Compute Optimization of Petri Net Controllers Using the Algebraic Method

• Published in: Applied sciences Vol. 9; no. 13; p. 2633
• Main Authors: Rezig, Sadok, Turki, Sadok, Rezg, Nidhal
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.07.2019; Multidisciplinary digital publishing institute (MDPI)
• Subjects: bounded petri nets; Combinatorial analysis; combinatorial explosion of states; Complex systems; Computer applications; Computer Science; Controllers; Design; discrete event systems; flexible manufacturing system; Manufacturing; Mathematics; Methods; Nuclear power plants; Optimization; Petri nets; Supervisors; theory of regions; flexible manufacturing system; discrete event systems; combinatorial explosion of states; theory of regions; bounded petri nets
• ISSN: 2076-3417; 2076-3417
• DOI: 10.3390/app9132633

This study attempted to calculate an optimal Petri net supervisor able to respect the control specifications imposed for a flexible manufacturing system. There are several theories around the control synthesis of discrete event systems. Unfortunately, these methods are very sensitive to the combinatorial explosion of states in the generated graph, especially when the complexity of the system increases. It is therefore necessary to move towards new ways based on formal methods allowing the synthesis of a supervisor. In this work, we propose an algebraic approach using the theory of regions. Our main contribution is to design a set of Petri net controllers based on the properties of Petri nets and not on reachability graph generation for bounded Petri nets. This will decrease significantly the production cost of the manufacturing system, since the computation burden of the supervisor is reduced. Our control policy was applied to a flexible manufacturing system implemented in our laboratory. Comparisons with previous studies using CPLEX software are provided in order to illustrate the effectiveness of our proposed method.