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This work investigates quantitative supervisory control of discrete event systems modeled with Petri nets under the fixed‐initial‐credit energy objective. A weight function referred to as an energy function is defined on a Petri net to characterize the energy level of a transition. The proposed fixed‐initial‐credit energy problem aims to design a supervisor such that the energy level of a transition sequence in a supervised system is higher than 0 under a given initial energy level. The problem is eventually transformed into a two‐player game between a system and a supervisor; supervisor synthesis is reduced to finding a winning strategy in the two‐player game. Instead of enumerating the complete state space of the underlying Petri net, two information structures are utilized, namely the conventional basis reachability graph and the newly proposed essential marking graph, to construct two‐player games based on each of them. It is shown that a winning strategy for a supervisor decoded from the game based on the basis reachability graph of the Petri net is a solution to the problem but is in general restrictive. Further, it is shown that the set of strategies for a supervisor in the game based on the essential marking graph is consistent with that from the game based on the reachability graph of a Petri net. The two developed approaches do not require an exhaustive exploration of the state space of a plant, thus achieving higher efficiency. [ABSTRACT FROM AUTHOR]

Recently, in semiconductor manufacturing, cluster tools have to process multiple wafer types concurrently due to product customization. Different wafer types may have different processing routes, which causes deadlocks and complicates the scheduling problem of cluster tools. This work aims to develop a general method to resolve the scheduling problem of single-arm cluster tools with a general mix of wafer types. To this end, a generic Petri net model controlled by self-loops is developed to optimally avoid deadlocks. Based on the Petri net model, an earliest starting strategy is adopted to operate single-arm cluster tools once wafers enter the tools. In order to maximize the productivity, a particle swarm optimization algorithm is constructed to determine the releasing sequence of raw wafers. Numerical examples are provided to validate the effectiveness and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Nowadays, high-throughput screening (HTS) systems are widely used in pharmaceutical industries and laboratories for the discovery of new drugs and biomedical substances. It is important to efficiently schedule them so as to reduce the cost. In the operation of an HTS system, a microplate may visit some resources more than once and complex time window constraints are imposed on some activities and activity sequences. Moreover, with the consistency requirement, a one-microplate cyclic schedule is necessary. Thus, its scheduling problem is very challenging. This article studies the scheduling problem of an HTS system for an enzymatic assay, a typical application of HTSs, from the perspective of control theory. The system is modeled by resource-oriented Petri nets (ROPNs). With the model, necessary and sufficient conditions under which a feasible cyclic schedule exists are established. Then, we determine how many microplates should be in the system for concurrent processing and the transition firing sequence to obtain the activity sequence for an optimal and feasible schedule. In this way, a feasible and optimal cyclic schedule can be found by very simple computations, which shows that polynomial algorithms for an optimal schedule exist, while the existing studies apply mathematical programming with exponential computation complexity. Also, its efficient implementation is given. [ABSTRACT FROM AUTHOR]

Given a discrete event system, it is said to be opaque if an intruder who can partially observe system behavior cannot infer that the system is necessarily in a predefined secret. A discrete event system is current-state opaque if an intruder is never able to verify whether the current state of the system is within the secret states. This article addresses the verification of current-state opacity of a discrete event system modeled with Petri nets, where the secret is defined as a set of states. The existing methods cannot deal with large-sized systems due to the curse of dimensionality. Multi-valued decision diagrams (MDDs) are widely accepted as an efficient and compact data structure for representing the extremely large reachability sets of Petri nets. We show that MDDs can be used in Petri nets with partial observable transitions and propose an approach for the verification of current-state opacity for bounded Petri nets. It is shown by experimental studies that the symbolic approach is practically more efficient than traditional techniques such as basis reachability graphs (BRGs). [ABSTRACT FROM AUTHOR]

Due to the proliferation of contemporary computer-integrated systems and communication networks, there is more concern than ever regarding privacy, given the potential for sensitive data exploitation. A recent cyber-security research trend is to focus on security principles and develop the foundations for designing safety-critical systems. In this work, we investigated the problem of verifying current-state opacity in discrete event systems using labeled Petri nets. A system is current-state opaque provided that the current-state estimate cannot be revealed as a subset of secret states. We introduced a new sub-model of the system, named an observer net. The observer net have the same structure as the plant, but it is distinguished by the use of colored markers as well as simultaneous and recursive transition enabling and firing, which offer an efficient state estimation. We considered two settings of the proposed approach: an on-line setting, in which a current-state opacity algorithm is proposed. The algorithm waits for the occurrence of an observable event and determines if the current observation of a plant reveals the secret behaviour, as well as, an off-line setting, where the verification problem is solved based on a state estimator called a colored estimator. In this context, necessary and sufficient conditions for verifying opacity are developed with illustrative examples to demonstrate the presented approach. [ABSTRACT FROM AUTHOR]

Deadlocks are a highly undesirable situation in flexible manufacturing systems (FMSs). This article presents a direct and novel method to detect such markings by constructing the resource flow graph of a Petri net that models an FMS and to recover such markings by adding a set of recovery transitions. First, an algorithm is developed to build a new kind of directed graph called the resource flow graph of a Petri net. Resource flow graphs can well represent the competition for shared resources by different processes. Second, based on the resource flow graph, loop graphs can be found. Furthermore, partial deadlock markings can be easily detected due to their relationship with loop graphs. Then, we propose an algorithm to design a set of recovery transitions for loop graphs that are enabled at partial deadlock markings. The proposed approach can detect partial deadlock markings without generating a complete reachability graph of a Petri net and the resulting net is deadlock-free with all reachable markings by adding the obtained recovery transitions. Finally, some widely used examples are provided to demonstrate the proposed approach. Note to Practitioners—The occurrence of deadlocks in an FMS tends to cause unnecessary productivity costs and even catastrophic results. In the framework of Petri nets, reachability graph analysis can usually obtain a maximally permissive supervisor of a plant. However, it is rather inefficient since it suffers from the state explosion problem. In this particular research, we develop an off-line deadlock detection and recovery policy by setting a group of virtual events that are not present in a physical model. The proposed approach is computationally efficient since it does not require to generate a reachability graph. It guarantees that the resulted system is deadlock-free with its all original reachable markings. [ABSTRACT FROM AUTHOR]

With integer linear programming problems (ILPPs) being formulated and solved, the existing approaches design optimal Petri-net supervisors via nonpure net structures, including self-loops and data inhibitor arcs. Nonpure net structures are powerful for control of Petri-net-modeled discrete-event systems. However, in the existing work, the formulated ILPPs contain a large number of constraints, which is computationally inefficient. In this article, we propose approaches that formulate ILPPs with fewer constraints such that the computational efficiency is significantly improved. To do so, in formulating ILPPs for optimal Petri-net controllers by using self-loops and data inhibitor arcs, we remove the reachability conditions for legal markings. By doing so, an obtained solution may result in some legal markings unreachable. To solve this problem, a novel technique is developed to design an optimal controller by modifying the initial marking and structure of the obtained supervisor. It is shown that, by the reduced ILPPs, one can find the same feasible solutions as that obtained by the existing work. Finally, the proposed approaches are demonstrated by examples. [ABSTRACT FROM AUTHOR]

This paper addresses the state estimation of timed discrete event systems, where the occurrence of an event is associated with a time delay and the initial state of the system belongs to a set of possible initial states. A discrete event system is modeled with a bounded timed labeled Petri net whose unobservable subnet is acyclic, and the behavior of the system under a global time clock can be observed. The procedure for state estimations of partially observed Petri nets is refined by the introduction of time in discrete event systems. We apply the symbolic techniques to the representation of states and transition relations of bounded timed labeled Petri nets. Then we propose an online algorithm for the computation of state estimations generated by timed observations. [ABSTRACT FROM AUTHOR]

Nowadays, wafer fabrication in semiconductor manufacturing is highly dependent on cluster tools. A cluster tool is equipped with several process modules (PMs) and a wafer handling robot. When the tool is operating, generally each PM is processing a wafer, and the robot is responsible for delivering the wafers from one PM to another. Thus, when a wafer is completed in a PM, the robot may be busy for performing other tasks such that it cannot immediately unload the completed wafer in the PM, resulting in that the wafer has to stay there for some extra time. The processing time of a wafer together with its delay time for waiting for the robot’s arrival for unloading is defined as wafer residency time in a PM. However, a long wafer delay time may deteriorate its quality. Therefore, it is highly desired and important to reduce the wafer delay time at each step as much as possible. This work aims to tackle this important issue for single-arm cluster tools (SACTs). Specifically, by using a Petri net model, this work analyzes the steady-state operational behavior of an SACT under the backward and earliest starting strategies. It is found that there must exist wafer delay time at the steps in the upstream of the bottleneck step, and such wafer delay time can be reduced by properly adjusting the robot waiting time. Thus, three algorithms are developed to reduce the wafer delay time at each step as much as possible by properly assigning the robot idle time. Finally, the application of the proposed method is illustrated by using examples. Note to Practitioners—In a modern semiconductor fab, there are hundreds of cluster tools for wafer fabrication. To ensure wafer quality, it is important to reduce the wafer delay time in PMs of cluster tools after a wafer is processed since the high temperature, chemical gas, and particles in the PMs may damage the wafer. To do so, this work proposes three algorithms with polynomial complexity to assign the robot idle time as robot waiting time such that the wafer delay time in PMs can be reduced as much as possible. Furthermore, the obtained schedule by these algorithms is optimal in terms of the cycle time. Besides, the developed algorithms can be easily embedded into the controller of cluster tools by facility engineers. Therefore, this work has a practical value. [ABSTRACT FROM AUTHOR]

A maximally permissive (or optimal) supervisory control of an automated manufacturing system (AMS) modeled by Petri nets (PNs) can be usually implemented by imposing constraints in the form of a set of linear inequalities. To find such a set of linear constraints, in the existing work, an integer linear programming (ILP) problem is generally formulated and solved for some dominant markings obtained by reachability analysis and vector covering theory, which is computationally inefficient due to the combinatorial nature of solving ILPs to decide the coefficients of optimal linear constraints. This paper addresses the deadlock prevention problem for AMSs by developing efficient methods to reduce the computational overhead through the establishment of conditions on deciding the maximal permissiveness of linear constraints imposed on a system. By taking the advantage of structural properties of a PN model under consideration, we identify the most part of minimal covered illegal markings that can be optimally controlled via policies obtained by specific linear inequality constraints. Also, algorithms are developed to implement the proposed policies. The proposed approach can verify the optimality of a linear constraint efficiently without solving ILP problems. A linear programming method is developed to deal with the markings that cannot be processed by the proposed structural analysis. It is shown that for the considered class of PNs, called system of simple sequential processes with resources (S3PR), no mixed ILP problem needs to solve and the computational burden is dramatically reduced. Two examples are employed to demonstrate the efficiency of the developed method. [ABSTRACT FROM AUTHOR]

To effectively respond to the changing market demands, a manufacturer should produce variety of products with small lots. Thus, multiple products (models) are assembled simultaneously on a same line. However, it is very challenging to balance such an assembly line. This paper conducts a study on balancing a mixed-model assembly line of Type E. To solve this problem, a coloured-timed Petri net model is developed to describe the task precedence relationship. Also, the optimisation problem is formulated as a mathematical programming model. Then, with the models, a two-stage heuristic algorithm is proposed to solve the problem. At the first stage, based on the Petri net model, a P-invariant algorithm (PA) is presented to minimise the number of workstations. At the second stage, a heuristic is proposed to further minimise the cycle time by combining the PA with a binary search algorithm (BSA). Performance of the proposed method is evaluated by an illustrative example and numerical experiments. It is shown that it works well in terms of both solution accuracy and computational efficiency for large size problems. [ABSTRACT FROM PUBLISHER]

State space techniques are one of the main approaches deployed for the analysis of concurrent systems. However, state space construction is stalled by a common phenomenon called the state explosion problem which makes it a tough task or even impossible when the state space computation demands prohibitive cost (time and memory). We limit general resource allocation systems (RASs) to a certain class whose state space can be hierarchically constructed, yet it comprises various enough types of real-world discrete event systems, such as automated manufacturing systems. This paper focuses on a class of RASs modeled with Petri nets (PNs), where, through pure algebraic operations, a novel method to compute the state spaces is proposed, which is motivated by the superposition property. Given a PN model of a system and a target resource configuration, we first propose a special initial marking called the initial basis marking and compute the corresponding reachability graph. Then, we increase the capacity of the resource places in an incremental way and generate the reachability graphs by taking advantage of the PN structure and the previously computed reachability graph until the capacity function of resources reaches the target resource configuration. A complete enumeration of reachable states can be obtained by a recursive scheme. Experimental studies also demonstrate the efficiency of the proposed approach in terms of computational cost and its high-potential to cope with the state-explosion problem. [ABSTRACT FROM AUTHOR]

In wafer manufacturing, extensive research on the operations of cluster tools under the steady state has been reported. However, with the shrinking down of wafer lot size, such tools are frequently required to switch from handling one lot of wafers to another, resulting in more transient processes, including start-up and close-down ones. Also, wafer residency time constraint is critical for many wafer fabrication processes. To cope with the transient scheduling problem of time-constrained single-arm cluster tools with parallel chambers, based on a generalized backward strategy, this paper first builds timed Petri net models for these two transient processes. Then, two linear programs are derived for the first time to search a feasible schedule with a minimal makespan. Two industrial examples are given to demonstrate the effectiveness of the obtained results at last. [ABSTRACT FROM AUTHOR]

Scheduling a cluster tool with wafer residency time constraints is challenging and important in wafer manufacturing. With a backward strategy, the scheduling problem of such single-robot-arm cluster tools is well-studied in the literature. It is much more challenging to schedule a more general case whose optimal scheduling strategy is not limited to the backward one. This work uses a timed Petri net (PN) to model the dynamic behavior of the system and presents a method to determine the optimal scheduling strategy for the system. Based on its PN model and the obtained strategy, it reveals that the key issue to schedule such a tool is to determine when and how long the robot should wait for. Based on this finding, this work establishes for the first time the necessary and sufficient conditions regarding the existence of an optimal and feasible one-wafer cyclic schedule for single-robot-arm cluster tools. It then formulates a computationally efficient linear program to find it if existing, and finally gives industrial examples to show the application and power of the proposed method. [ABSTRACT FROM AUTHOR]

Resource failures may happen in automated manufacturing systems (AMSs) because of different reasons in the real world, making most existing deadlock control policies unapplicable. This paper develops methods for the robust deadlock control of AMSs with unreliable resources based on Petri nets. The considered AMSs are modeled with generalized systems of simple sequential processes with resources (GS3PR). First, a method based on reachability graph partition technique is provided to analyze the robust legal markings and the forbidden ones in an unreliable GS3PR (U-GS3PR), in which resource failures and recovery procedures are modeled with recovery subnets. Then, the control problem for such a system is converted into a problem for controlling the forbidden states in a U-GS3PR and control places can be designed by solving the maximal number of forbidden markings problems. Since the robust legal reachability spaces computed may be nonconvex and such a system cannot be optimally controlled by the conjunctions of linear constraints, we propose an interval-inhibitor-arc-based robust deadlock control policy for a system with nonconvex legal reachability spaces by solving the maximal number of ${t_{q}}$ -critical marking/transition separation instances problems (MNTMPs(${t_{q}}$)). Finally, examples are presented to demonstrate the proposed methods. [ABSTRACT FROM AUTHOR]

It is theoretically and practically significant to synthesize a maximally permissive (optimal) controller to prevent deadlocks in an automated manufacturing system (AMS). With an AMS being modeled with Petri nets, by the existing methods, integer linear programming (ILP) problems are usually formulated and solved to obtain optimal policies by forbidding illegal markings at the same time no legal marking is excluded. Without an efficient technique for solving an ILP, such a method is usually computationally prohibitive. A resource-oriented Petri net (ROPN) is employed to model a class of AMS for resolving the deadlock control problem with maximal permissiveness in this paper. Efficient methods are developed to figure out the key structures in an ROPN model for deadlock prevention. Based on the structural properties of ROPN models, this work explores several types of illegal markings that can be prohibited optimally by structural analysis. For these markings, a deadlock prevention policy can be derived in an algebraic way without solving a notorious ILP problem. For the other markings, linear programming (LP), instead of ILP, approaches are developed to forbid them optimally. Thus, a maximally permissive controller can be developed while the computational cost is reduced greatly. The proposed methods are verified by typical examples in the literature. • Resource-oriented Petri nets are used to model systems for deadlock prevention. • Various types of illegal markings that can be simply prevented are structurally identified. • It finds that most of illegal markings can be prevented by using polynomial algorithms. • The other illegal markings can be prevented by solving a linear programming. [ABSTRACT FROM AUTHOR]

This paper deals with the identification problem of faulty behavior in a discrete event system, assuming that the fault-free model of a system is given in terms of Petri nets, where the set of transitions is divided into two disjoint subsets: 1) observable and 2) unobservable ones. The observed system output is defined as a transition-marking sequence, i.e., each transition is followed by a marking. First, a nonlinear integer programming model that characterizes the faults modeled by fault transitions is built according to the abnormal behavior extracted from the observed sequence. Then, it is converted into an integer linear programming (ILP) problem and a faulty net that preserves the structure of the fault-free one is obtained by solving this ILP model. In addition, an algorithm is developed to ensure acyclicity of the resulting unobservable subnet whose transition set is composed of the unobservable transitions of the fault-free net and the identified fault transitions. [ABSTRACT FROM AUTHOR]

A deluge of studies has been carried out on deadlock prevention and liveness enforcement for flexible manufacturing systems (FMSs). This paper reports an algebraic procedure to find a set of merged place invariants, aiming to reduce the structural complexity of a liveness-enforcing Petri net supervisor for an FMS. Firstly, given an uncontrolled Petri net model, a set of control places as well as their corresponding place invariants are computed by using the existing methods. A systematic approach is developed to find a set of merged place invariants that are much more compact than the original supervisor structure, which remarkably reduces the number of control places in a liveness-enforcing Petri net supervisor for an FMS. The structurally reduced supervisor provides the same or more permissive behavior than that of an original one. As an algebraic approach, the proposed method is computationally trivial and is applicable to all manufacturing-oriented Petri net classes currently available in the literature. Several typical manufacturing examples are used to demonstrate the approach reported in this research. [ABSTRACT FROM AUTHOR]

Power transmission lines of traditional power transmission systems (PTSs) may suffer from some faults that can lead to blackouts. This work proposes a methodology to construct hierarchical distributed control systems (DCSs) for the automatic fault detection and restoration of PTSs using colored Petri nets (CPNs). If faults occur in power transmission lines, they can be detected by supervisors, and local solutions can be computed to restore the faults. Each supervisor is coordinated by a coordination protocol to perform the computation of local solutions. The structures of traditional PTSs are simplified and defined by CPNs, and the derivation processes of fault detection and restoration based on the proposed coordination protocol are verified by the mathematical methods of CPNs. Finally, the complexity of the proposed hierarchical DCS and coordination protocol is discussed and an example is given to illustrate the proposed method. © 2018 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [ABSTRACT FROM AUTHOR]

A traditional power transmission system (TPTS) is composed of many electrical substations (ESs) and transmission lines. When the latter meet faults, the output of the ESs may be interrupted. In this paper, a methodology is proposed to construct controlled systems with battery energy storage systems to avoid the output interruption during the fault detection and restoration for some important ESs. In a TPTS, an important ES can be controlled by a supervisor that can be thought of as a control agent. Moreover, the ES can be preconnected with other ESs. If a fault occurs in the input lines of the ES, the fault can be detected by its supervisor and restored by its preconnected ESs. Furthermore, the ES can contain a battery energy storage system to store electric power for its temporary output during the fault detection and restoration. Therefore, the output interruption of the ES can be successfully avoided. This work formally models the structures of TPTSs and their control systems by using Petri nets and then verifies the correctness of fault detection and restoration. Finally, a case study is presented. [ABSTRACT FROM AUTHOR]

In wafer fabrication, a robotic cluster tool is required to be closed down in order for engineers to perform its on-demand and preventive maintenance and switch between different wafer lots. They often deal with a close-down process subject to wafer residency time constraints, i.e., a wafer must exit from a processing chamber before its quality degradation within a certain time limit. To obtain higher yield, it is very important to optimize a close-down process for a cluster tool. Yet the existing literature pays no or little attention to this issue. By focusing on a time-constrained single-arm cluster tool, this paper intends: 1) to build its Petri net model to analyze its schedulability and 2) to develop computationally efficient algorithms to find an optimal and feasible schedule for its closing-down process under different workloads at its steps. Industrial examples are used to illustrate the application of the proposed method. [ABSTRACT FROM PUBLISHER]

This paper proposes an iterative method to the synthesis of liveness-enforcing supervisors for flexible manufacturing systems (FMSs). The concept of a global idle place (GP) for an original uncontrolled net system is developed. A GP is used temporarily to simplify the reachability graph computation of the system and is finally removed when the liveness of the system is achieved. At each iteration, bad markings (BMs) are identified. By using a marking covering approach, a minimal covering set of BMs is computed and then controlled through a simplified invariant-based control method. A sufficient condition under which the proposed method can obtain an optimal supervisor is presented. The proposed method can generally lead to an optimal or near-optimal supervisor. Finally, several FMS examples are utilized to illustrate applicability and the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

A hybrid multirobot cluster tool is composed of both single and dual-arm robotic cluster tools. Since the behavior of different individual tools is different, it is very challenging to coordinate their activities in such a tool and to schedule it optimally. To find a one-wafer cyclic schedule to reach the shortest cycle time for a treelike hybrid multirobot cluster tool whose bottleneck tool is process-bound, this paper extends resource-oriented Petri nets to model it such that a schedule can be parameterized by its robots’ waiting time. Based on the model, this paper then establishes the conditions under which there is a one-wafer cyclic schedule such that the shortest cycle time can be obtained. An efficient algorithm is also given to test the existence of such a schedule and to find it if existing. At last, examples are used to illustrate the proposed approaches. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of developing a model for traffic signal control with transit priority using Hierarchical Colored Petri nets (HCPN). Petri nets (PN) are useful for state analysis of discrete event systems due to their powerful modeling capability and mathematical formalism. This paper focuses on their use to formalize the transit signal priority (TSP) control model. In a four-phase traffic signal control model, the transit detection and two kinds of transit priority strategies are integrated to obtain the HCPN-based TSP control models. One of the advantages to use these models is the clear presentation of traffic light behaviors in terms of conditions and events that cause the detection of a priority request by a transit vehicle. Another advantage of the resulting models is that the correctness and reliability of the proposed strategies are easily analyzed. After their full reachable states are generated, the boundness, liveness, and fairness of the proposed models are verified. Experimental results show that the proposed control model provides transit vehicles with better effectiveness at intersections. This work helps advance the state of the art in the design of signal control models related to the intersection of roadways. [ABSTRACT FROM AUTHOR]

Abstract: 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. [ABSTRACT FROM AUTHOR]

Scheduling a multicluster tool with wafer residency time constraints is highly challenging yet important in ensuring high productivity of wafer fabrication. This paper presents a method to find an optimal one-wafer cyclic schedule for it. A Petri net is developed to model the dynamic behavior of the tool. By this model, a schedule of the system is analytically expressed as a function of robots’ waiting time. Based on this model, this paper presents the necessary and sufficient conditions under which a feasible one-wafer cyclic schedule exists. Then, it gives efficient algorithms to find such a schedule that is optimal. These algorithms require determining the robots’ waiting time via simple calculation and thus are efficient. Examples are given to show the application and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Due to the trends of larger wafer diameters and smaller lot sizes, cluster tools need to switch from processing one lot of wafers to another frequently. This leads to more transient periods in wafer fabrication, which includes startup and close-down processes. Their efficient scheduling and control problems become more and more important. They become very difficult to solve especially when wafer residency time constraints must be considered. Most previous studies focused on the steady periodic schedule for cluster tools. Little research was on the transient processes of cluster tools despite their increasing importance. In order to optimize a startup transient process, this work develops a Petri net model to describe its behavior for a single-arm cluster tool. Then, based on the model, for the case that the workloads among the steps can be properly balanced, this work proposes a scheduling algorithm to find an optimal and feasible schedule for the startup process. For the other cases schedulable at the steady state, a linear programming model is developed to find an optimal and feasible schedule for the startup process. Finally, illustrative examples are given to show the applications of the proposed method. [ABSTRACT FROM PUBLISHER]

In semiconductor manufacturing, there are wafer fabrication processes with wafer revisiting. Some of them must meet wafer residency time constraints. Taking atomic layer deposition (ALD) as a typical wafer revisiting process, this paper studies the challenging scheduling problem of single-arm cluster tools for the ALD process with wafer residency time constraints. It is found that there are only several scheduling strategies that are applicable to this problem and one needs to apply each of them to decide whether a feasible schedule can be found or not. This work, for each applicable strategy, performs the schedulability analysis and derives the schedulability conditions for such tools for the first time. It proposes scheduling algorithms to obtain an optimal schedule efficiently if such conditions are met. It finally gives illustrative examples to show the application of the proposed concepts and approach. [ABSTRACT FROM PUBLISHER]

This work proposes a novel structure in Petri nets, namely data inhibitor arcs, and their application to the optimal supervisory control of Petri nets. A data inhibitor arc is an arc from a place to a transition labeled with a set of integers. A transition is disabled by a data inhibitor arc if the number of tokens in the place is in the set of integers labeled on it. Its formal definitions and properties are given. Then, we propose a method to design an optimal Petri net supervisor with data inhibitor arcs to prevent a system from reaching illegal markings with respect to control specifications. Two techniques are developed to reduce the supervisor structure by compressing the number of control places. Finally, a number of examples are used to illustrate the proposed approaches and experimental results show that they can obtain optimal Petri net supervisors for the net models that cannot be optimally controlled by pure net supervisors. A significant result is that the proposed approach can always lead to an optimal supervisor with only one control place for bounded Petri nets on the premise that such a supervisor exists. [ABSTRACT FROM PUBLISHER]

This work studies the scheduling problem of a single-arm multicluster tool with a linear topology and process-bound bottleneck individual tool. The objective is to find a one-wafer cyclic schedule such that the lower bound of cycle time is reached by optimally configuring spaces in buffering modules that link individual cluster tools. A Petri net (PN) model is developed to describe the dynamic behavior of the system by extending resource-oriented PNs such that a schedule can be parameterized by robots’ waiting time. Based on this model, conditions are presented under which a one-wafer cyclic schedule with the lower bound of cycle time can be found. With the derived conditions, an algorithm is developed to find such a schedule and optimally configure buffer spaces. The algorithm requires only simple calculation to set the robots’ waiting time and buffer size. Illustrative examples are presented to demonstrate the proposed method. [ABSTRACT FROM PUBLISHER]

The recent developments of technologies in Internet of Things (IoT) provide the opportunities for smart manufacturing with real-time traceability, visibility, and interoperability in production planning, execution, and control. To fulfill this target, this work presents a real-time production performance analysis and exception diagnosis model (PAEDM). By this model, hierarchical-timed-colored Petri net (HTCPN) with smart tokens that change just like smart objects in practice is used to analyze the sensor data such that the critical performance information can be perceived. Decision Tree is used to diagnose exceptions from the critical production performance, so that persuasive qualitative and quantitative exception information can be extracted accurately. The presented method is demonstrated by a case study and simulation results show that PAEDM can be used to effectively analyze production performance and exceptions in real-time for dynamic and stochastic manufacturing processes. [ABSTRACT FROM PUBLISHER]

Nondeterministic firing of concurrent transitions in Petri nets (PNs) may lead to the disappearance of conflicts. The disappearance implies that the partial conflicting transitions in a conflict become disabled before the resolution of the conflict. The phenomenon is called confusions that are caused by the interlacement of conflicting and concurrent transitions in PNs, which generates incomplete and faulty system conflicting behavior such that conflicts cannot be correctly resolved. In this paper, conflict-increasing confusions (CICs) and conflict-decreasing confusions (CDCs) in a PN are investigated. The relation graph of conflicts and confusions (RGC²) in a PN is proposed to detect the structure of confusions. To avoid the occurrence of confusions in a PN, an algorithm based on generalized mutual exclusion constraints (GMECs) is proposed, which can generate confusion-avoidance supervisors such that the occurrence of conflicts can be ensured in a PN. Finally, an example of confusion detection and avoidance in a flexible assembly system is presented. [ABSTRACT FROM AUTHOR]

This paper focuses on the enforcement of nonlinear constraints in Petri nets. An integer linear programming model is formulated to transform a nonlinear constraint to a minimal number of conjunctive linear constraints that have the same admissible marking space as the nonlinear one does in Petri nets. The obtained linear constraints can be easily enforced to be satisfied by a set of control places with a place invariant based method. The control places make up a supervisor that can enforce the given nonlinear constraint. For a case that the admissible marking space decided by a nonlinear constraint is nonconvex, another integer linear programming model is developed to obtain a minimal number of constraints whose disjunctions are equivalent to the nonlinear constraint with respect to the reachable markings. Finally, a number of examples are provided to demonstrate the proposed approach. [ABSTRACT FROM AUTHOR]

The loss of conflicting information in a Petri net (PN), usually called confusions, leads to incomplete and faulty system behavior. Confusions, as an unfortunate phenomenon in discrete event systems modeled with Petri nets, are caused by the frequent interlacement of conflicting and concurrent transitions. In this paper, confusions are defined and investigated in bounded generalized PNs. A reasonable control strategy for conflicts and confusions in a PN is formulated by proposing elementary conflict resolution sequences (ECRSs) and a class of local synchronized Petri nets (LSPNs). Two control algorithms are reported to control the appeared confusions by generating a series of external events. Finally, an example of confusion analysis and control in an automated manufacturing system is presented. [ABSTRACT FROM AUTHOR]

To effectively operate a refinery and make it competitive, efficient short-term scheduling techniques that utilize commercial software tools for practical applications need to be developed. However, cumbersome details make it difficult to solve the short-term scheduling problem (STSP) of crudeoil operations, and mathematical programming models fail to meet the industrial needs. This article proposes an innovative control-theoretic and formal model-based method to tackle this long-standing issue. This method first models the STSP as a hybrid Petri net (PN) and then derives critically important schedulability conditions. The conditions are used to decompose a complex problem into several tractable subproblems. In each subproblem, there are either continuous variables or discrete variables. For subproblems with continuous variables, this work proposes a linear programming-based method to solve them; while, for subproblems with discrete variables, this work adopts efficient heuristics. Consequently, the STSP is efficiently resolved,and the application of the proposed method is well illustrated via industrial case studies. [ABSTRACT FROM PUBLISHER]

This paper studies the challenging problem of scheduling single-arm multi-cluster tools with wafer residency time constraints. They have a linear topology and their bottleneck tool is process-bound. This work aims to find an optimal one-wafer cyclic schedule. With the Petri net model developed in our previous work and the minimal cycle time for a multicluster tool without wafer residency time constraints, it derives the necessary and sufficient schedulability conditions for multicluster tools with wafer residency time constraints for the first time. Then, it gives an algorithm to find an optimal one-wafer cyclic schedule if schedulable. This is done by simply setting the robots’ waiting time for each tool. Thus, it is very computationally efficient and applicable to practical problems. An example is presented to illustrate the proposed method. [ABSTRACT FROM PUBLISHER]

A multi-cluster tool is composed of a number of individual cluster tools linked by buffering modules (BMs). The capacity of a BM can be one or two. Aiming at finding an optimal one-wafer cyclic schedule, this paper explores the effect of two-space BMs on the performance of a multi-cluster tool. A Petri net (PN) model is developed to model it by extending resource-oriented PNs. The dynamic behavior of robot waiting and tasks, process modules, and buffers is well described by the model. This paper shows that there is always a one-wafer cyclic schedule that reaches the lower bound of the cycle time of a process-bound tool. Furthermore, a closed-form algorithm is revealed to find such a schedule for the first time for such multi-cluster tools. Illustrative examples are given to show the application and power of the proposed method. [ABSTRACT FROM AUTHOR]

Due to the different behavior of single-arm and dual-arm cluster tools, it is challenging to schedule a hybrid multi-cluster tool containing both of them. This paper aims to find an optimal one-wafer cyclic schedule for such a multi-cluster tool. It is assumed that the bottleneck individual cluster tool in it is process-bound, thereby making it process-dominant. To do so, this paper models a hybrid multi-cluster tool with Petri nets. With this model, it derives the conditions under which individual cluster tools can operate in a paced way. Based on these conditions, this paper shows that for any process-dominant hybrid multi-cluster tool there is always a one-wafer cyclic schedule. Then, it develops the algorithms to find the minimal cycle time and the optimal one-wafer cyclic schedule. It is computationally efficient and easy-to-implement in practice. Examples are given to show the application and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Cyclic scheduling and operation of a residency time-constrained single-arm cluster tool with failure-prone process modules are highly challenging. In some cases, when a failure occurs, there still exists a feasible cyclic schedule for the performance-degraded tool. In other cases, such a schedule no longer exists. For the latter, it is highly desired to respond to a process module failure properly such that the tool can continue working and the wafers in the tool can be completed in a feasible way. This work is the first one to study this important issue. The idea is to apply Petri nets to describe the dynamic behavior of a single-arm cluster tool. With the developed Petri net model, this paper formulates failure response policies to control the cluster tool such that it can keep working without violating any residency time constraint. The failure response policies are implemented via efficient real-time control laws. Illustrative examples are presented to show their usage. [ABSTRACT FROM AUTHOR]

In a multi-cluster tool, there may be both single and dual-arm cluster tools. Such a multi-cluster tool is called hybrid multi-cluster tool. To operate such a multi-cluster tool, one needs to coordinate different types of robots for accessing the shared buffering modules. Aiming at finding a one-wafer periodic schedule such that the lower bound of cycle time can be reached, this paper conducts a study on scheduling a hybrid multi-cluster tool with its bottleneck tool being process-bound. The tool is modeled by a kind of timed Petri net model. With this model, the scheduling problem is reduced to determining the robots' waiting time. Then, the conditions under which a one-wafer periodic schedule exists such that the lower bound of cycle time can be reached are presented. Based on them, a closed-form algorithm is given to check whether such a one-wafer periodic schedule exists. If so, it is found via simple calculation. Examples are given to show the application of the proposed method. [ABSTRACT FROM PUBLISHER]

In operating a multi-cluster tool, it needs to coordinate the activities of multiple robots. Thus, it is very challenging to schedule it. This paper conducts a study on one-wafer cyclic scheduling for multi-cluster tools whose bottleneck cluster tool is process-bound. The system is modeled by a Petri net. With this model, conditions under which a one-wafer cyclic schedule exists are developed. Based on them, it is shown that, for any multi-cluster tool whose bottleneck cluster tool is process-bound, there is always a one-wafer cyclic schedule. Then, a method is presented to find the minimal cycle time and the optimal one-wafer cyclic schedule. It is computationally efficient. Illustrative examples are used to show the applications and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

For some wafer fabrication processes, such as an atomic layer deposition (ALD) process, the wafers need to visit some process modules for a number of times. Using the existing swap-based strategy scheduling method in such systems leads to a 3-wafer cyclic schedule. Unfortunately, it is not optimal in the sense of cycle time. Aiming at searching for a better schedule, this paper models the system by a timed Petri net. With this model, the properties of the 3-wafer schedule are analyzed. Then, based on the analysis, it is found that, to improve the performance, it is necessary to reduce the number of wafers completed in a cycle. Hence, a 1-wafer schedule is developed by using a new swap-based strategy. By using the Petri net model, its cycle time is analyzed and shown to be optimal. Also, an effective method is presented to implement it. Illustrative examples are given to verify the research results obtained in this paper. [ABSTRACT FROM PUBLISHER]

With wafer residency time constraints, it is crucial to schedule a cluster tool in semiconductor fabrication such that the wafer sojourn time in a processing module is in a given range. However, because of the activity time variation in wafer fabrication by cluster tools, a feasible schedule obtained under the assumption of deterministic activity times may become infeasible. To solve this problem, it is critically important to reveal the wafer sojourn time fluctuations with bounded activity time variation. This paper targets at single-arm cluster tools. They are modeled by a Petri net to describe the fabrication processes. Based on the net, a real-time control policy is proposed such that its use offsets the effect of the activity time variation as much as possible. Then, the wafer sojourn time delay is analyzed and analytical expressions are given to calculate the upper bound. With the proposed method, we can check if a given schedule is feasible under bounded activity time variation. Examples are given to show the applications of the research results. [ABSTRACT FROM PUBLISHER]

Deadlocks are a rather undesirable situation in a highly automated flexible manufacturing system. Their occurrences often deteriorate the utilization of resources and may lead to catastrophic results in safety-critical systems. Graph theory, automata, and Petri nets are three important mathematical tools to handle deadlock problems in resource allocation systems. Particularly, Petri nets are considered as a popular formalism because of their inherent characteristics. They received much attention over the past decades to deal with deadlock problems, leading to a variety of deadlock-control policies. This study surveys the state-of-the-art deadlock-control strategies for automated manufacturing systems by reviewing the principles and techniques that are involved in preventing, avoiding, and detecting deadlocks. The focus is deadlock prevention due to its large and continuing stream of efforts. A control strategy is evaluated in terms of computational complexity, behavioral permissiveness, and structural complexity of its deadlock-free supervisor. This study provides readers with a conglomeration of the updated results in this area and facilitates engineers in finding a suitable approach for their industrial scenarios. Future research directions are finally discussed. [ABSTRACT FROM PUBLISHER]

With wafer residency time constraint of cluster tools in semiconductor manufacturing, activity time variation can make an originally feasible schedule infeasible. Thus, it is difficult to schedule them and schedulability is a vitally important issue. With bounded activity time variation considered, this paper addresses their real-time scheduling issues and conducts their schedulability analysis. A Petri net (PN) model and a control policy are presented. Based on them, this paper derives closed-form schedulability conditions. If schedulable, an algorithm is developed to obtain an offline periodic schedule. This schedule together with the control policy forms a real-time schedule. It is optimal in terms of cycle time and can be analytically computed, which represents significant advance in this area. [ABSTRACT FROM PUBLISHER]

As the traffic on roads becomes increasingly heavy, driving safety has widely become a concern. Thus, an advanced driving-assistance system (ADAS) becomes much more important, because it can improve driving safety. It is composed of a human driver and an automated system called a copilot. To make it effective, they should properly cooperate. Hence, it is very important to define and model their cooperation behavior such that an ADAS can effectively be designed and realized. This paper presents the colored hybrid Petri net (CHPN) model to describe their cooperation behavior. It shows how switch between the driver and the copilot should be done to control the vehicle. The model is shown to be deadlock-free and conflict-free. Therefore, it is useful for ADAS design, analysis, and simulation. [ABSTRACT FROM PUBLISHER]