Abstract
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.
Highlights
The control of automated systems has long been a matter of great interest to the scientific world.The tools for studying discrete event systems (DES) are numerous, but Petri nets (PNs) [1] are nowadays most used because of their various and interesting properties for complex systems, such as airplanes, nuclear power plants or oil refineries, etc
Since the calculation time of the control costs money according to the imposed constraints, the main contribution of this paper is to develop a control method which enables us to use the advantages of the PN properties and the theory of regions (TR) while avoiding its technical obstacles, i.e., the generation and the analysis of the reachability graph (RG)
Without RG generation, one can design the same number of PN controllers using the theory of regions
Summary
The control of automated systems has long been a matter of great interest to the scientific world. Chen et al [17] proposed a vector-covering approach to decrease the number of states to consider in the synthesis process of the PN supervisor These methods can reduce the number of PN monitors. Pan [22] developed a new method for deadlock prevention based on the TR This control policy sought to decrease the number of reachability conditions of the theory of regions in order to facilitate supervisor computation. In our previous works [25,26,27,28,29], a new method called minimal cuts in RG was developed Through this control policy, the computational cost of the PN supervisor was minimized by applying the TR on specific zones and not on the whole graph.
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