines), actuators, sensors and a dynam ic

model of the load. This model is representative of a

classical four cylinders

1.4

liter engine.

2.1.

Fuel dynamics

The fuel flow sub-model describes the fuel transport

from injection location to intake port. A two phase fuel

flow occurs in the intake manifold, with a thin film of

fuel on the manifold walls and droplets transported by

the main stream of air and fuel

[ I ] .

It

is

worth

emphasizing that the fuel film dynamic model is non-

linear in spite of its linear form. Indeed, the parameter

values depend on the engine operation states and are not

constant. Moreover their identification

is

relatively

complex.

It is assumed that at any time there are uniform

conditions in the intake manifold and that a fraction X of

the injected fuel is deposited on the wall as liquid film.

The evaporation is considered proportional to the mass

of the fuel film. The phenomena can he described by a

model with two time constants

[7]:

1

T

m, =-[-mfi+ l-x)m,)] ( 2 )

m

=

m +m s 3)

with mg fuel film mass flo w (kgkec),

mp injected fuel mass flow (kg/sec),

m,

fuel vapor mass f low (kdse c) ,

mf

cylinder port fuel mass flow (kgisec),

x

fraction of injected fuel deposited as fuel film,

z,

fuel vapor time constant (sec)

and

ry

fuel film time co nstant (sec).

In an injection system the vapor time constant r, can

usualIy be neglected with respect to the fuel film time

constant

zr

and equation

( 2 )

becomes:

Hence, the global equivalent transfer function that links

the fuel mass injected and the fuel mass admitted can be

described by:

5 )

From

3)

and

(4),

an ideal compensation for the

simplified model can he obtained:

m , = I - X ) k ,

4)

Mf s )

=

l + l - X ) z p

M j i W I+r f s

1

1-x

f i

=- m p -6,j-I ( 6 )

where m, is the desired fuel mass flow and

iff

he fuel

film mass flow estimation defined as in I ) by:

m g =-(-Gg

+Xm,)

1

z/

Linear compensation based on the equations above

cannot he achieved to give optimal compensation over

the entire operating range of an engine, especially

in

transient condition. This fact has been pointed out

in

several earlier publications and is very important in

practical applications

[7].

However, the compensation

presented above permits to sensibly reduce the fuel

dynamics effect on AFR and

so,

to better a ppreciate the

air estimation effects.

2.2. Air dynamics

The air intake sub-model describes the air mass flow

from the throttle to the cylinder port [ 2 ] .The only input

which can he controlled is the throttle angle that

modifies the intake manifold pressure:

dP 0

t = a Sthr(t) f s V P t ) / Putm)

( 8 4

(8h)

here a=-----Jp-- and f l =

30 Mu Vmun

-

Ne@ PltJ

f@ t), Ne(t).Ta)

y

R

Tu

Putm

Ma

Vmun R Tu

y R Ta

with P t)

Sthr(t)

Wt

W O

f a 0

Patm

Tu

Vmun

and b R . M a

manifold pressure (Pa),

effectiv e throttle s ection (m'),

engine speed (rpm),

Saint-Venant function,

filling function,

atmospheric pressure (Pa),

air temperature K),

manifold volume (m3),

thermodynamic constants.

The first term of (Sa) corresponds to the entering flow

from the throttle. The second term represents the exiting

flow that is admitted into the cylinder and depen ds

essentially on manifold pressure and engine speed. The

air dynamics is fairly com plex and non-linear, and

is

a

central problem in AF R regulation

2.3. Event-based model

A closer

look

at the engine processes shows that the

operations divide the physical processes into four distinct

regimes corresponding to the four events: intake,

compression, power and exhaust, and suggests an event-

based app roach according to the crank angle.

As a

result, the characteristic behavior

of

an engine

consists of a combination of two types of dynamics:

time-based and event-based. Event-based dynamics are

described in the crank angle domain. From the engine

control point of view, only one value

of

AFR exists at

each cycle for each cylinder, and the outputs of an

engine control system are synchronous with crank angle.

Hence, the fundamental sampling period

Te,

constant

in

7)

Proceedings Of the

American Control

Conference

1405 Denver,

Colorado

June 46.2003

8/9/2019 Beltrami 2003

3/6

8/9/2019 Beltrami 2003

4/6

4.2.

T h e

neural

model

As the v ariable to be estimated, here the air m ass, is not

measured, a simulation model, involving outputs

predicted by the model in the regression vector, is

needed. Hence, a Neural Output

Error

model

WOE)

i s

used. To predict j ( k ), he air mass to be admitted at

discrete time

k,

the following regressors have been

chosen:

Air mass prediction at

(k

) , $(k - ,

Manifold pressure

P k - )

and

P k - ) ,

Engine speed Ne(k - ),

Throttle angle reference Th+@(i),

i

=

k-l.k-b... k-6

.

This choice is clearly based on physical equations

8),

which involve a s dynamical inpu ts the ma nifold pressure

P o ) ,

effective throttle section

Sthr(t)

and engine speed

Ne(?). Including

P k

-

)

and P k

-

2) reflects the

presence of P(t) time derivative in 8). The engine

speed, beyond its role in air admission m odel, permits to

handle the variable sampling period

Te

issue. The last

regressors allow the prediction thanks to the delay

present in the throttle actuator which is aro und

30

ms. At

6000 rpm, the sampling period

is 5

ms and 6 samples are

then necessary. The same choice is m ade in [ I I] . The use

of a rapid throttle could reduce the delay and

so

the

number of regressors.

Training was performed by minimizing the mean

squared error function, with the Levenherg-Marquardt

method implemented in a specific Matlab toolbox

[15].

The different signals involved in training the network

should have been scaled to avoid saturation. A hidden

layer of n

=

14

neurons (see eq.

12)

was selected to

reach a good prediction accuracy.

The training data set was obtained by simulating the

engine on a large range of operation. The torque

reference signal consisted of steps of random length and

size, to which was added up a random step signal with

length and amp litude divided by IO, as shown figure 4.

in AFR regulation. A solution for air prediction is

proposed in the following section.

4 Neural air mass prediction

4.1.

In t roduc t ion

As the AFR m easurement presents a delay and the sensor

dynamics is slow with respect to the variation to he

detected during transient phases, a feedforward control

seems to be the solution during transients. For such a

scheme, the AFR regulation quality depends essentially

on the prediction of the air mass to be adm itted. From the

physical model of the air admission dynamics, given by

S), the goal is to obtain a discrete event-based model of

the air admission in order to predict the air mass

f low

to

be admitted in the cylinder. The delay between the angle

reference and the actual throttle position can be used to

develop an air charge anticipation algorithm. Magner a nd

Jankovic

2002)

develop such a solution using a neural

predictor [Ill . Other works [SI

[lo] [I21

already used

neural networks to optimize AFR control.

Because of their ability to represent complex non-linear

mappings with good flexibility and accuracy, neural

networks have become popular to model various

subsystems as discrete black boxes

[13]

[14].

As parsimonious and flexible universal approximator,

the on e hidden layer perceptron w ith linear output unit is

used here. Its form is given, for single output f ,by:

where pj, = I ; . . , p , are the inputs of the network,

wki

and

b k ,

k = f : . . , n ,

j = f : . . p

are the weights

and biases

of

the hidden layer, the activation function

g

is

a

sigmoid function, chosen here

as

often as the

hyperbolic tangent, 4 , = I ; . . , n , and bZ are the

weights and b ias of the outpu t neuron or node.

The non linear model ( 1 1 ) can be used as discrete

dynamical predictor of a variable

y :

where p k)= [pl(k)pz(k)...pp(k)P is the regression

vector and the parameter vector

B

is the concatenation

of all the weights w and biases

b .

Depending on the

choice o f the regressors in p@), ifferent models can be

derived.

m = f m ) , e 8 ) 13)

FIG.4 : Engine torque reference (daN .m) vs. time (sec)

The whole engine operation range

for

different engine

speeds was covered. The speed reference signal was

Proceedings of the American Contml Conference

Denver, Colorado June

4-6, 2003

407

8/9/2019 Beltrami 2003

5/6

varying from

1000

to 6000 rpm by step of 1000 rpm. As

the sampling period depends on the engine speed, the

step duration varied with th e speed reference

to

keep the

same learning points nu mber fo r each level.

5. Results

Two simulation scenarios can be considered for

validation: the engine speed scenario and the torque

scenario. In [4], it is shown that transients in torque are

the most disturbing. So the torque scenario is used here

for comp arison.

The main task was to obtain an air mass predictor in

order to enhance AFR control in transient phases. As the

transient fuel dynamics compensation was not the main

problem, results will be compared with the same fuel

admission corrected (in simulation) by the ideal

compensation 6) and

7).

Different simulations have been performed to test the

neural air mass predictor. The torque reference

represented on figure

5

is chosen to generate fast throttle

angle variations and thus rapid transient phases.

FIG. 5 : Torque refere nce (daN.m) vs. time (sec)

That signal is used with differe nt engine speed references

from 1000 to 6500 rpm by

500

rpm step to compare the

results with data similar but different from the learning

set. The simulations have been done with the ideal fuel

film compensation and a PI controller on AFR

measurement (in the AFR controller - figure 3) to avoid

bias.

The test results

of

the on e step ahead neural predictor are

reported in table 1. The engine speed reference value

used with the torque reference is reported in the first

row. The Root Mean Square Error (RMSE) values for

the air mass prediction with a traditional method (Air-t)

(prediction by a volumetric efficiency map from

estimated manifold pressure, given by I

I ,

and engine

speed) and for the neural prediction (Air-nn) are

reported in the second and third rows. The last two rows

give the RMSE on AFR control results with traditional

(AFR-t) and neural (AFR-nn) predictions.

Table I - Results

The results show that the neural prediction leads to a

very significant improvement in AFR control thanks tn

its better prediction of the air mass to be admitted. The

neural network interpolates the learning data very well,

hut, for extrapolatio n, the performan ces fall dow n

compared to traditional method (at 6500 rpm for

example).

Results at

3500

rpm are shown in figures 6 and 7, during

only 3 seconds to better illu strate the differences. Figure

6

shows the neural air mass prediction compared to the

real (simulated) air mass. It can he noticed that the

prediction errnr is very weak and the real and predicted

air masses are difficult to distinguish

Real air

mass

Neural prediction

redictionerror

I

1.5 8 1 8

8 5

10

FIG.

6 :

Predicted and real air mass (mg)

vs.

time (sec)

As previously mentioned, the good capability of the air

mass neural predictor allows to significantly enh ance the

AFR control. Figure

7

shows a comparison between the

AFR excursion with the traditional air mass flow

predictor (AFR-t) and the neural on e (AFR-nn).

In

all cases the AFR excursions are reduced (by

50%)

especially for high excursions, which are the most

problematic for consumption, agreement and pollutant.

However the static error compensation is rather slower

because the feedback controller has not been redefined.

Proceedingsof the American

Conlrol Conference

~enver

oioraao ne 4-6,

zw3

408

8/9/2019 Beltrami 2003

6/6

 

7 s 1 5 8 9 5 10

FIG. 7: Com parison ofth e AFR errors vs. time (sec)

6 . Conclusion

The need of an accurate prediction of the air mass to b e

admitted in the cylinder has been emphasized in the

framework of AFR control. A neural network can be

built and trained to provide a good dynamical air mass

prediction, much better than the prediction based on

classic observer and static volumetric efficiency map.

The neural predictor makes complete use of the delay in

the throttle actuator. For operating points inside the

learning domain, the neural network interpolates very

accurately.

A solution combining this neural air mass one step ahead

predictor and a transient fuel film compensation has been

proposed for AFR control. The results show that the

AFR excursions are drastically reduced on rapid torque

transients

if

the inputdoutputs

of

the air admission can

be correctly collected. It appears also that the feedback

controller must be redefined to optimize static error

compensation.

Although the neural dyn amical prediction of cylinder air

mass greatly improves the AFR control, further works

must be com pleted

for

application to handle the data set

collection and the system non-stationarity over time.

References

1. Arsie, C. Pianese,

G .

Rizzo, and V . Cioffi. An

adaptive estimator

of

fuel film dynamics in the

intake port of a spark ignition engine. 3 ' IFAC

Workshop Advances in Automotive Control,

pp,

293-298, Karlsruhe, Germany, 2001.

P. Anthoine and A. Dauron (1993). Dtpollution des

moteurs a essence: regulation de richesse avec

sonde proportionnelle et actionneur papillon.

Automatiquepour

les

vihicules, pp. 57-72, Amiens,

France, 1993.

M. Behnia and B.E. Milton. Fundamentals

of

fuel

film formation and motion

in

spark ignition engine

induction systems.

Energy Conversion. and

Management, 42,

1751-1768,2001.

Y . Chamaillard and C . Pem er. Air-fuel ratio control

by fuzzy logic, preliminary investigation. 3'd IFAC

Workshop Advances in Automotive Control, pp.

221-226, Karlsruhe, Germany, 2001.

C.F. Chang, ,N.P. Fekete, and

J.D.

Powell. Engine

air-fuel ratio control using an event-based observer.

SAE Paper 93 0766, Detroit, MI, 1993.

[6] R.M. Heck and

R.J. Farrauto. Automobile exhaust

catalysts.

Applied Catalysis, A : General, 221,

443-

457,2001.

[7] E. Hendricks, T. Vesterholm, P. Kaidantzis,

P.

Rasmussen, and

M.

Jensen. Nonlinear Transient

Fuel Film Compensation (NTFC).

SAE Paper

930767, Detroit, MI, 1993.

[8] R.J. How lett, S.D. alters, P.A. Howson, and L.A.

Park. Air-fuel ratio measurement in an internal

combustion engine using a neural network.

Advances in vehicle control and safety,

Amiens,

France, 1998.

M. Jankovic and S. Magner. Cylinder air-charge

estimation for advanced intake valve operation in

variable cam timing engines.

JSAE, 22,

445-452,

2001.

[IO] N. Li,

K. Li

and S. Thompson. Employing a new

type of neural network to optimise power plant air-

fuel ratio.

141h IFAC Triennial World Congress,

pp.

333-338, Beijing, China, 1999.

[ I l l S. Magner and M. Jankovic. Delta air charge

anticipation for mass air flow and electronic throttle

control based systems.

American Control

Conference,

pp. 1407-1412 , Anchorag e, AK, 2002.

[I21 M.

Majors, J.A. Stori, and D. ho (1994). Neural

network control of automotive fuel injection

systems. IEEE Conirol Systems Magazine, 14 3),

31-36, 1994

[I31

K.S.

Narendraand K. Parthasarathy. Identification

and control of dynamical systems using neural

networks. IEEE

Trans. on Neural Networks,

1(1),

4-27, 1990.

[I41 M. Norgaard, 0 Ravn, N.K. Poulsen and L.K.

Hansen.

Neural networks for modeling and control

of dynamic systems. Springer, 2000.

[I51 M. Norgaard. Neural Network Based System

Identification Toolbo x. Technical Report 95-E-7 73;

Institute of Automation, Technical University of

Denmark, 1995.

1161 R.W. Weeks and

J J

Moskwa. Transient airflow

rate estimation in a natural gas engine using a non-

linear observer.

SAE Paper 940759,

1994

[5]

[9]

Proceedings

of

the

American

Control

Conterence

Denver. Colorado June

4.62003

409