Designing Nonlinear Digital Controller for Switching Non Affine Process of Spark Ignition Engine Catalyst Warm-Up

This paper details a new method for model-based discrete sliding mode control of a spark ignition (S.I.) engine cold start considering nonlinear dynamic effects, modeling uncertainty and multiple switched dynamic configurations. Control algorithm deals with stabilization and tracking problems that correspond to crank-shaft velocity, air-to-fuel ratio (AFR) and catalyst temperature in cold start operating mode. To this end, an individual sliding function is assigned to each tracking problem which is subsequently used in construction of associated Lyapunov function. Crank-shaft velocity is regulated using air mass flow rate into intake manifold considering associated dynamic equations describing air mass flow. To ensure precise AFR control, the sliding control model is constructed considering the previously calculated air mass flow rate which leads to nonlinear expressions that are subsequently employed in calculation of appropriate fuel mass flow rate. Stabilization of catalyst temperature is conducted through definition of a virtual control input corresponding to spark angle. As catalyst temperature is described using logarithmic mathematical expressions, additional steps have to be considered to ensure feasibility of control algorithm in various operating conditions. The designed control was numerically applied to validated mathematical model of Toyota 2AZ-FE engine so as to render efficiency and precision of feedback performance.