Abstract
The present paper describes a model representation of multi-cyclic phenomena for a multi-cylinder engine system. The model is simplified for implementation as a practical engine controller. The simplified model with physically meaningful variables can be used in design considering practical objectives and constraints more effectively. The proposed approach consists of two steps. First, an approximate analytical discrete crank angle model (i.e., a periodically time-varying state space model) is derived from the conservation laws. Second, the concept of role state variables is proposed to transform the periodically time-varying state space model into a time-invariant state space model. The stabilizability and optimality of the time-invariant state space model imply those of the periodically time-varying state space model. The time-invariant state space model is used to design cold start feedforward and feedback controllers.
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