Design of Liveness-Enforcing Supervisors for S3PR Based on Complementary Places

In this article, an algorithm is proposed to design liveness-enforcing supervisors for systems of simple sequential processes with resources (S 3 PR) based on complementary places. Firstly, a mixed integer programming (MIP) based deadlock detection method is used to find unmarked strict minimal siphons from an infinite-capacity net. Next, the finite-capacity net, in which liveness can be enforced, is obtained by adding capacity function to the infinite-capacity net. Finally, complementary-place transformation is used to transform the finite-capacity net into an infinite-capacity net. This article focuses on adding a complementary place to each operation place that is related to unmarked siphons, deals with the deadlock problem from a new view point, and hence advances the deadlock control theory. Compared with the existing methods, the new policy is easier to implement for real industrial systems. More importantly, design of a complementary-place supervisor is very easy. Finally, in some cases, the new policy can obtain a structurally simpler supervisor with more permissive behavior than the existing methods do. A flexible manufacturing systems (FMS) example is used to compare the proposed policy with some other methods.