Analysis of Petri net based control algorithms - basic properties

Petri nets (PN) show good properties in modeling control algorithms. However, they provide no means for modeling the connection between an algorithm and its environment. To overcome this problem, different extensions of the basic PN model have been introduced. In this paper a model is used that associates transitions with firing conditions depending on external signals instead. Furthermore, the model called signal interpreted Petri net (SIPN) sets the output signals depending on its marking. The problems arising by applying results of standard PN analysis methods to SIPN are illustrated and the source of these problems, dynamic synchronization (DS), is identified. Based on DS, necessary and sufficient conditions for the validity of PN analysis are derived. For the cases where PN analysis is not sufficient to determine the properties of an SIPN, an algorithm for the calculation of the SIPN reachability graph is presented, and it is shown how the properties of the SIPN are determined using this reachability graph