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A deadlock prevention approach for flexible manufacturing systems without complete siphon enumeration of their Petri net models

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Abstract

Siphons are very important in the analysis and control of deadlocks in a Petri net. However, it is quite time-consuming or even impossible to get the complete siphon enumeration of a Petri net. This paper focuses on the deadlock prevention problems in flexible manufacturing systems that are modeled with S4PR, a general class of Petri nets. The analysis of S4PR leads us to characterize deadlock situations in terms of insufficiently marked siphons. The method proposed in this paper is an iterative approach. At each iteration, a non-max-marked siphon is computed by solving a mixed integer linear programming problem. Then the siphon is max-marked through a P-invariant by adding a monitor place. This process is carried out until no non-max-marked siphon can be found in the net. As a result all the siphons in the net are max-controlled. Then the net becomes live. Without computing all the siphons, a monitor-based liveness-enforcing Petri net supervisor can be found with more permissive behavior. A number of flexible manufacturing examples are used to demonstrate the proposed methods.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China under Grant No 60474018 and 60773001, and the National Research Foundation for the Doctoral Program of Higher Education, Ministry Education of China under Grant No. 20070701013. The authors would like to thank the anonymous reviewers whose comments and suggestions greatly helped us improve the quality and presentation of this paper.

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Authors and Affiliations

  1. School of Electro-Mechanical Engineering, Xidian University, 710071, Xi’an, People’s Republic of China

    Chunfu Zhong & Zhiwu Li

  2. Department of Computer Science, Halle-Wittenberg Martin-Luther University, 06120, Halle, Germany

    Zhiwu Li

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  1. Chunfu Zhong
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Correspondence to Zhiwu Li.

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Zhong, C., Li, Z. A deadlock prevention approach for flexible manufacturing systems without complete siphon enumeration of their Petri net models. Engineering with Computers 25, 269–278 (2009). https://doi.org/10.1007/s00366-008-0122-1

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