SIZING, CYCLE TIME AND PLANT CONTROL USING DIOID ALGEBRA

Saïd Amari (1) , Isabel Demongodin (2) , Jean Jacques Loiseau (3)

1 LURPA - Laboratoire Universitaire de Recherche en Production Automatisée
2 LSIS - Laboratoire des Sciences de l'Information et des Systèmes
3 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes

Using an industrial process from the car sector, we show how dioid algebra may be used for the performance evaluation, sizing, and control of this discrete-event dynamic system. Based on a Petri net model as an event graph, max-plus algebra and min-plus algebra permit to write linear equations of the behavior. From this formalism, the cycle time is determined and an optimal sizing is characterized for a required cyclic behavior. Finally, a strict temporal constraint the system is subject to is reformulated in terms of inequalities that the (min, +) system should satisfy, and a control law is designed so that the controlled system satisfies the constraint.

Mots clés: dioid algebra; Petri net; sizing; cycle time; control

Domaines: Automatique / Robotique

Saïd Amari, Isabel Demongodin, Jean Jacques Loiseau. SIZING, CYCLE TIME AND PLANT CONTROL USING DIOID ALGEBRA. A. Dolgui J. Soldek and O. Zaikin (Eds.), Springer. SIZING, CYCLE TIME AND PLANT CONTROL USING DIOID ALGEBRA, Springer, pp.71-85, 2004. ⟨hal-00362950⟩