α-Siphons of a Suboptimal Control Model of a Subclass of Petri Nets

Daniel Yuh Chao
DOI: 10.4236/ica.2011.21003                

Abstract

It has been a hot research topic to synthesize maximally permissive controllers with fewest monitors. So far, all maximally permissive control models for a well-known benchmark are generalized Petri net, which com-plicates the system. In addition, they all relied on time-consuming reachability analysis. Uzam and Zhou ap-ply First-met-bad-marking (FBM) method to the benchmark to achieve a near maximal permissive control policy with the advantage of no weighted control (WC) arcs. To improve the state of the art, it is interesting to synthesize optimal controller with as few weighted arcs as possible since it is unclear how to optimize the control for siphon involving WC arcs, This paper explores the condition to achieve optimal controller with-out WC and defining a new type of siphon, called α-siphon. If the condition is not met, one can apply the technique by Piroddi et al. to synthesize optimal controllers with WC.

Keywords

Petri Nets, Siphons, Controllability, FMS, S3PR

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	J. Ezpeleta, J. M. Colom and J. Martinez, “A Petri Net Based Deadlock Prevention Policy for Flexible Manufacturing Sys-tems,” IEEE Transactions on Robotics and Automation, Vol. 11, No. 2, April 1995, pp. 173-184. doi: 10.1109/70.370500
[2]	Z. W. Li, J. Zhang and M. Zhao, “Li-veness-Enforcing Supervisor Design for a Class of Generalized Petri Net Models of Flexible Manufacturing Systems,” IEE Proceedings Control Theory & Applications, Vol. 1, No. 4, 2007, pp. 955-967. doi:10.1049/iet-cta:20060218
[3]	C.-F. Zhong and Z.-W. Li, “Design of Liveness-Enforcing Supervisors via Transforming Plant Petri Net Models of FMS,” Asian Journal of Control (Special Issue on the Control of Discrete Event Systems), Vol. 6, No. 2, 2010, pp. 270-280.
[4]	J. W. Guo and Z. W. Li, “A Deadlock Prevention Approach for a Class of Timed Petri Nets Using Elementary Siphons,” Asian Journal of Control, Vol. 12, No. 3, 2010, pp. 347-363. doi:10.1002/asjc.189
[5]	M. Uzam and M. C. Zhou, “An Iterative Synthesis Approach to Petri Net Based Deadlock Pre-vention Policy for Flexible Manufacturing Systems,” IEEE Transactions on Systems, Man, and Cybernetics A, Vol. 37, No. 3, 2007, pp. 362-371. doi:10.1109/TSMCA.2007.893484
[6]	L. Piroddi, R. Cor-done and I. Fumagalli, “Selective Siphon Control for Deadlock Prevention in Petri Nets,” IEEE Transactions on Systems, Man, and Cybernetics A, Vol. 38, No. 6, 2008, pp. 1337-1348. doi:10.1109/TSM CA.2008.2003535
[7]	L. Piroddi, R. Cor-done and I. Fumagalli, “Combined Siphon and Marking Gen-eration for Deadlock Prevention in Petri Nets,” IEEE Transac-tions on Systems, Man, and Cybernetics A, Vol. 39, No. 3, May 2009, pp. 650-661. doi:10.1109/TSMCA.2009.2013189
[8]	M. Uzam, Z. W. Li and M. C. Zhou, “Identification and Elimination of Redundant Control Places in Petri Net Based Liveness Enforcing Supervi-sors of FMS,” International Journal of Advanced Manufactur-ing Technology, Vol. 35, No. 1-2, 2007, pp. 150-168. doi:10.1007/s00170- 006-0701-5
[9]	D. Y. Chao, “Improve-ment of Suboptimal Siphon- and FBM-Based Control Model of a Well-Known S3PR,” to appear in IEEE Transactions on Automation Science and Engineering, Vol. 8, 2011.
[10]	Y.-Y. Shih and D. Chao, “Sequence of Control in S3PMR,” Computer Journal, Vol. 53, No. 10, December 2010, pp. 1691-1703. doi:10.1093/comjnl/bxp081
[11]	D. Chao and G. J. Liu, “A Simple Suboptimal Siphon- Based Control Model of a Well-Known S3PR,” Asian Journal of Control, December 2010. http://onlinelibrary. wiley.com/doi/10.1002/asjc.292/full
[12]	D. Y. Chao, “Com-putation of Elementary Siphons in Petri Nets for Deadlock Con-trol,” Computer Journal, Vol. 49, No. 4, 2006, pp. 470-479. doi:10.1093/comjnl/bxl019
[13]	D. Y. Chao, “A Graphic-Algebraic Computation of Elementary Siphons of BS3PR,” Journal of Information Science and Engineering, Vol. 23, No. 6, 2007, pp. 1817-1831.
[14]	D. Y. Chao, “Incremental Approach to Computation of Elementary Siphons for Arbitrary S3PR,” IEE Proceedings Control Theory & Applications, Vol. 2, No. 2, 2007, pp. 168-179.