Design of liveness-enforcing supervisors with simpler structures for deadlock-free operations in flexible manufacturing systems using necessary siphons

Siphons can be used to characterize deadlock states and solve deadlock problems in Petri nets that model flexible manufacturing systems. This paper presents an iterative siphon-based control (ISC) deadlock prevention policy for Petri nets via the combination of mixed integer programming (MIP) and the concept of necessary siphons (NSs). At each iteration in this ISC policy, a maximal deadly marked siphon that is closely related to deadlocks in a Petri net can be conveniently found by an MIP-based deadlock detection method. Then the places in it are classified and an NS is derived from the classified places. For each NS found, depending on its complementary set, the proposed policy adds a proper control place (CP) to make it marked (max-controlled). Moreover, during the ISC procedure, a test for redundant NSs is carried out under a certain condition in order to avoid the addition of the corresponding CPs. The siphon control process proceeds iteratively until the controlled system is live. Compared with the existing approaches, the proposed policy usually leads to a structurally simple liveness-enforcing supervisor by adding as few CPs as possible and achieves better control results. Some examples are introduced to illustrate the proposed approach.