Modeling, analysis, simulation, scheduling, and control ofsemiconductor manufacturing systems: A Petri net approach

This paper presents a Petri net approach to modeling, analysis, simulation, scheduling, and control of semiconductor manufacturing systems. These systems can be characterized as discrete event systems that exhibit sequential, concurrent, and conflicting relations among the events and operations. Their evolution is dynamic over time. The system complexity is tremendous owing to the complex semiconductor manufacturing processes and test procedures. A formal approach such as Petri nets enables one to describe such complex discrete event systems precisely and thus allows one to perform both qualitative and quantitative analysis, scheduling and discrete-event control of them. This paper also serves as a tutorial paper. It briefly reviews applications of Petri nets in semiconductor manufacturing automation. It then introduces definitions and concepts of Petri nets. It proceeds with a discussion of basic Petri net modules in system modeling, a modeling method and a practical system's modeling example. Next, the paper presents their properties and their implications in manufacturing systems, as well as their analysis methods. Timed Petri nets are introduced for system simulation, performance evaluation, and scheduling purposes. An application-oriented case study is presented. Finally, the paper concludes with the active research areas in applying Petri nets to design of semiconductor manufacturing systems     

Comparing ladder logic diagrams and Petri nets for sequencecontroller design through a discrete manufacturing system

Design methods for sequence controllers play a very important role in advancing industrial automation. The increasing complexity and varying needs of modern discrete manufacturing systems have challenged the traditional design methods such as the use of ladder logic diagrams (LLDs) for programmable logic controllers. The methodologies based on research results in computer science have recently received growing attention by academic researchers and industrial engineers in order to design flexible, reusable, and maintainable control software. Particularly, Petri nets are emerging as a very important tool to provide an integrated solution for modeling, analysis, simulation, and control of industrial automated systems. This paper identifies certain criteria to compare LLDs and Petri nets in designing sequence controllers and responding to the changing control requirements. The comparison is performed through a practical system after introducing “real-time Petri nets” for discrete-event control purposes. The results reported in this paper will help: (a) further establish Petri net based techniques for discrete-event control of industrial automated systems; and (b) effectively convince industrial practitioners and researchers that it is worthy and timely to consider and promote the applications of Petri nets to their particular discrete-event control problems     

Modeling, qualitative analysis, and performance evaluation of theetching area in an IC wafer fabrication system using Petri nets

Integrated circuit (IC) wafer fabrication systems can be characterized as discrete event systems. Petri nets are tools that have been successfully used to model and analyze such systems. This paper reports a project of applying Petri net methodologies to detailed modeling, qualitative analysis, and performance evaluation of the etching area in a real-world IC wafer fabrication system located in Taiwan's Hsinchu Science-Based Industrial Park, To tackle the problem of building a large and complex system model, a synthesis technique is used. The resultant extended net model is checked for important qualitative properties in manufacturing. A simple control policy for deadlock prevention is proposed. To obtain performance measures, simulation is used. The simulation result shows that except a small number of machines, the errors between the simulated and actual utilizations are less than 5%, The validated model can be used to answer many “what-if” questions, such as predicting the maximal throughput and bottleneck machines     

Modeling and performance analysis of cluster tools using Petri nets

The performance of cluster tools is gaining ever-increasing importance as the semiconductor industry migrates to larger wafer sizes, and smaller device geometries. Customers demand higher throughput-to-footprint ratios for semiconductor equipment. Cluster tool throughput is the outcome of complex interactions of various subsystems, and there is a critical need for appropriate tools that aid in understanding these interactions, and their effects on throughput. Current methods for throughput analysis are not very well oriented toward understanding the dynamics in cluster tool processing. In this paper we present a procedure to model cluster tools using Petri nets. These models help designers to comprehend the flow of wafers during processing. While Petri nets have been used extensively in the modeling and analysis of diverse manufacturing processes/systems, this to the best of our knowledge is the first attempt to specifically model cluster tools. A state cycle analysis is discussed next; this method enables equipment designers to extract steady state throughput information, as well as understand the interplay of subsystems during the wafer Row. Two example configurations are used to illustrate Petri net-based model building and analysts. These two examples encompass a variety of design features found in the industry today, e.g., sequential and parallel processing, single and dual end effector robots, anticipatory and simple scheduling     

Modeling and Performance Evaluation of Inventory Systems Using Batch Deterministic and Stochastic Petri Nets

This paper presents our work on modeling and performance analysis of inventory systems using batch deterministic and stochastic Petri nets (BDSPNs). It addresses issues frequently raised by industrial companies, but did not receive enough attention by the Petri nets (PNs) community in spite of its important role in the study of discrete event systems. The BDSPN is a new class of PNs capable of describing the synchronization of discrete and batch token flows in discrete batch processes. Such processes appear in inventory systems or more general supply chains where materials are purchased in finite discrete quantities (batches of different sizes), and many operations such as inventory replenishment and customer order fulfillment are usually performed in a batch way because of the batch nature of customer orders and/or in order to take advantages of the economies of scale. In this paper, the BDSPN model is formally introduced, and its conflict resolutions of transitions and batch firing indexes are addressed. The model is then applied to the modeling and performance evaluation of various inventory systems. Analytic performance evaluation techniques are developed for the model with illustrative applications to the inventory systems. Our study shows that the model is powerful for both modeling and performance evaluation of the systems.     

Petri nets and integrality relaxations: A view of continuous Petri net models

Petri nets are formalisms for the modeling of discrete event dynamic systems (DEDS). The integrality of the marking and of the transitions firing counters is a clear reflection of this. To reduce the computational complexity of the analysis or synthesis of Petri nets, two relaxations have been introduced at two different levels: (1) at net level, leading to continuous net systems; (2) at state equation level, which has allowed to obtain systems of linear inequalities, or linear programming problems. These relaxations are mainly related to the fractional firing of transitions, which implies the existence of non-integer markings. We give an overview of this emerging field. It is focused on the relationship between the properties of (discrete) PNs and the corresponding properties of their continuous approximation. Through the interleaving of qualitative and quantitative techniques, surprising results can be obtained from the analysis of these continuous systems. For these approximations to be "acceptable", it is necessary that large markings (populations) exist. It can also be seen, however, that not every populated net system can be continuized. In fact, there exist systems with "large" populations for which continuation does not make sense. The possibility of expressing nonlinear behaviors may lead to deterministic continuous differential systems with complex behaviors.     

Differential Petri net models for industrial automation and supervisory control

Supervisory control systems play a central role in modern industrial automation. However, control theory has recently made significant advances in modeling mixed continuous/discrete event systems ("hybrid control systems"), whose typical instantiations include the industrial supervisory controller. This article shows how differential Petri nets, a model for hybrid control systems, can be used to represent industrial supervisory systems in a unified way. Typical industrial automation tests can be modeled, whereas the effect of communication protocols and software can be straightforwardly included using conventional Petri nets. Therefore, a global model for the operation of an industrial control system can be formed and its behavior analyzed.     

A modeling framework to evaluate performability parameters ingracefully degrading systems

A systematic approach to modeling and assessing gracefully degrading systems, exploiting the formalism offered by Petri nets, is provided. The procedure followed is based on the definition of some fundamental modules, the composition of which allows a complete model of the system to be obtained. The model can then be solved by computer simulation or analytically by means of a class of Petri nets to obtain interesting performability parameters either at steady state or when the system is time-varying. A number of real cases are examined and the results obtained are described     

基于层次实时有色Petri网的实时系统建模与分析方法研究

Petri网是一种基于图形进行模拟和分析的数学工具,能够描述系统的异步和并发行为,但是现有高级Petri网不能对嵌入式实时系统进行完整的模拟与实时性分析。该文首先通过扩展有色Petri网提出了层次实时有色Petri网模型,然后描述了嵌入式实时系统的建模和实时性分析方法。最后,将该文提出的方法应用于硬实时系统列车通信网络MVB总线控制器的建模和实时性分析过程,仿真和分析结果表明,该方法能够满足列车通信网络系统设计对MVB总线控制器的功能验证和实时性分析需求。     

Simulation of Semiconductor Manufacturing Supply-Chain Systems With DEVS, MPC, and KIB

The dynamics of high-volume discrete-part semiconductor manufacturing supply-chain systems can be described using a combination of Discrete EVent System Specification (DEVS) and model predictive control (MPC) modeling approaches. To formulate the interactions between the discrete process model and its controller, another model called Knowledge Interchange Broker (KIB) is used. A robust and scalable testbed supporting DEVS-based manufacturing process modeling, MPC-based controller design, and the ${hbox{KIB}}_{{{rm DEVS}/{rm{MPC}}}}$ interaction model is developed. A suite of experiments have been devised and simulated using this testbed. The flexibility of this approach for modeling, simulating, and evaluating stochastic discrete process models under alternative control schemes is detailed. The testbed illustrates the benefits and challenges associated with developing and using realistic manufacturing process models and process control policies. The simulation environment demonstrates the importance of explicitly defining and exposing the interactions between the manufacturing and control subsystems of complex semiconductor supply-chain systems.      

Petri nets: Properties, analysis and applications

Starts with a brief review of the history and the application areas considered in the literature. The author then proceeds with introductory modeling examples, behavioral and structural properties, three methods of analysis, subclasses of Petri nets and their analysis. In particular, one section is devoted to marked graphs, the concurrent system model most amenable to analysis. Introductory discussions on stochastic nets with their application to performance modeling, and on high-level nets with their application to logic programming, are provided. Also included are recent results on reachability criteria. Suggestions are provided for further reading on many subject areas of Petri nets     

Modeling a die bonder with Petri nets: a case study

The process of designing complex manufacturing machines involves problems of interdisciplinary communication, design space exploration as well as design evaluation and analysis that can best be solved by integrating modeling and simulation stages into the development process. Requirements necessary for a modeling environment are: support for hierarchical and modular structuring, module reuse, configurability of the model, executability of the model with a notion of time, and intuitive usability. The CodeSign object-oriented, temporal Petri net formalism with its associated tool is a modeling and simulation environment to meet those requirements. A case study conducted in an industrial setting is described that demonstrates the applicability of the CodeSign approach to the modeling of semiconductor manufacturing equipment with step-wise refinement. Results are given to show the accuracy of simulation results with respect to data actually measured on the machine. The CodeSign simulation results are shown to have superior accuracy compared to the output of a previous spreadsheet model of the same machine     

Tutorial: Petri nets as a graphical description medium for manyreliability scenarios

One of the basic problems of dependability modeling is the adequate abstraction of real-world technological problems to the principle terms of reliability/safety scenarios. This concerns primarily the definition of components and of faults on different system levels. Given these terms the rest of any modeling needs basic logical operations, mostly AND and OR, and delays, and often some counting (of time or events). All of these basic operations are offered by a fairly simple kind of Petri net (PN), i.e., timed stochastic Petri nets, allowing also for the modeling of immediate activities and of such with a deterministic delay. In this half-tutorial paper it is shown how such Petri nets modeling, i.e., the construction of the relevant nets, works in practice. No math will be needed for that. Several typical engineering virtues are needed; primarily imagination as to how to (i) find simple solutions, since often nonelegant solutions can be correct too, (ii) compose larger PN from elementary building blocks, and (iii) the ability to model the real world by interpreting the so-called tokens of a PN intelligently in different places of one and the same PN. In the appendix it is shown how the PN can also help in the analytical analysis of nonrepairable systems. In that context they are superior to state graphs since they show state durations explicitly     

Petri net as a modeling tool

Over the last decade, Petri nets have emerged as a most suitable, powerful and widely acceptable modeling tool for representing and studying the asynchronous concurrent hardware (or software) systems/processes. Petri nets can be viewed as formal automata or as an automation which can generate the formal languages or a model to analyse and synthesize various kinds of systems. The structure of Petri nets, their markings, extensions and subclasses are briefly discussed. Several examples of Petri net models of computer hardware and software are presented. Various applications of reachability concepts are also given.     

Modeling and analysis of message passing in distributedmanufacturing systems

This paper addresses the information flow between devices and programs in computer integrated manufacturing systems. Specifically, it presents modeling techniques and methods for detecting the existence of message paths among hardware and software components and the upper bound on time delays along that message path. The modeling technique can be used to analyze interoperability between hardware and software components in the system in initial design and specification. The modeling technique has three components: an object model to describe the message passing protocols between communicating components; a color timed Petri net to describe the dynamic behavior and state dependency within each individual component; and an object synthesis method that integrates the Petri nets of individual objects and message protocols between objects to describe the dynamics of the entire system. The graphical modeling can enhance communication among different groups involved in system design and the analytical method can provide component specifications. The use of the modeling technique and method in early system design can result in time and cost savings in system integration due to better communication, better component selection and early problem identification     

Structuring and composability issues in Petri nets modeling

Along Petri nets' history, numerous approaches have been proposed that try to manage model size through the introduction of structuring mechanisms allowing hierarchical representations and model composability. This paper proposes a classification system for Petri nets' structuring mechanisms and discusses each one of them. These include node fusion, node vectors, high-level nets, and object-oriented inspired Petri nets extensions, among others. One running example is used emphasizing the application of the presented mechanisms to specific areas, namely to automation systems modeling, and software engineering, where object-oriented modeling plays a major role.     

SMT-Based Symbolic Encoding and Formal Analysis of HML Models

Hybrid system is a dynamic system that involves continuous, discrete behaviors, and the interactions between continuous physical components and discrete controllers. In this paper a hybrid modeling language (called HML) for hybrid systems is extended with templates to achieve code reuse. For the formal analysis of the corresponding hybrid system models in this modeling language, these models are translated into SMT (satisfiability modulo theories) formulas as the input to an SMT solver dReal which retains the capability of bounded reachability analysis for non-linear hybrid systems. Moreover, dReal can produce data for potential traces of hybrid systems, thus it can be employed to simulate on hybrid systems. In this paper the simulation and reachability analysis are integrated in a prototype tool (open source). We present a case study for an inverted pendulum with PID (Proportional-Integral-Derivative) controllers and a rod reactor system for temperature control, both are verified to demonstrate the efficiency of the prototype tool. We conclude that, this modeling language is capable of modeling and verification of hybrid systems based on simulation and bounded reachability analysis.     

Ladder diagram and Petri-net-based discrete-event control design methods

Ladder diagrams (LDs) for a programmable logic controller are a dominant method in discrete event control of industrial automated systems. Yet, the ever-increasing functionality and complexity of these systems have challenged the use of LDs to design their discrete-event controllers. Researchers are constantly pursuing integrated tools that eliminate the limitations of LDs. These tools are aimed not only for control but also system analysis, evaluation, and simulation. For the past several decades, Petri nets (PNs) have emerged as an important tool to provide an integrated solution for modeling, analysis, simulation, and control of industrial automated systems. Different types of PN-based controllers are proposed and intended to apply in the industry. There is a need for more benchmark studies of PN and LD methods in order to form a structured and integrated framework for logic control software development. This paper, for the first time, presents a comprehensive survey on the recent methods for discrete event control design.