Abstract
Petri nets are an important and popular tool to model and analyze deadlocks in flexible manufacturing systems. The state space of a Petri net model can be divided into two disjoint parts: a live-zone and a dead-zone. Reachability graph analysis plays an important role in the modeling and control of Petri nets. Most existing studies have to fully enumerate the reachable markings of a Petri net to obtain the first-met bad markings (FBMs), which exacerbates the computational overheads. In this paper, a computationally efficient method to find dead markings in Petri nets is presented. We first introduce an algorithm to find dead markings by solving an integer linear programming problem. Then, the set of markings in the dead-zone is calculated, including the set of dead markings and the set of bad markings. Then we can find all the FBMs. By using a vector covering approach, the minimal covered set of FBMs is computed. The proposed approach can obtain the dead markings and FBMs by searching only a part of a reachability graph. Finally, examples are provided to demonstrate the proposed method.
Highlights
F LEXIBLE manufacturing systems (FMSs) can automatically finish various kinds of jobs by using shared resources such as robots, machines, and automated guided vehicles
Reachability graph analysis is an important technique to deal with the deadlock problem in Petri nets
Different from traditional methods, we propose a computationally efficient method to obtain the dead markings and first-met bad markings (FBMs) in Petri nets by searching only a part of a reachability graph
Summary
F LEXIBLE manufacturing systems (FMSs) can automatically finish various kinds of jobs by using shared resources such as robots, machines, and automated guided vehicles. Reachability graph analysis is an important technique to deal with the deadlock problem in Petri nets. An iterative approach is developed to obtain a supervisor to forbid all FBMs. This study can reduce the number of constraints in the ILPPs and lead to a maximally permissive supervisor with a small number of control places. All the aforementioned papers deal with deadlocks in Petri nets by using the concept of FBMs. It is not efficient to find FBMs by generating the whole reachability graph since the number of reachable markings increases exponentially with the size of a net model. Different from traditional methods, we propose a computationally efficient method to obtain the dead markings and FBMs in Petri nets by searching only a part of a reachability graph.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
