Skip to main content
Log in

Extremum seeking-based optimal EGR set-point design for combustion engines in lean-burn mode

  • Research Article
  • Published:
Control Theory and Technology Aims and scope Submit manuscript

Abstract

In lean combustion mode, exhaust gas ratio (EGR) is a significant factor that affects fuel economy and combustion stability. A proper EGR level is beneficial for the fuel economy; however, the combustion stability (coefficient of variation (COV) in indicated mean effective pressure (IMEP)) deteriorated monotonously with increasing EGR. The aim of this study is to achieve a trade-off between the fuel economy and combustion stability by optimizing the EGR set-point. A cost function (J) is designed to represent the trade-off and reduce the calibration burden for optimal EGR at different engine operating conditions. An extremum-seeking (ES) algorithm is adopted to search for the extreme value of J and obtain the optimal EGR at an operating point. Finally, a map of optimal EGR set-value is designed and experimentally validated on a real driving cycle.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Guzzella, L., & Amstutz, A. (1998). Control of diesel engines. IEEE Control Systems Magazine, 18(5), 53–71.

    Article  Google Scholar 

  2. Wahlström, J., Eriksson, L., & Nielsen, L. (2009). EGR-VGT control and tuning for pumping work minimization and emission control. IEEE Transactions on Control Systems Technology, 18(4), 993–1003.

    Article  Google Scholar 

  3. Van Nieuwstadt, M. J., Kolmanovsky, I. V., Moraal, P. E., Stefanopoulou, A., & Jankovic, M. (2000). EGR-VGT control schemes: Experimental comparison for a high-speed diesel engine. IEEE Control Systems Magazine, 20(3), 63–79.

    Article  Google Scholar 

  4. Jankovic, M., & Kolmanovsky, I. (2000). Constructive Lyapunov control design for turbocharged diesel engines. IEEE Transactions on Control Systems Technology, 8(2), 288–299.

    Article  Google Scholar 

  5. Joachim, R., Axel, S., Heinrich, R., Bert, K., Michael, K., & Stefan, P. (2000). Model based boost pressure and exhaust gas recirculation rate control for a diesel engine with variable turbine geometry. In Presented at the IFAC Workshop: Advanced Automotive Control (pp. 277–282). Karlsruhe, Germany.

  6. Rückert, J., Schloßer, A., Rake, H., Kinoo, B., Krüger, M., & Pischingert, S. (2001). Model based boost pressure and exhaust gas recirculation rate control for a diesel engine with variable turbine geometry. IFAC Proceedings Volumes, 34(1), 277–282.

    Article  Google Scholar 

  7. Jiang, W., & Shen, T. (2019). Lyapunov-based nonlinear feedback control design for exhaust gas recirculation loop of gasoline engines. Journal of Dynamic Systems, Measurement, and Control, 141(5), 051005.

    Article  Google Scholar 

  8. Jiang, W., & Shen, T. (2019). Nonlinear observer-based control design and experimental validation for gasoline engines with EGR. Control Theory and Technology, 17(3), 216–227.

    Article  MathSciNet  Google Scholar 

  9. Jiang, W., & Shen, T. (2021). Nonlinear observer-based exhaust manifold pressure estimation and fault detection for gasoline engines with exhaust gas recirculation. International Journal of Engine Research, 22(4), 1377–1392.

    Article  Google Scholar 

  10. Tan, Y., Moase, W. H., Manzie, C., Nešić, D., & Mareels, I. M. (2010). Extremum seeking from 1922 to 2010. In Proceedings of the 29th Chinese control conference (pp. 14–26). Beijing, China.

  11. Manzie, C., & Krstic, M. (2009). Extremum seeking with stochastic perturbations. IEEE Transactions on Automatic Control, 54(3), 580–585.

    Article  MathSciNet  Google Scholar 

  12. Liu, S. J., & Krstic, M. (2012). Stochastic averaging and stochastic extremum seeking. Springer.

    Book  Google Scholar 

  13. Robbins, H., & Monro, S. (1951). A stochastic approximation method. The Annals of Mathematical Statistics, 22(3), 400–407.

    Article  MathSciNet  Google Scholar 

  14. Chakrabartty, S., Shaga, R. K., & Aono, K. (2013). Noise-shaping gradient descent-based online adaptation algorithms for digital calibration of analog circuits. IEEE Transactions on Neural Networks and Learning Systems, 24(4), 554–565.

    Article  Google Scholar 

  15. Kushner, H. J., & Clark, D. S. (2012). Stochastic approximation methods for constrained and unconstrained systems. New York: Springer.

    MATH  Google Scholar 

  16. Spall, J. C. (1992). Multivariate stochastic approximation using a simultaneous perturbation gradient approximation. IEEE Transactions on Automatic Control, 37(3), 332–341.

    Article  MathSciNet  Google Scholar 

  17. Spall, J. C. (1998). Implementation of the simultaneous perturbation algorithm for stochastic optimization. IEEE Transactions on Aerospace and Electronic Systems, 34(3), 817–823.

    Article  Google Scholar 

  18. HellstrÖm, E., Lee, D., Jiang, L., Stefanopoulou, A. G., & Yilmaz, H. (2013). On-board calibration of spark timing by extremum seeking for flex-fuel engines. IEEE Transactions on Control Systems Technology, 21(6), 2273–2279.

    Article  Google Scholar 

  19. Lewander, M., Widd, A., Johansson, B., & Tunestål, P. (2012). Steady state fuel consumption optimization through feedback control of estimated cylinder individual efficiency. In Proceedings of the American Control Conference (ACC) (pp. 4210–4214). Montreal, Canada.

  20. Mohammadi, A., Manzie, C., & Nešić, D. (2014). Online optimization of spark advance in alternative fueled engines using extremum seeking control. Control Engineering Practice, 29, 201–211.

    Article  Google Scholar 

  21. Tan, Q., Divekar, P., Chen, X., Zheng, M., & Tan, Y. (2014). Exhaust gas recirculation control through extremum seeking in a low temperature combustion diesel engine. In Proceedings of the American Control Conference (pp. 1511–1516). Portland, OR, USA.

  22. Divekar, P., Tan, Q., Chen, X., Zheng, M., & Tan, Y. (2015). Diesel engine fuel injection control using a model-guided extremum-seeking method. In Proceedings of the 8th ASME Annual Dynamic Systems and Control Conference. Columbus, OH, USA.

  23. Killingsworth, N. J., Aceves, S. M., Flowers, D. L., Espinosa-Loza, F., & Krstic, M. (2009). HCCI engine combustion-timing control: Optimizing gains and fuel consumption via extremum seeking. IEEE Transactions on Control Systems Technology, 17(6), 1350–1361.

    Article  Google Scholar 

  24. Popovic, D., Jankovic, M., Magner, S., & Teel, A. R. (2006). Extremum seeking methods for optimization of variable cam timing engine operation. IEEE Transactions on Control Systems Technology, 14(3), 398–407.

    Article  Google Scholar 

  25. Lee, D., Jiang, L., Yilmaz, H., & Stefanopoulou, A. G. (2010). Preliminary results on optimal variable valve timing and spark timing control via extremum seeking. IFAC Proceedings Volumes, 43(18), 377–384.

    Article  Google Scholar 

  26. Corti, E., & Forte, C. (2011). Spark advance real-time optimization based on combustion analysis. Journal of Engineering for Gas Turbines and Power, 133(9), 092804.

    Article  Google Scholar 

  27. Zhang, Y., & Shen, T. (2017). Cylinder pressure based combustion phase optimization and control in spark-ignited engines. Control Theory and Technology, 15(2), 83–91.

    Article  MathSciNet  Google Scholar 

  28. Teodosio, L., De Bellis, V., & Bozza, F. (2015). Fuel economy improvement and knock tendency reduction of a downsized turbocharged engine at full load operations through a low-pressure EGR system. SAE International Journal of Engines, 8(4), 1508–1519.

    Article  Google Scholar 

  29. Guzzella, L., & Onder, C. (2009). Introduction to modeling and control of internal combustion engine systems. Springer.

    Google Scholar 

  30. Xu, Z., Zhang, Y., Di, H., & Shen, T. (2019). Combustion variation control strategy with thermal efficiency optimization for lean combustion in spark-ignition engines. Applied Energy, 251, 113329.

    Article  Google Scholar 

  31. Shi, H., Jiang, W., & Shen, T. (2019). Lyapunov Function based Nonlinear Control of EGR-VVT Dual Loop in IC Engines. In IEEE International Conference on Cybernetics and Intelligent Systems (CIS) and IEEE Conference on Robotics, Automation and Mechatronics (RAM) (pp. 239–244). Bangkok, Thailand.

  32. Gao, J., Wu, Y., & Shen, T. (2016). Experimental comparisons of hypothesis test and moving average based combustion phase controllers. ISA Transactions, 65, 504–515.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Haoyun Shi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shi, H., Zhang, Y. & Shen, T. Extremum seeking-based optimal EGR set-point design for combustion engines in lean-burn mode. Control Theory Technol. 19, 354–364 (2021). https://doi.org/10.1007/s11768-021-00047-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11768-021-00047-x

Keywords

Navigation