应用控制变迁的柔性制造系统死锁控制策略
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摘要
不同于目前许多文献中基于添加控制库所的死锁预防策略,本文提出了控制变迁方程(CTE)的概念和相应的基于添加控制变迁(CT)的死锁控制策略(DCP).通过分析存在死锁的原网(N0, M0)的可达图(RG),该DCP求解出所有死锁标识(DM).基于CTE,构造出所需的控制变迁.然后,对每个DM添加相应的CT,进而消除了原网(N_0, M_0)中的死锁标识,得到了活性受控网系统(N~?, M~?).通过理论分析和相关算例的应用,该DCP的正确性和有效性得到了验证.此外,该DCP获取的活性受控网系统(N~?, M~?)可达数目与原网(N_0, M_0)是相同的,即最大可达数(MRN).
Unlike the deadlock prevention policies by adding control places(CPs) in most existing literature, this paper proposes a concept of control transition equation(CTE) and the corresponding deadlock control policy(DCP) by adding control transitions(CTs). By analyzing the reachability graph(RG) of an original net(N_0, M_0) with deadlocks, all deadlock markings(DMs) are found by this DCP. The desired CTs are constructed on the basis of the proposed CTE. Accordingly,the corresponding CT is added to each DM in order to make all DMs in the original net(N_0, M_0) eliminated. So a live controlled system(N~?, M~?) is obtained. The correctness and efficiency of the proposed DCP is verified via the theoretical analysis and the relevant examples in the existing literature. Moreover, the reachable number of the live controlled system(N~?, M~?) obtained by the proposed DCP is the same as that of the original net(N_0, M_0), i. e., maximally reachable number(MRN).
Unlike the deadlock prevention policies by adding control places(CPs) in most existing literature, this paper proposes a concept of control transition equation(CTE) and the corresponding deadlock control policy(DCP) by adding control transitions(CTs). By analyzing the reachability graph(RG) of an original net(N_0, M_0) with deadlocks, all deadlock markings(DMs) are found by this DCP. The desired CTs are constructed on the basis of the proposed CTE. Accordingly,the corresponding CT is added to each DM in order to make all DMs in the original net(N_0, M_0) eliminated. So a live controlled system(N~?, M~?) is obtained. The correctness and efficiency of the proposed DCP is verified via the theoretical analysis and the relevant examples in the existing literature. Moreover, the reachable number of the live controlled system(N~?, M~?) obtained by the proposed DCP is the same as that of the original net(N_0, M_0), i. e., maximally reachable number(MRN).
引文
[1]LI Z W,ZHOU M C.Deadlock resolution in automated manufacturing systems.A Novel Petri Net Approach.London,UK:Springer,2009.
[2] LI Z W, WU N Q, ZHOU M C. Deadlock control of automated manufacturing systems based on Petri nets:a literature review. IEEE Transactions on Systems, Man, and Cybernetics, Part C, 2012, 42(4):437–462.
[3] LI Shaoyong, XIAO Xingda, CAI Ying, et al. A two-stage deadlock control policy with maximally reachable number for ordinary Petri nets. Control Theory&Applications, 2017, 34(2):243–250.(李绍勇,肖兴达,蔡颖,等.普通Petri网最大可达数的两段式死锁控制策略.控制理论与应用, 2017, 34(2):243–250.)
[4] HUANG Y S, PAN Y L, SUN P J. Transition-based deadlock detection and recovery policy for fmss using graph technique. ACM Transactions on Embedded Computing Systems, 2013, 12(1):1–13.
[5] CHEN Y F, LI Z W. Design of a maximally permissive livenessenforcing supervisor with compressed supervisory structure for flexible manufacturing systems. Automatica, 2011, 47(5):1028–1034.
[6] CHAO D Y. A new optimal policy for a well-known S3PR. International Journal of Production Research, 2012, 50(22):1–13.
[7] HUANG B, ZHOU M C, ZHANG G X. Synthesis of Petri net supervisors for FMS via redundant constraint elimination. Automatica,2015, 61(6):156–163.
[8] LI S Y, LI Z W. Solving siphons with the minimal cardinality in Petri nets and its applications to deadlock control. International Journal of Production Research, 2012, 50(22):6203–6218.
[9] UZAM M, ZHOU M C. An improved iterative synthesis method for liveness enforcing supervisors of flexible manufacturing systems. International Journal of Production Research, 2006, 44(10):1987–2030.
[10] LI Shaoyong, AN Aimin, CAI Ying, et al. A deadlock control policy for a subclass of Petri nets G-system. Control Theory&Applications,2013, 30(11):1429–1436.(李绍勇,安爱民,蔡颖,等. Petri网的子类G-system网的死锁控制策略.控制理论与应用, 2013, 30(11):1429–1436.)
[11] LI S Y, AN A M, WU H M, et al. Policy to cope with deadlocks and livelocks for flexible manufacturing systems using the max′-controlled new smart siphons. IET Control Theory and Applications,2014, 8(16):1607–1616.
[12] CHEN Y F, LI Z W, ZHOU M C. Behaviorally optimal and structurally simple liveness-enforcing supervisors of flexible manufacturing systems. IEEE Transactions on Systems, Man, and Cybernetics,Part A, 2012, 42(3):615–629.
[13] PARK J, REVELIOTIS S A. Deadlock avoidance in sequential resource allocation systems with multiple resource acquisitions and fle-xible routings. IEEE Transactions on Automatic Control, 2001,46(10):1572–1583.
[14] ZHONG C F, LI Z W. A deadlock prevention approach for flexible manufacturing systems without complete siphon enumeration of their Petri net models. Engineering with Computers, 2009, 25(11):269–278.
[15] INA:Integrated Net Analyzer, a tool package for analysis of Petri nets.Version 2.2, http://www.informatik.hu-berlin.de/starke/ina. html,2002.
[2] LI Z W, WU N Q, ZHOU M C. Deadlock control of automated manufacturing systems based on Petri nets:a literature review. IEEE Transactions on Systems, Man, and Cybernetics, Part C, 2012, 42(4):437–462.
[3] LI Shaoyong, XIAO Xingda, CAI Ying, et al. A two-stage deadlock control policy with maximally reachable number for ordinary Petri nets. Control Theory&Applications, 2017, 34(2):243–250.(李绍勇,肖兴达,蔡颖,等.普通Petri网最大可达数的两段式死锁控制策略.控制理论与应用, 2017, 34(2):243–250.)
[4] HUANG Y S, PAN Y L, SUN P J. Transition-based deadlock detection and recovery policy for fmss using graph technique. ACM Transactions on Embedded Computing Systems, 2013, 12(1):1–13.
[5] CHEN Y F, LI Z W. Design of a maximally permissive livenessenforcing supervisor with compressed supervisory structure for flexible manufacturing systems. Automatica, 2011, 47(5):1028–1034.
[6] CHAO D Y. A new optimal policy for a well-known S3PR. International Journal of Production Research, 2012, 50(22):1–13.
[7] HUANG B, ZHOU M C, ZHANG G X. Synthesis of Petri net supervisors for FMS via redundant constraint elimination. Automatica,2015, 61(6):156–163.
[8] LI S Y, LI Z W. Solving siphons with the minimal cardinality in Petri nets and its applications to deadlock control. International Journal of Production Research, 2012, 50(22):6203–6218.
[9] UZAM M, ZHOU M C. An improved iterative synthesis method for liveness enforcing supervisors of flexible manufacturing systems. International Journal of Production Research, 2006, 44(10):1987–2030.
[10] LI Shaoyong, AN Aimin, CAI Ying, et al. A deadlock control policy for a subclass of Petri nets G-system. Control Theory&Applications,2013, 30(11):1429–1436.(李绍勇,安爱民,蔡颖,等. Petri网的子类G-system网的死锁控制策略.控制理论与应用, 2013, 30(11):1429–1436.)
[11] LI S Y, AN A M, WU H M, et al. Policy to cope with deadlocks and livelocks for flexible manufacturing systems using the max′-controlled new smart siphons. IET Control Theory and Applications,2014, 8(16):1607–1616.
[12] CHEN Y F, LI Z W, ZHOU M C. Behaviorally optimal and structurally simple liveness-enforcing supervisors of flexible manufacturing systems. IEEE Transactions on Systems, Man, and Cybernetics,Part A, 2012, 42(3):615–629.
[13] PARK J, REVELIOTIS S A. Deadlock avoidance in sequential resource allocation systems with multiple resource acquisitions and fle-xible routings. IEEE Transactions on Automatic Control, 2001,46(10):1572–1583.
[14] ZHONG C F, LI Z W. A deadlock prevention approach for flexible manufacturing systems without complete siphon enumeration of their Petri net models. Engineering with Computers, 2009, 25(11):269–278.
[15] INA:Integrated Net Analyzer, a tool package for analysis of Petri nets.Version 2.2, http://www.informatik.hu-berlin.de/starke/ina. html,2002.
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