Studies Of Petri Net Control Method For Discrete Event System

Petri net is a powerful tool of simulating and analyzing system Recently it is widely applied to the field of computer science and discrete event dynamic systemIn this paper the control theory and method are studied deeply based on Petri net model of the discrete event dynamic system .The Petri net concepts of path gains and merge operation for the place invariant are introduced . The relations between path gain and place invariant and between paths. basic circles and their corresponding place invariants are presented. Also the relation between Petri net figure operation and the place invariant operation is established. And a sufficient and necessary condition of existence of place invariants for a weighted state machine is proved. Petri net geometrical significance of place invariants is unveiled, So that the node significance of Petri net is expended .The existence of loop-free weighted event graph place invariant is proved and the forms of its place invariant and the minimum place invariant are embodied based on the concept of path gain .The place invariant of Petri net which is merged by two Petri nets on places is discussed A geometrical approach to compute place invariant and judge its existence is presented via decomposing loop-free Petri net into some weighed event graphs merged on places Those not only are very importance to Petri net theory but also provided the base for the Petri net controller studies and synthesis of discrete event dynamic system . The problem of implementation of the equality constraints in discrete event system is discussed based on the concept of place invariant modeled by Petri net .By adding some new arcs to the system Petri net ,a approach to implementation equality constraints for DEDS is presented ,The method is efficient in design and computation . This paper studies the problem of Petri net controllers for discrete event system modeled by Petri nets with uncontrollable transitions. And a sufficient and necessary condition of existence of place invariant for a class of Petri net is proved . The controller for the Petri net without competition structure is implemented based on the Petri net concept of path gains .The deadlock avoidance in a class of sequential manufacturing systems is discussed based on Petri net model in this paper. By analysis of system structure ,a necessary and sufficient condition for liveness of system model is proved .Deadlock avoidance controller which is a Petri net is presented . The controlled closed-looped system may be live.