A Deadlock Prevention Policy for Flexible Manufacturing Systems Modeled With Petri Nets Using Structural Analysis

Abstract

This paper derives an iterative deadlock prevention policy for systems of simple sequential processes with resources (S 3 PRs) based on structural analysis, which consists of two stages. The first stage is called siphons control. Strict minimal siphons (SMSs) in an S 3 PR net are computed and control places are added by imposing P-invariants associated with the complementary sets of the SMSs, which restricts no legal system behavior. The original resource places are removed and the newly added control places are regarded as resource places, resulting in a new net, which needs to add control places for its SMSs if deadlocks persist. Repeat this step until a new net without SMSs is obtained. Then, an S 4 PR, called the first-controlled net, is obtained by integrating all added control places into the original net. The second stage, called non-maxmarked siphons control, is performed in an iterative way if the system is not live yet. At each iteration, a mixed integer linear programming (MILP) problem is formulated to compute a non-max-marked siphon, and a control place is added for the siphon to the first-controlled net, resulting in an augmented net. The iteration is executed until a final-augmented net generates no new non-max-marked siphon. In general, based on the above two stages, this paper can obtain a supervisor with more behavior permissiveness compared to the previous studies. Moreover, an optimal supervisor can be found if a first-controlled net has no nonmax-marked siphon, implying that the second stage is not necessary. Finally, some examples are provided to demonstrate the proposed policy.INDEX TERMS Flexible manufacturing system, Petri net, deadlock prevention policy, structural analysis.

Modeling and Control for Deadlock-Free Operation of Single-Arm Cluster Tools With Concurrently Processing Multiple Wafer Types via Petri Net

“…Since Petri nets can deal with concurrent activities for discrete manufacturing system, they have been widely applied for modeling [Reisig, 1985;Murata, 1989;Bai et al, 2016;Zhang et al, 2017 andZhang et al, 2018], deadlock analysis [Suzuki and Murata, 1983;Li et al, 2008 andKaroui et al, 2018;Chen et al, 2019;and Duan et al, 2019], and supervisor control [Liu et al, 2013 andWang et al, 2015;and Zhang et al, 2015]. This work adopts them to model cluster tools for wafer fabrication.…”

Optimal Scheduling of Flexible Manufacturing System Using Improved Lion-Based Hybrid Machine Learning Approach

“…Duan et al [28] developed an iterative deadlock mitigation strategy dependent on structural analysis for devices with simple sequential processes with resources (S3PR), which comprised two stages. The first stage was called the ''control of the siphons.''…”

“…Bio-inspired meta-heuristics are becoming popular for various applications these days [39], [40]. MILP [28] can solve various kinds of complex problems; however, it does not provide an optimal solution to large problems, and its computational time is long. In contrast to other conventional methods, the iterative intersection approach [29] is effective and efficient and does not require ILPPs (integer linear programming problem) to be solved.…”

A Customized Supervisory Control Approach for Flexible Manufacturing Systems

“…Liu et al proposed a deadlock controller synthesis approach for FMS based on the max-controllability of siphons [31]. Duan et al proposed a deadlock prevention policy for FMS modeled by Petri nets using structural analysis [32]. Du et al proposed a control policy for the robust deadlock avoidance and control of FMS [33].…”