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Evaluation analytique du temps de réponse des systèmes de commande en réseau en utilisant l’algèbre (max,+)

Abstract : Networked automation systems (NAS) are more and more used in industry, given the several advantages they provide like flexibility, low cost, ease of maintenance, etc. However, the use of a communication network in SCR means in essence sharing some resources and therefore strikingly impacts their time performances. For instance, a control signal does get to its destination (actuator) only after a non zero delay. So, to guarantee that such a delay is shorter than a given threshold or other time constraints well respected, an a priori evaluation is necessary before operating the SCR. In our research activities, we are interested in client/server SCR reactivity and the evaluation of their response time.Our contribution in this investigation is the introduction of a (Max,+) Algebra-based analytic approach to solve some problems, faced in the existing methods like state explosion of model checking or the non exhaustivity of simulation. So, after getting Timed Event Graphs based models of the SCR and their linear state (Max,+) representation, we obtain formulae that enables to calculate straightforwardly the SCR response times. More precisely, we obtain formulae of the bounds of response time by adopting a deterministic analysis and other formulae to calculate the probability density of response time by considering a stochastic analysis. Moreover, in our investigation we take into account every single elementary delay involved in the response time, including the end-to-end delays, due exclusively to crossing the communication network. This latter being however constituted of shared resources, making by the way the use of TEG and (Max,+) Algebra impossible, we introduce a novel approach to model the communication network. This approach brings to life a new class of Petri nets, called Conflicting Timed Event Graphs (CTEG), which enables us to solve the problem of the shared resources. We also manage to represent the CTEG dynamics using recurrent (Max,+) equations and therefore calculate the end to-end delays. An Ethernet-based network is studied as an example to apply this novel approach. Note by the way that the field of application of this approach borders largely communication networks and is quite possible when dealing with other systems.Finally, to validate the different results of our research activities and the related hypotheses, especially the maximal bound of response time formula, we carry out lots of experimental measurements on a lab facility. We compare the measures to the formula predictions and check their agreement under different conditions.
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Boussad Addad. Evaluation analytique du temps de réponse des systèmes de commande en réseau en utilisant l’algèbre (max,+). Autre. École normale supérieure de Cachan - ENS Cachan, 2011. Français. ⟨NNT : 2011DENS0023⟩. ⟨tel-00661602⟩

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