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Title:Model-based control of spatially extended systems
Author(s):Shermer, Russel Duane
Doctoral Committee Chair(s):Packard, Norman H.
Department / Program:Physics
Subject(s):model-based control
spatially extended systems
partial differential equations
Abstract:We extend a new method of control, model-based control, to the realm of partial differential equations. The hallmark of model-based control is that a particular goal dynamics is achieved by using a model for the observed dynamics to create the appropriate driving needed to make the goal dynamics an attractor for the system, alleviating the need for constant feedback, as is necessary with traditional control methods. First an introduction to general control methods is given, followed by a detailed explanation of model-based control. A general convergence analysis is presented for the purpose of establishing the criteria necessary for successful control. We investigate model-based control analytically for several classes of partial differential equations and use computer simulations to explore systems beyond analytic tractability such as the Burgers and the N avier-Stokes equations. With the Burgers equation a systematic investigation into the control behavior was conducted with particular attention to sensitivity of the control to model inaccuracies, boundary errors, and noise. For the Navier-Stokes equations some simple tests are conducted for the purpose of demonstrating the viability of the control method for spatially complex systems. Additionally, the idea of simplifying the application of the driving force is discussed and illustrated with examples.
Issue Date:1991
Genre:Dissertation / Thesis
Rights Information:1991 Russel Duane Shermer
Date Available in IDEALS:2011-04-27
Identifier in Online Catalog:3478201

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