Modeling and Reduction With Applications to Semiconductor Processing
HARVARD UNIV BOSTON MA
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This thesis consists of several somewhat distinct but connected parts, with an underlying motivation in problems pertaining to control and optimization of semiconductor processing. The first part Chapters 3 and 4 addresses problems in model reduction for nonlinear state-space control systems. In 1993, Scherpen generalized the balanced truncation method to the nonlinear setting. However, the Scherpen procedure is not easily computable and has not yet been applied in practice. We offer a method for computing a working approximation to the controllability energy function, one of the main objects involved in the method. Moreover, we show that for a class of second-order mechanical systems with dissipation, under certain conditions related to the dissipation, an exact formula for the controllability function can be derived. We then present an algorithm for a numerical implementation of the Morse-Palais lemma, which produces a local coordinate transformation under which a real-valued function with a non-degenerate critical point is quadratic on a neighborhood of the critical point. Application of the algorithm to the controllability function plays a key role in computing the balanced representation. We then apply our methods and algorithms to derive balanced realizations for nonlinear state-space models of two example mechanical systems a simple pendulum and a double pendulum.
- Electrical and Electronic Equipment