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The burned gas remaining in the cylinder after the exhaust stroke of an SI engine, i.e. the residual gas fraction, has a significant influence on both the torque production and the composition of the exhaust gas. This work investigates the behavior of the residual gas fraction over the entire operating range of the engine. A combined discrete-continuous linear model is identified, which describes the dynamic effects of the gas composition from when the gases enter the cylinder up to the measurement with a specific sensor. In this investigation, that sensor is a fast NO measurement device. The system is modelled by three elements in series: the in-cylinder mixing, the transport delay, and the exhaust mixing. The resulting model contains three elements in series connection: the in cylinder mixing, the transport delay, and the exhaust gas mixing. The model is able to calculate the fuel mass entering the cylinder during a fuel injection transient.

In this paper we introduce an improved model for the fuel supply dynamics in an SI engine. First, we briefly investigate all the thermodynamic phenomena which are assumed to have a significant impact on fuel flow into the cylinder (i.e., fuel atomization, droplet decay, wall-wetting, film evaporation, and mixture flow back). This theoretical analysis results in a basic set of dynamic equations. Unfortunately, these equations are not convenient to use for control purposes. Therefore, we proceed to a simplified formulation. Several unknown parameters remain, describing phenomena which are difficult to quantify, such as heat and material transfer characteristics. These parameters are subject to operating conditions and are not discussed further. In order to validate the model dynamics, we refer to frequency and step response measurements performed on a 4-cylinder, 1.8 liter BMW engine with sequential fuel injection.