Model-Based Stochastic Optimal Air–Fuel Ratio Control With Residual Gas Fraction of Spark Ignition Engines

In this paper, a stochastic optimal control scheme for the air-fuel ratio is proposed, which considers the cyclic variations of the residual gas fraction (RGF). Initially, a cylinder pressure-based measurement of the RGF is derived by following the physics of inlet-exhaust process. Then, a dynamical model is presented to describe the cyclic variation of the air charge, fuel charge, and combustion products under a cyclically varied RGF, where the RGF is modeled as a Markovian stochastic process. Using this model, a feedback control law is derived, which optimizes the quadratic cost function in the stochastic sense with respect to the stochastic property of the residual gas. The cost function reflects the tradeoff between the accuracy of the regulation of the air-fuel ratio with the fluctuation in the fuel injection. Finally, a sampling process-based statistical analysis for the RGF is presented based on the experiments conducted on a full-scaled gasoline engine test bench, and the proposed control law is validated based on a numerical simulation and experiments.