Control of Hybrid Petri Nets using Max-Plus Algebra

In this paper, Hybrid Petri Nets are proposed as a modelling methodology to control production in a large class of manufacturing processes. A hybrid Petri net (HPN) is a combination of a ‘classical’ Petri net and a continuous Petri net, the ‘fluid’ version of a timed Petri net. The two parts of an HPN can affect each other. In the particular model proposed, the discrete part of the HPN ‘regulates’ the continuous Petri net. In fact, whenever an event occurs which changes the present system behavior, the discrete Petri net manages the provoked changes adapting the production process functioning, that is, the continuous Petri net functioning, so as to cope with the new conditions and still fulfil the production requirements. The introduced model allows to realize the control of production by solving suitable optimization problems. The characteristic of the model that makes it specially interesting for analysis and optimization purposes is the special structure of its discrete part, which turns out to be a Timed Event Graph (TEG). TEG’s are Petri nets with peculiar structural characteristics, which makes them be analytically represented by means of state equations linear in the Max-Plus algebra. This capability is exploited to state the constraints imposed by the manufacturing system behavior on the cost functionals to be optimized to solve the control problems of interest. Key-Words: Hybrid Petri nets, modelling, manufacturing systems, Timed Event Graphs, Max-plus algebra,