Liveness and boundedness analysis of Petri net synthesis

2014 ◽  
Vol 24 (5) ◽  
Author(s):  
CHUANLIANG XIA
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Flexible Manufacturing ◽  
Manufacturing System ◽  
Flexible Manufacturing System ◽  
Dynamic Properties ◽  
Synthesis Method ◽  
Sufficient Conditions ◽  
Sufficient And Necessary Conditions ◽  
Petri Net Synthesis

We provide motivation for and then study the synthesis of Petri nets. Synthesis can avoid the state exploration problem by guaranteeing correctness for the Petri net. We propose conditions to be imposed on a synthesis shared pb-type subnet for systems specified in Petri nets that ensure the preservation of the liveness and boundedness structural properties. Specifically, we propose a group of sufficient conditions, or both sufficient and necessary conditions, for liveness preservation and boundedness preservation. Possible applications of this synthesis method are illustrated through an example in the form of a flexible manufacturing system. These results are useful for studying the static and dynamic properties of Petri nets for analysing the properties of large complex systems.

Extraction of elementary siphons in a class of generalized Petri nets using graph theory

2014 ◽  
Vol 31 (2) ◽  
pp. 331-352 ◽  
Author(s):  
YiFan Hou ◽  
ZhiWu Li ◽  
Mi Zhao ◽  
Ding Liu
Keyword(s):  
Graph Theory ◽  
Petri Nets ◽  
Petri Net ◽  
Flexible Manufacturing ◽  
Design Methodology ◽  
Manufacturing System ◽  
Flexible Manufacturing System ◽  
Structural Complexity ◽  
Compact Set ◽  
Content Type

Purpose – Siphon-based deadlock control in a flexible manufacturing system (FMS) suffers from the problems of computational and structural complexity since the number of siphons grows exponentially with respect to the size of its Petri net model. In order to reduce structural complexity of a supervisor, a set of elementary siphons derived from all strict minimal siphons (SMS) is explicitly controlled. The purpose of this paper is through fully investigating the structure of a class of generalized Petri nets, WS3PR, to compute all SMS and a compact set of elementary siphons. Design/methodology/approach – Based on graph theory, the concepts of initial resource weighted digraphs and restricted subgraphs are proposed. Moreover, the concept of augmented siphons is proposed to extend the application of elementary siphons theory for WS3PR. Consequently, the set of elementary siphons obtained by the proposed method is more compact and well suits for WS3PR. Findings – In order to demonstrate the proposed method, an FMS example is presented. All SMS and elementary siphons can be derived from initial resource weighted digraphs. Compared with those obtained by the method in Li and Zhou, the presented method is more effective to design a structural simple liveness-enforcing supervisor for WS3PR. Originality/value – This work presents an effective method of computing SMS and elementary siphons for WS3PR. Monitors are added for the elementary siphons only, and the controllability of every dependent siphon is ensured by properly supervising its elementary ones. A same set of elementary siphons can be admitted by different WS3PR with isomorphic structures.

Petri Net Supervisory Method for Linear Constraints and its Applications to Flexible Manufacturing Systems

2013 ◽  
pp. 20-35
Author(s):  
Jiliang Luo
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Flexible Manufacturing ◽  
Flexible Manufacturing Systems ◽  
Manufacturing Systems ◽  
Manufacturing System ◽  
Flexible Manufacturing System ◽  
Linear Constraints ◽  
Supervisor Synthesis ◽  
Synthesis Procedure

An algorithm is proposed to equivalently transform original linear constraints on Petri nets, where the uncontrollable subnets are forward-concurrent free nets, into admissible ones. Consequently, this algorithm can be used to design both efficient and optimal supervisors for enforcing linear constraints on Petri nets since the problem on how to enforce admissible constraints has been well solved. Further, the supervisor synthesis procedure is presented using this algorithm. Lastly, it is illustrated by an example where an optimal supervisor is designed for a flexible manufacturing system.

Update to "Extraction of elementary siphons in a class of generalized Petri nets using graph theory" [Engineering Computations (2014) 31(2)331-352]

2016 ◽  
Vol 33 (2) ◽  
Author(s):  
YiFan Hou ◽  
Mi Zhao
Keyword(s):  
Graph Theory ◽  
Petri Nets ◽  
Petri Net ◽  
Flexible Manufacturing ◽  
Design Methodology ◽  
Manufacturing System ◽  
Flexible Manufacturing System ◽  
Type Design ◽  
Published Paper

Purpose The purpose of this paper is to correct some mistakes in recently published paper (Hou, Y.F., Li, Z.W., Zhao, M., and Liu, D. (2014) “Extraction of elementary siphons in a class of generalized Petri nets using graph theory”, Engineering Computations, Vol.31, No.2, pp.331-352). Design/methodology/approach In (Hou et al., 2014), based on the concepts of initial resource weighted digraphs and restricted subgraphs, a structurally simple liveness-enforcing supervisor for WS3PR was designed. To demonstrate the effectiveness and applicability of the proposed method, a flexible manufacturing system (FMS) example was presented. However, there are some mistakes in the considered example. The derived monitors were incorrect, which caused the result that the final controlled net system is not live. Findings In order to correct the errors in (Hou et al., 2014), a liveness-enforcing Petri nets supervisor with revised monitors for the considered example was redesigned by applying the method in (Hou et al., 2014). Originality/value This paper corrected the mistakes in (Hou et al., 2014). Consequently, a liveness-enforcing Petri net supervisor is redesigned.

scholarly journals Compute Optimization of Petri Net Controllers Using the Algebraic Method

2019 ◽  
Vol 9 (13) ◽  
pp. 2633
Author(s):  
Sadok Rezig ◽  
Sadok Turki ◽  
Nidhal Rezg
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Flexible Manufacturing ◽  
Manufacturing System ◽  
Flexible Manufacturing System ◽  
Discrete Event ◽  
Algebraic Approach ◽  
Control Policy ◽  
Algebraic Method ◽  
Control Synthesis

This study attempted to calculate an optimal Petri net supervisor able to respect the control specifications imposed for a flexible manufacturing system. There are several theories around the control synthesis of discrete event systems. Unfortunately, these methods are very sensitive to the combinatorial explosion of states in the generated graph, especially when the complexity of the system increases. It is therefore necessary to move towards new ways based on formal methods allowing the synthesis of a supervisor. In this work, we propose an algebraic approach using the theory of regions. Our main contribution is to design a set of Petri net controllers based on the properties of Petri nets and not on reachability graph generation for bounded Petri nets. This will decrease significantly the production cost of the manufacturing system, since the computation burden of the supervisor is reduced. Our control policy was applied to a flexible manufacturing system implemented in our laboratory. Comparisons with previous studies using CPLEX software are provided in order to illustrate the effectiveness of our proposed method.

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