Centralized and decentralized supervisory controller design to enforce boundedness,liveness, and reversibility in Petri nets

Supervisory controller design to enforce boundedness, liveness, and reversibility in Petri nets is considered. The Petri nets considered may have non-unity weight arcs and both controllable and uncontrollable transitions. Algorithms for a centralized controller design approach are first developed. The developed algorithms always find a controller whenever it exists. This controller enforces boundedness, liveness, and reversibility; it also avoids deadlock. Furthermore, it is shown that the controller obtained is the least restrictive controller among all controllers which enforce desired properties. A decentralized controller design approach, based on overlapping decompositions, is then introduced. Algorithms to design decentralized controllers based on this approach are also developed. These controllers, when they exist, also guarantees boundedness, liveness, reversibility and deadlock freeness. The decentralized controllers have two main advantages over the centralized ones. First, they have reduced on-line computation and communication requirements. Second, the computational time required to design decentralized controllers is considerably less than that required for centralized controllers.     

离散制造装配系统的活性控制

首次研究离散制造装配系统的活性控制问题.建立了系统的工件加工过程Petri网 模型.通过对系统Petri网模型的结构分析,提出了导致系统死锁的两类元素结构及活性特 征.对一类离散制造装配系统提出了避免死锁的Petri网控制器,这类控制器容易实现,对系 统的限制小,而且使得受控系统仍具Petri网模型.对一般离散制造装配系统提出了保证系统 活性的控制策略.     

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。     

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     

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.     

离散制造装配系统的活性控制1)

首次研究离散制造装配系统的活性控制问题.建立了系统的工件加工过程Petri网模型.通过对系统Petri网模型的结构分析,提出了导致系统死锁的两类元素结构及活性特征.对一类离散制造装配系统提出了避免死锁的Petri网控制器,这类控制器容易实现,对系统的限制小,而且使得受控系统仍具Petri网模型.对一般离散制造装配系统提出了保证系统活性的控制策略.     

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.     

Designs of Bisimilar Petri Net Controllers With Fault Tolerance Capabilities

This paper proposes an approach for providing tolerance against faults that may compromise the functionality of a given controller modeled by a Petri net. The method is based on embedding the given Petri net controller into a larger (redundant) Petri net controller that retains the original functionality and properties, and uses additional places, connections, and tokens to impose invariant conditions that allow the systematic detection and identification of faults via linear parity checks. In particular, this paper considers two types of redundant Petri net controllers: 1) nonseparate redundant Petri net controllers have the same functionality as the given Petri net controller and allow for fault detection and identification, but do not necessarily retain the given controller intact; and 2) separate redundant Petri net controllers are a special case of the nonseparate redundant controllers that retain the given Petri net controller intact but enhance it with additional places to enable fault detection and identification. The work in this paper obtains complete characterizations of both types of redundant controllers along with necessary and sufficient conditions for them to be bisimulation equivalent to the given original Petri net controller. In addition, this paper discusses how each type of redundant controllers can be designed to have desirable fault detection and identification capabilities. When the bisimulation equivalence requirement is not directly enforced, nonseparate redundant controllers can potentially have advantages over separate ones (e.g., they can use fewer connections to detect and identify the same number of faults). An example of a Petri net controller for a production cell and its fault tolerance capabilities using separate and nonseparate embeddings is used to illustrate the approach.     

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.     

Design and fault diagnosis of Petri net controllers for Petri nets with uncontrollable and unobservable transitions

This paper presents a methodology for diagnosing faults of controllers which are modeled by Petri nets with uncontrollable and unobservable transitions. The inadmissible constraints with uncontrollable and unobservable transitions are transformed into admissible conditions in this method. And we can design controllers easily using reduction technique. In order to provide tolerance against faults in controllers, we embed the given Petri net controller into a larger Petri net controller that retains the functionality of original controllers, and encode the large Petri net controller. Separate redundant Petri net controllers using additional places, connections and tokens to impose invariant conditions allow the systematic detection and identification of faults via Hamming code. The proposed method is attractive because it can check faults (place faults, transition faults or mixed faults) easily. A manufacturing cell is taken as an example to illustrate the approach.     

基于变迁指标分解的Petri网性质分析

Petri网的分解技术是复杂网系统分析的一种重要手段,基于变迁指标的分解方法将系统分解为一组T-网。通过获得分解子网的结构性质以及子网与原网间的性质保持关系,得到了判定原网结构性质的一些方法和结论;同时给出了判定原网系统活性的一个条件。所得结果为结构复杂Petri网的性质分析提供了有效的方法。     

具有多项式时间复杂性的避免制造系统死锁控制策略

基于系统 Petri 网模型, 研究自动制造系统的避免死锁问题. 对不含中心资源的制造系统, 证明了它只包含安全和死锁两类可达状态. 通过一步向前看的方法, 给出了系统多项式时间复杂性的最佳避免死锁策略. 对一般系统定义了一种辅助 Petri 网. 利用辅助网的最佳避免死锁策略, 提出了综合一般制造系统多项式复杂性的避免死锁策略的方法.     

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.     

Deadlock prevention for flexible manufacturing system

Deadlock must be prevented via the shop controller during the flexible manufacturing system （FMS） performing. Various models have been tried for the analysis and design of shop controller. Petri net is suitable to describe the dynamic behavior of the discrete event system, such as concurrency, conflict and deadlock, however, the verification of the .system behavior needs structure analysis with complex theoretical proof method. Temporal logic model checking has important advantages over traditional theorem prover. It is flatly automatic and can produce possible counter-example which is particularly important in finding subtle error in complex transition systems. In this paper, a new method for the deadlock prevention based on Petri net and Temporal Logic model checking is presented. The specification in the Temporal Logic is expressed according to some result of structure analysis of the Petri net. The model checking is employed to execute the formal verification, which will conduct an exhaustive exploration of all possible behaviors. Finally, an example is presented to demonstrate how the method works.     

Deadlock p revention f or flexible manufacturing system

Deadlock must be prevented via the shop controller during the flexible manufacturing system (FMS) performing. Various models have been tried for the analysis and design of shop controller. Petri net is suitable to describe the dynamic behavior of the discrete event system , such as concurrency , conflict and deadlock , however , the verification of the system behavior needs ructure analysis with complex theoretical proof method. Temporal logic model checking has important advantages over traditional theorem prover. It is fully automatic and can produce possible unter- example which is particularly important in finding subtle error in complex transition systems. In this paper ,a new method for the deadlock prevention based on Petri net and Temporal Logic model checking is presented. The specification in the Temporal Logic is expressed according to some result of structure analysis of the Petri net . The model checking is employed to execute the formal verification ,which will conduct an exhaustive exploration of all possible behaviors. Finally ,an example is presented to demonstrate how the method works.     

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.     

具有不可控变迁离散事件系统的Petri网控制器

考虑可用具有不可控变迁的受控Petri网建模的离散事件动态系统.提出了在这类 系统中实现一组不等式约束的控制器的综合方法.所提出的控制器可通过给系统Petri网模 型增加一些Petri网元素来实现,其计算是建立在本文提出的Petrl网的路增益概念基础上 的.方法是系统、简单、计算量小.     

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.     

Liveness Problem of Petri Nets Supervisory Control Theory for Discrete Event Systems

A quite great progress of the supervisory control theory for discrete event systems (DES) has been made in the past nearly twenty years, and now, automata, formal language and Petri nets become the main research tools. This paper focus on the Petri nets based supervisory control theory of DES. Firstly, we review the research results in this field, and claim that there generally exists a problem in Petri nets based supervisory control theory of DES, that is, the deadlock caused by the controller introduced to enforce the given specification occurs in the closed-loop systems, especially the deadlock occurs in the closed-loop system in which the original plant is live. Finally, a possible research direction is presented for the solution of this problem.     

基于有色Petri网并发进程模型及死锁避免方法

并发进程具有明显的异步并发性,而Petri网是描述异步并发系统的有效工具,但是目前将Petri网用于并发进程控制问题的研究还几乎没有。为此通过引入扩展有色Petri网,为并发进程建立了模型,并给出了避免死锁的有效方法。