A physical model for engine control design via role state variables

The present paper describes a model representation of the multi-cyclic phenomena of a multi-cylinder engine system. The model is simplified for the implementation of a practical engine controller. The simplified model is described by physically meaningful state variables, which enables controller designers to effectively consider practical objectives and constraints. The proposed approach consists of two steps. First, an approximate analytical discrete-crank angle model, which is a periodic state equation, is derived from the gas equations, the conservation laws, and the motion dynamics. Second, the concept of role state variables is proposed to transform the periodic state equation into a time-invariant state equation. The stabilizability and detectability of the time-invariant state equation are shown to be equivalent to those of the periodic state equation. The time-invariant state equation is used to design cold start feedforward and feedback controllers.