Super-Twisting Air/Fuel Ratio Control for Spark Ignition Engines

Abstract

In this work, a model-based controller for the air to fuel ratio (represented by \(\lambda \)) is designed for spark ignition (SI) engines in order to rise the fuel consumption efficiency and to reduce the emission of pollutant gases to the atmosphere. The proposed control method is based on an isothermal mean value engine model (MVEM) developed by Elbert Hendricks and in the super-twisting sliding mode control algorithm that results to be robust to matched perturbations and alleviates the chattering problem. The dynamics for \(\lambda \) depends on the time derivative of the control input, i.e., the injected fuel mass flow (\(\dot{m}_{fi}\)). This term is estimated by means of the well-known robust sliding mode differentiator which is feedback to the control algorithm. To solve the time-delay measurement problem (due to combustion process and the transportation of gases) at the Universal Exhaust Gas Oxygen (UEGO) sensor, the delay represented with an exponential function in the frequency domain is approximated by means of a Pade method which yields to a transfer function. Then, this transfer function is taken to a state space representation in order to design an observer based on the super-twisting sliding mode algorithm, where the real \(\lambda \) factor is finally determined by the equivalent control method and used for feedback. Digital simulations were carried on, where the proposed control scheme is simulated with two observers based on a second and third order Pade approximations. Also, the proposed controller is simulated without an observer, where \(\lambda \) is directly taken from the UEGO sensor. Simulations predict a better output behavior in the case of a controller based observer design, and in particular, the observer based on the third order approximation provides the best results. Therefore, the controller based on the third order observer is chosen for parametric uncertainties and noise measurement simulation, where the air to fuel ratio still performs well.