Deadlock control policy for a class of automated
manufacturing systems with key resources
Huixia Liu
State Key Laboratory of Industrial Control Technology &
Institute of Cyber-Systems and Control
Zhejiang University
Hangzhou, China
School of Information and Electrical Engineering
Ludong University
Yantai, China
huixialiu@126.com
Weimin Wu
State Key Laboratory of Industrial Control Technology &
Institute of Cyber-Systems and Control
Zhejiang University
Hangzhou, China
wmwu@iipc.zju.edu.cn
Abstract—For automated manufacturing systems (AMSs)
without center resources that are one-unit resources shared by
two or more maximal perfect resource transition circuits, the
optimal Petri net-based polynomial complexity deadlock
avoidance policies are synthesized in our previous work. Based
on Petri net models of AMSs, this work focuses on the deadlock
control problem for AMSs with center resources. First, the
concepts of key resources and key transitions are presented. It
can prove that key transitions can bring AMSs with key
resources into secondary-deadlock, i.e. the controlled Petri nets
of AMSs with key resources are not live. Second, for a class of
AMSs with key resources, secondary-deadlock can be
characterized by maximal perfect control transition circuits
(MPCT-circuits) that are saturated at a reachable marking of the
controlled system. Then, by adding a control place and related
arcs to each MPCT-circuit, secondary-deadlock can be
prevented. Thereby, a deadlock control policy for a class of
AMSs with center resources is synthesized. Finally, a few
examples are provided to demonstrate the presented policy and
used to compare them with the state-of-the-art methods.
Keywords—Automated manufacturing systems, deadlock
control, Petri net
I. INTRODUCTION
An automated manufacturing system (AMS) is a
computer-controlled manufacturing system containing
multiple concurrent flows of job processes, and often exploits
shared resources to reduce the production cost. The
introduction of heavy resource sharing can increase flexibility,
but may lead to deadlock when two or more jobs keep waiting
indefinitely for the other jobs in a production sequence to
release resources. Deadlocks can reduce productivity
drastically or lead to the entire stagnancy. Therefore, it is
necessary to develop an efficient deadlock control policy to
guarantee that deadlocks never happen in AMSs [2], [6].
Petri nets are a powerful tool for modeling and analyzing
FMSs [10]. Based on Petri nets, three types of approaches are
developed for AMSs, i.e., deadlock detection and recovery [5],
deadlock prevention [1], [3]-[4], [7]-[9], [15], and deadlock
avoidance [11]-[12], [14].
This work focuses on deadlock prevention methods. A
number of such methods characterize deadlocks in terms of
deadlock structures of Petri nets, such as siphons and
resource-transition circuits [13]. Ezpeleta et al. described an
AMS using a special class of Petri nets named by systems of
simple sequential processes with resources (S
3
PRs) [1]. They
proved that a marked S
3
PR net is live if and only if each
minimal siphon has at least one token at each reachable
marking from the initial markings. Huang et al proposed
another prevention policy for S
3
PRs without complete
computation of siphons [4]. This policy is an iterative
approach and consists of two main stages. The first stage is
known as siphon control, and the second stage is known as
augmented siphon control.
Xing et al utilized resource transition circuits (RT-circuits)
to characterize deadlock states in S
3
PRs [12]. An RT-circuit is
a circuit that only contains resource places and transitions. For
a marked S
3
PR without center resources, Xing et al derived an
optimal Petri-net-based polynomial complexity deadlock
avoidance policy. For a marked S
3
PR with center resources,
by reducing it and applying the design of an optimal deadlock
avoidance policy to the reduced one, a suboptimal deadlock
avoidance policy is established, and its computation is of
polynomial complexity. Based on the concept of RT-circuits,
Han et al proposed the concept of crucial resources and
control transition circuits and established a two-stage deadlock
prevention policy for S
3
PRs with crucial resources [3]. In [15],
You et al presented a liveness-enforcing Petri net supervisor
for a class of S
3
PRs with B-ξ-resources.
By enlightening the concept of crucial resources and
control transition circuits, the concepts of key resources and
key transitions are first presented. It proves that key transitions
can result S
3
PRs with key resources into secondary-deadlock,
i.e. the controlled Petri nets of S
3
PRs with key resources are
not live. Second, for a class of S
3
PRs with key resources,
secondary-deadlock can be characterized by maximal perfect
control transition circuits (MPCT-circuits) that are saturated at
This work was supported in part by the National Nature Science
Foundation of China under Grants 61304052, 61374066 and 61273152, in par
y the Outstanding Young Research Award Fund of Shandong Province unde
Grant BS2013DX005, in part by China Post-Doctoral Science Foundation o
the 55
th
Grant Program under Grant 2014M551741, in part by the Doctoral
Fund of Ludong University under Grant LY2013008.
Proceedings of 2015 IEEE 12th International Conference on Networking, Sensing and Control
Howard Civil Service International House, Taipei, Taiwan, April 9-11, 2015
978-1-4799-8069-7/15/$31.00 ©2015 IEEE