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.
From the frequency response measurements we first extract the time constants of the oxygen sensor used throughout the experiments. Provided with these parameters we investigate the transient behavior of the model due to both steps in air and in fuel supply. In order to vary fuel supply we control injection time, whereas air supply variations are generated by controlling the throttle set point. For this purpose, the amount of air residing in the cylinder is calculated according to intake manifold pressure, thereby eliminating intake manifold dynamics.
We verify that the model proposed is sufficient to describe most of the dynamic phenomena in fuel supply.