An improved deadlock control policy using elementary siphons and MIP approach

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/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 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.

In this paper we deal with deadlock problems for a class of resource allocation systems, namely G-system, which allows multiple resource acquisitions and flexible routings with machining, assembly, and disassembly operations. A deadlock prevention methodology that is an iterative approach consisting of two stages is proposed. The first one is called siphons control, which is to add a control place to the original net for each insufficiently marked minimal siphon. The objective is to prevent a minimal siphon from being insufficiently marked. The second one, called control-induced siphons control, is to add a control place to the augmented net with its output arcs connecting to source transitions, which assures that there is no new insufficiently marked siphon generated. A mixed integer programming approach is adopted for generalized Petri nets to obtain an insufficiently marked minimal siphon from the maximal deadly marked siphon. This way avoids complete siphon enumeration that is much more time-consuming for a sizeable plant model than the existing method. This paper makes the application of presented deadlock control methods to G-systems.

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.

Deadlocks in automated flexible manufacturing systems (FMS)is a crucial problem in production process. This paper presents an effective deadlock prevention policy for a special class of Petri nets, S3PR. Based on siphon method, a set of generalized mutual exclusion constraints (GMEC) expressed by the marking vector can be found. Then monitors based on the GMEC are added to the plant model such that the siphons in the resultant net are all invariant-controlled and no emptiable siphon is generated due to the addition of the monitors. This novel deadlock prevention policy can usually lead to a maximally permissive supervisor by adding a number of monitors and arcs, the number of monitors is decided by the number of emptiable siphon in the net system, the proposed policy can work excellently in proper size petri net system. Finally two manufacturing examples are utilized to illustrate the proposed method.

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.

Deadlocks are a rather undesirable phenomenon in flexible manufacturing systems (FMSs). This work, by adding monitors, develops a deadlock prevention policy for FMSs that can be modeled by a class of Petri nets called α-S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> PR with i-resources. First, an algorithm is presented to reduce an S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> PR via a i-resource. Based on the algorithm, i-resources in α-S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> PRs are classified into two types: 1) A-ξ-resources and 2) B-ξ-resources. Next, for an α-S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> PR with only B-ξ-resources, it is proved that a maximally permissive liveness-enforcing supervisor can be designed by controlling all emptied strict minimal siphons. For an α-S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> PR containing A-ξ-resources, a liveness-enforcing supervisor can be designed by iteratively reducing the net via A-ξ-resources and adding the corresponding monitors. Finally, a deadlock prevention algorithm for α-S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> PRs is presented. Two FMS examples are used to illustrate its application. Its comparison results with other state-of-the-art deadlock prevention policies validate its overall advantages in terms of computational complexity, structural complexity, and behavior permissiveness.

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

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.

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 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.

Elementary siphons have been extensively studied to solve deadlock problems inPetri nets. However, most of the existing approaches based on elementary siphons can deal with thePetri nets in which all the transitions are supposed to be controllable and observable. This paper develops an elementary‐siphon‐based deadlock control policy for flexible manufacturing systems with uncontrollable and unobservable transitions. For elementary siphons, their complementary sets are successively expanded by considering unobservability and uncontrollability of transitions. Monitors are designed for the expanded complementary sets. The proposed method permits that there are arcs from monitors to a set of special uncontrollable transitions. Moreover, we show that the dependent siphons are always marked in the controlled system that is derived from the proposed method when there exist uncontrollable and unobservable transitions.

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.

Li and Zhou propose simpler Petri net controllers based on the concept of elementary siphons (generally much smaller than the set of all strict minimum siphons (SMSs) in large Petri nets) to minimise the addition of control places. SMSs can be divided into two groups: elementary and dependant; characteristic T-vectors of the latter are linear combinations of that of the former. A T-vector η is associated with each siphon S such that η(i) is the number of tokens gained in or lost from S by firing transition ti once. A dependent siphon S0 strongly depends on elementary siphons S1, S2, … , Sk if η0 = a1η1 + a2η2 + ⋅⋅⋅ + akηk with all ai (i = 1, 2, 3, … , k) positive. S0 is a weakly dependent siphon if some ai is negative. The T-vectors (resp. number) for elementary siphons are mutually independent (linear to the size of the net). In an earlier paper, we show that there exists a third siphon S3 such that ηβ = η1 + η2 - η3. This equation (called η relationship) plays an important role for optimal control of weakly dependent siphons. However, it assumes that all above S span between exactly two processes. For a well-known benchmark, however, most dependent siphons span more than two processes. This paper improves by removing this restriction and shows that ηβ = η1 + η2 - η3 holds as long as S1∩S2 is another emptiable siphon.