A deadlock prevention approach for a class of timed Petri nets using elementary siphons

To solve the problem of deadlock prevention for timed Petri nets, an effective deadlock prevention policy based on elementary siphons is proposed in this paper. Without enumerating reachable markings, deadlock prevention is achieved by adding monitors for elementary siphons, increasing control depth variables when necessary, and removing implicit, liveness-restricted and redundant control places. The final supervisor is live. First, a timed Petri net is stretched into a stretched Petri net (SPN). Unchanging the system performance, each transition in the SPN has a unit delay time. Then the siphon-control-based approach is applied. Monitors computed according to the marking constraints are added to the SPN model to ensure all strict minimal siphons in the net invariant-controlled. A liveness-enforcing supervisor with simple structure can be obtained by reverting the SPN into a TdPN.

[1]  MengChu Zhou,et al.  A deadlock control method using elementary siphons of Petri nets , 2003, SMC'03 Conference Proceedings. 2003 IEEE International Conference on Systems, Man and Cybernetics. Conference Theme - System Security and Assurance (Cat. No.03CH37483).

[2]  José Manuel Colom,et al.  Implicit places in net systems , 1999, Proceedings 8th International Workshop on Petri Nets and Performance Models (Cat. No.PR00331).

[3]  Jiacun Wang,et al.  Timed Petri Nets: Theory and Application , 1998 .

[4]  Alessandro Giua,et al.  Observer-based state-feedback control of timed Petri nets with deadlock recovery , 2004, IEEE Transactions on Automatic Control.

[5]  Altug Iftar,et al.  Supervisory controller design for timed Petri nets , 2006, 2006 IEEE/SMC International Conference on System of Systems Engineering.

[6]  Kamel Barkaoui,et al.  On Liveness and Controlled Siphons in Petri Nets , 1996, Application and Theory of Petri Nets.

[7]  Jiacun Wang,et al.  Timed Petri Nets , 1998, The Kluwer International Series on Discrete Event Dynamic Systems.

[8]  MengChu Zhou,et al.  Control of Elementary and Dependent Siphons in Petri Nets and Their Application , 2008, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[9]  MengChu Zhou,et al.  Clarifications on the Definitions of Elementary Siphons in Petri Nets , 2006, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[10]  L. Recalde,et al.  Improving the decision power of rank theorems , 1997, 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation.

[11]  F. D. J Bowden,et al.  A brief survey and synthesis of the roles of time in petri nets , 2000 .

[12]  MengChu Zhou,et al.  Elementary siphons of Petri nets and their application to deadlock prevention in flexible manufacturing systems , 2004, IEEE Trans. Syst. Man Cybern. Part A.

[13]  Latif Salum.  Petri nets and time modelling , 2008 .

[14]  MengChu Zhou,et al.  Identification and elimination of redundant control places in petri net based liveness enforcing supervisors of FMS , 2007 .

[15]  Feng Chu,et al.  Deadlock analysis of Petri nets using siphons and mathematical programming , 1997, IEEE Trans. Robotics Autom..

[16]  Latif Salum.  New perspectives in time(d) Petri nets and their analysis , 2003, Proceedings of 2003 IEEE Conference on Control Applications, 2003. CCA 2003..

[17]  ZhiWu Li,et al.  A deadlock prevention approach using elementary siphons for a class of Petri nets , 2004, 2004 IEEE International Conference on Systems, Man and Cybernetics (IEEE Cat. No.04CH37583).

[18]  Robin P. Fawcett,et al.  Theory and application , 1988 .

[19]  Hoda A. ElMaraghy,et al.  Deadlock prevention and avoidance in FMS: A Petri net based approach , 1998 .

[20]  Zhiwu Li,et al.  Deadlock Resolution in Automated Manufacturing Systems: A Novel Petri Net Approach , 2009 .

[21]  Javier Martínez,et al.  A Petri net based deadlock prevention policy for flexible manufacturing systems , 1995, IEEE Trans. Robotics Autom..

[22]  MuDer Jeng,et al.  A deadlock prevention policy for flexible manufacturing systems using siphons , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[23]  MengChu Zhou,et al.  Modeling, Simulation, and Control of Flexible Manufacturing Systems - A Petri Net Approach , 1999, Series in Intelligent Control and Intelligent Automation.

[24]  Tadao Murata,et al.  Petri nets: Properties, analysis and applications , 1989, Proc. IEEE.

[25]  Gang Xu,et al.  Reachability Analysis of Real-Time Systems Using Time Petri Nets , 2000 .