A divide-and-conquer-method for the synthesis of liveness enforcing supervisors for flexible manufacturing systems

In this paper a divide-and-conquer-method for the synthesis of liveness enforcing supervisors (LES) for flexible manufacturing systems (FMS) is proposed. Given the Petri net model (PNM) of an FMS prone to deadlocks, it aims to synthesize a live controlled Petri net system. For complex systems, the use of reachability graph (RG) based deadlock prevention methods is a challenging problem, as the RG of a PNM easily becomes unmanageable. To obtain the LESs from a large PNM is usually intractable. In this paper, to ease this problem the PNM of a system is divided into small connected subnets. Each connected subnet prone to deadlocks is then used to compute the LES for the original PNM. Starting from the simplest subnet prone to deadlocks to make the subnet live, monitors (control places) are computed. The RG of each subnet is considered and split into a dead-zone (DZ) and a live-zone. All states in the DZ are prevented from being reached by means of a well-established invariant-based control method. Next, the computation of monitors is followed for bigger subnets. Previously computed monitors are included within the bigger subnets based on a criterion. This process keeps the DZ of the bigger subnets smaller compared with the original uncontrolled subnets. When all subnets are live we obtain a set of monitors that are included within the PNM to obtain a partially controlled PNM (pCPNM). A new set of monitors is also computed for the pCPNM. Finally, a live controlled Petri net system is obtained. The proposed method is generally applicable, easy to use, effective and straightforward although its off-line computation is of exponential complexity in theory. Its use for FMS control guarantees deadlock-free operation and high performance in terms of resource utilization and system throughput. Two FMS deadlock problems from the literature are used to illustrate the applicability and the effectiveness of the proposed method.     

Comments on “An Iterative Synthesis Approach to Petri Net Based Deadlock Prevention Policy for Flexible Manufacturing Systems”

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.     

An iterative method for synthesizing non-blocking supervisors for a class of generalized Petri nets using mathematical programming

This paper presents a novel and computational deadlock prevention policy for a class of generalized Petri nets, namely G-systems, which allows multiple resource acquisitions and flexible routings with machining, assembly and disassembly operations. In this research, a mixed integer programming (MIP)-based deadlock detection technique is used to find an insufficiently marked minimal siphon from a maximal deadly marked siphon for generalized Petri nets. In addition, two-stage control method is employed for deadlock prevention in Petri net model. Such proposed method is an iterative approach consisting of two stages. The first one is called siphons control, which adds a control place to the original net for each insufficiently marked minimal siphon. The objective is to prevent minimal siphons 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 due to the addition of the monitors. Compared with the existing approaches, the proposed deadlock prevention policy can usually lead to a non-blocking supervisor with more permissive behavior and high computational efficiency for a sizeable plant model due to avoiding complete siphon enumeration. Finally, a practical flexible manufacturing system (FMS) example is utilized to illustrate the proposed method.     

Design of a maximally permissive liveness-enforcing supervisor with a compressed supervisory structure for flexible manufacturing systems

In this paper, a deadlock prevention policy for flexible manufacturing systems (FMS) is proposed, which can obtain a maximally permissive liveness-enforcing Petri net supervisor while the number of control places is compressed. By using a vector covering approach, the sets of legal markings and first-met bad markings (FBM) are reduced to two small ones, i.e., the minimal covering set of legal markings and the minimal covered set of FBM. A maximally permissive control purpose can be achieved by designing control places such that all markings in the minimal covered set of FBM are forbidden and no marking in the minimal covering set of legal markings is forbidden. An integer linear programming problem is designed to minimize the number of control places under an assumption that a control place is associated with a P-semiflow. The resulting net has the minimal number of control places on the premise that the assumption holds, and possesses all permissive states of a plant. The only problem of the proposed method is its computational complexity that makes it inapplicable to large-scale Petri net models. An FMS example from the literature is presented to illustrate the proposed method.     

Deadlock avoidance policy for Petri-net modeling of flexiblemanufacturing systems with shared resources

Multiple products through a flexible manufacturing system (FMS) with limited resources can lead to deadlock. In this paper, the authors study the problem of deadlock avoidance by using the Petri net (PN) model for FMSs and introducing the concept of deadlock structure. The necessary and sufficient conditions to prevent deadlock are characterized. The authors use a state feedback restriction policy which prevents some enabled transitions from firing for avoiding deadlock in the system. In particular, when the number of any key kind of resources is greater than one, this policy is minimally restrictive and allows the maximal use of resources in the system. The authors present the PN realization of these restriction policies when the closed-loop system can be modeled by a live PN. The restriction policies can be easily implemented. An example is provided for illustration     

Design of liveness-enforcing supervisors with simpler structures for deadlock-free operations in flexible manufacturing systems using necessary siphons

Siphons can be used to characterize deadlock states and solve deadlock problems in Petri nets that model flexible manufacturing systems. This paper presents an iterative siphon-based control (ISC) deadlock prevention policy for Petri nets via the combination of mixed integer programming (MIP) and the concept of necessary siphons (NSs). At each iteration in this ISC policy, a maximal deadly marked siphon that is closely related to deadlocks in a Petri net can be conveniently found by an MIP-based deadlock detection method. Then the places in it are classified and an NS is derived from the classified places. For each NS found, depending on its complementary set, the proposed policy adds a proper control place (CP) to make it marked (max-controlled). Moreover, during the ISC procedure, a test for redundant NSs is carried out under a certain condition in order to avoid the addition of the corresponding CPs. The siphon control process proceeds iteratively until the controlled system is live. Compared with the existing approaches, the proposed policy usually leads to a structurally simple liveness-enforcing supervisor by adding as few CPs as possible and achieves better control results. Some examples are introduced to illustrate the proposed approach.     

A deadlock prevention approach for flexible manufacturing systems without complete siphon enumeration of their Petri net models

Siphons are very important in the analysis and control of deadlocks in a Petri net. However, it is quite time-consuming or even impossible to get the complete siphon enumeration of a Petri net. This paper focuses on the deadlock prevention problems in flexible manufacturing systems that are modeled with S⁴PR, a general class of Petri nets. The analysis of S⁴PR leads us to characterize deadlock situations in terms of insufficiently marked siphons. The method proposed in this paper is an iterative approach. At each iteration, a non-max-marked siphon is computed by solving a mixed integer linear programming problem. Then the siphon is max-marked through a P-invariant by adding a monitor place. This process is carried out until no non-max-marked siphon can be found in the net. As a result all the siphons in the net are max-controlled. Then the net becomes live. Without computing all the siphons, a monitor-based liveness-enforcing Petri net supervisor can be found with more permissive behavior. A number of flexible manufacturing examples are used to demonstrate the proposed methods.     

Liveness-enforcing supervisors synthesis for a class of generalised Petri nets based on two-stage deadlock control and mathematical programming

In this article we deal with deadlock prevention problems for S⁴PR, a class of generalised Petri nets, which can well model a large class of flexible manufacturing systems where deadlocks are caused by insufficiently marked siphons. We present a deadlock prevention methodology that is an iterative approach consisting of two stages. The first one is called siphon control, which is to add for each insufficiently marked minimal siphon a control place to the original net. Its objective is to prevent a minimal siphon from being insufficiently marked. The second one, called control-induced siphon control, is to add a control place to the augmented net with its output arcs connecting to the source transitions, which assures that there are no new insufficiently marked siphons generated. At each iteration, a mixed integer programming approach is adopted for generalised Petri nets to obtain an insufficiently marked minimal siphon from the maximal deadly siphon. This way complete siphon enumeration is avoided that is much more time-consuming for a sizeable plant model than the proposed method. The relation of the proposed method and the liveness and reversibility of the controlled net is obtained. Examples are presented to demonstrate the presented method.     

A Maximally Permissive Deadlock Prevention Policy for FMS Based on Petri Net Siphon Control and the Theory of Regions

This paper addresses the deadlock problems in flexible manufacturing systems (FMS) by using a Petri net siphon control method and the theory of regions. The proposed policy consists of two stages. The first one, called siphons control, is to add, for every siphon that we identify, a monitor to the original net model such that it is optimally invariant controlled. In the second stage, the theory of regions is utilized to derive the net supervisors such that deadlocks can be prevented. The first-stage work significantly lowers the computational cost compared with the approach where the theory of regions is used alone. An FMS example is presented to illustrate the technique. By varying the markings of given net structures, this paper shows its computational advantages.     

A deadlock prevention approach for a class of timed Petri nets using elementary siphons

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     

避免FMS死锁的控制策略

本文利用ＦＭＳ的Ｐｅｔｒｉ网模型讨论系统的死锁问题，给出了系统死锁的必要充分条件，提出了避免系统死锁的反馈控制策略，这种策略对系统的限制小，在许多情形下是最优的。     

一类FMS的最佳活Petri网模型的综合

利用Petri网为一类柔性制造系统建模,并讨论避免系统死锁问题.通过Petri网模 型的结构分析,证明了系统产生死锁的一个充分必要条件.给出了避免死锁的最佳控制器,它 可以通过给系统的Petri网模型增加一些新的位置与相应的弧来实现.从而导出了这类制造 系统的最佳活Petri网模型.     

无冲突Petri网系统活标识判定的结构化方法

为了有效求解无冲突Petri网系统活标识的判定及配置优化问题,提出无冲突Petri网系统活标识判定的一种结构化方法。该方法首先求取无冲突Petri网的各强连通分支;然后对每一含有元素个数大于2的强连通分支求取其无同步变迁库所索引集合;最终得到无冲突Petri网系统的无前置库所索引集合,基于该库所元素集合即可实现对活标识的快速判定及配置优化。通过例子具体说明了该方法的实现及应用。分析结果表明,所提方法具有多项式时间复杂度,较易于操作和程序化实现。     

部分可控Petri网分布式死锁监控器设计

研究了部分可控Petri网柔性制造系统中的死锁避免的问题。为了保证死锁避免和资源最大允许利用,提出了基于分支定界法的Petri网死锁监控器的优化设计方法,采用多个子控制节点对全局状态建立分布式监控器,通过行为可行和分布可行对分布式监控器下合法状态空间进行检测,对最大行为可行子集建立线性规划模型求解最大分布可行合法状态集,得到分布式监控器下的最大合法状态子空间。最后,建立了柔性制造系统的部分可控Petri网模型,针对系统的死锁避免等多个行为特性要求,分别设计了集中式监控器和分布式监控器,分布式监控器能有效地避免死锁。     

基于Petri网的柔性制造系统一种预防死锁方法

基于Petri网的结构特性分析,研究了FMS(柔性制造系统)一种预防死锁方法.提出了 Petri网的一种特殊拓扑结构--基本信标的概念.在Petri网中基本信标的集合是SMS(严格极 小信标)集合的一个真子集.尤其在大型Petri网系统中,基本信标的集合比SMS的集合要小得 多.对于Petri网的一个子类S3PR,只对每一个基本信标添加一个库所使其不被清空,就可实现 预防死锁,也就是说无须控制S3PR的所有SMS而达到无信标被清空的目的.此外,对于S3PR, 还提出了一种求取SMS和基本信标的方法.相对于现在普遍采用的控制所有SMS来预防死锁 的策略,其具三方面优势.1)只需控制少量的SMS即所谓的基本信标.相应地,添加少量的控制 库所和连接弧,就可得到无死锁或活的Petri网.2)不需要先行计算出极小信标的集合.3)明显 地,这种方法更适合大型Petri网系统.我们通过穿插在文中的一个例子来说明这些方法.     

基于变迁覆盖的制造系统死锁控制策略

基于系统Petri网模型,研究柔性制造系统的死锁控制问题.论文利用变迁覆盖为系统设计活性控制器.变迁覆盖是由一组极大完备资源变迁回路组成的集合,其变迁集覆盖了Petri网中所有极大完备资源变迁回路的变迁集.验证变迁覆盖的有效性,然后仅对有效变迁覆盖中的极大完备资源变迁回路添加控制位置,就得到系统的活性受控Petri网.这种受控Petri网包含的控制位置个数少,从而结构相对简单.最后通过一个例子说明了所提出的死锁控制策略的构成与特点.     

基于Petri网模型的FMS死锁结构

死锁是柔性制造系统中容易发生的异常现象，如不加以消除，将会导致整个系统的瘫痪。文中通过Petri网模型对FMS的结构分析，揭示出导致FMS死锁的结构元素和活性特征，在此基础上，提出了FMS的无死锁Petri网控制器算法，并举例说明这种控制器算法在FMS中的应用。     

基于混合法的叶片FMS控制系统研究

本文基于Ｐｅｔｒｉ网建模的混合法，建立了叶片ＦＭＳ控制系统活的、安全和可逆的Ｐｅｔｒｉ网模型，应用该模型开发了叶片ＦＭＳ控制系统仿真器，可成功地避免叶片ＦＭＳ的死锁产生。     

Observer-based state-feedback control of timed Petri nets with deadlock recovery

This paper discusses the problem of controlling a timed Petri net whose marking cannot be measured but is estimated using an observer. The control objective is that of enforcing a set of generalized mutual exclusion constraints (GMEC) and all transitions are assumed to be controllable. We show that the use of marking estimates may significantly reduce the performance of the closed-loop system and in particular may lead to a deadlock. First, we present a linear algebraic characterization of deadlock markings based on siphon analysis. Second, we show how this characterization may be used to derive a procedure that may be invoked to recover from a controller induced deadlock. Finally, we assume that the timing delays associated to transitions are known and show how this knowledge can be used to improve the marking estimate and to recover the net from partial deadlocks. This procedure is similar to the one used for deadlock recovery and may be invoked whenever a transition has not fired for a time longer than its expected delay.