Parameter Identification of Nonlinear System on Combustion Engine Based MVEM using PEM

Trigas Badmianto(1*), Eka Firmansyah(2), Adha Imam Cahyadi(3)

(1) Department of Electrical Engineering and Information Technology, Universitas Gadjah Mada
(2) Department of Electrical Engineering and Information Technology, Universitas Gadjah Mada
(3) Department of Electrical Engineering and Information Technology, Universitas Gadjah Mada
(*) Corresponding Author


In four-stroke engine injection system, often called spark ignition (SI) engine, the air-fuel ratio (AFR) is taken from the measurement of lambda sensor in the exhaust. This sensor does not directly describe how much AFR in the combustion chamber due to the large transport delay. Therefore, the lambda sensor is used only as a feedback in AFR control "correction", not as the "main" control. The purpose of this research is to identify the parameters of the non-linear system in SI engines to produce AFR estimator. The AFR estimator is expected to be used as a feedback of the main "AFR" control system. The process of identifying the parameters using the Gauss-Newton method, due to its rapid computation to Achieve convergence, is based on prediction error minimization (PEM). The models of AFR estimator is an open-loop system without a universal exhaust gas oxygen (UEGO) sensors as feedback, called a virtual AFR sensor. The high price of UEGO sensors makes the virtual AFR sensor can be a practical solution to be applied in AFR control. The model in this research is based on the mean value engine models (MVEM) with some modifications. The research dataset was taken from a Hyundai Verna 2002 with the additional UEGO type of lambda sensors. The throttle opening angle (input) is played by stepping on the gas pedal and the signal to the injector (input) is set to a certain quantity to produce the AFR (output) value read by the UEGO sensor. This research produces an open loop estimator model or AFR virtual sensors with normalized root mean square error (NRMSE) = 0.06831 = 6.831%.


Parameter identification, Air-Fuel Ratio, MVEM, Spark-ignition engines, fuel injection system, Prediction error minimization

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Y. Shi, D.-L. Yu, Y. Tian, and Y. Shi, “Air–Fuel Ratio Prediction and NMPC for SI Engines With Modified Volterra Model and RBF Network,” Eng. Appl. Artif. Intell., Vol. 45, pp. 313–324, Oct. 2015.

Tom Dentom, Automobile Electrical and Electronic System. Burlington, MA: Elsevier Butterworth-Heinemann, 2004.

Christian Winge Vigild, Elbert Hendricks, and Spencer C Sorenson, “The Internal Combustion Engine Modelling: Modelling, Estimation and Control Issues,” Technical University of Denmark, Lyngby, 2002.

H. Tang, L. Weng, ZY Dong, and R. Yan, “Adaptive and Learning Control for SI Engine Model With Uncertainties,” IEEEASME Trans. Mechatron, Vol. 14, No. 1, pp. 93–104, Feb. 2009.

DG Copp, KJ Burnham, and FP Lockett, “Model Comparison for Feedforward Air/Fuel Ratio Control,” Control '98. UKACC International Conference on (Conf. Publ. No. 455), 1998, Vol. 1, pp. 670–675.

Toyota Computer Controlled System (TCCS), Toyota Technical Training, 1997.

D. Marin, I. Hiticas, and L. Mihon, “Fuzzy Logic Control Applied on SI Engine Concerning the Injection Time Evolution,” 2012 IEEE 13th International Symposium on Computational Intelligence and Informatics (CINTI), 2012, pp. 279–284.

E. Hendricks and J. Luther, “Model and Observer Based Control of Internal Combustion Engines,” Proceedings of the 1st International Workshop on Modeling Emissions and Control in Automotive Engines, MECA'01, 2001, pp. 9–20.

H. Melgaard, E. Hendricks, and H. Madsen, “Continuous Identification of a Four-Stroke SI Engine,” American Control Conference, 1990, 1990, pp. 1876–1881.

E. Hendricks, J. Poulsen, MB Olsen, PB Jensen, M. Fons, and C. Jepsen, “Alternative Observers for SI Engine Air/Fuel Ratio Control,” Proceedings of 35th IEEE Conference on Decision and Control, 1996, Vol. 3, pp. 2806–2811.

EL Hanzevack, TW Long, CM Atkinson, and M. Traver, “Virtual Sensors for Spark Ignition Engines Using Neural Networks,” Proceedings of the 1997 American Control Conference, 1997, Vol. 1, pp. 669–673.

SS Kamat, H. Javaherian, VV Diwanji, JG Smith, and KP Madhavan, “Virtual Air-Fuel Ratio Sensors for Engine Control and Diagnostics,” 2006 American Control Conference, 2006, pp. 7.

X. Donghui, L. Yuelin, and Zhouzhe, “Study on Transient Air-Fuel Ratio Predictive Model of Gasoline Engine Based on Artificial Intelligence,” 2014 7th International Conference on Intelligent Computation Technology and Automation, 2014, pp. 742–745.

N. Cesario, M. Lavorgna, and F. Pirozzi, “Modelling On-Off Virtual Lambda Sensors Based on Multi-Spread Probabilistic Neural Networks,” 10th IEEE Conference on Emerging Technologies and Factory Automation 2005 (ETFA 2005), 2005, Vol. 1, pp. 6.

L. Wu and JJ Liu, “Comparative Research Transient Air-Fuel Ratio Control Strategy Based on Fuzzy Control and Neural Network,” Appl. Mech. Mater., Vol. 643, pp. 66–71, Sep. 2014.

WK Yap and V. Karri, “ANN virtual sensors for emissions prediction and control,” Appl. Energy, Vol. 88, No. 12, pp. 4505–4516, Dec. 2011.

SW Wang, DL Yu, JB Gomm, GF Page, and SS Douglas, “Adaptive Neural Network Model Based Predictive Control for Air–Fuel Ratio of SI Engines,” Eng. Appl. Artif. Intell., Vol. 19, No. 2, pp. 189–200, Mar. 2006.

I. Arsie, C. Pianese, and M. Sorrentino, “A Procedure to Enhance Identification of Recurrent Neural Networks for Simulating Air–Fuel Ratio Dynamics in SI Engines,” Eng. Appl. Artif. Intell., Vol. 19, No. 1, pp. 65–77, Feb. 2006.

R. Pradhan, P. Ramkumar, and S. Suhan, “Estimation of Air-Fuel Ratio (AFR) in a Sark-Ignition (SI) Engine from Cylinder Pressure Measurements”, IJRRAS, Vol. 13, No. 3, pp. 707-715, Dec. 2012.

A. Yazdani et al., “Air Charge and Residual Gas Fraction Estimation for a Spark-Ignition Engine Using In-Cylinder Pressure,” SAE Technical Paper, 2017.

M. Kumar and T. Shen, “Estimation and Feedback Control of Air-Fuel Ratio for Gasoline Engines,” Control Theory Technol., Vol. 13, No. 2, pp. 151–159, May 2015.

D. Efimov, S. Li, Y. Hu, S. Muldoon, H. Javaherian, and VO Nikiforov, “Application of Interval Observers to Estimation and Control of Air-Fuel Ratio in a Direct Injection Engine,” American Control Conference 2015 (ACC), 2015, pp. 25–30.

T. Laurain, Z. Lendek, J. Lauber, and RM Palhares, “A New Air-Fuel Ratio Model Fixing the Transport Delay: Validation and Control,” 2017 IEEE Conference on Control Technology and Applications (CCTA), 2017, pp. 1904–1909.

E. Hendricks and S. Sorenson, “Mean Value SI Engine Model for Control Studies,” American Control Conference 1990, 1990, pp. 1882–1887.

E. Hendricks and SC Sorenson, “SI Engine Controls and Mean Value Engine Modelling,” SAE Technical Paper, 1991.

E. Hendricks, “A Generic Mean Value Engine Model for Spark Ignition Engines,” Proceedings of the 41st Simulation Conference, SIMS 2000, 2000.

J. Na, G. Herrmann, C. Rames, R. Burke, and C. Brace, “Air-Fuel-Ratio Control of Engine System with Unknown Input Observer,” 2016 UKACC 11th International Conference on Control (CONTROL), 2016, pp. 1–6.

J. Espinoza-Jurado, E. Dávila, J. Rivera, JJ Raygoza-Panduro, and S. Ortega, “Robust Control of the Air to Fuel Ratio in Spark Ignition Engines with Delayed Measurements from a UEGO Sensor,” Math. Probl. Eng., Vol. 2015, pp. 1–13, 2015.

M. Lei, Z. Chunnian, L. Hong, L. Jie, L. Wen, and L. Xianghua, “Research on Modeling and Simulation of SI Engine for AFR Control Application,” Biotechnol. Indian J., Vol. 10, No. 24, 2014.

Lennart Ljung, “System Identification ToolboxTM User's Guide.” The MathWorks, Inc, Sep-2012.

F. Spuri and L. Goes, “Modeling and Parametric Identification of a Variable-Displacement Pressure-Compensated Pump,” The 15th Scandinavian International Conference on Fluid Power, SICFP'17, 2017.

Lennart Ljung, System Identification Theory for the User (Second Edition). Prentice Hall, 1999.

A. Croeze, L. Pittman, and W. Reynolds, “Nonlinear Least-Squares Problems with the Gauss-Newton and Levenberg-Marquardt Methods,” Technical report, University of Mississipi, Department of Mathematics, June 2012.


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