Algebraic Synthesis of Timed Supervisor for Automated Manufacturing Systems Using Petri Nets

For practical automated manufacturing systems (AMSs), the time dimension is of great significance and should be integrated in their plant models. Reasonably, many of the realistic general mutual exclusion constraints (GMECs) imposed on these discrete models should be timed rather than merely algebraic or logic. In the past, such a problem was studied on the basis of the Ramadge-Wonham supervisory control technique (SCT) and the theory of regions. It proves to be NP-hard since it necessitates the generation of reachability graphs. This paper shows that it can be solvable in polynomial time by using generalized linear constraints, which are originally proposed to increase the expressive power of the linear marking constraints. By dividing each constraint into marking, firing vector, and Parikh terms, its respective control place can be synthesized algebraically without considering the separation of dangerous states and events. Several examples are used to validate the effectiveness and efficiency of the proposed approach. Note To Practitioners-This paper concerns about the supervisor design with the involvement of global time information, which is motivated by industrial applications where time dimension is crucial for their elaborate characterization. These applications, particularly arising in AMS, show that supervisory control specifications may be strongly related to time and would be quite impractical without taking into account indices such as global time. Previously, such a problem is proposed to be dealt with through a methodology based on the Ramadge-Wonham approach and the theory of regions, which is ineffective owing to the excessive computational time. The goal of this paper is to propose an algebraic synthesis method that can tackle this problem effectively yet remain tractable. Both theoretical and experimental results demonstrate that effective supervisors can be obtained in a computationally efficient way. Practitioners can easily implement these supervisors.