| The problem of controlling a modern semiconductor fabrication facility (fab) is one of the most challenging problems facing the semiconductor industry. This work addresses the modeling and control of a modern fab. A virtual five-machine six-step mini-fab benchmark is used to focus the presentation. The benchmark-developed by Intel corporation in collaboration with Arizona State University-contains the features that make modeling and control of a real line challenging.; A Discrete Event System (DES) is one that changes state only at discrete points in time, in response to the occurrence of certain events. Most manufacturing systems fall in the category of discrete event systems, including semiconductor fabrication facilities. Other examples of DESs include: telecommunication networks, parallel processing systems and traffic control systems. One framework that is suitable for analyzing such systems is Max-Plus algebra. In this formalism, maximization and addition are the basic operations. For certain classes of DESs, using this formalism results in linear models, allowing great insight. For this reason, the framework was chosen for modeling the fab.; A technique was developed to model the factory benchmark at the lowest level, using Max-Plus algebra. It is shown that, under certain assumptions, the resulting models are linear in this framework. A factory model building block that allows arbitrary factories of this class to be modeled was developed. Several simple machine policies were evaluated for stability and performance using this framework.; General stability results were developed for systems governed by linear dynamic equations in the Max-Plus framework. Necessary and sufficient conditions for autonomous stability are presented herein. This work extends previously available results for a subclass of Max-Plus linear systems, namely those modeled by strongly connected graphs. The problem of input-output stability is also investigated.; The problem of stabilizing the factory in the presence of disturbances and parameter variation is addressed, and a release policy governor—that regulates the release of starts int the factory has been developed. These results are an extension of previously available results that were developed for higher-level flow models. |
