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A deluge of studies has been carried out on deadlock prevention and liveness enforcement for flexible manufacturing systems (FMSs). This paper reports an algebraic procedure to find a set of merged place invariants, aiming to reduce the structural complexity of a liveness-enforcing Petri net supervisor for an FMS. Firstly, given an uncontrolled Petri net model, a set of control places as well as their corresponding place invariants are computed by using the existing methods. A systematic approach is developed to find a set of merged place invariants that are much more compact than the original supervisor structure, which remarkably reduces the number of control places in a liveness-enforcing Petri net supervisor for an FMS. The structurally reduced supervisor provides the same or more permissive behavior than that of an original one. As an algebraic approach, the proposed method is computationally trivial and is applicable to all manufacturing-oriented Petri net classes currently available in the literature. Several typical manufacturing examples are used to demonstrate the approach reported in this research. [ABSTRACT FROM AUTHOR]

This paper proposes an iterative method to the synthesis of liveness-enforcing supervisors for flexible manufacturing systems (FMSs). The concept of a global idle place (GP) for an original uncontrolled net system is developed. A GP is used temporarily to simplify the reachability graph computation of the system and is finally removed when the liveness of the system is achieved. At each iteration, bad markings (BMs) are identified. By using a marking covering approach, a minimal covering set of BMs is computed and then controlled through a simplified invariant-based control method. A sufficient condition under which the proposed method can obtain an optimal supervisor is presented. The proposed method can generally lead to an optimal or near-optimal supervisor. Finally, several FMS examples are utilized to illustrate applicability and the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]