Supervisor Design Approach For FMS Based On Time Scheduling

The deadlock problem is a subject that can not be ignored in flexible manufacturing systems (FMS). This paper mainly focuses on a study of deadlock control policy under the Petri nets formalism. All of the existing deadlock control methods, no matter structure analysis-based or reachability graph-based, need to add some control places to the original Petri nets. As the size of a Petri net grows exponentially with the numbers of nodes and the initial tokens, which makes the complexity of structure and computation increased with the controlled net system. To solve the problem, this paper applies the thought of marking/transition separation instance in the theory of regions. Its aim is to prevent the permissive behavior running into the forbidden states in the net system. By introducing the concept of time scheduling, adding time constraints to transitions to achieve the change of transitions firing sequences. And then, the deadlock in the net system can be forbidden effectively. Since the deadlocks are eliminated in the design and planning stage, the system-down caused by the deadlocks can be avoided.Reachability analysis is a basic method which is widely used in the Petri net model analysis. The deadlock control is a type of problem of forbidden states. In this paper, an entire reachability graph is calculated. According to the theory of regions, the reachable markings can be divided into four classes:deadlocks, bad markings, dangerous markings and good markings. The dangerous markings and good markings constitute the maximal legal behavior of a system. In order to remove the forbidden behavior to get the controller, we need to find all the marking/transition separation instances. The theory of regions prevents the firing of transitions which can lead to deadlocks by adding some control places, which makes the controlled net more complex. In this paper, by adding the time constraints to the transitions enabled simultaneously, we can control the firing sequences to avoid unnecessary states, such as LILs (local isolated loops), deadlocks and bad markings. Through the above strategy, deadlock prevention can be realized.Through the analysis of some Petri net models, the author discovered and defined a phenomenon called LILs which existing in the reachability graph. From the perspective of the Petri net dynamic activity, although the states from the LILs are not dead, the existence of local isolated loops can cause the system-down as the deadlock does. At the end of the paper, two FMS examples, called LS3PR, are given to demonstrate the proposed algorithm.