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The problem of adaptively controlling the mixture ratio can be reduced to the problem of identifying the respective non-linear system dynamics [ 19]. In the present paper, convenient models of the significant dynamic processes, i.e., intake manifold, wall-wetting and oxygen sensor dynamics, arc deduced. We will separate the analysis in terms of an air and a fuel path. Concerning the fuel path we restrict our attention exclusively to linear sensor models in order to keep the modelling overhead small. Nevertheless, considering the overall dynamics, we will have to deal with some inherent non-linearities. Suitable parametrizations of these models with respect to the demands imposed by the filtering techniques are then introduced. In the case of linear dynamics we aim to achieve a linear regression form whereas in the case of non-linear dynamics, we will augment the system state and apply extended Kalman filter theory.

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.

This paper introduces a model-based adaptive controller designed to compensate mixture ratio dynamics in an SI engine. In the basic model the combined dynamics of wall-wetting and oxygen sensor have to be considered because the only information about process dynamics originates from measuring exhaust λ. The controller design is based on the principles of indirect Model Reference Adaptive Control (MRAC). The indirect approach connotes that explicit identification of the system parameters is required for the determination of the controller parameters. Due to nonlinearities and delays inherent in the process dynamics, an adaptive extended Kalman filter is used for identification purposes. The Kalman filter method has already been described in detail within an earlier paper [1]. It proves to be ideally suited to deal with nonlinear identification problems. The estimated parameters are further used to tune an adaptive observer for wall-wetting dynamics.