New regulations for emission control require the improvement of the system composed by spark ignition internal combustion engine and three-way catalytic converter (TWC). In particular, an important problem is to minimize harmful emissions during the transient warm-up phase where the TWC is not working yet and, hence, a large amount of pollutants are emitted in the air. Toward this goal we present a dynamical thermo-chemical TWC model simple enough for the design and test of warm-up control strategies. The model is obtained through an asymptotic approximation of a more detailed model, i.e., by letting the adsorption coefficient between gas and substrate tend to infinity. Further, we present a fast integration algorithm based partly on a “method of lines” space-discretization, partly on the “method of characteristics” for “quasi linear” hyperbolic partial differential equations, the separation being allowed by a two time scale analysis of the system. The model has been identified, through a purposely designed genetic algorithm, and validated on experimental data.
Issue Section:
Technical Papers
Keywords:
partial differential equations,
internal combustion engines,
air pollution control,
integration,
parameter estimation,
adsorption,
genetic algorithms
Topics:
Air pollution control,
Algorithms,
Approximation,
Catalytic converters,
Emissions,
Genetic algorithms,
Internal combustion engines,
Partial differential equations,
Pollution,
Simulation,
Temperature,
Design,
Transients (Dynamics),
Gases,
Boundary-value problems,
Chemical reactions,
Ignition,
Regulations
1.
Levenspiel, O., 1972, Chemical Reaction Engineering, 2nd Edition, Wiley, New York, Chap. 14.
2.
Abate, G., Glielmo, L., Milano, M., Rinaldi, P., Santini, S., and Serra, G. 1997, “Numerical Simulation and Identification of the Dynamic Behavior of Three Way Catalytic Converters,” ICE97-3rd International Conference on Internal Combustion Engines: Experiments and Modelling, September, Capri, Italy, pp. 409–412.
3.
Chen, D. K. S., Bissett, E. J., Oh, S. H., and Van Ostrom, D. L., 1988, “A Three-Dimensional Model for the Analysis of Transient Thermal and Conversion Characteristics of Monolithic Catalytic Converters,” SAE paper 880282.
4.
Leveroni, E., Pattas, K. N., Stamatelos, A. M., Pistikopoulos, P. K., Koltsakis, G. C., Konstandinidis, P. A., and Volpi, E., 1994, “Transient Modeling of 3-Way Catalytic Converters,” SAE paper 940934.
5.
Montreuil, C. N., Williams, S. C., and Adamczyk, A. A., 1992, “Modeling Current Generation Catalytic Converters. Laboratory Experiments and Kinetic Parameter Optimization—Steady State Kinetics,” SAE paper 920096.
6.
Oh
, S. H.
, and Cavendish
, J. C.
, 1985
, “Mathematical Modeling of Catalytic Converter Lightoff. Part III: Prediction of Vehicle Exhaust Emissions and Parametric Analysis
,” AIChE J.
, 31
, No. 6
, pp. 943
–949
.7.
Koltsakis
, G. C.
, Kostantinidis
, P. A.
, and Stamatelos
, A. M.
, 1997
, “Development and Application Range of Mathematical Models for 3-way Catalytic Converters
,” Appl. Catal., B, Environ.
, 12
, pp. 161
–191
.8.
Koltsakis
, G. C.
, Kandylas
, I. P.
, and Stamatelos
, A. M.
, 1998
, “Three-Way Catalytic Converter Modeling and Applications
,” Chem. Eng. Commun.
, 164
, pp. 153
–189
.9.
Brandt, E. P., Grizzle, J. W., and Wang, Y., 1997, “A Simplified Three-Way catalyst Model for Use in On-Board SI Engine Control and Diagnostics,” Proceedings of the ASME Dynamic System and Control Division, Vol. 61, pp. 653–659.
10.
Glielmo, L., Rinaldi, P., Santini, S., and Serra, G., 1998, “Modelling and Numerical Simulation of the Dynamic Behavior of Three Way Catalytic Converters,” IEEE Conference on Control Applications, September, Trieste, Italy, pp. 731–735.
11.
Baba, N., Ohsawa, K., and Sugiura, S., 1996, “Numerical Approach for Improving the Conversion Characteristics of Exhaust Catalysts under Warming-Up Condition,” SAE paper 962076.
12.
Faraoni, V., Santini, S., Continillo, G., and Glielmo, L., 1999, “Role of Mass Transport and Chemical Kinetics in the Dynamics of Monolith Catalytic Reactors,” 4th International Conference ICE99, Internal Combustion Engines: Experiments and Modeling, Capri, 12–16 September, pp. 605–611.
13.
Hawthorn
, R. D.
, 1974
, “Afterburner Catalysis: Effect of Heat and Mass Transfer between Gas and Catalyst Surface
,” AIChE Symp. Ser.
, 70
, No. 137
, pp. 428
–438
.14.
Aimard
, F.
, Li
, S.
, and Sorine
, M.
, 1996
, “Mathematical Modeling of Automotive Three-Way Catalytic Converters with Oxygen Storage Capacity
,” Control Eng. Practice
, 4
, No. 8
, pp. 1119
–1124
.15.
Cussenot, C., Basseville, M., and Aimard, F., 1996, “Monitoring the Vehicle Emission System Components,” Proc. 13th IFAC World Congress, San Francisco, USA.
16.
John, F., 1975, Partial Differential Equations, Springer-Verlag, New York.
17.
Chester, C. R., 1971, Techniques in Partial Differential Equations, McGraw-Hill, NY.
18.
Jeffrey, A., 1976, Quasilinear Hyperbolic Systems and Waves, Pitman, London.
19.
Lin, C. C., and Segel, L. A., 1988, Mathematics Applied to Deterministic Problems in the Natural Sciences, Society for Industrial & Applied Mathematics.
20.
Kokotovic´, P. V., Khalil, H. K., and O’Reilly, J., 1986, Singular Perturbation Methods in Control: Analysis and Design, Academic Press, London.
21.
Schiesser, W. E., 1991, The Numerical Method of Lines: Integration of Partial Differential Equations, Academic Press, San Diego.
22.
Goldberg, D. E., 1989, Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley, Reading, MA.
23.
Michalewicz, Z., 1996, Genetic Algorithms+Data Structures=Evolution Programs, 3rd ed., Springer-Verlag, New York.
24.
Davis, L., 1991, Handbook of Genetic Algorithms, Van Nostrand Reinhold, New York.
25.
Booker, L., 1989, “Improving Search in Genetic Algorithms,” L. Davis, ed., Genetic Algorithms and Simulated Annealing, Pitman, NY, pp. 61–73.
26.
Davis, L., 1989, “Adapting Operator Probabilities in Genetic Algorithms,” Proc. 3st Int. Conf. Genetic Algorithms, pp. 61–69.
27.
Grefenstette
, J. J.
, 1986
, “Optimization and Control Parameters for Genetic Algorithms
,” IEEE Trans. Syst. Man Cybern.
, SMC-16
, Jan/Feb.
, pp. 122
–128
.28.
Davis, L., 1985, “Job Shop Scheduling with Genetic Algorithms,” Proc. 1st Int. Conf. Genetic Algorithms, pp. 136–140.
29.
Heywood J. B., 1988, Internal Combustion Engine Fundamentals, McGraw-Hill, New York.
30.
Bender, C. M., and Orszag, S. A., 1999, Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory, Springer-Verlag, New York.
31.
Kevorkian, J., and Cole, J. D., 1996, Multiple Scale and Singular Perturbation Methods, Springer-Verlag, New York.
Copyright © 2001
by ASME
You do not currently have access to this content.
