Petri网的子类G–system网的死锁控制策略

由于柔性制造系统中的死锁问题与对应建模Petri网中信标密切相关, 如何准确和快捷地求解这样的信标, 对于基于信标可控的死锁控制策略设计而言, 是十分重要的. 本文提出了基于G-system网灵巧信标的迭代式求解与受控的死锁控制策略. 与目前求解导致死锁信标所采用的部分枚举方法相比, 该方法避免了先求解出最大的死标识信标, 进而从中提取极小信标的步骤, 提高了信标的计算效率. 同时, 通过添加适当的控制库所, 使得灵巧信标满足max'-controlled, 获取的活性受控G–system网系统的许可行为数目可以得到进一步的提升. 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.     

基于混合整数规划的一般Petri网死锁检测方法

信标的受控性是检测柔性制造系统(flexible manufacturing system,FMS)Petri网模型是否存在死锁的关键因素.对于普通Petri网,在任何可达标识下所有信标不被清空是检测网系统非死锁的充分条件.然而,该条件对于建模能力更强的一般Petri网并不适用,max可控性条件由此产生.研究证明,该条件对于一般Petri网的死锁检测过于严格了.虽然其后有很多研究者通过改进max可控性条件以求给出条件更宽松的一般Petri网非死锁的充分条件,但大部分的研究成果都仅仅局限于一种顺序资源共享分配系统Petri网模型S4PR(systems of sequential systems with shared resources)网.因此,本文在max可控性条件的基础上提出了新的名为max#可控的信标可控性条件,并在此条件的基础上实现了基于混合整数规划(mixed integer programming,MIP)的死锁检测方法.与现有研究成果相比,max#可控性条件更宽松,可适用于更多类型的一般网,为解决大规模柔性制造系统中死锁监督控制器的结构复杂性问题提供了有力的理论支撑.     

基于信标的柔性制造系统的优化死锁预防策略

针对柔性制造系统（FMS）中的死锁问题，根据矩阵理论给出了Petri网中基本信标的概念，进而提出一种基于基本信标和混合整数规划法（MIP）的死锁预防策略．该策略将最优基本信标作为控制对象，以混合整数规划法给出的系统无死锁条件为目标函数．不考虑从属信标受控条件便可在多项式时间内使系统受控．该控制策略的显著特点是以较低的计算复杂度实现整个系统受控，并使需要添加的控制库所和连接弧大大减少．控制实例证明了其有效性．     

柔性制造系统非阻塞监督控制器优化设计

针对一类含有并发执行装配过程的柔性制造系统G-systems,提出一种新的死锁预防策略保证该系统的非阻塞性,即在控制下,受控系统从任意可达状态都可以到达理想状态.首先对Petri网模型中基本信标实施控制,保证了基本信标的最大可控,然后通过线性规划算法求取所有从属信标满足可控性的条件,即获得基本信标的控制深度变量.与现有方法相比,该策略优点在于只需加入少量的控制库所,就可避免不必要的迭代过程;其次是提出控制器输出弧位置优化策略,得到了结构更为简单、许可行为更多的非阻塞Petri网控制器.     

基于混合整数规划的非阻塞监督控制器设计

提出一种新的死锁控制策略, 保证含有并发执行装配过程的一类柔性制造系统(Flexible manufacturing system, FMS) G-system的非阻塞性, 即在控制下, 受控系统从任意可达状态都可到达理想状态. 首先对Petri网模型运用混合整数规划算法求取一个最大的死信标, 然后从最大的死信标中求取一个需要受控的极小信标, 并对其添加控制库所, 从而保证所有信标的最大可控. 和现有方法相比, 该策略避免了求取所有的信标, 且添加较少的控制库所即可获得结构简单、许可行为趋于最优的控制器.     

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.     

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.     

一类活性Petri网控制器的冗余检测及结构简化

S4R(systems of sequential systems with shared resources)网是分析和解决柔性制造系统死锁现象常用的一种重要的Petri网子类模型,现有的基于S4R网的死锁预防方法通常采用对部分或者全部严格极小信标添加控制库所来实现.此类方法的不足在于得到的活性S4R控制器中往往存在冗余控制库所.针对已为网中每一个严格极小信标都逐一添加了控制库所和相关连接弧的活性S4R控制器,本文提出并设计了一种基于整数规划技术的冗余检测及结构简化方法,由此得到结构更简单、行为允许度更高的活性S4R控制器.该方法的核心思想是:如果网中已经存在一个p-不变式使得某个严格极小信标满足最大受控条件,那么为该严格极小信标添加的控制库所就是冗余的.由于该方法无需进行Petri网的可达性分析,避免了状态组合爆炸问题,因此具有较高的可行性和计算效率.最后用实验验证了本文方法的正确性和有效性.     

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.     

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.     

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.     

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.     

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.     

应用必需信标的Petri网死锁预防策略

本文提出了表征一个Petri网子类,即S4R网(system of sequential systems with shared resources)中死锁问题的必需信标的概念和一种将混合整数规划算法与必需信标控制相结合的死锁预防策略.在该策略的迭代过程中,混合整数规划算法发现被控的Petri网中是否存在最大的死标识信标,若存在,则通过库所分类和迭代式的信标提取,得到必需信标,添加相应的控制库所,满足必需信标的最大可控性,从而实现被控的Petri网活性的目的.理论分析和算例验证表明了该策略的正确性和有效性.     

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.     

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。     

Necessary and sufficient liveness condition of GS3PR Petri nets

Structural analysis is one of the most important and efficient methods to investigate the behaviour of Petri nets. Liveness is a significant behavioural property of Petri nets. Siphons, as structural objects of a Petri net, are closely related to its liveness. Many deadlock control policies for flexible manufacturing systems (FMS) modelled by Petri nets are implemented via siphon control. Most of the existing methods design liveness-enforcing supervisors by adding control places for siphons based on their controllability conditions. To compute a liveness-enforcing supervisor with as much as permissive behaviour, it is both theoretically and practically significant to find an exact controllability condition for siphons. However, the existing conditions, max, max′, and max″-controllability of siphons are all overly restrictive and generally sufficient only. This paper develops a new condition called max*-controllability of the siphons in generalised systems of simple sequential processes with resources (GS³PR), which are a net subclass that can model many real-world automated manufacturing systems. We show that a GS³PR is live if all its strict minimal siphons (SMS) are max*-controlled. Compared with the existing conditions, i.e., max-, max′-, and max″-controllability of siphons, max*-controllability of the SMS is not only sufficient but also necessary. An example is used to illustrate the proposed method.