Design of deadlock prevention supervisors using Petri nets

This paper proposes a methodology to synthesize supervisors for a class of sequential resource allocation system for flexible manufacturing systems. The type of Petri nets are called S3PR, where deadlocks are related to emptied siphons. In a former paper (Huang et al., IEEE Trans Syst Man Cybern, 2007), a deadlock prevention policy was proposed based on Petri nets siphons for the type of Petri nets. Since all minimal siphons should be controlled, the deadlock prevention policy is very time-consuming when the system is large. In this research, a concept of the elementary siphon is used to reduce the number of control places. A new siphon-based policy of deadlock prevention for the type of Petri nets is presented. This policy consists of two main stages: The first stage, called elementary siphons control, adds control places to the original net model to prevent elementary siphons from being emptied. The second stage, called generalized siphons control, adds control places that adopt a conservative policy of controlling only the release of parts into the system are used. Compared to the existing approaches, the new deadlock prevention policy can obtain a structurally compact deadlock prevention supervisor by adding only a few control places. Finally, numerical experiments under reachable states illustrate that the proposed algorithm appears to be more permissive than the closely related approaches.     

自动制造系统的一种死锁避免策略

基于Petri网的结构分析理论，提出了自动制造系统Petri网模型的一种死锁控制方法，在这种策略的控制下，避免了系统中死锁的产生，从而许多制造系统的Petri网模型具有活性，提出了一种保证所有严格极小信标至少含有一个托肯的方法，对冗余严格极小信标的研究，提高了Petri网复杂自动制造系统的建模能力。结果表明，在设计无死锁的Petri网格型时，不是所有的严格极小信标都要考虑，从而简化了设计结果和控制算法。     

Deadlock control of concurrent manufacturing processes sharing finite resources

A novel deadlock control policy is developed for modeling the concurrent execution of manufacturing processes with limited shared resources through a class of nets, ES³PR. A relevant property of the system behavior is that it is deadlock-free. Recent work has shown that deadlock situations in a plant system can be easily characterized by the structural analysis of the system, particularly, in terms of unmarked or insufficiently marked siphons in its Petri net model. The strict minimal siphons in a plant ES³PR net model are divided into elementary and dependent ones. The proposed deadlock prevention policy is to make all siphons satisfy maximal cs-property when the elementary siphons in the plant Petri net model are properly supervised via explicitly adding monitors for them with appropriate initial markings. Compared with the existing approaches in the literature, the advantage of the policy is that a much smaller number of supervisory places (monitors) are added and unnecessary iterative processes are avoided. Finally, its application is illustrated by a flexible manufacturing example.     

Efficient deadlock prevention policy in automated manufacturing systems using exhausted resources

To design supervisors enforcing liveness of automated manufacturing systems (AMS), an efficient deadlock prevention policy based on the exhausted resources is proposed. This policy exploits a special structure of Petri nets in the sense that the liveness of a specific system can be guaranteed if no shared resource can be emptied. In contrast to the typical conventional policies, the explicit enumeration of either the reachable states or the siphons can be avoided. Experimental results verify the efficient implementation of the proposed policy.     

The use of the Petri net reduction approach for an optimal deadlock prevention policy for flexible manufacturing systems

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.     

Deadlock control of flexible manufacturing systems via invariant–controlled elementary siphons of petri nets

Effective resolution for deadlock problems plays an important role in the operation of automated flexible manufacturing systems (FMS). Based on P-invariants and elementary siphons of Petri nets, a deadlock prevention policy is developed for a special class of Petri nets that can well model many FMS. Siphons in a plant net model are divided into elementary and dependent ones. For each elementary siphon, a monitor is added to the plant model such that the siphon is invariant-controlled. Our method guarantees that no emptiable control-induced siphon is generated due to the addition of the monitors. When all elementary siphons are controlled, the controllability of a dependent siphon is ensured by properly setting the control depth variables of its related elementary siphons. An FMS example is utilized to illustrate the proposed methods.     

On a deadlock prevention policy for a class of Petri nets S3PMR

In Yan et al. (J Inf Sci Eng 25(1): 167–183, 2009), a deadlock prevention policy is proposed for a subclass of Petri nets, S³PMR, that can well model a large class of flexible manufacturing systems (FMS) where deadlocks are caused by unmarked siphons in their Petri net models. To validate the effectiveness and efficiency of the proposed approach, two examples were demonstrated in Yan et al. (J Inf Sci Eng 25(1): 167–183, 2009). This paper shows that there is a problem with one of the control places computed for one of the examples. In Yan et al. (J Inf Sci Eng 25(1): 167–183, 2009), for another example, two different deadlock prevention supervisors were proposed. It is also shown in this paper that, for these two supervisors, it is possible to obtain two subsets of control places. Thus, the structures of the two supervisors are further simplified with the same permissive system behaviours.     

S3PMR网的一种死锁预防优化策略

针对Petri网的S3PMR中的死锁预防问题,提出一种优化的控制器设计方法.当控制器的优化性不能保证时,要对所添加的控制器进行结构分析,提出了一个输出弧位置最优化的死锁预防控制算法.将S3PMR中的严格极小信标分为基本信标和从属信标,对每一个基本信标添加一个控制库所,使其P-不变式可控,且不会产生新的可被清空信标,对从属信标的控制则通过调整基本信标的控制深度变量来实现.从而用少量的控制库所得到结构更简单、许可行为更多的活性Petri网控制器.     

冗余信标及其在Petri网结构控制中的应用

提出了冗余严格极小信标的概念 ,冗余信标是网拓扑的一种特殊结构。在保证网系统的所有信标不被清空时 ,只需要考虑那些非冗余的严格极小信标即可。这样便降低无死锁Petri控制器设计的复杂性 ,大大增强了Petri网处理复杂系统的能力。同时提出了一种死锁控制的迭代算法 ,使用冗余信标的概念可以大大简化Petri网的设计。以自动制造系统为例 ,说明了这种概念的应用。     

Identification and elimination of redundant control places in petri net based liveness enforcing supervisors of FMS

In the past two decades, a number of Petri-net-based approaches were proposed for deadlock prevention in flexible manufacturing systems (FMS). An FMS is modeled as a Petri net, and then the controller or the liveness enforcing supervisor (LES) is computed as a Petri net. A live Petri net (LPN) guarantees deadlock-free operations of the modeled FMS. An LES consists of a number of control places (CPs) and their related arcs. To-date most of the attention has been paid to make the underlying Petri net models live without questioning whether or not all of the computed CPs are necessary. It is often the case that the number of CPs determined by these approaches is not minimal. Reducing it in order to reduce the complexity of the controlled system is an important issue that was not tackled before. To address this problem, this paper proposes a redundancy test for an LES of an FMS. The proposed approach takes an LPN model, controlled by n CPs, as input and in the existence of any redundant CPs it produces redundant and necessary CPs. The proposed approach is applicable to any LPN consisting of a Petri net model (PNM), controlled by means of a set of CPs.     

On a maximally permissive deadlock prevention policy for automated manufacturing systems by using resource-oriented Petri nets

It is theoretically and practically significant to synthesize a maximally permissive (optimal) controller to prevent deadlocks in an automated manufacturing system (AMS). With an AMS being modeled with Petri nets, by the existing methods, integer linear programming (ILP) problems are usually formulated and solved to obtain optimal policies by forbidding illegal markings at the same time no legal marking is excluded. Without an efficient technique for solving an ILP, such a method is usually computationally prohibitive. A resource-oriented Petri net (ROPN) is employed to model a class of AMS for resolving the deadlock control problem with maximal permissiveness in this paper. Efficient methods are developed to figure out the key structures in an ROPN model for deadlock prevention. Based on the structural properties of ROPN models, this work explores several types of illegal markings that can be prohibited optimally by structural analysis. For these markings, a deadlock prevention policy can be derived in an algebraic way without solving a notorious ILP problem. For the other markings, linear programming (LP), instead of ILP, approaches are developed to forbid them optimally. Thus, a maximally permissive controller can be developed while the computational cost is reduced greatly. The proposed methods are verified by typical examples in the literature.     

Revised dependent siphons

The number of problematic siphons grows exponentially with the size of net, resulting in many monitors to prevent from reaching deadlocks. Li and Zhou propose the concept of elementary siphons so that many problematic siphons, called dependent siphons, do not need monitors. They indicate that it is not limited to simple sequential processes with resources (S³PR) and may be extended to arbitrary nets. S³PMR is a generalization of S³PR by allowing a job place to use more than one resource. Also, when entering the next operation place, it may not release the resource. We demonstrate a counter-example by showing that the dependent condition may be relaxed so that an elementary siphon, while requiring a monitor previously, may be controlled after some elementary siphons get controlled.     

USING COLORED TIMED PETRI NET FOR THE SOLUTION OF DEADLOCK IN A FLEXIBLE ASSEMBLY SYSTEM

0 INTRODUCTIONThe manufacturing process and assembly inworkshop are regarded as discrete events.Thesystem,which involves these process is called discreteevent dynamic system (DEDS). Many modeling toolshave been employed for modeling this kind of system,such as, queuing theory, critical path method, max-min algebra, perturbation analysis and Petrinet.AInong these tools, Petri nets are graphical andmathematical modeling too1 which is applicable tomany systems. They are promising tools fo…     

Deadlock prevention using Petri nets and their unfoldings

Unfoldings of Petri nets (PN) provide a method for the analysis of concurrent systems without restoring the state space of a system. This allows one to overcome the state explosion problem. Many properties of the initial PN (boundedness, safety, persistency and hazards) can be checked by constructing the unfolding. A deadlock prevention procedure first detects deadlocks using an unfolding. Then, the first method reduces the unfolding to a set of deadlock-free subunfoldings that cover all live behaviours. The second method uses a direct transformation at the level of the original PN. The methods are implemented as subroutines in the Berkeley program SIS. Although the deadlock detection problem is known to be NP-complete, experimental results show that for highly parallel specifications deadlock prevention by unfoldings is typically more efficient than deadlock prevention based on symbolic BDD (binary decision diagrams) traversal of the corresponding reachability graph.     

平面包络环面蜗杆基于坐标测量的高精度制造方法

用坐标测量的方法实现了平面包络环面蜗杆齿形偏差的测量，提出了由齿形偏差的测量结果诊断蜗杆加工时机床工具的调整误差，并根据诊断结果修正机床工具的调整参数，从而提高蜗杆制造精度的方法，加工测量的试验表明本文方法十分有效。     

An Optimal Deadlock Prevention Policy for Flexible Manufacturing Systems Using Petri Net Models with Resources and the Theory of Regions

In this paper, an optimal deadlock prevention policy for flexible manufacturing systems (FMSs) is proposed. In an FMS, dead-locks can arise because of a limited number of shared resources, i.e. machines, robots, buffers, fixtures etc. Deadlock is a highly undesirable situation, where each of a set of two or more jobs keeps waiting indefinitely for the other jobs in the set to release resources. The proposed optimal deadlock prevention policy is based on the use of reachability graph analysis of a 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, which is a formal synthesis technique toderive Petri nets from automaton-based models. The policy proposed is optimal in the sense that it allows the maximal use of resources in the system according to the production requirements. Two examples are provided for illustration. RID=" ID=" <E5>Correspondence and offprint requests to</E5>: M. Uzam, Ni&gbreve;de &Uuml;niversitesi, M&uuml;hendislik-Mimarlik Fak&uuml;ltesi, Elektrik-Elektronik M&uuml;hendisli&gbreve;i B&ouml;l&uuml;m&uuml;, Kamp&uuml;s, 51100, Ni&gbreve;de, Turkey. E-mail: murat_uzam&commat;hotmail.com     

Enhancement of an efficient liveness-enforcing supervisor for flexible manufacture systems

This paper presents an enhanced efficient control method to obtain a maximally permissive deadlock prevention policy for flexible manufacturing systems (FMSs) based on Petri nets and the theory of regions. It is well known that the marking/transition-separation instances (MTSIs) method with the theory of regions has been extensively studied as one of optimal policies (i.e., maximally permissive) in FMS deadlock problems. However, all MTSIs are required to identify for controlling the deadlock problems. Therefore, this paper proposes novel crucial MTSIs (CMTSIs) to alleviate the computation cost due to the involvement of few MTSIs. This article elucidates CMTSI is the foundation of MTSI. Moreover, a maximally permissive liveness-enforcing supervisor with efficient computation can be implemented based on the experimental results, demonstrating that the proposed control policy is the most efficient algorithm among the closely related approaches.     

An optimal-elementary-siphons-based iterative deadlock prevention policy for flexible manufacturing systems

Petri nets have been proved to be a tool with prominent capabilities to describe discrete event systems, such as flexible manufacturing systems (FMS), thanks to their excellent properties over other models. Characterization in terms of special structural elements in a Petri net called siphons has been a major approach for the investigation of deadlock-freeness in context of FMS. Utilizing the optimal elementary siphons and the modified mixed integer programming (MIP) algorithm proposed in this paper, one can detect and solve deadlock problems arising in FMS in an iterative mode with tractable computational complexity. Moreover, the MIP approach can be exploited to implement the flexibility enhancement in the resultant net system so that the obtained system is less restricted. In contrast to the conventional typical policies, this approach evolves without explicitly enumerating all the strict minimal siphons. Its legitimacy and feasibility are proved and validated through an experimental study.     

Application of Petri nets for deadlock analysis and avoidance in flexible manufacturing systems

Unreasonable dispatching resources to jobs in flexible manufacturing system (FMS) may result in a deadlock situation. This serious situation is studied and avoided through Petri net (PN) analysis techniques in this paper. Firstly, a production Petri net (PPN) model for a given FMS is developed. Based on a certain set of resources in PPN, the concepts of a deadlock state and a potential deadlock state are introduced. Then, we present a deadlock avoidance method that consists of two parts. One is the construction of a deadlock state equation that describes the intrinsic relationship between resources assignation and a deadlock state in PPN. This equation is a necessary and sufficient condition for the occurrence of a deadlock situation. The other is the construction of a restrictive PN controller for each deadlock state equation. This restrictive PN controller can control the resources dispatching by excluding some enabled transitions from firing, consequently avoiding the deadlock. This method is minimally restrictive and allows the maximal use of resources not only for normal FMS, but also for special FMS with cyclic deadlock structure chain (i.e., a pathological type of circular waiting structure). Finally, two applications are given to illustrate the validity of this method. The results show that this method can be efficiently implemented in practical FMS.