Small-Size Liveness-Enforcing Supervisor for Automated Manufacturing Systems Using the Theory of Transition Cover

The supervisor simplification problem for automated manufacturing systems (AMSs) has been receiving increasing attention in recent years. This article uses a well-known class of Petri nets, namely, systems of sequential systems with shared resources (S(4)Rs) to model general AMSs. We aim to simplify the liveness-enforcing supervisor for (SR)-R-4 by using the concept of transition cover (TC). Deadlocks in (SR)-R-4 can be characterized by a kind of special structural object called perfect activity circuits (PACs). First, a set of special PACs are defined as a TC and its effectness is also verified. Then, by adding a monitor with a control variable to each PAC in an effective TC (ETC), we establish a liveness-enforcing supervisor for (SR)-R-4. The control variables are determined by solving an integer linear programming problem so as to increase the supervisor's permissiveness as much as possible. Under the proposed control methodology, it is analyzed that the upper bound of the number of monitors equates to that of transitions in (SR)-R-4. Especially for the system with a few transitions, since not many monitors are added, the proposed supervisor has relatively small-scaled structures or a small number of control places. In addition, we present algorithms to get an ETC from any nonlive (SR)-R-4. Based on this ETC, we can design one liveness-enforcing supervisor of small size for the underlying S4R. Finally, some examples are used to illustrate the proposed approach.