On Algebraic Identification of Critical States for Deadlock Control in Automated Manufacturing Systems Modeled With Petri Nets

Dajiang Sun,Mohamed Abdel Fattah Sharaf,Yufeng Chen,Mohammed A El-Meligy,Naiqi Wu,Zhiwu Li

doi:10.1109/access.2019.2936052

Abstract

Petri nets are an important and popular tool to model and analyze deadlocks in automated manufacturing systems. The state space of a Petri net model can be divided into two disjoint parts: a live-zone and a dead-zone. A first-met bad marking (FBM) is a marking in the dead-zone, representing the very first entry from the live-zone to the dead-zone, and the calculation of FBMs to a large extent contributes to the complexity of designing optimal liveness-enforcing supervisors. Most existing studies have to fully enumerate the reachable markings of a Petri net model to obtain the FBMs, which exacerbates the computational overheads. This paper first explores a variation mechanism of calculating FBMs with respect to the resource capacity in a class of S 3 PR (Systems of Simple Sequential Processes with Resources) from the structural analysis perspective, which contains a ξ-resource. More generally, for the class of S 3 PR with an η-resource as defined in this paper, the FBMs can be calculated in an algebraic way by a customized structural analysis technique without enumerating all the reachable markings. Finally, the variation mechanism of calculating FBMs is revealed for these considered classes of Petri net models. Examples are given to demonstrate the proposed method.

Highlights

Over the passed two decades, the development of science and technology has reached an unprecedented height
System blocking caused by deadlocks may lead to catastrophic consequences and enormous economic losses, which should be considered when designing a supervisory controller for automated manufacturing systems (AMSs)
For the class of Petri nets, η-S3PR, we show that the first-met bad marking (FBM) can be directly computed in an algebraic way, without enumerating all reachable markings

Summary

INTRODUCTION

Over the passed two decades, the development of science and technology has reached an unprecedented height. According to Section IV.C in [36], in an η-S3PR with a ξ -resource, there exists a marking M in DZ, for all S ∈ , M (S) = 0, where S ∈ is a strict minimal siphon These kinds of markings are called spurious-safe markings whose set is denoted by DZ ∗. If strict minimal siphon S3 = {p3, p6, ra, rη, rb} ∪ Prm ∪ Prn ∪ Pru ∪ Prq is emptied, the markings in MFBM have been analyzed in the case that. For-loop structure (Lines 8–11) means concatenating marking vectors of n HR-circuits which directly obtains FBMs. Note that the number of siphons in a Petri net, even in an S3PR, is exponential with respect to its structural size.

IDENTIFICATION OF FBMS IN AN η-S3PR WITHOUT ξ -RESOURCES

CONCLUSION