A deadlock prevention approach for flexible manufacturing systems without complete siphon enumeration of their Petri net models

Siphons are very important in the analysis and control of deadlocks in a Petri net. However, it is quite time-consuming or even impossible to get the complete siphon enumeration of a Petri net. This paper focuses on the deadlock prevention problems in flexible manufacturing systems that are modeled...

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Bibliographic Details
Published in:Engineering with computers 2009-09, Vol.25 (3), p.269-278
Main Authors: Zhong, Chunfu, Li, Zhiwu
Format: Article
Language:English
Subjects:
CAE) and Design
Calculus of Variations and Optimal Control
Optimization
Classical Mechanics
Computation
Computer Science
Computer-Aided Engineering (CAD
Control
Enumeration
Flexible manufacturing systems
Iterative methods
Linear programming
Math. Applications in Chemistry
Mathematical and Computational Engineering
Mathematical models
Monitors
Original Article
Siphons
Studies
Supervisors
Systems Theory
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Summary:Siphons are very important in the analysis and control of deadlocks in a Petri net. However, it is quite time-consuming or even impossible to get the complete siphon enumeration of a Petri net. This paper focuses on the deadlock prevention problems in flexible manufacturing systems that are modeled with S 4 PR, a general class of Petri nets. The analysis of S 4 PR leads us to characterize deadlock situations in terms of insufficiently marked siphons. The method proposed in this paper is an iterative approach. At each iteration, a non-max-marked siphon is computed by solving a mixed integer linear programming problem. Then the siphon is max-marked through a P -invariant by adding a monitor place. This process is carried out until no non-max-marked siphon can be found in the net. As a result all the siphons in the net are max-controlled. Then the net becomes live. Without computing all the siphons, a monitor-based liveness-enforcing Petri net supervisor can be found with more permissive behavior. A number of flexible manufacturing examples are used to demonstrate the proposed methods.
ISSN:0177-0667
1435-5663
DOI:10.1007/s00366-008-0122-1