On the suboptimal liveness-enforcing supervisors based on Petri net structural analysis and the theory of regions

Abstract

This paper develops a new methodology to derive deadlock prevention policies for flexible manufacturing systems based on a Petri net formalism. It designs a supervisor for a plant net model by adding monitors or control places and using the theory of regions to gain maximally permissive behavior. Then, the strict minimal siphons in the maximally permissive supervisor are computed and divided into elementary and dependent ones. To prevent them from being emptied, algebraic expressions about the markings of the additional monitors in the supervisor and the resource places in the plant net model are derived, under which the supervisor is live. The expressions are used to derive the live initial markings for the supervisor without changing its structure when the number of jobs to be processed and the capacity of manufacturing resources in a plant change. The case study shows that our combined method is computationally efficient compared to existing ones, in which the theory of regions is used alone, and the permissive behavior of the supervisor is near-optimal.