On the lower bound of monitor solutions of maximally permissive supervisors for a subclass α-S³PR of flexible manufacturing systems

Abstract

Recently, a novel and computationally efficient method – based on a vector covering approach – to design optimal control places and an iteration approach that computes the reachability graph to obtain a maximally permissive liveness enforcing supervisor for FMS (flexible manufacturing systems) have been reported. However, it is unclear as to the relationship between the structure of the net and the minimal number of monitors required. This paper develops a theory to show that the minimal number of monitors required cannot be less than that of basic siphons in α-S³PR (systems of simple sequential processes with resources). This confirms that two of the three controlled systems by Chen et al. are of a minimal monitor configuration since they belong to α-S³PR and their number in each example equals that of basic siphons.

Keywords:

• Petri net
• flexible manufacturing system (FMS)
• deadlock prevention

Acknowledgements

This work was supported by the National Science Council under Grant NSC 99-2221-E-004-002.

Additional information

Notes on contributors

Daniel Yuh Chao

D.Y. Chao (M91SM04) received the Ph.D degree in electrical engineering and computer science from the University of California, Berkeley in 1987. He is currently a distinguished full professor at the Department of Management and Information Systems, National ChengChi University (NCCU). His research interest was in the application of Petri nets to the design and synthesis of communication protocols and the computer aided design (CAD) implementation of a multi-function Petri net graphic tool. He is now working on the optimal control of flexible manufacturing systems. He has published 153 (including 81 journal) papers in the area of communication protocols, Petri nets, DQDB, networks, FMS, data flow graphs and neural networks. He has been awarded the title of Distinguished Research Lecture Professor since 2005 and six times of excellent research at NCCU.