Liveness Analysis And Controller Design Of Time Petri Nets Based On Transition Priority

In flexible manufacturing systems(FMS), deadlock problems should not be ignored. Most of the previous research was carried out under the framework of Petri nets without consideration of the time factor.However,from the point of view of performance analysis and real-time control,the concept of time should be integrated into Petri nets.This paper is devoted to the study of deadlock control policy based on the transition priority under time Petri nets framework.Traditional deadlock prevention policies need to add monitors to the original net, which makes the net structure more complex.In this paper, the deadlock prevention policy based on transition priority does not need to add any places and arcs, but set up the proper priorities of transitions. The controlled net has simpler structure, which is easier to implement in the actual system control.The uncertainty of the moment that the transition fires makes difficult to analyze the performance and control the time Petri nets.On the basis of the class states of a time net, the concept of state sub class is put forward in paper.Under the same P-marking, the states that have the same emission transition set are classified as a subclass.The division of the sub class is concerned with the transition set in the state, and no longer concerned about the transition firing time.It does not only reduce the complexity of the analysis of the time net, but also can use the correspondence between the state class of time net and the state of the source net to control a special kind of time Petri nets that satisfy certain conditions.In this paper, based on the transition priority,we obtain a class of time Petri nets which are equivalent to their consponding source net in liveness. An effective method to solve the problem of deadlock prevention for this class of time Petri nets is proposed. Firstly, by analyzing the reachable states of the given 3LS PR, net a transition priority vector is obtained by given algorithm. Under the constraints of the transition priority vector, the controlled net is live. Then based on the transition priority vector, the time parameters are obtained for a kind of time Petri nets. The dangerous states of the net are equivalent to those of the corresponding source nets.Therefore they have the same liveness proper as controller based on transition priorities. Finally, the effectiveness of the presented method is demonstrated by an example.