A deadlock control algorithm using control transitions for flexible manufacturing systems modelling with Petri nets

ABSTRACT This paper develops a concept of control transition equation (CTE) and the corresponding deadlock control algorithm (DCA) using control transitions (CTs) to eliminate deadlocks in Petri nets. By analysing the reachability graph (RG) of an original net with deadlocks, this DCA firstly find all deadlock markings (DMs) and then the corresponding CTs are solved on the basis of the proposed CTE. Secondly, a linear programming problem that can minimise the number of CTs is applied to these CTs. In addition, in order to furtherly simplify the structure of these CTs, the reconstruction of the necessarily added CTs is performed by a circulating sequence number method. Finally, a live controlled system with the simpler structure is obtained by adding the desired CTs to , which can reach the same number of states as the original plant model , i. e. live maximally reachable number. The proposed DCA is different from deadlock prevention policies using control places (CPs) in most existing literature and whose correctness and efficiency are verified via the theoretical analysis and the relevant several examples.

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