Controllability of Strongly and Weakly Dependent Siphons under Disturbanceless Control
ABSTRACT
Li and Zhou propose to add monitors Vs to elementary siphons S only while controlling the rest of dependent siphons - important for large systems but far from being maximally permissive. The control policy for weakly dependent siphons (WDS) is rather conservative due to some negative terms in the controllability. We show that this is no longer true as can be shown that it has the same controllability as that for strongly dependent siphons.
Li and Zhou propose to add monitors Vs to elementary siphons S only while controlling the rest of dependent siphons - important for large systems but far from being maximally permissive. The control policy for weakly dependent siphons (WDS) is rather conservative due to some negative terms in the controllability. We show that this is no longer true as can be shown that it has the same controllability as that for strongly dependent siphons.
Cite this paper
nullD. Chao, K. Wu, J. Chen and M. Lee, "Controllability of Strongly and Weakly Dependent Siphons under Disturbanceless Control," Intelligent Control and Automation, Vol. 2 No. 4, 2011, pp. 310-319. doi: 10.4236/ica.2011.24036.
nullD. Chao, K. Wu, J. Chen and M. Lee, "Controllability of Strongly and Weakly Dependent Siphons under Disturbanceless Control," Intelligent Control and Automation, Vol. 2 No. 4, 2011, pp. 310-319. doi: 10.4236/ica.2011.24036.
References
[1] D. Y. Chao, “Computation of Elementary Siphons in Petri Nets for Deadlock Control,” The Computer Journal, Vol. 49, No. 4, 2006, pp. 470-479. [2] 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. [3] 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. [4] D. Y. Chao, “Technical Note-Reaching More States for Control of FMS,” International Journal of Production Research, Vol. 48, No. 4, 2008, pp. 1217-1220. doi:10.1080/00207540701747210 [5] D. Y. Chao, “Comments on Deadlock Prevention and Avoidance in FMS: A Petri Net Based Approach,” The International Journal of Advanced Manufacturing Technology, Vol. 39, No. 3-4, 2008, pp. 317-318. doi:10.1007/s00170-007-1190-x [6] D. Y. Chao, “An Incremental Approach to Extract Minimal Bad Siphons,” Journal of Information Science and Engineering, Vol. 23, No. 1, 2007, pp. 203-214. [7] D. Y. Chao, “Revised Dependent Siphons,” The International Journal of Advanced Manufacturing Technology, Vol. 43, No. 1, 2009, pp. 182-188, doi:10.1007/s00170-008-1684-1 [8] D. Y. Chao, “Conservative Control Policy for Weakly Dependent Siphons in S3PR Based on Elementary Siphons,” IET Control Theory & Applications, Vol. 4, No. 7, 2010, pp. 1298-1302. [9] D. Y. Chao, “Structure of Weakly Dependent Siphons,” Unpublished Manuscript. [10] D. Y. Chao, “Improvement of Suboptimal Siphon- and FBM-Based Control Model of a Well-Known S3PR,” IEEE Transactions on Automation Science and Engineering, Vol. 8, No. 2, 2011, pp. 404-411. doi:10.1109/TASE.2010.2088120 [11] J. Ezpeleta, J. M. Colom and J. Martinez, “A Petri Net Based Deadlock Prevention Policy for Flexible Manufacturing Systems,” IEEE Transactions on Robotics and Automation, Vol. 11, No. 2, 1995, pp. 173-184. doi:10.1109/70.370500 [12] M. V. Iordache, J. O. Moody and P. J. Antsaklis, “A Method for the Synthesis of Liveness Enforcing Supervisors in Petri Nets,” Proceedings of the 2001 American Control Conference, Arlington, 25-27 June 2001, pp. 4943-4948. [13] Z. W. Li and M. C. Zhou, “Elementary Siphons of Petri Nets and Their Application to Deadlock Prevention in Flexible Manufacturing Systems,” IEEE Transactions on Systems, Man, and Cybernetics Part A: Systems and Humans, Vol. 34, No. 1, 2004, pp. 38-51. [14] Z. W. Li and M. C. Zhou, “Clarifications on the Definitions of Elementary Siphons in Petri Nets,” IEEE Transactions on Systems, Man, and Cybernetics Part A: Systems and Humans, Vol. 35, No. 6, 2006, pp. 1227-1229. [15] M. Uzam and M. C. Zhou, “An Iterative Synthesis Approach to Petri Net Based Deadlock Prevention Policy for Flexible Manufacturing Systems,” IEEE Transactions on Systems, Man, and Cybernetics Part A: Systems and Humans, Vol. 37, No. 3, 2007, pp. 362-371. [16] Z. W. Li and M. C. Zhou, “Control of Elementary and Dependent Siphons in Petri Nets and Their Application,” IEEE Transactions on Systems, Man, and Cybernetics Part A: Systems and Humans, Vol. 38, No. 1, 2008, pp. 133-148. [17] Z. W. Li and M. C. Zhou, “On Controllability of Dependent Siphons for Deadlock Prevention in Generalized Petri Nets,” IEEE Transactions on Systems, Man, and Cybernetics Part A: Systems and Humans, Vol. 38, No. 2, 2008, pp. 369-384. doi:10.1109/TSMCA.2007.914741 [18] Z. W. Li and M. C. Zhou, “On Siphon Computation for Deadlock Control in a Class of Petri Net,” IEEE Transactions on Systems, Man, and Cybernetics Part A: Systems and Humans, Vol. 38, No. 3, 2008, pp. 667-679. [19] L. Piroddi, R. Cordone and I. Fumagalli, “Selective Siphon Control for Deadlock Prevention in Petri Nets,” IEEE Transactions on Systems, Man, and Cybernetics Part A: Systems and Humans, Vol. 38, No. 6, 2008, pp. 1337-1348. [20] L. Piroddi, R. Cordone and I. Fumagalli, “Combined Siphon and Marking Generation for Deadlock Prevention in Petri Nets,” IEEE Transactions on Systems, Man, and Cybernetics Part A: Systems and Humans, Vol. 39, No. 3, 2009, pp. 650-661. [21] Y. Y. Shih and D. Y. Chao, “Sequence of Control in S3PMR,” Computer Journal, Vol. 53, No. 10, 2010, pp. 1691-1703. doi:10.1093/comjnl/bxp081 [22] M. Uzam, Z. W. Li and M. C. Zhou, “Identification and Elimination of Redundant Control Places in Petri Net Based Liveness Enforcing Supervisors of FMS,” The International Journal of Advanced Manufacturing Technology, Vol. 35, No. 1-2, 2007, pp. 150-168. doi:10.1007/s00170-006-0701-5 [23] 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.
[1] D. Y. Chao, “Computation of Elementary Siphons in Petri Nets for Deadlock Control,” The Computer Journal, Vol. 49, No. 4, 2006, pp. 470-479. [2] 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. [3] 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. [4] D. Y. Chao, “Technical Note-Reaching More States for Control of FMS,” International Journal of Production Research, Vol. 48, No. 4, 2008, pp. 1217-1220. doi:10.1080/00207540701747210 [5] D. Y. Chao, “Comments on Deadlock Prevention and Avoidance in FMS: A Petri Net Based Approach,” The International Journal of Advanced Manufacturing Technology, Vol. 39, No. 3-4, 2008, pp. 317-318. doi:10.1007/s00170-007-1190-x [6] D. Y. Chao, “An Incremental Approach to Extract Minimal Bad Siphons,” Journal of Information Science and Engineering, Vol. 23, No. 1, 2007, pp. 203-214. [7] D. Y. Chao, “Revised Dependent Siphons,” The International Journal of Advanced Manufacturing Technology, Vol. 43, No. 1, 2009, pp. 182-188, doi:10.1007/s00170-008-1684-1 [8] D. Y. Chao, “Conservative Control Policy for Weakly Dependent Siphons in S3PR Based on Elementary Siphons,” IET Control Theory & Applications, Vol. 4, No. 7, 2010, pp. 1298-1302. [9] D. Y. Chao, “Structure of Weakly Dependent Siphons,” Unpublished Manuscript. [10] D. Y. Chao, “Improvement of Suboptimal Siphon- and FBM-Based Control Model of a Well-Known S3PR,” IEEE Transactions on Automation Science and Engineering, Vol. 8, No. 2, 2011, pp. 404-411. doi:10.1109/TASE.2010.2088120 [11] J. Ezpeleta, J. M. Colom and J. Martinez, “A Petri Net Based Deadlock Prevention Policy for Flexible Manufacturing Systems,” IEEE Transactions on Robotics and Automation, Vol. 11, No. 2, 1995, pp. 173-184. doi:10.1109/70.370500 [12] M. V. Iordache, J. O. Moody and P. J. Antsaklis, “A Method for the Synthesis of Liveness Enforcing Supervisors in Petri Nets,” Proceedings of the 2001 American Control Conference, Arlington, 25-27 June 2001, pp. 4943-4948. [13] Z. W. Li and M. C. Zhou, “Elementary Siphons of Petri Nets and Their Application to Deadlock Prevention in Flexible Manufacturing Systems,” IEEE Transactions on Systems, Man, and Cybernetics Part A: Systems and Humans, Vol. 34, No. 1, 2004, pp. 38-51. [14] Z. W. Li and M. C. Zhou, “Clarifications on the Definitions of Elementary Siphons in Petri Nets,” IEEE Transactions on Systems, Man, and Cybernetics Part A: Systems and Humans, Vol. 35, No. 6, 2006, pp. 1227-1229. [15] M. Uzam and M. C. Zhou, “An Iterative Synthesis Approach to Petri Net Based Deadlock Prevention Policy for Flexible Manufacturing Systems,” IEEE Transactions on Systems, Man, and Cybernetics Part A: Systems and Humans, Vol. 37, No. 3, 2007, pp. 362-371. [16] Z. W. Li and M. C. Zhou, “Control of Elementary and Dependent Siphons in Petri Nets and Their Application,” IEEE Transactions on Systems, Man, and Cybernetics Part A: Systems and Humans, Vol. 38, No. 1, 2008, pp. 133-148. [17] Z. W. Li and M. C. Zhou, “On Controllability of Dependent Siphons for Deadlock Prevention in Generalized Petri Nets,” IEEE Transactions on Systems, Man, and Cybernetics Part A: Systems and Humans, Vol. 38, No. 2, 2008, pp. 369-384. doi:10.1109/TSMCA.2007.914741 [18] Z. W. Li and M. C. Zhou, “On Siphon Computation for Deadlock Control in a Class of Petri Net,” IEEE Transactions on Systems, Man, and Cybernetics Part A: Systems and Humans, Vol. 38, No. 3, 2008, pp. 667-679. [19] L. Piroddi, R. Cordone and I. Fumagalli, “Selective Siphon Control for Deadlock Prevention in Petri Nets,” IEEE Transactions on Systems, Man, and Cybernetics Part A: Systems and Humans, Vol. 38, No. 6, 2008, pp. 1337-1348. [20] L. Piroddi, R. Cordone and I. Fumagalli, “Combined Siphon and Marking Generation for Deadlock Prevention in Petri Nets,” IEEE Transactions on Systems, Man, and Cybernetics Part A: Systems and Humans, Vol. 39, No. 3, 2009, pp. 650-661. [21] Y. Y. Shih and D. Y. Chao, “Sequence of Control in S3PMR,” Computer Journal, Vol. 53, No. 10, 2010, pp. 1691-1703. doi:10.1093/comjnl/bxp081 [22] M. Uzam, Z. W. Li and M. C. Zhou, “Identification and Elimination of Redundant Control Places in Petri Net Based Liveness Enforcing Supervisors of FMS,” The International Journal of Advanced Manufacturing Technology, Vol. 35, No. 1-2, 2007, pp. 150-168. doi:10.1007/s00170-006-0701-5 [23] 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.