Disturbance attenuation in time-delay systems — A case study on engine air-fuel ratio control
Proceedings of the 2011 American Control Conference
In this paper we analyze relative performance of several approaches to disturbance attenuation for systems with time delay including the conventional Proportional-Integral controller, the Smith Predictor, and the Model Reduction controller. The paper proposes a measure of disturbance attenuation capability and computes it analytically for each of the controllers considered. The results are applied to the air-fuel ratio regulation in automotive engines. To meet strict emission regulations,
... ne engines must operate at stoichiometric airfuel ratio over most of its operating range. A major component towards accomplishing this goal is the closed loop fuel controller. The feedback uses an exhaust-gas oxygen sensor which introduces a long transport delay. This paper discusses the air-fuel ratio regulation problem, explores options in control design for disturbance attenuation in system with time-delay, and shows simulation and experimental, in-vehicle validations. I. INTRODUCTION In practical applications, feedback control is used to stabilize unstable or marginally stable systems, achieve good tracking of reference signals, or attenuate effects of disturbances. These goals may not be completely aligned as fast reference trajectory tracking may not produce good disturbance attenuation and vice-versa. In particular, and this is relevant for the problem considered in this paper, the Smith Predictor delay compensation method is well known for achieving fast reference tracking, but not necessarily good disturbance attenuation (see, for example,  ). This paper considers the problem of disturbance attenuation for the air-fuel ratio regulation system in gasoline engines. The three way catalytic converters, employed to remove the three main regulated components (hydrocarbons, oxides of nitrogen, and carbon monoxide) from engine exhaust, achieve very high efficiency only in a very narrow range of air-fuel ratios around stoichiometry (about 14.6 for gasoline). Thanks to their oxygen storage capability, the catalytic converters can operate efficiently for a brief period of time away from stoichiometry. If the oxygen storage gets depleted or saturated, the efficiency drops significantly. Hence, it is very important to keep the air-fuel ratio excursions away from stoichiometry as brief and as shallow as possible. Details on operation of three way catalysts can be found in Section 2.8.2 of  . † M.