Extension of Elementary Siphons in a Class of Generalized Petri Nets

Abstract:

This work presents an effective method on computing strict minimal siphons and elementary siphons based on the concept of initial resource weighted digraphs for a class of generalized Petri nets, namely WS³PR. In addition, the controllability conditions of dependent siphons are developed. Monitors are added for the elementary siphons only and the controllability of a dependent siphon is ensured by properly supervising its elementary siphons. Through fully investigating the structure of the net, especially weight information, the set of elementary siphons obtained by the proposed method is more compact and well suits for WS³PR. An example is illustrated to demonstrate the proposed method.

• Periodical: Applied Mechanics and Materials (Volumes 284-287)
• Pages: 2238-2243
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.284-287.2238
• Online since: January 2013
• Authors: Yi Fan Hou, Zhi Wu Li, Mi Zhao, Ding Liu
• Keywords: Deadlock Prevention, Elementary Siphon, Flexible Manufacturing System, Petri Net

References

[1] M.P. Fanti and M.C. Zhou: Deadlock control methods in automated manufacturing systems, IEEE Trans. Syst. Man Cybern. A, Vol. 34 (2004), No. 1, pp.5-22.

DOI: 10.1109/tsmca.2003.820590

[2] J. Ezpeleta and L. Recalde: A deadlock avoidance approach for nonsequential resource allocation systems, IEEE Trans. Syst. Man Cybern. A, Vol. 34 (2004), No. 1, pp.93-101.

DOI: 10.1109/tsmca.2003.820575

[3] N.Q. Wu and M.C. Zhou: Modeling and deadlock avoidance of automated manufacturing systems with multiple automated guided vehicles, IEEE Trans. Syst. Man Cybern. B, Vol. 35(2005), No. 6, pp.1193-1202.

DOI: 10.1109/tsmcb.2005.850141

[4] Z.W. Li and M.C. Zhou: Elementary siphons of Petri nets and their application to deadlock prevention in flexible manufacturing systems, IEEE Trans. Syst. Man Cybern. A, Vol. 34 (2004), No. 1, pp.38-51.

DOI: 10.1109/tsmca.2003.820576

[5] Z.W. Li and M.Z. Zhou: Two-stage method for synthesizing liveness-enforcing supervisors for flexible manufacturing systems using Petri nets, IEEE Trans. Ind. Inf., Vol. 2 (2006), No. 4, pp.313-325.

DOI: 10.1109/tii.2006.885185

[6] Z.W. Li, M.C. Zhou and M.D. Jeng: A maximally permissive deadlock prevention policy for FMS based on Petri net siphon control and the theory of regions, IEEE Transactions on Autom. Sci. Eng., Vol. 5 (2008), No. 1, pp.182-188.

DOI: 10.1109/tase.2006.884674

[7] M. Zhao, Y.F. Hou and D. Liu: Liveness-enforcing supervisors synthesis for a class of generalized Petri nets based on two-stage deadlock control and mathematical programming, " Int. J. Control, Vol. 83 (2010), No. 10, p.2053-(2066).

DOI: 10.1080/00207179.2010.504785

[8] Z.W. Li and M.C. Zhou: Deadlock resolution in automated manufacturing systems: a novel Petri net approach, Springer, London (2009).

[9] D. Liu, Z.W. Li, and M.C. Zhou: Liveness of an extend S3PR, Automatica, Vol. 46(2010), No. 6, pp.1008-1018.

DOI: 10.1016/j.automatica.2010.03.011

[10] M. Zhao and Z.W. Li: Deadlock control for a class of generalized Petri net models of flexible manufacturing systems, Int. J. Prod. Res., Vol. 47(2009), No. 21, pp.6085-6107.

DOI: 10.1080/00207540802101945