Abstract
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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Cassandras C.G. and S. Lafortune. 1999. Introduction to discrete event systems. Kluwer Academic.
Baccelli F., G. Cohen, G. Olsder, et J. Quadrat. 1992. Synchronization and Linearity: An algebra for Discrete Event Systems. Willey.
Martinez C. and P. Castagna. 2003. Sizing of an industrial plant using tight time constraints using complementary approaches: (max, +) algebra and computer simulation. Simulation Modelling Practice and Theory 11, 75–88.
Olsder G.J., Subiono, M.Mc Guettrick. 1998. On large scale max-plus algebra model in railway systems. Actes de la 26ièmeécole de printemps d’informatique théorique: algebre max-plus et applications en informatique et automatique, INRIA, LIAFA, IRCyN, France, 177–192.
Mairesse J. 1998. Petri nets, (max,+) algebra and scheduling. Actes de la 26ièmeécole de printemps d’informatique théorique: algebre max-plus et applications en informatique et automatique, INRIA, LIAFA, IRCyN, France, 329–357.
Cochet-Terrasson J., G. Cohen, S. Gaubert, M.Mc Gettrick, J.P. Quadrat. 1998. Numerical computation of spectral elements in max-plus algebra. IF AC conference on system structure and control, France, 699–706.
Gaubert S. 1995. Resource optimization and (min,+) spectral theory. IEEE trans. on automatic control 40(11), 1931–1934.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer Science + Business Media, Inc.
About this chapter
Cite this chapter
Amari, S., Demongodin, I., Loiseau, JJ. (2005). Sizing, Cycle Time and Plant Control Using Dioid Algebra. In: Dolgui, A., Soldek, J., Zaikin, O. (eds) Supply Chain Optimisation. Applied Optimization, vol 94. Springer, Boston, MA. https://doi.org/10.1007/0-387-23581-7_6
Download citation
DOI: https://doi.org/10.1007/0-387-23581-7_6
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-23566-0
Online ISBN: 978-0-387-23581-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)