Simple Engine Exhaust Temperature Modeling and System Identification Based on Markov Chain Monte Carlo

Article Preview

Abstract:

Even though actual composition of engine exhaust gases varies across diverse types of engines, such as gasoline, diesel, gas turbine and natural gas engines, engine exhaust temperature is always a major factor with strong impact on emission levels and catalytic converting efficiency. For spark ignition engines, exhaust temperature depends on various engine parameters, such as engine speed, engine load, A/F ratio, intake air temperature, coolant temperature and spark timing, etc. Due to complexity, it is impossible to share a unique analytical model of engine exhaust temperature. Instead, it is mostly modeled as a complicated nonlinear system. The model complexity increases significantly however accuracy cannot be guaranteed. On the other hand, a simple linear model with accurate system identification could serve as a versatile alternative to represent the engine exhaust temperature, while engine parameters are subject to model identification to be adaptable across different types of engines. Combination of linear functions in terms of dominant engine parameters of engine speed and engine load is used for exhaust temperature modeling. To identify optimal parameters, Markov Chain Monte Carlo (MCMC) is applied. The discrete-time Markov chain is introduced where the stationary probability replaces posterior density in Monte Carlo integration for numerical integration. Compared with the high order nonlinear approaches, low computation cost is involved in the simplified model. Good agreement between the model prediction data and testing results is observed. The approach could be easily extended to other types of engines.

You might also be interested in these eBooks

Info:

Periodical:

Pages:

224-228

Citation:

Online since:

July 2014

Export:

Price:

Permissions CCC:

Permissions PLS:

Сopyright:

© 2014 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

* - Corresponding Author

[1] J. Heywood, Internal Combustion Engine Fundamentals, McGraw-Hill Publisher, (1988).

Google Scholar

[2] Z. Ye, H. Mohamadian, L. Li, Q. Meng and Z. Li, Theoretical and Practical Mechanisms on Lowering Exhaust Emission Levels for Diverse Types of Spark Ignition Engines, SAE International PFL Congress, 2008-01-1545, June 23-25, 2008, Shanghai, China.

DOI: 10.4271/2008-01-1545

Google Scholar

[3] Z. Ye, Modeling, Identification, Design and Implementation of Nonlinear Automotive Idle Speed Control Systems-An Overview, IEEE Transactions on Systems, Man and Cybernetics, Part C: Applications and Reviews, Vol. 37, No. 6, pp.1137-1151, November, (2007).

DOI: 10.1109/tsmcc.2007.905810

Google Scholar

[4] Z. Ye and Z. Li, Impact of Lean-Burn Control Technology on the Fuel Economy and NOx Emission of Gasoline Engines, pp.1041-1058, Vol. 224, No. 8, Proceedings of the Institution of Mechanical Engineers, Part D, Journal of Automobile Engineering, August, (2010).

DOI: 10.1243/09544070jauto1409

Google Scholar

[5] B. Delphine, L. Thomas, and P. Nicolas, Control-Oriented Time-Varying Input-Delayed Temperature Model for SI Engine Exhaust Catalyst, American Control Conference, pp.2189-2195, June 17 - 19, 2013, Washington DC, USA.

DOI: 10.1109/acc.2013.6580160

Google Scholar

[6] J. Zavala, P. Sanketi, Simplified Models of Engine HC Emissions, Exhaust Temperature and Catalyst Temperature for Automotive Cold Start, Vol. 5, No. 1, pp.199-206.

DOI: 10.3182/20070820-3-us-2918.00028

Google Scholar

[7] M. Firoozabadi, M. Shahbakhti, Thermodynamic Control-Oriented Modeling of Cycle-To-Cycle Exhaust Gas Temperature in an HCCI engine, Applied Energy 110 (2013) 236–243.

DOI: 10.1016/j.apenergy.2013.04.055

Google Scholar

[8] Z. Ye, Temperature Impact on Modeling and Control of Lean NOx Trap, SAE Transactions, Journal of Fuels and Lubricants, Vol. 112-4, pp.790-795, September, (2004).

Google Scholar

[9] Lars Eriksson, Mean Value Models for Exhaust System Temperatures, SAE Technical Paper Series 2002-01-0374, SAE World Congress, Detroit, USA.

DOI: 10.4271/2002-01-0374

Google Scholar

[10] Q. Zhang, G. Yin, On Nearly Optimal Controls of Hybrid LQG Problems, IEEE Transactions on Automatic Control, Vol. 44, No. 12, pp.2271-81, (1999).

DOI: 10.1109/9.811209

Google Scholar

[11] Z. Ye, Y. Ye, Maximum Likelihood Estimation on Mismatch for Stochastic Nearly Optimal Control, American Control Conference, Boston, USA, pp.4388-4392, June 30 – July 2, (2004).

DOI: 10.23919/acc.2004.1383999

Google Scholar

[12] B. Boroujeny, H. Zhu, and Z. Shi, MCMC Algorithms for CDMA and MIMO Communication Systems, pp.1896-1909, IEEE Transactions on Signal Processing, Vol. 54, No. 5, May (2006).

DOI: 10.1109/tsp.2006.872539

Google Scholar

[13] Z. Ye, H. Mohamadian, Model Predictive Control on Wall Wetting Effect Using MCMC, IEEE Latin-American Conference on Communications, Santiago, Chile, Nov. 24-26, (2013).

DOI: 10.1109/latincom.2013.6759836

Google Scholar