Skip to main content
SpringerLink
Log in

Deadlock control of flexible manufacturing systems via invariant–controlled elementary siphons of petri nets

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

Effective resolution for deadlock problems plays an important role in the operation of automated flexible manufacturing systems (FMS). Based on P-invariants and elementary siphons of Petri nets, a deadlock prevention policy is developed for a special class of Petri nets that can well model many FMS. Siphons in a plant net model are divided into elementary and dependent ones. For each elementary siphon, a monitor is added to the plant model such that the siphon is invariant-controlled. Our method guarantees that no emptiable control-induced siphon is generated due to the addition of the monitors. When all elementary siphons are controlled, the controllability of a dependent siphon is ensured by properly setting the control depth variables of its related elementary siphons. An FMS example is utilized to illustrate the proposed methods.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Abdallah IB, ElMaraghy HA (1998) Deadlock prevention and avoidance in FMS: a Petri net based approach. Int J Adv Manuf Tech 14:704–715, Sept

    Article  Google Scholar 

  2. Banaszak ZA, Krogh BH (1990) Deadlock avoidance in flexible manufacturing systems with concurrently competing process flows. IEEE Trans Robot Automat 6:724–734, Dec

    Article  Google Scholar 

  3. Barkaoui K, Abdallah IB (1995) A deadlock prevention method for a class of FMS. In Proc IEEE Int Conf Syst Man Cybern, Vancouver, BC, Canada, pp 4119–4124

  4. Barkaoui K, Chaoui A, Zouari B (1997) Supervisory control of discrete event systems based on structure theory of Petri nets. In Proc IEEE Int Conf Syst Man Cybern, Orlando, Florida, USA, pp 3750–3755

  5. Cho H, Kumaran TK, Wysk RA (1995) Graph-theoretic deadlock detection and resolution for flexible manufacturing systems. IEEE Trans Robot Automat 11:413–421, June

    Article  Google Scholar 

  6. Chu F, Xie XL (1997) Deadlock analysis of Petri nets using siphons and mathematical programming. IEEE Trans Robot Automat 13:793–804, Dec

    Article  Google Scholar 

  7. Desel J, Esparza J (1995) Free choice petri nets. Cambridge: Cambridge University Press, UK

    MATH  Google Scholar 

  8. Ezpeleta J, Colom JM, Martinez J (1995) A Petri net based deadlock prevention policy for flexible manufacturing systems. IEEE Trans Robot Automat 11:173–184, Apr

    Article  Google Scholar 

  9. Ezpeleta J, Tricas F, Garcia-Valles F, Colom J (2002) A banker’s solution for deadlock avoidance in FMS with flexible routing and multisource states. IEEE Trans Robot Automat 18:621–625, Aug

    Article  Google Scholar 

  10. Ezpeleta J, Recalde L (2004) A deadlock avoidance approach for non-sequential resource allocation systems. IEEE Trans Syst Man Cybern A 34:93–101, Jan

    Article  Google Scholar 

  11. Fanti MP, Zhou MC (2004) Deadlock control methods in automated manufacturing systems. IEEE Trans Syst Man Cybern A 34:5–22, Jan

    Article  Google Scholar 

  12. Fanti MP, Maione B, Mascolo S, Turchiano A (1997) Event-based feedback control for deadlock avoidance in flexible production system. IEEE Trans Robot Automat 13:347–363, June

    Article  Google Scholar 

  13. Ghaffari A, Nidhal N, Xie XL (2003) Design of a live and maximally permissive Petri net controller using the theory of regions. IEEE Trans Robot Automat 19:137–141, Feb

    Article  Google Scholar 

  14. Hsieh FS, Chang SC (1994) Dispatching-driven deadlock avoidance controller synthesis for flexible manufacturing systems. IEEE Trans Robot Automat 10:196–209, Apr

    Article  Google Scholar 

  15. Huang YS, Jeng MD, Xie XL, Chung SL (2001) Deadlock prevention policy based on Petri nets and siphons. Int J Prod Res 39:283–305

    Article  MATH  Google Scholar 

  16. Iordache MV, Moody JO, Antsaklis PJ (2002) Synthesis of deadlock prevention supervisors using Petri nets. IEEE Trans Robot Automat 18:59–68, Feb

    Article  Google Scholar 

  17. Jeng MD, Xie XL (1999) Analysis of modularly composed nets by siphons. IEEE Trans Syst Man Cybern A 29:399–406, July

    Article  Google Scholar 

  18. Kumaran TK, Chang W, Cho H, Wysk RA (1994) A structural approach for deadlock detection and, avoidance, and resolution in flexible manufacturing systems. Int J Prod Res 32:2361–2379, Oct

    Article  Google Scholar 

  19. Lautenbach K (1987) Linear algebraic calculation of deadlocks and traps. In: Voss K, Genrich HJ, Rozenberg G (eds) Concurrency and Nets. Springer, Berlin Heidelberg New York, pp 315–336

    Google Scholar 

  20. Lautenbach K, Ridder H (1994) Liveness in bounded Petri nets which are covered by T-invariants. In: Valette R (ed) Proc. 13th Int. Conf. Application and Theory of Petri Nets 1994, Lecture Notes in Computer Science, vol. 815, Springer, Berlin Heidelberg New York, pp 358–375

    Google Scholar 

  21. Lawley MA, Reveliotis SA, Ferreira PM (1998) A correct and scalable deadlock avoidance policy for flexible manufacturing systems. IEEE Trans Robot Automat 14:796–809, Oct

    Article  Google Scholar 

  22. Li ZW, Zhou MC (2004) Elementary siphons of Petri nets and their application to deadlock prevention in flexible manufacturing systems. IEEE Trans Syst Man Cybern A 34:38–51, Jan

    Article  Google Scholar 

  23. Li ZW, Hu HS, Jeng MD (2004) An algorithm for elementary siphons in PN. In Proc. IEEE Int. Conf. Networking, Sensing, and Control, Taipei, Taiwan, March 21–25, pp 519–524

  24. Li ZW, Zhou MC (2006) Clarifications on the definition of elementary siphons of Petri nets. To appear in IEEE Trans Syst Man Cybern A

  25. Murata T (1989) Petri nets: properties, analysis, and applications. Proc IEEE 77:541–580, Apr

    Article  Google Scholar 

  26. Park J, Reveliotis SA (2001) Deadlock avoidance in sequential resource allocation systems with multiple resource acquisitions and flexible routings. IEEE Trans Automat Contr 46:1572–1583, Oct

    Article  MATH  MathSciNet  Google Scholar 

  27. Reveliotis SA (2003) On the siphon-based characterization of liveness in sequential resource allocation systems. In: van der Aalst WMP, Best E (eds) Proc. Int. Conf. Application and Theory of Petri Nets 2003, Lecture Notes in Computer Science, vol. 2679, Springer, Berlin Heidelberg New York, pp 241–255

    Google Scholar 

  28. Reveliotis SA, Ferreira PM (1996) Deadlock avoidance policies for automated manufacturing cells. IEEE Trans Robot Automat 12:845–857, Dec

    Article  Google Scholar 

  29. Reveliotis SA, Lawely MA, Ferreira PM (1997) Polynomial-complexity deadlock avoidance policies for sequential resource allocation systems. IEEE Trans Automat Contr 42:1344–1357, Oct

    Article  MATH  Google Scholar 

  30. Schrijver A (1998) Theory of linear and integer programming. Wiley, New York, pp 259

    MATH  Google Scholar 

  31. Starke PH (1992) INA: Integrated Net Analyzer. Handbuch

  32. Tricas F, Valles FG, Colom JM, Ezpeleta J (2002) An iterative method for deadlock prevention in FMSs. In: Boel R, Stremersch G (eds) Discrete Event Systems: Analysis and Control, Kluwer Academic Publishers, Boston, pp 139–148

    Google Scholar 

  33. Viswanadham N, Narahari Y, Johnson T (1990) Deadlock prevention and deadlock avoidance in flexible manufacturing systems using Petri net models. IEEE Trans Robot Automat 6:713–723, Dec

    Article  Google Scholar 

  34. Wysk RA, Yang NS, Joshi S (1991) Detection of deadlocks in flexible manufacturing systems. IEEE Trans Robot Automat 7:853–859, Dec

    Article  Google Scholar 

  35. Xing KY, Hu BS, Chen HX (1996) Deadlock avoidance policy for Petri-net modelling of flexible manufacturing systems with shared resources. IEEE Trans Automat Contr 41:289–295, Feb

    Article  MATH  MathSciNet  Google Scholar 

  36. Yamalidou E, Moody JO, Antsaklis PJ (1994) Feedback control of Petri nets based on place invariants. Automatica 32:15–28

    Article  MathSciNet  Google Scholar 

  37. Zhou MC, DiCesare F (1991) Parallel and sequential mutual exclusions for Petri net modelling for manufacturing systems. IEEE Trans Robot Automat 7:515–527, Aug

    Article  Google Scholar 

  38. Zhou MC, Venkatesh K (1998) Modelling, simulation and control of flexible manufacturing systems: a petri net approach. World Scientific, Singapore

    Google Scholar 

Download references

Acknowledgments

The authors would like to thank the National Nature Science Foundation of China under Grant No 60474018, the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry of China, under Grant No 2004-527, and the Youth Workstation Foundation of Xidian University, China, under Grant No 2002-04-001.

Author information

Authors and Affiliations

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

    Zhiwu Li & Na Wei

Authors
  1. Zhiwu Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Na Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhiwu Li.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, Z., Wei, N. Deadlock control of flexible manufacturing systems via invariant–controlled elementary siphons of petri nets. Int J Adv Manuf Technol 33, 24–35 (2007). https://doi.org/10.1007/s00170-006-0452-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-006-0452-3

Keywords

Search

Navigation