Linear Stochastic Modeling and Control of Diluted Combustion for SI Engines

The combustion process in spark-ignition (SI) engines exhibits cycle-to-cycle variability, which imposes limits on engine operation. When exhaust gas recirculation (EGR) is used to increase engine efficiency, the combustion variability (CV) increases and spark advance (SA) must be re-tuned to achieve maximum brake torque. In order to maximize EGR benefits without excessive cyclic CV, feedback control can be applied to modify EGR and SA accordingly. This paper presents a control-oriented combustion model that captures the stochastic properties of combustion features. A linear quadratic Gaussian (LQG) controller is used to modify SA and EGR to achieve a particular combustion shape, characterized by the initiation and duration angles. Using stochastic control theory for linear Gaussian systems, analytical solutions for the cyclic variability of the combustion process and the control commands under closed-loop operation are derived. This methodology is validated against experimental engine data and results at transient and steady state operation are presented.