23 research outputs found

    A behavioral approach to balanced representations of dynamical systems

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    AbstractThe behavioral approach to linear systems provides an alternative framework for studying the notion of balanced representations. A new definition for balanced representations is proposed that is one-to-one related to a set of system invariants that is obtained by assuming a specific Hilbert space structure on the system behavior. This notion of balancing is more general than the prevailing notion of balancing in that it is well defined for nonstable systems and is independent of a particular (input-output) representation of the system. It is shown that Lyapunov, LQ̧G, and H∞ balanced representations are obtained as a special case. An application for the problem of model approximation is discussed

    Covariance and Gramian matrices in control and systems theory.

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    Covariance and Gramian matrices in control and systems theory and pattern recognition are studied in the context of reduction of dimensionality and hence complexity of large-scale systems. This is achieved by the removal of redundant or 'almost' redundant information contained in the covariance and Grarrdan matrices. The Karhunen-Loeve expansion (principal component analysis) and its extensions and the singular value decomposition of matrices provide the framework for the work presented in the thesis. The results given for linear dynamical systems are based on controllability and observability Gramians and some new developments in singular perturbational analysis are also presented

    Digital Filters and Signal Processing

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    Digital filters, together with signal processing, are being employed in the new technologies and information systems, and are implemented in different areas and applications. Digital filters and signal processing are used with no costs and they can be adapted to different cases with great flexibility and reliability. This book presents advanced developments in digital filters and signal process methods covering different cases studies. They present the main essence of the subject, with the principal approaches to the most recent mathematical models that are being employed worldwide

    Conditioning, reduction, and disturbance analysis of large order integrated models for space-based telescopes

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    Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2001.Includes bibliographical references (p. 211-215).by Scott Alan Uebelhart.S.M

    Estimation and control of non-linear and hybrid systems with applications to air-to-air guidance

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    Issued as Progress report, and Final report, Project no. E-21-67

    Modeling and Reduction with Applications to Semiconductor Processing

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    This thesis consists of several somewhat distinct but connected parts, withan underlying motivation in problems pertaining to control and optimizationof semiconductor processing. The first part (Chapters 3 and 4) addressesproblems in model reduction for nonlinear state-space control systems. In1993, Scherpen generalized the balanced truncation method to the nonlinearsetting. However, the Scherpen procedure is not easily computable and hasnot yet been applied in practice. We offer a method for computing a workingapproximation to the controllability energy function, one of the mainobjects involved in the method. Moreover, we show that for a class ofsecond-order mechanical systems with dissipation, under certain conditionsrelated to the dissipation, an exact formula for the controllabilityfunction can be derived. We then present an algorithm for a numericalimplementation of the Morse-Palais lemma, which produces a local coordinatetransformation under which a real-valued function with a non-degeneratecritical point is quadratic on a neighborhood of the critical point.Application of the algorithm to the controllabilty function plays a key rolein computing the balanced representation. We then apply our methods andalgorithms to derive balanced realizations for nonlinear state-space modelsof two example mechanical systems: a simple pendulum and a double pendulum. The second part (Chapter 5) deals with modeling of rapid thermal chemicalvapor deposition (RTCVD) for growth of silicon thin films, viafirst-principles and empirical analysis. We develop detailedprocess-equipment models and study the factors that influence depositionuniformity, such as temperature, pressure, and precursor gas flow rates,through analysis of experimental and simulation results. We demonstratethat temperature uniformity does not guarantee deposition thicknessuniformity in a particular commercial RTCVD reactor of interest. In thethird part (Chapter 6) we continue the modeling effort, specializing to acontrol system for RTCVD heat transfer. We then develop and apply ad-hocversions of prominent model reduction approaches to derive reduced modelsand perform a comparative study
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