Transition cover-based design of Petri net controllers for automated manufacturing systems

In automated manufacturing systems (AMSs), deadlock problems must be well solved. Many deadlock control policies, which are based on siphons or Resource-Transition Circuits (RTCs) of Petri net models of AMSs, have been proposed. To obtain a live Petri net controller of small size, this paper proposes for the first time the concept of transition covers in Petri net models. A transition cover is a set of Maximal Perfect RTCs (MPCs), and the transition set of its MPCs can cover the set of transitions of all MPCs. By adding a control place with the proper control variable to each MPC in an effective transition cover to make sure that it is not saturated, it is proved that deadlocks can be prevented, whereas the control variables can be obtained by linear integer programming. Since the number of MPCs in an effective transition cover is less than twice that of transition vertices, the obtained controller is of small size. The effectiveness of a transition cover is checked, and ineffective transition covers can be transformed into effective ones. Some examples are used to illustrate the proposed methods and show the advantage over the previous ones.