Generalized state equation for petri nets

Petri nets (PN) are becoming more common as a tool for analysis and design of industrial automation systems (IAS). As an important advantage, PN is able to represent the systems both mathematically and graphically. We can utilize mathematical features of PN to carry out modeling, simulation, testing and verification phases of IAS. Thus, the entire analysis and design process of large-scale systems is greatly simplified and system modeling can be performed accurately and efficiently. However, there is no state equation available defined for PN in the literature, when dealing with the inhibitor and enabling arcs. In addition, although resetting mechanism is frequently used for IAS, there is no arc type directly representing such a mechanism in the literature. In this study, the state equation of PN is revisited and novel mathematical descriptions of both inhibitor and enabling arcs are introduced. Additionally, a new type of arc, called "nullifier arc", and its corresponding modified state equation are proposed for modeling of the resetting mechanism. The state equation of all three arc types are combined and expressed as "generalized state equation". New software is developed and utilized to demonstrate the application of generalized state equation on an IAS. Finally, it is revealed that this novel generalized state equation is capable of representing the special arcs, which facilitates analysis of large scale systems.