Siphon basis-based design of Petri net controllers for a class of flexible manufacturing systems

This paper develops a new deadlock prevention policy for a class of flexible manufacturing systems called as systems of simple sequential processes with resources (S³PRs). Siphon basis is introduced to obtain a compact Petri net controller by considering the complementary sets of siphons in S³PRs. A siphon basis consists of strict minimal siphons (SMSs) whose complementary sets can cover the complementary set of each SMS in Petri nets. It is proved that a live Petri net controller can be constructed based on a controllable siphon basis. The structural complexity of the obtained controller is largely reduced because the number of SMSs in a controllable siphon basis is no more than that of the operation places in S³PRs. Based on a controllable siphon basis, a new deadlock prevention policy is established for S³PRs. An example is utilized to demonstrate the proposed method.