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Packard, Norman H. Shermer, Russel Duane 2011-04-27T16:32:24Z 2011-04-27T16:32:24Z 10000-01-01 1991 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. Submitted by Carolyn Mead (cmead2@illinois.edu) on 2011-04-27T16:32:24Z No. of bitstreams: 1 1991_shermer.pdf: 3491958 bytes, checksum: 494f8177cbc13c1a5df764b3fd9dd48a (MD5) Made available in DSpace on 2011-04-27T16:32:24Z (GMT). No. of bitstreams: 1 1991_shermer.pdf: 3491958 bytes, checksum: 494f8177cbc13c1a5df764b3fd9dd48a (MD5) Previous issue date: 1991 Restriction data tranferred 2014-07-01T11:12:19-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: Thesis Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Carolyn Mead (cmead2@illinois.edu) on 2011-04-27T16:32:24Z Item is restricted indefinitely. Thesis U of I Only 3478201 http://hdl.handle.net/2142/18894 en 1991 Russel Duane Shermer model-based control spatially extended systems partial differential equations dynamics Model-based control of spatially extended systems Dissertation / Thesis text Physics Physics University of Illinois at Urbana-Champaign Dissertation Ph.D.