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.     

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.     

Deadlock-free Supervisor Design for Robotic Manufacturing Cells With Uncontrollable and Unobservable Events

In this paper,a deadlock prevention policy for robotic manufacturing cells with uncontrollable and unobservable events is proposed based on a Petri net formalism.First,a Petri net for the deadlock control of such systems is defined.Its admissible markings and first-met inadmissible markings(FIMs)are introduced.Next,place invariants are designed via an integer linear program(ILP)to survive all admissible markings and prohibit all FIMs,keeping the underlying system from reaching deadlocks,livelocks,bad markings,and the markings that may evolve into them by firing uncontrollable transitions.ILP also ensures that the obtained deadlock-free supervisor does not observe any unobservable transition.In addition,the supervisor is guaranteed to be admissible and structurally minimal in terms of both control places and added arcs.The condition under which the supervisor is maximally permissive in behavior is given.Finally,experimental results with the proposed method and existing ones are given to show its effectiveness.     

基于Petri网结构分析的监控器综合

在基于Petri网建模的离散事件系统中, 提出利用局部关联信息进行约束转换, 并实现Petri网结构监控器综合的方法. 对以Parikh矢量约束形式给出的控制规范, 不可控不可观变迁会导致约束成为非法约束, 分析了不可控变迁的前向关联结构和不可观变迁的后向关联结构, 利用局部关联变迁实现对不可控和不可观变迁的间接控制, 从而将非法矢量约束转换为合法约束, 并保证初始控制规范的实现. 与基于矩阵的监控器综合方法相比, 本文的方法只需利用局部信息, 最后通过实例对该方法进行了说明.     

Maximally permissive supervisor synthesis based on a new constraint transformation method

The method is proposed to design the maximally permissive and efficient supervisor for enforcing linear constraints, in which the weights of places are not negative, on ordinary Petri nets with uncontrollable transitions. First, the weakly admissible linear constraint is introduced. Second, a method is proposed to design the monitor place for enforcing a weakly admissible linear constraint on Petri nets. Third, a theorem proving that a linear constraint can be equivalently transformed at an uncontrollable transition into a disjunction of new constraints is proposed. Fourth, using this theorem, an algorithm is presented to equivalently transform a linear constraint, each place weight of which is not negative, into a disjunction of weakly admissible ones. Lastly, the supervisor, which consists of the plant net and a set of monitor places, is designed for the weakly admissible linear constraints calculated by the above algorithm.     

Synthesis of supervisors enforcing general linear constraints in Petri nets

Efficient techniques exist for the design of supervisors enforcing constraints consisting of linear marking inequalities. This note shows that without losing the benefits of the prior techniques, the class of constraints can be generalized to linear constraints containing marking terms, firing vector terms, and Parikh vector terms. We show that this extended class of constraints is more expressive. Furthermore, we show that the extended constraints can describe any supervisor consisting of control places arbitrarily connected to the transitions of a plant Petri net (PN). The supervisor design procedure we propose is as follows. For PNs without uncontrollable and unobservable transitions, a direct method for the design of a PN supervisor that is least restrictive is given. For PNs with uncontrollable and/or unobservable transitions, we reduce the problem to the design of supervisors enforcing linear marking inequalities.     

Control Synthesis of Petri Nets Based on S-Decreases

A method for constructing a controller for a discrete event system modeled by a Petri net is presented in this paper. The control specification of the system is given by a set of linear inequality constraints defined on the marking of the net. The controller that forces the net to obey the constraints is an extended Petri net, which is synthesized based on minimal support S-decreases. The method can deal with general Petri nets with uncontrollable transitions, and then provides a systematic way for synthesizing net-based controllers for discrete event systems.     

基于GMEC转换算法的Petri网结构控制器综合方法

针对含不可控变迁Petri网系统禁止状态控制器设计问题,提出了一种基于矩阵变换和整数线性规划的结构控制器综合方法。该方法的关键是对代表系统合法状态的广义互斥约束(generalized mutual exclusion constraint, GMEC)进行转换。首先,根据Petri网系统的关联矩阵,将库所集分为无关库所集、不可控库所集和补足库所集。其次,通过对非允许GMEC中补足库所的权值和不可控库所的权值进行处理,并运用整数线性规划将非允许GMEC转换为允许GMEC。在允许GMEC的基础上,根据库所不变量原理设计出Petri网系统的结构控制器。最后,以某零件加工系统为例验证了所提方法的泛用性和高效性,为实际智能制造系统的监督控制器设计提供有效参考方案。     

Maximally Permissive Petri Net Supervisors for Flexible Manufacturing Systems with Uncontrollable and Unobservable Transitions

This paper presents a deadlock prevention policy to obtain behaviorally optimal supervisors for flexible manufacturing systems with uncontrollable and unobservable transitions. The conditions of uncontrollability and unobservability of transitions are revealed in the sense of the implementation of a Petri net supervisor. Then, integer linear programming models are designed to obtain a Petri net supervisor such that all legal markings are reachable and the number of control places is reduced. We also show that a controllable transition can be unobservable and self‐loops can be used to disable the transition but do not observe its firing. Finally, examples are provided to illustrate the proposed approach.     

基于有限容量库所的离散事件系统的Petri网控制器综合——第1部分

针对由Petri网建模的离散事件系统, 提出了一种新的控制器设计方法. 控制器是基于有限容量库所的概念构造而成的, 并使被控对象在给定的一组线性不等式约束下运行, 而给定的线性不等式约束是定义在库所标识上的. 控制器的综合利用了有限容量库所Petri网转换为 (普通 )无限容量库所Petri网的技术. 针对约束的不同情况, 给出了相应的Petri网的控制器的设计方法.     

针对一般线性约束的Petri网控制器设计方法

针对基于Petri网离散事件系统关于标识向量和Parikh向量的不等式约束反馈控制器设计问题,提出一种新的控制器设计方法.该方法首先利用Petri网的状态方程把关于标识向量和Parikh向量的不等式约束转变成关于Parikh向量的不等式约束,然后基于Petri网库所是关于Parikh向量的不等式约束的观点构造控制器.最后将该方法与Iordache和Moody提出的方法作比较,实验结果显示该方法更简单、有效.     

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.     

Modeling admissible behavior using event signals

We describe here how to obtain a model for the admissible behavior of a discrete event system that is represented by a safe Petri net (PN) model. The transitions of this PN model may be controllable or uncontrollable. Also given is a sequential specification which is modeled with a special state machine. Then, using the condition and event arcs of net condition/event systems, a combined model of plant and specification is obtained. We use only the structure of this combined model to develop a method which gives the admissible behavior of the system. Thus, we avoid the complexity of a complete state enumeration.     

Suboptimal supervisory control of Petri nets in presence of uncontrollable transitions via monitor places

This paper deals with the problem of enforcing generalized mutual exclusion constraints (GMEC) on place/transition nets with uncontrollable transitions. An efficient control synthesis technique, which has been proposed in the literature, enforces GMEC constraints by introducing monitor places to create suitable place invariants. The method has been shown to be maximally permissive and to give a unique control structure in the case that the set of legal markings is controllable. This paper investigates on and formally shows that the class of controllers obtained by this technique may not have a supremal element for uncontrollable specifications. Moreover, it is shown that the family of monitor places enforcing an uncontrollable specification can be parameterized with respect to the solution of a linear system of equation. An algorithm to obtain such parameterization is presented here.     

A deadlock prevention approach for flexible manufacturing systems with uncontrollable transitions in their Petri net models

Deadlocks are a highly undesired situation in a fully automated flexible manufacturing system, whose occurrences are tied to the existence of shared resources that are competed by different production processes. In the last two decades, a fair amount of research has been done on deadlock analysis and control for flexible manufacturing systems, leading to a variety of strategies in the literature. Petri nets are a promising mathematical tool to handle deadlock problems in flexible manufacturing systems. However, most deadlock control policies based on a Petri net formalism assume that all the transitions in a plant model are controllable. However, uncontrollability of events are a natural feature in a real‐world production system. This paper proposes a deadlock prevention policy for a class of Petri nets by considering the existence of uncontrollable transitions. Deadlocks are prevented by adding monitors to a plant Petri net model, whose addition does not inhibit the firings of uncontrollable transitions. Linear programming techniques are employed to find transitions to which a monitor points in order that a more permissive liveness‐enforcing Petri net supervisor can be found. A number of manufacturing examples are used to demonstrate the proposed methods. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Structuring Acyclic Petri Nets for Reachability Analysis and Control

The incidence matrices—from places to transitions and vice versa—of an acyclic Petri net can obtain a block-triangular structure by reordering their rows and columns. This allows the efficient solution of some reachability problems for acyclic Petri nets. This result is further used in supervisory control of Petri nets; supervisors for Petri nets with uncontrollable transitions are constructed by extending the method of Yamalidou et al. (1996) to Petri nets where transitions can be executed simultaneously. A large class of Petri nets with uncontrollable transitions is given for which the maximally permissive supervisor can be realized by a Petri net. The original specification is algorithmically transformed—by using the results for acyclic Petri nets—into a new specification to take the presence of uncontrollable transitions into account. The supervisor is obtained by simple matrix multiplications and no linear integer programs need to be solved. Furthermore, a class of Petri nets is given for which the supervisor can be realized by extending the enabling rule with OR-logic.     

Supervisor synthesis for discrete event systems under partial observation and arbitrary forbidden state specifications

In this paper, we consider the forbidden state problem in discrete event systems modeled by partially observed and partially controlled Petri nets. Assuming that the reverse net of the uncontrollable subnet of the Petri net is structurally bounded, we compute a set of weakly forbidden markings from which forbidden markings can be reached by firing a sequence of uncontrollable/unobservable transitions. We then use reduced consistent markings to represent the set of consistent markings for Petri nets with structurally bounded unobservable subnets. We determine the control policy by checking if the firing of a certain controllable transition will lead to a subsequent reduced consistent marking that belongs to the set of weakly forbidden markings; if so, we disable the corresponding controllable transition. This approach is shown to be minimally restrictive in the sense that it only disables behavior that can potentially lead to a forbidden marking. The setting in this paper generalizes previous work by studying supervisory control for partially observed and partially controlled Petri nets with a general labeling function and a finite number of arbitrary forbidden states. In contrast, most previous work focuses on either labeling functions that assign a unique label to each observable transition or forbidden states that are represented using linear inequalities. More importantly, we demonstrate that, in general, the separation between observation and control (as considered in previous work) may not hold in our setting.     

Suboptimal time management of discrete event systems with uncontrollable events modeled by Petri nets

Preventing systems from entering to forbidden states is a crucial issue in discrete event systems control. Adding supervisors to the system is a common method to avoid entering to forbidden states. In discrete event systems modeled by Petri net adding a supervisor could be done by means of control places. Since, the time is not considered in designing this supervisor, in presence of uncontrollable transitions adding control places can lead to increase the operation time of the system modeled by timed Petri net. Because, the firing of some transitions is prevented when it is not necessary. So, to design a more efficient controller, we will be required to use time information of the system component. Therefore, in this paper, a method for optimizing the time behavior of a supervised timed Petri net will be proposed. To obtain an efficient operation, some timed places as timer will be added to the net. The time of this timer places is calculated to permit firing of some controllable transitions in order to enter into some weakly forbidden states while entering to forbidden states is prevented. This concept leads to increase the speed of system as well as obtain an acceptable operation. This method can be applied for all systems modeled by Petri nets. The efficiency of proposed approach will be discussed and validated with a case study.     

Analysis of Hybrid Systems Based on Hybrid Net Condition/Event System Model

In thispaper, hybrid net condition /event systems are introducedas a model for hybrid systems. The model consists of a discretetimed Petri net and a continuous Petri net which interact eachother through condition and event signals. By introducing timeddiscrete places in the model, timing constraints in hybrid systemscan be easily described. For a class of hybrid systems that canbe described as linear hybrid net condition /eventsystems whose continuous part is a constant continuous Petrinet, two methods are developed for their state reachability analysis.One is the predicate-transformation method, which is an extensionof a state reachability analysis method for linear hybrid automata.The other is the path-based method, which enumerates all possiblefiring seqenences of discrete transitions and verifies if a givenset of states can be reached from another set by firing a sequenceof discrete transitions. The verification is performed by solvinga constraint satisfaction problem. A technique that adds additionalconstraints to the problem when a discrete state is revisitedalong the sequence is developed and used to prevent the methodfrom infinite enumeration. These methods provide a basis foralgorithmic analysis of this class of hybrid systems.     

Fault detection for discrete event systems using Petri nets with unobservable transitions

In this paper we present a fault detection approach for discrete event systems using Petri nets. We assume that some of the transitions of the net are unobservable, including all those transitions that model faulty behaviors. Our diagnosis approach is based on the notions of basis marking and justification, that allow us to characterize the set of markings that are consistent with the actual observation, and the set of unobservable transitions whose firing enable it. This approach applies to all net systems whose unobservable subnet is acyclic. If the net system is also bounded the proposed approach may be significantly simplified by moving the most burdensome part of the procedure off-line, thanks to the construction of a graph, called the basis reachability graph.