Petri net controllers - Modeling

The behavior of all logic controllers can be modeled using Petri nets. This tool is designed to represent discrete-event systems whose state variables change abruptly from one value to another, without the need to represent transient phenomena. This class includes control systems with or without simultaneous evolutions, processes or systems controlled by discrete-event models, and automatic systems (control and process). The asynchronous evolution mode of Petri nets makes them the model par excellence for distributed applications and, of course, communication protocols. Last but not least, they are widely used for performance evaluation by simulation or formal calculation on model extensions involving statistical or stochastic data.

The descriptive capacity of the Petri net model is limited when absolute dates appear in the specifications. Indeed, time is not explicitly taken into account by this model. It is therefore difficult to represent applications containing recommendations such as "at date t, ...". On the other hand, duration can be taken into account thanks to the temporal extensions of the basic model. It is therefore quite natural to envisage a Petri net representation of a specification containing: "after a 10-second wait, ...". The distinction is not always immediate, but derives from a reference to absolute time (date) or relative time (duration). Another major limitation of the Petri net model is the lack of an abstraction mechanism. Apart from the use of the activity concept described in this article, which is not specific to this model, no aggregation mechanism is really offered by Petri nets.

Of course, other modeling tools can also be used for discrete-event modeling. For example, finite-state automata can easily capture the sequential behavior of an application. On the other hand, as soon as simultaneous evolutions need to be represented, especially if they need to be synchronized from time to time, state graph representation becomes complex (we speak of a combinatorial explosion in the number of states) and, above all, the overall behavior of the model becomes difficult to grasp. Grafcet (functional graph of transition step control, a standardized language for PLCs) can be used instead of Petri nets. It should be noted that the Grafcet, which was defined by an Adepa working group in the 1980s, is in fact a derivative of binary Petri nets. Grafcet may be preferred for reasons of implementation. On the other hand, it quickly becomes difficult to use when the need for counting (of parts, messages, etc.) arises, and Petri nets are used instead. Finally, it should be noted that the Grafcet rule stipulating that "all traversable transitions are traversed simultaneously", introduced to make it deterministic, transforms a choice into a parallel departure...