Deadlock Control in Generalized Petri Nets

This chapter proposes a number of deadlock prevention polices for a class of generalized Petri nets, namely G-systems, which is usually considered to be the most generalized Petri nets that can model Flexible Manufacturing Systems (FMSs) with machining, assembly, and disassembly operations. First, a deadlock prevention policy based on elementary siphons theory is presented, which indicates that structural complexity and behavioral permissiveness can be improved effectively. In order to reduce the computational complexity, a Mixed Integer Programming (MIP)-based deadlock detection approach is proposed, then two deadlock control polices combined with MIP method are introduced. Finally, comparison among deadlock prevention policies reported in this chapter is done in terms of structural complexity, behavioral permissiveness, and computational complexity of the resulting supervisor through a typical case study. Importantly, future research directions related to this area are presented at the end of this chapter.

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Petri Net Based Deadlock Prevention Approach for Flexible Manufacturing Systems

Reconfigurable Embedded Control Systems ◽

10.4018/978-1-60960-086-0.ch015 ◽

2011 ◽

pp. 416-433 ◽

Cited By ~ 1

Author(s):

Chunfu Zhong ◽

Zhiwu Li

Keyword(s):

Petri Nets ◽

Petri Net ◽

Flexible Manufacturing ◽

Mixed Integer Linear Programming ◽

Flexible Manufacturing Systems ◽

Manufacturing Systems ◽

Iteration Step ◽

Mixed Integer ◽

Deadlock Prevention ◽

Prevention Approach

In flexible manufacturing systems, deadlocks usually occur due to the limited resources. To cope with deadlock problems, Petri nets are widely used to model these systems. This chapter focuses on deadlock prevention for flexible manufacturing systems that are modeled with S4R nets, a subclass of generalized Petri nets. The analysis of S4R leads us to derive an iterative deadlock prevention approach. At each iteration step, a non-max-controlled siphon is derived by solving a mixed integer linear programming. A monitor is constructed for the siphon such that it is max-controlled. Finally, a liveness-enforcing Petri net supervisor can be derived without enumerating all the strict minimal siphons.

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Deadlock Prevention Policy with Behavioral Optimality or Suboptimality Achieved by the Redundancy Identification of Constraints and the Rearrangement of Monitors

Discrete Dynamics in Nature and Society ◽

10.1155/2015/579623 ◽

2015 ◽

Vol 2015 ◽

pp. 1-15 ◽

Cited By ~ 7

Author(s):

Liang Hong ◽

YiFan Hou ◽

JunFeng Jing ◽

AnRong Wang ◽

Dmitry A. Litvin

Keyword(s):

Flexible Manufacturing ◽

Manufacturing Systems ◽

Mixed Integer ◽

Deadlock Prevention ◽

Second Phase ◽

Deadlock Detection ◽

Prevention Policy ◽

Prevention Method ◽

Two Phases ◽

Redundancy Identification

This work develops an iterative deadlock prevention method for a special class of Petri nets that can well model a variety of flexible manufacturing systems. A deadlock detection technique, called mixed integer programming (MIP), is used to find a strict minimal siphon (SMS) in a plant model without a complete enumeration of siphons. The policy consists of two phases. At the first phase, SMSs are obtained by MIP technique iteratively and monitors are added to the complementary sets of the SMSs. For the possible existence of new siphons generated after the first phase, we add monitors with their output arcs first pointed to source transitions at the second phase to avoid new siphons generating and then rearrange the output arcs step by step on condition that liveness is preserved. In addition, an algorithm is proposed to remove the redundant constraints of the MIP problem in this paper. The policy improves the behavioral permissiveness of the resulting net and greatly enhances the structural simplicity of the supervisor. Theoretical analysis and experimental results verify the effectiveness of the proposed method.

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Global Supervisory Structure for Decentralized Systems of Flexible Manufacturing Systems Using Petri Nets

Processes ◽

10.3390/pr7090595 ◽

2019 ◽

Vol 7 (9) ◽

pp. 595 ◽

Cited By ~ 2

Author(s):

Muhammad Bashir ◽

Liang Hong

Keyword(s):

Computational Complexity ◽

Petri Nets ◽

Petri Net ◽

Flexible Manufacturing ◽

Flexible Manufacturing Systems ◽

Manufacturing Systems ◽

Structural Complexity ◽

Decentralized Systems ◽

The Cost ◽

Global Controller

Decentralized supervisory structure has drawn much attention in recent years to address the computational complexity in designing supervisory structures for large Petri net model. Many studies are reported in the paradigm of automata while few can be found in the Petri net paradigm. The decentralized supervisory structure can address the computational complexity, but it adds the structural complexity of supervisory structure. This paper proposed a new method of designing a global controller for decentralized systems of a large Petri net model for flexible manufacturing systems. The proposed method can both reduce the computational complexity by decomposition of large Petri net models into several subnets and structural complexity by designing a global supervisory structure that can greatly reduce the cost at the implementation stage. Two efficient algorithms are developed in the proposed method. Algorithm 1 is used to compute decentralized working zones from the given Petri net model for flexible manufacturing systems. Algorithm 2 is used to compute the global controller that enforces the liveness to the decentralized working zones. The ring assembling method is used to reconnect and controlled the working zones via a global controller. The proposed method can be applied to large Petri nets size and, in general, it has less computational and structural complexity. Experimental examples are presented to explore the applicability of the proposed method.

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Deadlock Prevention for Automated Manufacturing Systems with Uncontrollable and Unobservable Transitions

Formal Methods in Manufacturing Systems - Advances in Civil and Industrial Engineering ◽

10.4018/978-1-4666-4034-4.ch015 ◽

2013 ◽

pp. 367-387

Author(s):

Meng Qin

Keyword(s):

Petri Nets ◽

Petri Net ◽

Flexible Manufacturing ◽

Flexible Manufacturing Systems ◽

Manufacturing Systems ◽

Deadlock Prevention ◽

Sufficient Condition ◽

Prevention Policy ◽

Automated Manufacturing Systems ◽

Partial Observability

Many deadlock prevention policies on the basis of Petri nets dealing with deadlock problems in flexible manufacturing systems exist. However, most of them do not consider uncontrollable and unobservable transitions. This chapter solves deadlock problems in Petri nets with uncontrollable and unobservable transitions. A sufficient condition is developed to decide whether an existing deadlock prevention policy is still applicable in a Petri net with uncontrollable and unobservable transitions, when the policy itself is developed under the assumption that all the transitions are controllable and observable. Moreover, the author develops a deadlock prevention policy to design liveness-enforcing supervisors for a class of Petri nets with partial observability and controllability of transitions. Furthermore, a sufficient condition to decide the existence of a monitor to enforce a liveness constraint is developed.

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Smart deadlock prevention policy for flexible manufacturing systems using Petri nets

IET Control Theory and Applications ◽

10.1049/iet-cta:20070399 ◽

2009 ◽

Vol 3 (3) ◽

pp. 362-374 ◽

Cited By ~ 25

Author(s):

Z. Li ◽

M. Shpitalni

Keyword(s):

Petri Nets ◽

Flexible Manufacturing ◽

Flexible Manufacturing Systems ◽

Manufacturing Systems ◽

Deadlock Prevention ◽

Prevention Policy

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An Efficient Siphon-Based Deadlock Prevention Policy for a Class of Generalized Petri Nets

Discrete Dynamics in Nature and Society ◽

10.1155/2016/8219424 ◽

2016 ◽

Vol 2016 ◽

pp. 1-12 ◽

Cited By ~ 4

Author(s):

YiFan Hou ◽

Mi Zhao ◽

Ding Liu ◽

Liang Hong

Keyword(s):

Petri Nets ◽

Flexible Manufacturing ◽

Flexible Manufacturing Systems ◽

Manufacturing Systems ◽

Synthesis Method ◽

Deadlock Avoidance ◽

Deadlock Prevention ◽

Prevention Policy ◽

Supervisor Synthesis ◽

Resource Allocation Systems

We propose a new deadlock prevention policy for an important class of resource allocation systems (RASs) that appear in the modeling of flexible manufacturing systems (FMSs). The model of this class in terms of generalized Petri nets is, namely, S4PR. On the basis of recent structural analysis results related to the elementary siphons in generalized Petri nets on one hand and an efficient deadlock avoidance policy proposed for the class of conjunctive/disjunctive (C/D) RASs on the other hand, we show how one can generate monitors to be added to a net system such that all its strict minimal siphons aremax′-controlled and no insufficiently marked siphon is generated. Thereby, a new, simple, and more permissive liveness-enforcing supervisor synthesis method for S4PR is established.

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