Modelling and temporal performances evaluation of networked control systems using (max, plus ) algebra

In this paper, we address the problem of temporal performances evaluation of producer/consumer networked control systems. The aim is to develop a formal method for evaluating the response time of this type of control systems. Our approach consists on modelling, using Petri nets classes, the behaviour of the whole architecture including the switches that support multicast communications used by this protocol. (max, +) algebra formalism is then exploited to obtain analytical formulas of the response time and the maximal and minimal bounds. The main novelty is that our approach takes into account all delays experienced at the different stages of networked automation systems. Finally, we show how to apply the obtained results through an example of networked control system.