Uwe Kiencke

Lars Nielsen

Automotive Control Systems

For Engine, Driveline, and Vehicle

Uwe Kiencke

Lars Nielsen

AutomotiveControl SystemsFor Engine, Driveline, and Vehicle

Second edition

With 345 figures and 13 tables

Library of Congress Control Number: 2005922217

ISBN 3-540-23139-0 Springer Berlin Heidelberg New York

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Prof. Dr.-Ing. Uwe KienckeUniversität Karlsruhe (TH)Department of Electrical Engineering76187 KarlsruheGermanykiencke@iiit.uni-karlsruhe.de

Prof. Dr. Lars Nielsen Division of Vehicular Systems Department of Electrical Engineering Linköping University 581 83 LinköpingSweden lars@isy.liu.se

64 3. ENGINE MANAGEMENT SYSTEMS

between 2000 and 3000 rpm. For even lower resonant frequencies the geometricdimensions of the inlet pipes become too large. The frequency of air pulsation inthe inlet pipe is

fp =n · CY L

2. (3.38)

The factor 2 is due to the fact that air is aspirated only every second cycle ina four stroke process. For example, the pulsation frequency for a six cylinderengine (CY L = 6) at an engine speed of n = 6000 rpm is fp = 300Hz. The airmass per cylinder can be calculated by integrating the mass air flow ma over onepulsation period.

ma =

tb

ta

ma dt (3.39)

The limits (begin ta and end tb) of integration are given by

tb − ta =1

fp=

2

n · CY L, (3.40)

and therefore, the aspirated air for one cylinder per cycle is

ma =

1fp

0

ma dt . (3.41)

The air supply ma can be calculated by integration of the mass air flow signal.The sampling rate must be high enough to avoid aliasing, and therefore it isabout 5 − 10 times higher as the highest pulsation frequency. Eventual non-linear characteristics of the air flow meter must be compensated for before theintegration. A linear characteristic can be obtained by e.g. multiplying thesensor characteristic with it’s inverse. Thus an eventual bias introduced by theintegration can be avoided [68].

The proper timing for integration (ta, tb) can be derived from the crankshaftangle αcs signal. For example, if the crankshaft sensor has 60 teeth, the durationof tb − ta = 1

fpis equivalent to ∆αCS = 120◦ in a six cylinder engine. This is

given by the shift of 20 teeth of the crankshaft sensor. Unfortunately, mass airflow is synchronized to time and not to the crankshaft angle αCS . Since mass airflow ma is not sampled at start and stop times ta and tb, it must be interpolated:

ma(ta) = ma(t0)t1 − ta

Ts+ ma(t1) 1 − t1 − ta

Ts

ma(tb) = ma(tn)tn+1 − tb

Ts+ ma(tn+1) 1 − tn+1 − tb

Ts

The integration is approximated e.g. by the trapezoidal rule:

ma ≈ Ts

CY L(ma(ta) + ma(t1))

t1 − taTs

+ ma(t1) + 2ma(t2) + · · ·

· · · + 2ma(tn−1) + ma(tn) + (ma(tn) + ma(tb)) 1 − tn+1 − tbTs