Robust fueling strategy for an SI engine modeled as an linear parameter varying time-delayed system

This paper presents a new approach to the widely discussed problem of air-fuel ratio (AFR) control in a spark ignition (SI) engine. Precise regulation of the air-fuel ratio is required to attain high catalytic converter efficiency and minimize tailpipe emissions. This regulation is achieved by manipulating the fuel pulse width based on the feedback received from an exhaust gas oxygen sensor. The fuel path of an SI engine exhibits time-varying dynamics including a delay. In this work, the fuel path is modeled as a linear parameter-varying (LPV) time-delayed system. The time delay existing in the system is not approximated using the Pade formula, but it appears explicitly as a time-varying delay in the state. The design of parameter dependent state feedback controller guaranteeing stability and induced ℒ₂ norm performance is explored using Lyapunov-Krasovskii functional. The synthesis conditions are formulated in terms of Linear Matrix Inequalities (LMIs) that can be easily solved. A gain-scheduled ℋ_∞ controller is designed to track reference air-fuel ratio and minimize the effects of disturbances on the air-fuel ratio, over complete operating range of the SI engine. Simulation results are presented to validate the proposed control design methodology.