Modern spark ignited (SI) internal combustion engines maintain their air-to-fuel ratio (AFR) at a desired level to maximize the three-way catalyst conversion efficiency and durability. However, maintaining the engine AFR during its transient operation is quite challenging due to rapid changes of driver demand or engine throttle. Conventional transient AFR control is based upon the inverse dynamics of the engine fueling dynamics and the measured mass air flow (MAF) rate to obtain the desired AFR of the gas mixture trapped in the cylinder. This paper develops a linear quadratic (LQ) tracking controller to regulate the transient AFR based upon a control-oriented model of the engine port fuel injection (PFI) wall wetting dynamics and the air intake dynamics from the measured airflow to the manifold pressure. The LQ tracking controller is designed to optimally track the desired AFR by minimizing the error between the trapped in-cylinder air mass and the product of the desired AFR and fuel mass over a given time interval. The performance of the optimal LQ tracking controller was compared with the conventional transient fueling control based on the inverse fueling dynamics through simulations and showed improvement over the baseline conventional inverse fueling dynamics controller. To validate the control strategy on an actual engine, a 0.4 l single cylinder direct-injection (DI) engine was used. The PFI wall wetting dynamics were simulated in the engine controller after the DI injector control signal. Engine load transition tests for the simulated PFI case were conducted on an engine dynamometer, and the results showed improvement over the baseline transient fueling controller based on the inverse fueling dynamics.

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