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Deadlock avoidance problems are investigated for automated manufacturing systems with flexible routings. Based on the Petri net models of the systems, this paper proposes, for the first time, the concept of perfect maximal resource-transition circuits and their saturated states. The concept facilitates the development of system liveness characterization and deadlock avoidance Petri net supervisors. Deadlock is characterized as some perfect maximal resource-transition circuits reaching their saturated states. For a large class of manufacturing systems, which do not contain center resources, the optimal deadlock avoidance Petri net supervisors are presented. For a general manufacturing system, a method is proposed for reducing the system Petri net model so that the reduced model does not contain center resources and, hence, has optimal deadlock avoidance Petri net supervisor. The controlled reduced Petri net model can then be used as the liveness supervisor of the system.
Based on the Petri net models of the systems, this paper proposes, for the first time, the concept of perfect maximal resource-transition circuits and their saturated states. The concept facilitates the development of system liveness characterization and deadlock avoidance Petri net supervisors. Deadlock is characterized as some perfect maximal resource-transition circuits reaching their saturated states. For a large class of manufacturing systems, which do not contain center resources, the optimal deadlock avoidance Petri net supervisors For a general manufacturing system, a method is proposed for reducing the system Petri net model so that the reduced model does not contain center resources and, hence, has optimal deadlock avoidance Petri net supervisor. The controlled reduced Petri net model can then be used as the liveness supervisor of the system.