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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 989674, 13 pages
Research Article

Robust Control of the Air to Fuel Ratio in Spark Ignition Engines with Delayed Measurements from a UEGO Sensor

1Department of Electronic Engineering, CUCEI UDG, 44430 Guadalajara, JAL, Mexico
2CONACYT, CINVESTAV del IPN, 45019 Zapopan, JAL, Mexico
3Department of Electronic Engineering, CINVESTAV del IPN, 45019 Zapopan, JAL, Mexico

Received 17 July 2015; Revised 8 October 2015; Accepted 8 October 2015

Academic Editor: Zhike Peng

Copyright © 2015 Javier Espinoza-Jurado et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A precise control of the normalized air to fuel ratio in spark ignition engines is an essential task. To achieve this goal, in this work we take into consideration the time delay measurement presented by the universal exhaust gas oxygen sensor along with uncertainties in the volumetric efficiency. For that purpose, observers are designed by means of a super-twisting sliding mode estimation scheme. Also two control schemes based on a general nonlinear model and a similar nonlinear affine representation for the dynamics of the normalized air to fuel ratio were designed in this work by using the super-twisting sliding mode methodology. Such dynamics depends on the control input, that is, the injected fuel mass flow, its time derivative, and its reciprocal. The two latter terms are estimated by means of a robust sliding mode differentiator. The observers and controllers are designed based on an isothermal mean value engine model. Numeric and hardware in the loop simulations were carried out with such model, where parameters were taken from a real engine. The obtained results show a good output tracking and rejection of disturbances when the engine is closed loop with proposed control methods.