Gain-Scheduling Control of Air-Fuel Ratio in Spark Ignition Engines with Time-Delay Effects

This thesis addresses a variety of gain-scheduling control design schemes for the air-fuel ratio (AFR) control problem in spark ignition (SI) engines. Fueling strategy design has drawn significant attention in the past decades since it is essential for maximizing the fuel economy while minimizing harmful exhaust emissions. The fuel path of the SI engine, as well as the three-way catalyst (TWC) dynamics, have been captured by a continuous-time linear parameter-varying (LPV) system with varying time-delay. LPV systems are linear dynamical systems whose dynamic characteristics rely on a measurable scheduling parameter vector, where the scheduling parameter vector is used to capture the dynamics of time-varying systems. In the first part, a classical frequency-domain control method of parameter-varying loop-shaping is utilized to tackle the challenges imposed by the non-minimum phase (NMP) system and provide stability and desired performance. The second part of the thesis deals with the delay-dependent output-feedback LPV controller synthesis by using parameter-dependent Lyapunov-Krasovskii functionals. Stability conditions and a prescribed induced L2-norm in terms of the disturbance rejection performance are derived in a convex linear matrix inequalities (LMIs) setting. The proposed control methodology has a distinct advantage over previously developed methods as it results in less conservative results and able to handle LPV systems with arbitrary varying large time-delays. In the last part, a delay-dependent sampled-data LPV controller is proposed. Due to the discrete nature of the controllers, the main goal of this part is to find a discrete-time controller to satisfy the objectives. The interconnection of the continuous-time plant and a digital controller through converter devices forms a hybrid closed-loop configuration, which is challenging to analyze mathematically. The input-delay method has been employed to transfer the hybrid system into the continuous-time domain. The designed sampled-data gain-scheduled LPV controller is proposed to take the inter-sample behavior into account and is required to establish the closed-loop asymptotic stability and a prescribed level of performance for the closed-loop hybrid LPV system with an arbitrarily varying time delay and sampling time. Finally, conducted simulation scenarios assess the performance of the proposed digital controller in the sense of reference AFR tracking and disturbance attenuation.