A control-oriented air-fuel ratio path model is developed to represent a spark-ignited, port-fuel-injected, twin-independent variable cam timing engine. Following a recent publication [Genç et al., SAE 2002-01-2752 (2002)] showing that cam timing not only affects the cylinder air flow but also the transient cylinder fuel flow, this paper constructs a mean value model that describes both air and fuel dynamics. While steady-state engine tests have been performed in order to identify the air path dynamics, a combination of linear and nonlinear identification methods have been used in order to identify the fuel path model including the wall-wetting dynamics. The resulting parameter-varying model has been validated with independent experimental data and can be used in powertrain controller design and development.

1.
Leone
,
T. G.
,
Christenson
,
E. J.
, and
Stein
,
R. A.
, 1996, “
Comparison of Variable Camshaft Timing Strategies at Part Load
,” SAE 960584.
2.
Stein
,
R. A.
,
Galietti
,
K. M.
, and
Leone
,
T. G.
, 1995, “
Dual Equal VCT-A Variable Camshaft Timing Strategy for Improved Fuel Economy and Emissions
,” SAE 950975.
3.
Genç
,
A. U.
,
Glover
,
K.
, and
Ford
,
R.
, 2001, “
Nonlinear Control of Hydraulic Camshaft Actuators in Variable Cam Timing Engines
,” in
MECA International Workshop
,
University of Salerno
, Italy, September, pp.
49
54
.
4.
Jankovic
,
M.
, and
Frischmuth
,
F.
, 1997, “
Disturbance Rejection in SI Engines With Variable Cam Timing
,” in ACC, Albuquerque, NM, June, pp.
289
293
.
5.
Jankovic
,
M.
,
Frischmuth
,
F.
,
Stefanopoulou
,
A. G.
, and
Cook
,
J. A.
, 1998, “
Torque Management of Engines With Variable Cam Timing
,”
IEEE Control Syst.
1066-033X,
18
(
5
) p.
34
.
6.
Hsieh
,
S. C.
,
Stefanopoulou
,
A. G.
,
Freudenberg
,
J. S.
, and
Butts
,
K. R.
, 1997, “
Emissions and Drivability Tradeoffs in a Variable Cam Timing SI Engine With Electronic Throttle
,” in ACC, Albuquerque, NM, June, pp.
284
288
.
7.
Hsieh
,
C. S.
,
Freudenberg
,
S. J.
, and
Stefanopoulou
,
A. G.
, 1999, “
Multivariable Controller Structure in a Variable Cam Timing Engine With Electronic Throttle and Torque Feedback
,” in
Conf. on Control Appl.
, Hawaii, pp.
465
470
.
8.
Gorinevsky
,
D.
,
Cook
,
J.
,
Feldkamp
,
L.
, and
Vukovich
,
G.
, 1999, “
Predictive Design of Linear Feedback/Feedforward Controller for Automotive VCT Engines
,” in ACC, June, Vol.
1
, pp.
207
211
.
9.
Kang
,
J. M.
, and
Grizzle
,
J. W.
, “
Dynamic Control of a SI Engine With Variable Valve Timing
,” to appear in International Journal of Robust and Nonlinear Control.
10.
Jankovic
,
M.
, and
Magner
,
S. W.
, 2002, “
Variable Cam Timing: Consequences to Automotive Engine Control Design
,” in
IFAC, 15th Triennial World Congress
.
11.
Genç
,
A. U.
,
Ford
,
R.
,
Glover
,
K.
, and
Collings
,
N.
, 2002, “
Experimental Investigation of Changing Fuel Path Dynamics in Twin-Independent Variable Cam Timing Engines
,” SAE 2002-01-2752.
12.
Chin
,
Y.
, and
Coats
,
F. E.
, 1986, “
Engine Dynamics: Time-Based Versus Crank-Angle Based
,” SAE 860142.
13.
Heywood
,
J. B.
, 1998,
Internal Combustion Engine Fundamentals
,
McGraw-Hill
, New York.
14.
Genç
,
A. U.
, 2002, “
Linear Parameter-Varying Modeling and Robust Control of Twin Independent Variable Cam Timing Engines
,” PhD thesis, University of Cambridge, Department of Engineering, UK, November.
15.
Moskwa
,
J. J.
, and
Hedrick
,
J. K.
, 1992, “
Modeling and Validation of Automotive Engines for Control Algorithm Development
,”
J. Dyn. Syst., Meas., Control
0022-0434,
114
, pp.
278
285
.
16.
Chevalier
,
A.
,
Vigild
,
C. W.
, and
Hendricks
,
E.
, 2000, “
Predicting the Port Air Mass Flow of SI Engines in Air/Fuel Ratio Control Applications
,” SAE 2000-01-0260.
17.
Stefanopoulou
,
A. G.
,
Cook
,
J. A.
,
Grizzle
,
J. W.
, and
Freudenberg
,
J. S.
, 1998, “
Control-Oriented Model of a Dual Equal Variable Cam timing Spark Ignition Engine
,”
J. Dyn. Syst., Meas., Control
0022-0434,
120
, pp.
257
266
.
18.
Aquino
,
C. F.
, 1981, “
Transient A/F Control Characteristics of the 5Liter Central Fuel Injection Engine
,” SAE 810494.
19.
Hires
,
S. D.
, and
Overington
,
M. T.
, 1981, “
Transient Mixture Strength Excursions—An Investigation of Their Causes and the Development of a Constant Mixture Strength Fueling Strategy
,” SAE 810495.
20.
Turin
,
R. C.
, and
Geering
,
H. P.
, 1993, “
On-Line Identification of Air-to-Fuel Ratio Dynamics in a Sequentially Injected SI Engine
,” SAE 930857.
21.
Purdy
,
G. R.
, and
Douglas
,
R.
, 1993, “
Wall-Wetting Theories Applied to the Transient Operation of a Single Cylinder Four-Stroke Gasoline Engine
,” SAE 932446.
22.
Turin
,
R. C.
,
Casartelli
,
E. G. B.
, and
Geering
,
H. P.
, 1994, “
A New Model for Fuel Supply Dynamics in an SI Engine
,” SAE 940208.
23.
Onder
,
C. H.
, and
Geering
,
H. P.
, 1994, “
Measurement of the Wall-Wetting Dynamics of a Sequential Injection Spark Ignition Engine
,” SAE 940447.
24.
Onder
,
C. H.
,
Roduner
,
C. A.
, and
Geering
,
H. P.
, 1997, “
Model Identification for the A/F Path of an SI Engine
,” SAE 970612.
25.
Jurgen
,
R.
, 1995,
Automotive Electronics Handbook
,
McGraw-Hill
, New York.
26.
Ljung
,
L.
, 1999,
System Identification-Theory for the User
,
2nd ed.
,
Prentice Hall
, Englewood Cliffs, NJ.
27.
Ogata
,
K.
, 1987,
Discrete-Time Control Systems
,
Prentice-Hall
, Englewood Cliffs, NJ.
28.
Simons
,
M. R.
,
Locatelli
,
M.
,
Onder
,
C. H.
, and
Geering
,
H. P.
, 2000, “
A Nonlinear Wall-Wetting Model for the Complete Operating Region of a Sequential Fuel Injected SI Engine
,” SAE 2000-01-1260.
You do not currently have access to this content.