T-网的活性分析及其判断算法

Petri网的活性反映了实际系统的元死锁性.本文讨论了一类结构简单的Petri网-T-网的活性问题,给出了各类T-网的活性判定定理并给出了判定算法.算法主要计算工作是变迁的前序库所集和后继变迁集以及回路的判断,这三个过程实际上是一个树的搜索过程,因此算法易于实现,判定效率也大大提高.     

具有不可靠资源柔性制造系统的鲁棒控制器设计

如果柔性制造系统包含不可靠资源,则在对系统进行控制器设计时,不仅要考虑由于资源分配不合理带来的死锁现象,还要考虑不可靠资源发生损坏带来的堵塞现象.对此,首先利用Petri网对具有不可靠资源的柔性制造系统进行建模,结合Petri网图形结构(资源变迁回路),模拟系统中的死锁和堵塞现象;然后,利用有效变迁覆盖的概念,为系统设计一种结构简单、鲁棒性强的Petri网控制器;最后,利用两个例子验证所设计控制器的有效性.     

普通Petri网最大可达数的两段式死锁控制策略

针对普通Petri网的死锁问题,本文提出了可实现最大可达数的两段式死锁控制策略(deadlock control policy,DCP).第1步,该策略求解原网(N0,M0)的基本信标(elementary siphons,ES)和从属信标(dependent siphons,DS),对每个基本信标添加控制库所(control place,CP)和控制变迁(control transition,CT),获得拓展网系统(N′,M′).第2步,构建拓展网系统的P–不变式整数规划问题,测试原网中从属信标的可控性.若所有从属信标满足可控条件,则直接得到活性受控网系统(N*,M*);反之,对不满足可控条件的从属信标也添加控制库所和变迁,从而也得到了(N*,M*).通过理论分析和算例验证,表明了该死锁控制策略的正确性和有效性.相比目前文献中的可实现最大许可行为数目(number of maximally permissive behavior,NMPB)的普通Petri网死锁预防策略,该DCP获取的活性受控网系统(N*,M*)可达数目与原网(N0,M0)是相同的,且最大可达数(maximally reachable number,MRN)高于最大许可行为数目NMPB.     

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.     

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.     

应用控制变迁的柔性制造系统死锁控制策略

不同于目前许多文献中基于添加控制库所的死锁预防策略,本文提出了控制变迁方程(CTE)的概念和相应的基于添加控制变迁(CT)的死锁控制策略(DCP).通过分析存在死锁的原网(N0, M0)的可达图(RG),该DCP求解出所有死锁标识(DM).基于CTE,构造出所需的控制变迁.然后,对每个DM添加相应的CT,进而消除了原网(N_0, M_0)中的死锁标识,得到了活性受控网系统(N~?, M~?).通过理论分析和相关算例的应用,该DCP的正确性和有效性得到了验证.此外,该DCP获取的活性受控网系统(N~?, M~?)可达数目与原网(N_0, M_0)是相同的,即最大可达数(MRN).     

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.     

一类受控Petri网的反馈控制

受控Petri网是离散事件动态系统(DEDS)的一种控制理论模型.通过模型来研究实现 禁止状态避免的最大允许反馈控制是DEDS控制理论中的一个重要课题.文中对受控Petri网 的一个子类(非受控变迁子集的外延子网为TC网)讨论控制综合问题,给出求这类受控网中实 现禁止状态避免的最大允许反馈控制的一个算法.     

面向资源Petri网的自动制造系统死锁预防

在自动制造系统(automated manufacturing systems, AMSs)中,死锁是一个急需解决的问题,其主要由资源的循环等待造成.为了解决该问题,本文首先基于面向资源Petri网(resource-oriented Petri nets, ROPNs)的特征,建立特殊资源标记图(special resource marked graphs, SRMGs).其次,在SRMGs中建立死锁与饱和回路之间的关系.最后通过为一些特殊回路添加控制器,阻止系统出现不安全标记.考虑到资源故障问题,为危险库所添加资源缓冲子网,保证需要故障资源的零件不会阻塞其他零件的持续生产.相比现有的控制器,本文的监督控制器具有控制开关,其通过实时改变控制库所的容量可以允许更多安全标记发生.     

一类Petri网—S4R的死锁预防策略

S4R网作为一种特殊的Petri网子类,与S' PR网相比可以建模更为复杂的、拥有多个并行加工进程的资源分配系统。针对S4R网提出了一种综合的死锁预防策略。利用MIP检验由S4R网建模的柔性制造系统的活性,在新的信标控制概念的基础上对需要控制的系统进行控制。再利用MIP检验受控网系统的活性,进一步控制不活的网系统。避免了对一些网不必要的控制以及一些网过于保守的控制,得到许可行为较多的控制器。     

Optimal deadlock avoidance Petri net supervisors for automated manufacturing systems

Deadlock avoidance problems are investigated for automated manufacturing systems with flexible routings. Based on the Petri net models of the systems, this paper proposes, for the first time, the concept of perfect maximal resourcetransition circuits and their saturated states. The concept facilities the development of system liveness characterization and deadlock avoidance Petri net supervisors. Deadlock is characterized as some perfect maximal resource-transition circuits reach their saturated states. For a large class of manufacturing systems, which do not contain center resources, the optimal deadlock avoidance Petri net supervisors are presented. For an general manufacturing system, a method is proposed for reducing the system Petri net model so that the reduced model does not contain center resources and, hence, has optimal deadlock avoidance Petri net supervisor. The controlled reduced Petri net model can then be used as the liveness supervisor of the system.     

Optimal deadlock avoidance Petri net supervisors for automated manufacturing systems

Deadlock avoidance problems are investigated for automated manufacturing systems with flexible routings. Based on the Petri net models of the systems, this paper proposes, for the first time, the concept of perfect maximal resource-transition circuits and their saturated states. The concept facilitates the development of system liveness characterization and deadlock avoidance Petri net supervisors. Deadlock is characterized as some perfect maximal resource-transition circuits reaching their saturated states. For a large class of manufacturing systems, which do not contain center resources, the optimal deadlock avoidance Petri net supervisors are presented. For a general manufacturing system, a method is proposed for reducing the system Petri net model so that the reduced model does not contain center resources and, hence, has optimal deadlock avoidance Petri net supervisor. The controlled reduced Petri net model can then be used as the liveness supervisor of the system.     

On Controllability of Dependent Siphons for Deadlock Prevention in Generalized Petri Nets

A fair amount of research has shown the importance of siphons in the analysis and control of deadlocks in a variety of resource allocation systems by using a Petri net formalism. In this paper, siphons in a generalized Petri net are classified into elementary and dependent ones, as done for ordinary nets in our previous work. Conditions are derived under which a dependent siphon is controlled by properly supervising its elementary siphons, which indicates that the controllability of dependent siphons in an ordinary Petri net is a special case of that in a generalized one. The application of the controllability of dependent siphons is shown by considering the deadlock prevention problem for a class of resource allocation systems, namely, G-system that allows multiple resource acquisitions and flexible routings in a flexible manufacturing system with machining, assembly, and disassembly operations. We develop a monitor-based deadlock prevention policy that first adds monitors for elementary siphons only to a G-system plant model such that the resultant net system satisfies the maximal controlled-siphon property (maximal cs-property). Then, by linear programming, initial tokens in the additional monitors are decided such that liveness is enforced to the supervised system. Also, a simplified live marking relationship for a G-system between the initial tokens of the source places and those of the resource places is derived. Finally, the proposed deadlock prevention methods are illustrated by using an example.     

An Iterative Synthesis Approach to Petri Net-Based Deadlock Prevention Policy for Flexible Manufacturing Systems

This paper proposes an iterative synthesis approach to Petri net (PN)-based deadlock prevention policy for flexible manufacturing systems (FMS). Given the PN model (PNM) of an FMS prone to deadlock, the goal is to synthesize a live controlled PNM. Its use for FMS control guarantees its deadlock-free operation and high performance in terms of resource utilization and system throughput. The proposed method is an iterative approach. At each iteration, a first-met bad marking is singled out from the reachability graph of a given PNM. The objective is to prevent this marking from being reached via a place invariant of the PN. A well-established invariant-based control method is used to derive a control place. This process is carried out until the net model becomes live. The proposed method is generally applicable, easy to use, effective, and straightforward although its off-line computation is of exponential complexity. Two FMS are used to show its effectiveness and applicability     

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.     

信标基底的可选择性在制造系统死锁控制中的应用

本文基于Petri网模型,讨论柔性制造系统的死锁控制问题.为了建立结构简单的Petri网控制器,本文在以前的工作中提出了信标基底的概念.信标基底是一组满足特定条件的严格极小信标集合.本文证明基于不同的信标基底,建立的受控系统其容许性能也不同.而容许性是评价死锁控制策略优劣的重要标准之一.故如何选择信标基底,提高受控系统的容许性能是值得研究的问题.本文讨论了使受控系统容许性能大大提高的信标基底的选择条件.基于该条件,为柔性制造系统建立有效的死锁控制策略.最后,通过两个例子解释该条件和策略.     

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.     

A Polynomial Algorithm for Computing Elementary Siphons in a Class of Petri Nets

A set of elementary siphons plays a key role in the development of deadlock prevention policies for automated manufacturing systems. This paper addresses the computation problem for elementary siphons in a subclass of Petri nets which are basic systems of simple sequential processes with resources (BS³PR) and can model many automated manufacturing systems. An algorithm for enumerating elementary siphons is established by the one‐to‐one relationship between maximal perfect resource‐transition circuits (MPCs) and strict minimal siphons. A set of MPCs is first computed, followed by a set of elementary siphons in a BS³PR. The presented algorithm is proved to have polynomial‐time complexity. An example is used to illustrate the algorithm.