Petri Net Based Deadlock Prevention Approach for Flexible Manufacturing Systems

Purpose – Siphon-based deadlock control in a flexible manufacturing system (FMS) suffers from the problems of computational and structural complexity since the number of siphons grows exponentially with respect to the size of its Petri net model. In order to reduce structural complexity of a supervisor, a set of elementary siphons derived from all strict minimal siphons (SMS) is explicitly controlled. The purpose of this paper is through fully investigating the structure of a class of generalized Petri nets, WS3PR, to compute all SMS and a compact set of elementary siphons. Design/methodology/approach – Based on graph theory, the concepts of initial resource weighted digraphs and restricted subgraphs are proposed. Moreover, the concept of augmented siphons is proposed to extend the application of elementary siphons theory for WS3PR. Consequently, the set of elementary siphons obtained by the proposed method is more compact and well suits for WS3PR. Findings – In order to demonstrate the proposed method, an FMS example is presented. All SMS and elementary siphons can be derived from initial resource weighted digraphs. Compared with those obtained by the method in Li and Zhou, the presented method is more effective to design a structural simple liveness-enforcing supervisor for WS3PR. Originality/value – This work presents an effective method of computing SMS and elementary siphons for WS3PR. Monitors are added for the elementary siphons only, and the controllability of every dependent siphon is ensured by properly supervising its elementary ones. A same set of elementary siphons can be admitted by different WS3PR with isomorphic structures.

Deadlock analysis and control using Petri net decomposition techniques

Deadlock/livelock problems can cause catastrophic results in flexible manufacturing systems (FMS) by forcing them to stop production processes at an unpredictable stage of production. Therefore, they must be handled properly in order to obtain flawless production in FMS. Petri net (PN) based deadlock/livelock studies for FMS have been widely carried out to obtain live PN models. When a PN model is live, this ensures that the modelled FMS is deadlock-free. Firstly, an uncontrolled (plant) PN model is constructed for the FMS suffering from deadlocks/livelocks. Then reachability graph (RG) analysis of this PN model is carried out to provide all possible reachable states of the modelled system. An RG of a PN model of an FMS suffering from deadlock/livelock problems can be split into the live zone (LZ) and the deadlock zone (DZ). The former is the set of system states considered to be legal (good), while the latter is the set of system states regarded to be illegal (bad). The LZ represents the optimal (maximally permissive) system behavior that must be provided by an optimal control policy. Generally, in PN based liveness studies, a liveness enforcing supervisor (LES) consisting of a set of control places (CP) is computed. Then the controlled (closed-loop) PN model is obtained by merging the plant PN model and the LES. If the number of reachable live states of the controlled PN model is the same as the ones that exist in the LZ, then the controlled model is optimal. Otherwise, it is suboptimal. The greater the number of live reachable states of the RG, the more products to be produced within the FMS. Therefore, the number of reachable live states of the controlled PN model is considered as a quality measure. It defines the behavioral permissiveness of the controlled model. In the literature, to verify the behavioral permissiveness of the PN models, the PN tool called INA (Integrated Net Analyzer) has been widely used. Recently, by means of INA, a method was proposed to compute the number of states within the LZ and the DZ of a given PN model suffering from deadlocks/livelocks. Unfortunately, INA cannot compute RGs of large PNs having a few millions of states. Therefore, in this paper by means of TINA (TIme petri Net Analyzer), an alternative faster and much more efficient method is proposed for the computation of the number of states within the LZ and the DZ for PN models with large RGs. In addition, in order to enable the development of new PN based deadlock prevention methods, further computations are also proposed. These include the computation of the set of states in the DZ, LZ and first met bad markings (FBMs) for a given PN model suffering from deadlocks/livelocks. The applicability and the effectiveness of the proposed methods are demonstrated by considering several well-known examples of FMS from the relevant literature.INDEX TERMS Flexible manufacturing systems (FMS), deadlock, deadlock prevention, Petri Nets (PN), liveness enforcing supervisor (LES), PN computation tools.

Petri nets are an effective way to model, analyze, and control deadlocks in automated manufacturing systems (AMS). There are three important criteria in designing and evaluating a liveness-enforcing supervisor for a system to be controlled: behavioral permissiveness, structural complexity, and computational complexity. A maximally permissive supervisor can lead to high utilization of system resources. A supervisor with a simple structure can decrease the hardware and software costs. As for the computational complexity, means that a deadlock control policy can be applied to large systems. The objective of this paper is to design liveness-enforcing supervisors for different flexible manufacturing systems, simulate the controlled systems, and estimate the utilization of resources and throughput of the system. The siphon control methods (Strict Minimal Siphons and Elementary Siphons) are used to solve the deadlock control problems for a number of AMSs with different sizes. Moreover, the paper aims to evaluate the performance of selected methods such as utilization of resources, throughput, and the number of monitors, arcs, and states. Finally, the computational results indicate that the elementary siphons based policy provides better structural complexity and computational complexity than the strict minimal siphons based policy. However, strict minimal siphons based policy leads to better behavioral permissiveness than elementary siphons methods.

Petri nets are a popular mathematical tool to investigate the deadlock problems in resource allocation systems. As an important problem solution paradigm in computer science, the divide-and-conquer strategy is used in this paper to investigate the deadlock prevention for flexible manufacturing systems (FMSs) that are modeled with Petri nets. Based on the concept of resource circuits, a plant net model is divided into an idle subnet, an autonomous subnet, and a number of small but independent subnets, called toparchies, from the viewpoint of deadlock control. A liveness-enforcing supervisor, called toparch, is designed for each toparchy. If a particular separation condition holds in a plant net model, the computational complexity of toparches is significantly reduced. This research shows that the resultant net, called monarch, by composing the toparches derived for the toparchies can serve as a liveness-enforcing Petri net supervisor for the whole plant model. FMS examples are given to illustrate the proposed method.

In the flexible manufacturing system deadlock prevention domain, researchers’ almost final target is to seek the maximally permissive controllers for solving the deadlock problems of flexible manufacturing systems. However, it seems a challenging work. Whatever you adopt, what kinds of methods, policies, and strategies, it seems complicated to obtain optimal controllers for deadlock prevention even if they claim their algorithms are optimal until the deadlock recovery is developed. Therefore, many experts, including us, have decided to design all kinds of actual maximally permissive recovery policies based on control transitions. It is a pity that these policies usually solve some particular flexible manufacturing systems’ deadlock problems. The controllers failed to recover the deadlock situation of flexible manufacturing systems once the idle or resource places were changed. In other words, these policies could never know or identify the real number of maximally permissive controllers in the same structure with different idle places. The precise combination of the number of idle places is called the saturated line, and it divides the reachability states into two region (saturated region and unsaturated region). Accordingly, this paper proposes a novel concept that achieves the precise maximum permissiveness and fits all kinds of flexible manufacturing systems. The experimental results show how our policy does in practice.

An important Petri net-based method to prevent deadlocks arising in flexible manufacturing systems (FMS) is to add control places and related arcs to strict minimal siphons (SMS) such that no siphon can be emptied. Its disadvantage lies in that the method often adds too many additional places to the net. This paper explores ways to minimize the new additions of places while achieving the same control purpose. It proposes the concept of elementary siphons that are a special class of SMS and proves that by adding a control place for each elementary siphon to make sure that it is always marked, deadlock can be successfully prevented. Compared with the existing methods, the new method requires a much smaller number of control places and, therefore, is suitable for large-scale Petri nets. An FMS example is used to illustrate the proposed concepts and policy.

In the above paper, it proposes a deadlock prevention policy for a flexible manufacturing system (FMS), which needs the complete state enumeration of the FMS that is modeled with Petri nets. The reachability graph of a Petri-net model is divided into two parts: the live zone (LZ) and the deadlock zone (DZ). The states in the LZ of the reachability graph of a Petri net constitute the legal behavior of the net from the viewpoint of deadlock prevention. The concept of first-met bad markings is proposed. A first-met bad marking is a node in DZ, whose father nodes are in LZ. The deadlock prevention policy is used in an iterative way. At each iteration, a first-met bad marking is identified from the reachability graph of a Petri net to be controlled. The reachability of a first-met bad marking is prohibited by adding a monitor, establishing a marking invariance relationship between the additional monitor and the activity places that are marked under the first-met bad marking. To achieve this, without a formal proof, [Lemma 1] is developed as shown in this article.

On the basis of the assumption that no resource failure occurs, a variety of deadlock control policies have been developed for automated manufacturing systems (AMSs). However, in practical manufacturing systems, the occurrence of resource failures is always inescapable. In case, if resources fail to work, the existing deadlock control strategies can no longer be applied to the changed system; therefore, redesigning a new strategy is necessary. Because of their powerful modeling capabilities, Petri nets are used to model the considered AMSs allowing multi-type and multi-quantity resource acquisition. This paper focuses on extending a deadlock prevention method to be applied to AMSs with unreliable resources. Strict minimal siphons are controlled by added control places (monitors) to ensure the system’s liveness. To prevent blocking issues caused by resource failures, we develop a set of shared resource constraints represented by a set of inequalities based on the minimal resource requirements of processes and the capacity of shared resources. Robust monitors are designed for them to limit the distribution of tokens in unreliable neighborhood places. Our objective is to control resource allocation such that those parts not necessarily requiring any failed resource can continue progressing smoothly even if some unreliable resources break down. Examples are given to elucidate our proposed method clearly.

Based on elementary siphons of Petri nets and the mixed integer programming approach, an improved deadlock prevention policy is developed for S/sup 3/PR. Siphons in such a plant Petri net model are divided into elementary and dependent ones. Our policy consists of two stages: siphon control and control-induced siphon control. At first stage, a monitor (control place) is added for each elementary siphon such that it is invariant-controlled. Due to the addition of monitors to plant model, control-induced siphons are possibly generated in the augmented S/sup 3/PR, which is an RCN-merged net. The second stage sees that monitors are added to make always marked control-induced siphons in the resultant RCN-merged net without generating new control-induced siphons. Compared with our previous work, the deadlock prevention policy developed in this paper can lead to a structurally simple liveness-enforcing Petri net supervisor by adding only a small number of monitors and arcs. An FMS example is utilized to illustrate the proposed methods.

In this paper, we use Petri nets to analyse flexible manufacturing systems (FMS) to achieve the following objectives. The first objective is to derive a theorem for checking the buffer overflows in an FMS. The second objective is to schedule the earliest starting times for a sequence of operations in an FMS by the timed Petri net. The FMS may involve many part types, machines, pallets and so on. The third objective is to detect the deadlock phenomenon by a corrected algorithm of the P-invariant theory for Petri nets. This method will enable us to know whether there exists any deadlock in an FMS. The algorithm is implemented in the Turbo Pascal language. The fourth objective is to search for the optimal scheduling rule in an FMS. The search procedure is also implemented in the Turbo Pascal language¨ The optimal machine scheduling rule can result in a better throughput.

To simulate and debug or diagnose manufacturing systems is always challenging. This paper presents a hybrid PLC-controlled and PC Visual Basic (VB)-based Human-Machine Interface (HMI) platform based on Petri net (PN) theory for Manufacturing Systems. An augmented PN model was adopted to design and simulate the operational sequence of the Flexible Manufacturing System (FMS) at the National Kaohsiung First University of Science and Technology (NKFUST). With the simulated PN model, the control sequences were quickly translated into PLC programs. A PC-based HMI monitoring system based on the PN model was developed to provide an intuitive offline simulation and online diagnostic tools for the FMS. This hybrid system shows many of advantages by using the economical discrete control unit with PLC, and PC-based HMI using PN model as a base. The discrete event control sequence of an FMS can be easily modeled and evaluated before its build-up. More importantly, it can be diagnosed online when the system is malfunctioning. That is, the presented system provides an adequate means for offline system design, simulation, performance evaluation, and quick online system diagnostic.

Petri nets have been recognized as one of the most powerful tools for modeling flexible manufacturing systems (FMSs). Deadlock prevention policies are used to solve the deadlock problems of FMSs. It is well known that theory of regions is the efficient method for obtaining maximally permissive controllers. All legal and live maximal behavior of Petri net models can be preserved by using marking/transition-separation instances (MTSIs) or event-state-separation-problem (ESSP) methods. However, computing all sets of inequalities are an extremely time consuming problem due to the reachability graph of the deadlocked system. In our previous works, we proposed CMTSI method to improve the computational cost. In this paper, the selective siphon method is merged in our new deadlock prevention policy. The merit of the proposed policy is that the number of two types CMTSIs can then be simplified. Experimental results indicate that it is the most efficient policy to obtain maximal permissive behavior of Petri net models.

To solve the problem of deadlock prevention for timed Petri nets, an effective deadlock prevention policy based on elementary siphons is proposed in this paper. Without enumerating reachable markings, deadlock prevention is achieved by adding monitors for elementary siphons, increasing control depth variables when necessary, and removing implicit, liveness‐restricted and redundant control places. The final supervisor is live. First, a timed Petri net is stretched into a stretched Petri net (SPN). Unchanging the system performance, each transition in the SPN has a unit delay time. Then the siphon‐control‐based approach is applied. Monitors computed according to the marking constraints are added to the SPN model to ensure all strict minimal siphons in the net invariant‐controlled. A liveness‐enforcing supervisor with simple structure can be obtained by reverting the SPN into a TdPN. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

The use of structure theory of Petri nets to develop efficient deadlock prevention and deadlock avoidance methods for flexible manufacturing systems (FMSs) modelled by S4R nets is demonstrated. Major synchronisation patterns, such as generalised parallel and sequential mutual exclusion, frequently observed in FMS contexts can be represented by this class. The liveness property of a given S4R net (deadlock-freeness in the context of FMSs) is characterised in terms of structural Petri net elements called siphons. An efficient method for controlling minimal siphons of a given S4R net is developed where local control places are added to the net. A sufficient condition for liveness of the augmented net is provided. This constitutes a deadlock prevention approach. When the net liveness condition is not satisfied, an on-line controller, using a dynamic resource allocation policy, is developed for the augmented net. The performance of the proposed approaches is illustrated using several examples.