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.     

Petri net supervisors for DES with uncontrollable and unobservabletransitions

A supervisor synthesis technique for Petri net plants with uncontrollable and unobservable transitions, that enforces the conjunction of a set of linear inequalities on the reachable markings of the plant, is presented. The approach is based on the concept of Petri net place invariants. Each step of the procedure is illustrated through a running example involving the supervision of a robotic assembly cell. The controller is described by an auxiliary Petri net connected to the plant's transitions, providing a unified Petri net model of the closed-loop system. The synthesis technique is based on the concept of admissible constraints. Procedures are given for identifying all admissible linear constraints for a plant with uncontrollable and unobservable transitions, as well as methods for transforming inadmissible constraints into admissible ones. A technique is described for creating a modified Petri net controller that enforces the union of all of these control laws. The method is practical and computationally inexpensive in terms of size, design time, and implementation complexity     

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.     

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.     

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.     

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.     

标注Petri网中的最小初始标识估计

为获得制造系统初始化时的最小资源以实现最优资源分配,利用标注Petri网对系统进行建模,并研究标注Petri网的最小初始标识估计问题。给定一个标注Petri网,在不可观测变迁组成无环子网的情况下,基于动态规划提出一种新的最小初始标识估计算法。在观察到给定的标注序列后,放宽不可观测变迁发生个数的限制,并根据该算法构建节点的演化过程。当出现相同的发生数向量时,仅保留当前极小的初始标识估计,并通过节点的演化过程对极小初始标识估计的托肯总数进行对比。为验证算法的有效性,给出一个制造系统的标注Petri网模型实例,最终得到的最小初始标识为［1000］^T,且对应的变迁发生序列为t₁t₃t₄t₆,满足给定标注Petri网的结构要求。实验结果表明,与传统基于动态规划的算法相比,该算法获得的最小初始标识估计具有更小的托肯总数。     

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.     

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     

Bounds on the Number of Markings Consistent With Label Observations in Petri Nets

In this paper, we consider state estimation in discrete-event systems (DESs) modeled by labeled Petri nets and present upper bounds on the number of system states (or markings) that are consistent with an observed sequence of labels. Our analysis is applicable to Petri nets that may have nondeterministic transitions (i.e., transitions that share the same label) and/or unobservable transitions (i.e., transitions that are associated with the null label). More specifically, given knowledge of a labeled Petri net structure and its initial state, we show that the number of consistent markings in a Petri net with nondeterministic transitions is at most polynomial in the length of the observation sequence (i.e., polynomial in the number of labels observed). This polynomial dependency of the number of consistent markings on the length of the observation sequence also applies to Petri nets with unobservable transitions under the assumption that their unobservable subnets are structurally bounded. The bounds on the number of markings established in this paper imply that the state estimation problem in labeled Petri nets can be solved with complexity that is polynomial in the length of the observation sequence.     

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.     

Design of Optimal Petri Net Supervisors for Flexible Manufacturing Systems via Weighted Inhibitor Arcs

This paper develops an approach to the design of an optimal Petri net supervisor that enforces liveness to flexible manufacturing systems. The supervisor contains a set of observer places with weighted inhibitor arcs. An observer place with a weighted inhibitor arc is used to forbid a net from yielding an illegal marking by inhibiting the firing of a transition at a marking while ensuring that all legal markings are preserved. A marking reduction technique is presented to decrease the number of considered markings, which can dramatically lower the computational burden of the proposed approach. An integer linear program is presented to simplify the supervisory structure by minimizing the number of observer places. Finally, several examples are used to shed light on the proposed approach which can lead to an optimal supervisor for the net models that cannot be optimally controlled via pure Petri net supervisors.     

On systematic methods to remove redundant monitors from liveness-enforcing net supervisors

Petri nets based deadlock prevention for flexible manufacturing systems has received much attention over the past decade, primarily due to the seminal work of Ezpeleta et al. in 1995. A Petri net based deadlock prevention mechanism is usually implemented by adding monitors or control places to a plant Petri net model such that liveness can be enforced. The significance of this methodology lies in that both a plant model and its supervisor are in a same formalism-Petri nets. Due to the inherent complexity of Petri nets, in theory, the number of additional monitors that have to been added to achieve liveness-enforcement purpose for an uncontrolled plant model is exponential with respect to the size of the model. This paper first proposes a systematic method to minimize the number of additional monitors in a liveness-enforcing Petri net supervisor such that the resultant net system has the same permissive behavior while liveness can still be preserved. Furthermore, for the liveness-enforcing Petri net supervisors of flexible manufacturing systems, which have some particular property, an algorithm is developed such that more permissive liveness-enforcing Petri net supervisors can be obtained after liveness-restrictive monitor removal. Compared with the existing techniques of eliminating redundant monitors in the literature, the complete state enumeration of a supervisor is avoided, which implies the high computational efficiency of the methods in this paper. Flexible manufacturing examples are used to demonstrate the proposed approaches.     

Marking Estimation of Petri Nets With Silent Transitions

In this paper, we deal with the problem of estimating the marking of a labeled Petri net system based on the observation of transitions labels. In particular, we assume that a certain number of transitions are labeled with the empty string , while unique labels taken from a given alphabet are assigned to each of the other transitions. Transitions labeled with the empty string are called silent because their firing cannot be observed. Under some technical assumptions on the structure of the unobservable subnet, we formally prove that the set of markings consistent with the observed word can be represented by a linear system with a fixed structure that does not depend on the length of the observed word.     

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     

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.     

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.