Elementary Siphons of Petri Nets and Their Application to Deadlock Prevention in Flexible Manufacturing Systems (original) (raw)
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Deadlock Prevention for Flexible Manufacturing Systems via Controllable Siphon Basis of Petri Nets
IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2015
Siphons are a kind of special structural objects in a Petri net, and plays a key role in synthesizing a live Petri net controller for flexible manufacturing systems. In order to obtain a small size Petri net controller, this paper introduces the concept of a controllable siphon basis. It then proves that a live Petri net controller can be established by adding a control place and related arcs to each strict minimal siphon (SMS) in a controllable siphon basis. The initial markings of control places are determined by an integer linear program. The number of control places in the obtained controllers is the same as the number of SMSs in the controllable siphon basis, while the latter is no more than that of the activity places in a Petri net model. An algorithm for constructing a controllable siphon basis is proposed, and a new deadlock prevention policy based on it is established. A few examples are provided to demonstrate the proposed concepts and policy and used to compare them with the state-of-the-art methods. Index Terms-Discrete event systems, flexible manufacturing systems, integer linear program (ILP), Petri nets. I. INTRODUCTION A FLEXIBLE manufacturing system (FMS) handles multiple concurrent flows of job processes that can make different products at the same time, and often exploits shared
A Petri net based deadlock prevention policy for flexible manufacturing systems
IEEE Transactions on Robotics and Automation, 1995
In this paper we illustrate a compositional method for modeling the concurrent execution of working processes in flexible manufacturing systems (FMS) through a special class of Petri Nets that we call S 'PI?. In essence, this class is built from state machines sharing a set of places modeling the availability of system resources. The analysis of S ' P R leads us to characterize deadlock situations in terms of a zero marking for some structural objects called siphons. In order to prevent the system from deadlocks, we propose a policy for resource allocation based on the addition of new places to the net imposing restrictions that prevent the presence of unmarked siphons (direct cause of deadlocks). Finally, we present the application of this technique to a realistic FMS case.
A deadlock prevention policy for flexible manufacturing systems using siphons
Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164), 2001
In this paper, we present a new deadlock prevention algorithm for the class Petri nets. A new class of net that is extended from S 3 PR, called ES 3 PR where deadlocks are related to unmarked siphons. This method is an iterative approach by adding two kinds of control places called ordinary control place and weighted control place to the original model to prevent siphons from being unmarked. We have obtained the relation of the algorithm and the liveness and reversibility of the controlled net. Finally, a flexible manufacturing example is presented for illustrating the method.
Elementary Siphons of Petri Nets and Deadlock Control in FMS
For responsiveness, in the Petri nets theory framework deadlock prevention policies based elementary siphons control are often utilized to deal with deadlocks caused by the sharing of resources in flexible manufacturing system (FMS) which is developing the theory of efficient strict minimal siphons of an S3PR. Analyzer of Petri net models and their P-invariant analysis, and deadlock control are presented as tools for modelling, efficiency structure analysis, control, and investigation of the FMSs when different policies can be implemented for the deadlock prevention. We are to show an effective deadlock prevention policy of a special class of Petri nets namely elementary siphons. As well, both structural analysis and reachability graph analysis and simulation are used for analysis and control of Petri nets. This work is successfully applied Petri nets to deadlock analysis using the concept of elementary siphons, for design of supervisors of some supervisory control problems of FMS and simulation of Petri net tool with MATLAB.
Siphon-Based Deadlock Prevention Policy for Flexible Manufacturing Systems
IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, 2006
A siphon-based algorithm for deadlock prevention of a type of Petri nets called S 3 PMR, which is a subclass of S 3 PGR 2 , is presented in this correspondence. The proposed method is an iterative approach by adding two kinds of control places called ordinary control (OC) places and weighted control (WC) places to the original model to prevent siphons from being unmarked. An OC place with ordinary arcs, which optimally prevent a siphon from becoming unmarked, is employed whenever it is possible, and otherwise, the WC places that adopt a conservative policy of controlling the release of parts into the system are used. Furthermore, this algorithm is not only for the subclass Petri nets but also for S 3 PR, ES 3 PR, S 2 LSPR, and S 3 PGR 2 nets. The authors prove the liveness and reversibility of the controlled net, and hence establish the correctness of the deadlock prevention policy. Finally, numerical experiments indicate that the proposed policy appears to be more permissive than closely related approaches in the literature.
Deadlock control policy for a class of Petri nets without complete siphon enumeration
Siphons are special structures of a Petri net. Their number grows exponentially with the net size. Hence, the traditional siphon-based deadlock control policies have two problems, that is, generating very structurally complex supervisory controllers and requiring intractable computation efforts. This paper intends to use the newly proposed concept, elementary siphons, and a mixed integer programming (MIP) method to design structurally simple supervisory controllers and reduce the computational burden. This method is applicable to a class of Petri nets, System of Simple Sequential Processes with Resources that can well model a wide class of discrete manufacturing systems. Siphons are divided into elementary and dependent ones. The proposed policy consists of three stages: siphon control, control-induced siphon control, and the elimination of control-redundant monitors. First, a monitor (control place) is added for each elementary siphon such that it is invariant-controlled. Because of the addition of monitors to the plant model, control-induced siphons are possibly generated in the augmented net. Next, monitors are added to make control-induced siphons in the augmented net always marked sufficiently without generating new problematic siphons. A MIP technique is used to guarantee that no siphon is insufficiently marked. Finally, we systematically remove control-redundant monitors. Compared with previous work in the literature, the deadlock prevention policy developed in this paper can lead to a structurally simple liveness-enforcing Petri net supervisor with more permissive behaviour by adding only a small number of monitors and arcs. Moreover, complete siphon enumeration is avoided. A manufacturing system example is utilised to illustrate the proposed methods.
The International Journal of Advanced Manufacturing Technology, 2004
In a flexible manufacturing system (FMS) with multiple products, deadlocks can arise due to limited shared resources, such as machines, robots, buffers, fixtures etc. The development of efficient deadlock prevention policies, which can optimise the use of system resources, while preventing deadlocks from occurring, has long been an important issue to be addressed. In [1], an optimal deadlock prevention policy was proposed, based on the use of reachability graph (RG) analysis of the Petri net model (PNM) of a given FMS and the synthesis of a set of new net elements, namely places with initial marking and related arcs, to be added to the PNM, using the theory of regions. The policy proposed in [1] is optimal in the sense that it allows the maximal use of resources in the system according to the production requirements. For very big PNMs, the reachability graph of the PNMs becomes very large and the necessary computations to obtain an optimal deadlock prevention policy become more difficult. In this paper, we propose the use of the Petri net reduction approach to simplify very big PNMs so as to make necessary calculations easily in order to obtain an optimal deadlock prevention policy for FMSs. An example is provided for illustration.
Smart deadlock prevention policy for flexible manufacturing systems using Petri nets
IET Control Theory & Applications, 2009
Deadlocks are a highly undesired situation in automated production systems including flexible manufacturing systems. Based on a Petri net formalism, a novel deadlock prevention policy is proposed for a class of Petri nets, S 3 PR, by using an MIP-based deadlock detection method and elementary siphons of Petri nets. Deadlock prevention is achieved by synthesising a set of monitors that are added to the plant net model. The concept of dominated transitions is proposed, to which the output arcs of the monitors are led. The monitors are computed according to a set of elementary siphons in a plant net model, which is found by using an established algorithm in the literature. When compared with the existing policies, the proposed method leads to a liveness-enforcing Petri net supervisor with a small number of monitors but more permissive behaviour. Examples are used to demonstrate the proposed method.
Maximally Permissive Deadlock Prevention Controlled in FMSs Based on the Siphons Petri Nets
IEEE 2021 Inter. Seminar on Machine Learning, Optimization, and Data Science (ISMODE), Jakarta, Indonesia, IEEE, (2022), pp. 307-312 , 2021
This article focuses on the presentation of maximally permissiѵe supervisors and control deadlock in flexible manufacturing systems (FMSs) presented with Petri nets(PNs). Siphons are targeted with the liveness of PNs models of FMSs, which requires analyzing the structural analyses and reachability graph (RG). The first approach is to analyze structural PNs for the purpose of solving them by controlling places used Pinѵariant which can be attributed to the existence of them would be empty. This can be done by using Petri net models, and the effectiveness is elucidated for the interactions, and operational resource sharing in FMS, which can be utilized as a class of an S 3 PR_net for modelling shows viable effectiveness. The simulation PNs are sufficient motivation for studying FMSs by controlling transitions (CTs) to prevent deadlocks to ensure that the second approach is liveness and maximal reachable number. These new paradigms allow formally are described by siphons-based systems. Specifically, examples of the supervisory design methods based on PNs are represented being to description control, liveness, and reversibility of the net productivity acquired that can be achieved liveness system by siphons PNs.