Discrete-Event Models

Abstract

Discrete-event models (DEM) of selected engine subsystems are the subject of in this chapter. The input and output signals of these systems either are not defined or are not relevant continuously, but only at certain discrete instances. Thus, the system behavior associated with the sampling of the signals, the delays caused by the timing relations, and the interaction with the ECU (which operates in a discrete-time way as well), become important.

Crank-angle based representations are often used for IC engine models. This change in the independent variable from time t to crank angle φ has advantages for certain control problems. Specifically, the feedforward action of the air/fuel ratio control system needs this special representation because it must be realized with the maximum bandwidth achievable. It is thus very sensitive to any errors in modeling the delays and the timing relations.

The following items are discussed in this chapter:

• When are DEM required?

• Various ECU operation modes and time scales.

• Precise timing of injection and ignition commands.

• DEM of torque production in IC engines.

• DEM of the air flow in IC engines.

• DEM of the fuel flow in IC engines.

• DEM of back-flow dynamics of CNG engines.

• DEM of residual gas dynamics.

• DEM of exhaust pipe dynamics.

• DEM based on measurements data of the cylinder pressure.

Most of these models are control-oriented models. Only the last model represents a first step toward thermodynamically more detailed ones.

One fundamental assumption that underlies the derivation of all of these models is that the engine speed does not significantly change during one engine cycle. This assumption has been justified in Sect. 2.5.2. Therefore, the models, although being defined in the crank-angle domain, are formulated on the basis of constant sampling times.