Modeling by Petri Net with Place Invariants for Sequential Control Systems.

It is difficult to model a discrete system than a continuous system. Recently, a great number of applications of Petri nets to the design and the analysis of discrete systems have been reported. However, a common problem in its applications is that the required computer memories and the computation times increase explosively in accordance with the increase in the number of systems' components. Some methods to divide or to reduce Petrinets have been proposed to solve this problem. Although the liveness and boundedness of Petri nets are held in the divided or reduced Petri nets, the reachability problem can not be solved by these methods.In this paper, we propose another method to model discrete systems by Petri nets with place invariants. Sequential control system will be described as a typical kind of discrete systems, and its structural characteristics will be used in modeling. Each component of a sequential control system will be modeled by a sub Petri net with place invariants. There are many components in one sequential control system, but each one is not necessarily complicated. Most sub Petri nets do not have so many places or transitions. It is also well known that a Petri net with place invariants is bounded and can be live by being put sufficient tokens into its initial marking. Besides, the reachability problem is not so difficult to solve in a small sub Petri net. Further, we define an activating relation to combine two or more sub Petri nets. And, some rules to reduce conflicts among enabled transitions will be described for simulations.