Analysis of Petri Net based Control Algorithms - Basic Properties.
Proceedings of the American Control Conference ACC 2000, Chicago, June 28-30, 2000, pp. 3172-3176.
- 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. The synchronized PN and its further extension to the interpreted PN are the most common ones. In these models, transitions are associated with firing conditions depending on external events. In this contribution 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 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.