Design of Liveness-Enforcing Supervisors for Flexible Manufacturing Systems Using Petri Nets

Abstract

This correspondence develops a methodology to synthesize supervisors for a special class of Petri nets that can well model many flexible manufacturing systems. In our previous work, siphons in a Petri net are divided into elementary and dependent ones on the condition that all emptiable minimal siphons are computed. In this research, a mixed integer programming (MIP)-based deadlock detection technique is used to find some, in general not all, minimal siphons in a plant model without complete siphon enumeration. For each siphon found, depending on its noncontrollability, a monitor is added such that it is invariant-controlled. Our siphon control method guarantees that no emptiable control-induced siphon is generated due to the addition of the monitors. The siphon control process proceeds iteratively until there is no unmarked siphon in the supervisor of a plant model. Compared with the existing approaches, the novel deadlock prevention policy can usually lead to a structurally simple liveness-enforcing supervisor by adding only a small number of monitors and arcs. More importantly, complete siphon enumeration is avoided. A practical flexible manufacturing system (FMS) example is utilized to illustrate the proposed methods.Index Terms-Deadlock prevention, elementary siphon, flexible manufacturing system (FMS), Petri net.

Theory of Regions for Control Synthesis without Computing Reachability Graph

“…The places P 1 , P 2 and P 5 represent the central conveyor, while the annex conveyor is modeled by P 3 . Its capacity is modeled by P 4 . If the piece to manufacture is not in compliance with recommended standard, it will be placed in the waste conveyor represented by the place P 6 .…”

“…Indeed, PNs can be analyzed by linear algebras. They play an important role in addressing the deadlock problems and analyzing the behavior of flexible manufacturing system [2][3][4][5]; a flexible manufacturing system can be defined as a computer controlled production system capable of processing a variety of part types. The flexibility of the system gives manufacturing firms an advantage in a quickly changing manufacturing environment [6].…”

An elementary siphon-based deadlock control algorithm with maximally reachable number to cope with deadlock problems in ordinary Petri nets

“…[7][8][9][10][11][12][13] In the past two decades, the research of resolving deadlocks has become the hot issues and many scholars and researchers have achieved a lot of remarkable results in theory and practical applications. 6,[14][15][16][17][18][19][20][21][22][23][24][25][26] Because of their own characteristics to easily and concisely describe the concurrent execution of processes and the reasonable distribution of shared resources in an FMS, 12,27 Petri nets have been widely used to model, analyze, and simulate the static and dynamic behaviors of an FMS, especially in deadlock problems. Using Petri nets, three policies, called deadlock detection and recovery (DDR), 1,28 deadlock avoidance (DA), 1,4 and deadlock prevention (DP) 6,10,[23][24][25][28][29][30][31][32] , respectively, are developed to cope with deadlock problems in FMSs.…”

A Computationally Improved Optimal Solution for Deadlocked Problems of Flexible Manufacturing Systems Using Theory of Regions

“…Their analysis methods used for deadlock prevention in FMS include structural analysis and reachability graphs. Deadlock prevention and avoidance schemes have been developed for controlling FMS [3][4][5][6][7][8] by using the former. In particular, deadlock prevention problems are solved using the concept of siphons [3][4][5][6] .…”

“…Deadlock prevention and avoidance schemes have been developed for controlling FMS [3][4][5][6][7][8] by using the former. In particular, deadlock prevention problems are solved using the concept of siphons [3][4][5][6] . Li & Zhou propose an elementary siphon control policy (ESCP) to reduce the redundant siphons to obtain structurally simpler controllers [9][10] .…”