Optimal liveness Petri net controllers with minimal structures for automated manufacturing systems

This paper considers deadlock avoidance problems for manufacturing systems with flexible routings. Based on system Petri net (PN) models, this paper proposes for the first time the concept of perfect resource-transition circuits (PRTC). The system liveness is characterized as no PRTCs can reach saturated states. PRTC-based methods for designing deadlock avoidance PN controllers/supervisors are presented. For systems without center resources, the presented controller is optimal, and more, if every elementary maximal PRTC can also reach its saturated state, then the controllers structure is minimal. For a system with center resources, the system PN model is first reduced so that the reduced PN model doesn't contain center resources and hence has optimal deadlock avoidance PN controller. Then the controlled reduced PN model can be used as a supervisor for the system liveness.