Control Algorithm Using a Revised MIP Method to Deal with Livelocks in S~4R of Petri Nets
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摘要
Livelocks, like deadlocks, can result in serious results in running process of flexible manufacturing systems(FMSs). Current deadlock control policies(DCPs) based on mixed integer programming(MIP) cannot detect siphons that cause and cope with livelocks in Petri nets. This study proposes a revised mixed integer programming(RMIP) method to directly solve the new smart siphons(NSSs) associated with livelocks in a system of sequential systems with shared resources(S~4 R), a typical subclass of generalized Petri net models. Accordingly,the solved NSSs are max'-controlled by adding the corresponding control places(CPs). As a result, an original S~4 R system with livelocks can be converted into the live controlled Petri net system. The related theoretical analysis and an example are given to demonstrate the proposed RMIP and the corresponding control algorithm(CA).
Livelocks, like deadlocks, can result in serious results in running process of flexible manufacturing systems(FMSs). Current deadlock control policies(DCPs) based on mixed integer programming(MIP) cannot detect siphons that cause and cope with livelocks in Petri nets. This study proposes a revised mixed integer programming(RMIP) method to directly solve the new smart siphons(NSSs) associated with livelocks in a system of sequential systems with shared resources(S~4 R), a typical subclass of generalized Petri net models. Accordingly,the solved NSSs are max'-controlled by adding the corresponding control places(CPs). As a result, an original S~4 R system with livelocks can be converted into the live controlled Petri net system. The related theoretical analysis and an example are given to demonstrate the proposed RMIP and the corresponding control algorithm(CA).
Livelocks, like deadlocks, can result in serious results in running process of flexible manufacturing systems(FMSs). Current deadlock control policies(DCPs) based on mixed integer programming(MIP) cannot detect siphons that cause and cope with livelocks in Petri nets. This study proposes a revised mixed integer programming(RMIP) method to directly solve the new smart siphons(NSSs) associated with livelocks in a system of sequential systems with shared resources(S~4 R), a typical subclass of generalized Petri net models. Accordingly,the solved NSSs are max'-controlled by adding the corresponding control places(CPs). As a result, an original S~4 R system with livelocks can be converted into the live controlled Petri net system. The related theoretical analysis and an example are given to demonstrate the proposed RMIP and the corresponding control algorithm(CA).
引文
[1] LI Z W, ZHOU M C. Deadlock resolution in automated manufacturing systems:A novel Petri net approach[M]. Berlin:Springer-Verlag, 2009.
[2] CHAO D Y. Max’-controlled siphons for liveness of S3PGR2[J]. IET Control Theory and Application,2007, 1(4):933-936.
[3] LIU G Y, LI Z W. General mixed integer programming-based liveness test for system of sequential systems with shared resources nets[J]. IET Control Theory and Application, 2010, 4(12):2867-2878.
[4] LI S Y, LI Z W. Solving siphons with the minimal cardinality in Petri nets and its applications to deadlock control[J]. International Journal of Production Research, 2012, 50(22):6203-6218.
[5] LI S Y, AN A M, WANG Y, et al. Design of liveness-enforcing supervisors with simpler structures for deadlock-free operations in flexible manufacturing systems using necessary siphons[J]. Journal of Intelligent Manufacturing, 2013, 24(6):1157-1173.
[6] LI Z W, ZHOU M C. On siphon computation for deadlock control in a class of Petri nets[J]. IEEE Transaction on Systems, Man, and Cybernetics, 2008, 38(3):667-679.
[7] ZHONG C F, LI Z W. A deadlock prevention approach for flexible manufacturing systems without complete siphon enumeration of their Petri net models[J]. Engineering with Computers, 2009, 25(3):269-278.
[8] LI Z W, LIANG J W, LU Y, et al. A deadlock prevention method for FMS with multiple resource acquisitions[C]//8th International Conference on Control,Automation, Robotics and Vision. Kunming, China:IEEE, 2004:2117-2122.
[9] LI Z W, WANG A R, WEI N. Liveness-enforcing supervisors for flexible manufacturing systems with multiple resource acquisitions[C]//International Conference on Networking, Sensing and Control. Ft. Lauderdale, FL, USA:IEEE, 2006:710-714.
[10] ZHONG C F, LI Z W. Self-liveness of a class of Petri net models for flexible manufacturing systems[J]. IET Control Theory and Applications, 2010, 4(3):403-410.
[11] LI S Y, LI Z W. Structure reduction of livenessenforcing Petri nets using mixed integer programming[J]. Asian Journal of Control, 2012, 14(2):384-399.
[2] CHAO D Y. Max’-controlled siphons for liveness of S3PGR2[J]. IET Control Theory and Application,2007, 1(4):933-936.
[3] LIU G Y, LI Z W. General mixed integer programming-based liveness test for system of sequential systems with shared resources nets[J]. IET Control Theory and Application, 2010, 4(12):2867-2878.
[4] LI S Y, LI Z W. Solving siphons with the minimal cardinality in Petri nets and its applications to deadlock control[J]. International Journal of Production Research, 2012, 50(22):6203-6218.
[5] LI S Y, AN A M, WANG Y, et al. Design of liveness-enforcing supervisors with simpler structures for deadlock-free operations in flexible manufacturing systems using necessary siphons[J]. Journal of Intelligent Manufacturing, 2013, 24(6):1157-1173.
[6] LI Z W, ZHOU M C. On siphon computation for deadlock control in a class of Petri nets[J]. IEEE Transaction on Systems, Man, and Cybernetics, 2008, 38(3):667-679.
[7] ZHONG C F, LI Z W. A deadlock prevention approach for flexible manufacturing systems without complete siphon enumeration of their Petri net models[J]. Engineering with Computers, 2009, 25(3):269-278.
[8] LI Z W, LIANG J W, LU Y, et al. A deadlock prevention method for FMS with multiple resource acquisitions[C]//8th International Conference on Control,Automation, Robotics and Vision. Kunming, China:IEEE, 2004:2117-2122.
[9] LI Z W, WANG A R, WEI N. Liveness-enforcing supervisors for flexible manufacturing systems with multiple resource acquisitions[C]//International Conference on Networking, Sensing and Control. Ft. Lauderdale, FL, USA:IEEE, 2006:710-714.
[10] ZHONG C F, LI Z W. Self-liveness of a class of Petri net models for flexible manufacturing systems[J]. IET Control Theory and Applications, 2010, 4(3):403-410.
[11] LI S Y, LI Z W. Structure reduction of livenessenforcing Petri nets using mixed integer programming[J]. Asian Journal of Control, 2012, 14(2):384-399.