Analysis of Petri-Net based Control Algorithms.
Proceedings SDPS, Fifth World Conference on Integrated Design and Process Technologies, Dallas, (CD-ROM), June 2000.
Petri nets (PN) have shown good properties in modeling control algorithms. However, they provide no means for modeling the connection between the 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, the transitions are associated with a firing condition that depends on external events. However, the notion of external events is not necessary in the description of control algorithms. Hence, in this contribution a model is used that associates transitions with firing conditions depending on external signals instead. Furthermore the model sets output signals depending on its marking. This model is called Signal Interpreted Petri Net (SIPN). However, the impact of such extensions on the formal analysis of the PN has to be considered. 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 results are given. The described problems caused by DS show that an SIPN analysis based on the underlying PN is not sufficient to determine the SIPNs properties. Therefore, an algorithm for the calculation of the SIPNs reachability graph is presented and it is shown how the SIPNs properties can be determined using this reachability graph.