Supervisor Optimization for Deadlock Resolution in Automated Manufacturing Systems With Petri Nets

As more and more producers move to use flexible and agile manufacturing as a way to keep them with a competitive edge, the investigations on deadlock resolution in automated manufacturing have received significant attention for a decade. Deadlock and related blocking phenomena often lead to catastrophic results in automated manufacturing systems. Their efficient handling becomes a necessary condition for a system to gain high productivity. This paper intends to present a tutorial survey of state-of-the art modeling and deadlock control methods for discrete manufacturing systems. It presents the updated results in the areas of deadlock prevention, detection and recovery, and avoidance. It focuses on three modeling methods: digraphs, automata, and Petri nets. Moreover, for each approach, the main and relevant contributions are selected enlightening pros and cons. The paper concludes with the future research needs in this important area in order to bridge the gap between the academic research and industrial needs.

Automated manufacturing systems (AMSs) are developing rapidly with increasingly sophisticated operations and complex topologies. In this paper, we propose a new kind of AMS structure, namely, AESMs, with processes expressed by flexible routes and embedded by marked graph blocks. Flexible routes and assembly operations are combined organically in this model, making it structurally complex and applicably adaptable. Deadlock resolution in AMSs is a fundamental and prerequisite issue. Conventional approach is based on monolithic methodologies by means of siphons, i.e., a special structural object closely related to deadlocks. Analysis shows that siphon-based mechanism is of limited applicability to control AESMs. On the contrary, we utilize a distributed approach in accordance with the philosophy of model predictive control techniques, which can create a trajectory dynamically leading the entire system to its desired destination. In our strategy, whether or not concerned tokens can reach critical places or critical place unities determines the feasibility of each step's execution. Control strategy is applied to processes locally such that they can concurrently proceed at the same pace. Global goals become attainable through the local observation, control, and execution upon local processes without knowing external and extra information.

Since the 1980s, Petri nets (PN) have been widely used to model automated manufacturing systems (AMS) for analysis, performance evaluation, simulation, and control. They are mostly based on process‐oriented modeling methods and thus termed as process‐oriented PN (POPN) in this paper. The recent study of deadlock avoidance problems in AMS led to another type of PN called resource‐oriented PN (ROPN). This paper, for the first time, compares these two modeling methods and resultant models in terms of modeling power, model complexity for analysis and control, and some critical properties. POPN models the part production processes straightforwardly, while ROPN is more compact and effective for deadlock resolution. The relations between these two models are investigated. Several examples are used to illustrate them. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Modelling automated manufacturing systems using a modification of coloured petri nets

This paper presents a new scheduling method for a flexible manufacturing system (FMS) in a Petri net framework. Petri nets can concisely model multiple lot sizes for each job, the strict precedence constraint, multiple kinds of resources, and concurrent activities. To decrease the likelihood of rejecting the critical markings, our algorithm adopts an improved checking method for previous generated marking. To reduce the computation complexity, an elaborate scheme is applied, which performs A* search locally and backtracking search globally in the reachability graph of the Petri net. Some numerical experiments are carried out to demonstrate usefulness of the algorithm.

For automated manufacturing systems (AMSs), deadlock-free operation is an important control objective, encouraging many researchers to focus their efforts on obtaining a computationally tractable and efficient control policy for the sake of deadlock resolution. However, much of the work existing in the literature obtains such control policies, by restricting the research model to some structurally simple ones, implying that extending these currently existing results to more complex models is usually nontrivial. In this work, we develop an on-line distributed control method for deadlock problem arising in the Petri nets where subnets are forward-conflict free nets. Without knowing the external and extra information, deadlocks can be avoided in real-time through local observation, control, and execution upon processes, thus greatly reducing computational complexity and time. Moreover, the results concluded by our control method can be easily extended to more structurally complex AMSs.

Modern complex systems require intensive application of complicated supervisors. Structural simplification techniques are one of the fundamental researches in the context of automated manufacturing systems (AMSs). They can reduce implementation cost, mitigate fabrication complexity, and improve reliability. Several typical methods are developed along this direction. In order to thoroughly explore their effectiveness and performance, we make a comparison and contrast investigation among them. Several analytical results and performance measures are proposed for their qualitative and quantitative comparison. Our approach can assist researchers and practitioners better comprehend the inherit mechanisms and relative merits of these simplification methodologies and their applicability in AMSs. This research is motivated by AMSs' control; however, they are also applicable to other systems with discrete event controllers.

In flexible manufacturing system (FMS) scheduling problems, the production process and constraints can be modeled by Petri nets concisely. However, the search space for an optimal or suboptimal schedule will exponentially grow with the increase of problem size. In this paper, we consider the scheduling problems of FMS in the framework of timed-transition Petri nets. In the framework, each token owns a individual timestamp which faciliates the analysis of the concurrency characteristic of modeled system. To save search effort, we provide an admissible heuristic function which also considers the available time of shared machine resources and subparts during calculating the lower bound of the remaining time for unprocessed operations. We prove the heuristic function is more effective than prior ones. Thus, an optimal scheduling strategy can be obtained at much less effort. Several numerical experiments are provided to demonstrate the effect of the improved heuristic function.

This paper presents a liveness analysis method for sequential automated manufacturing systems (AMSs), which can be modeled by a class of Petri nets named systems of sequential systems with shared resources (S4PR). We show that deadlocks in S4PR can be characterized by the saturation of its structural object named a perfect activity circuit (PA-circuits). Thus, S4PR is live if and only if no PA-circuits in it is saturated at all reachable states. A PA-circuits of an S4PR may not be saturated at any state; hence, we propose an integer linear program (ILP) to determine whether a PA-circuits can be saturated or not. Then an algorithm is proposed to compute the set of PA-circuits that may be saturated. This presented method nontrivially generalizes deadlock characterization and liveness condition of ordinary Petri nets to a broader class of nonordinary ones. Note to Practitioners —In the context of AMS, liveness is the most important property since it implies that there is no partial deadlock during the system evolution, and hence, all part types can be produced smoothly. We study the problem of liveness for AMS with the most general resource allocation and flexible routing, which can be modeled by S4PRs or disjunctive/conjunctive (D/C) resource allocation systems (RASs). Given such a complex AMS, based on its Petri net model, this paper presents a sufficient and necessary liveness condition by utilizing the structural properties, and develops an algorithm to identify all the structural objects that may lead the systems to deadlocks. This paper is significant in liveness-enforcing supervisor design for S4PR.

Individuals, populations and fluid approximations: A Petri net based perspective

Logical modelling and Petri nets constitute two complementary approaches for the dynamical modelling of biological regulatory networks. Leaning on a translation of logical models into standard Petri nets, we propose a formalisation of the notion of circuit functionality in the Petri net framework. This approach is illustrated with the modelling and analysis of a molecular regulatory network involved in the control of Th-lymphocyte differentiation.

To cope with the complexities of flexible manufacturing system FMS scheduling, this paper proposes and evaluates an improved search strategy and its application to FMS scheduling in a Petri net framework. Petri nets can concisely model multiple lot sizes for each job, the strict precedence constraint, multiple kinds of resources and concurrent activities. On the execution of the Petri nets, our algorithm can use both admissible heuristic functions and nonadmissible heuristic functions having the upper supports of the relative errors in A * heuristic search algorithm. In addition, the search scheme can ensure the results found are optimal and invokes quicker termination conditions. To demonstrate it, the scheduling results are derived and evaluated through a simple FMS with multiple lot sizes for each job. The algorithm is also applied to a set of randomly-generated FMSs with such characteristics as multiple resources and alternative routings.

Timed Petri nets (TPNs) have been widely used for modeling discrete-event systems of diverse manufacturing and service industries. In this article, we introduce a reachability tree-based optimization algorithm to optimize cyclic schedules of TPNs. In particular, we focus on a special class of cyclic schedules that are referred to as one-cyclic schedules, i.e., the algorithm efficiently finds the optimal one-cyclic transition firing schedule of a TPN. The proposed scheduling method can be robustly applied and extended to a number of different scheduling models since the methodology is not bounded to a specific domain. To enhance the computational performance, we establish a set of transition ordering constraints that can reduce the tree size during the search procedure. We evaluate the computational efficiency of the suggested algorithm by examining robotized manufacturing systems where one-cyclic schedules are popularly being used. It is numerically shown that the proposed algorithm is computationally more efficient than the previously studied Petri net-based optimization methods. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Resource scheduling is one of the most important managerial issues in diverse industrial systems. An optimal scheduling method for a certain industrial system is often locally developed by utilizing domain-specific operational properties. Although such domain-dependent knowledge can contribute to enhancing the computational efficiency of an optimization method, such an approach has a weak point that the method might not be applicable to scheduling problems of different industrial fields. Our motivation is to develop an algorithm for optimizing steady-state schedules that can be robustly applied for various types of discrete-event systems. The algorithm is developed on the basis of the Petri net modeling framework as it is widely being used for describing cyclic behaviors of diverse manufacturing systems, service systems, and social systems. It is experimentally shown that the proposed algorithm is computationally efficient compared with the existing cyclic scheduling methods.

The paper addresses the fault detection problem for discrete event systems modeled by Petri nets (PN). Assuming that the PN structure and initial marking are known, faults are modeled by unobservable transitions. The paper recalls a previously proposed diagnoser that works online and employs an algorithm based on the definition and solution of some integer linear programming problems to decide whether the system behavior is normal or exhibits some possible faults. To reduce the on-line computational effort, we prove some results showing that if the unobservable subnet enjoys suitable properties, the algorithm solution may be obtained with low computational complexity. We characterize the properties that the PN modeling the system fault behavior has to fulfill and suitably modify the proposed diagnoser.

On the basis of the assumption that no resource failure occurs, a variety of deadlock control policies have been developed for automated manufacturing systems (AMSs). However, in practical manufacturing systems, the occurrence of resource failures is always inescapable. In case, if resources fail to work, the existing deadlock control strategies can no longer be applied to the changed system; therefore, redesigning a new strategy is necessary. Because of their powerful modeling capabilities, Petri nets are used to model the considered AMSs allowing multi-type and multi-quantity resource acquisition. This paper focuses on extending a deadlock prevention method to be applied to AMSs with unreliable resources. Strict minimal siphons are controlled by added control places (monitors) to ensure the system’s liveness. To prevent blocking issues caused by resource failures, we develop a set of shared resource constraints represented by a set of inequalities based on the minimal resource requirements of processes and the capacity of shared resources. Robust monitors are designed for them to limit the distribution of tokens in unreliable neighborhood places. Our objective is to control resource allocation such that those parts not necessarily requiring any failed resource can continue progressing smoothly even if some unreliable resources break down. Examples are given to elucidate our proposed method clearly.