Fuel–air ratio control for a spark ignition engine using gain-scheduled delay-dependent approach

A novel approach to fuel-air ratio (FAR) control for spark ignition (SI) engines is presented in this study. The FAR dynamics are modelled as a first-order plus time-varying delay system. Time delay in the control plant is not approximated using the Pade formula. For controller design purposes, it is described as a time-varying delay in the measurement output. A gain-scheduled delay-dependent controller, regarding the time delay as a time-varying parameter, is then designed to track FAR reference and minimise the effects of disturbances on FAR regulation. The proposed controller guarantees the stability of closed-loop system and induced L₂ norm performance using Lyapunov-Krasovskii functional. The design method is then formulated in terms of linear matrix inequalities that leads to a convex optimisation problem and can be solved by parameter gridding technique. Simulation results validate the FAR regulation of proposed controller over the large range of time delay, which covers most engine operating conditions in practice.