University of Illinois Urbana-Champaign

Model-based control of spatially extended systems

Shermer, Russel Duane

This item is only available for download by members of the University of Illinois community. Students, faculty, and staff at the U of I may log in with your NetID and password to view the item. If you are trying to access an Illinois-restricted dissertation or thesis, you can request a copy through your library's Inter-Library Loan office or purchase a copy directly from ProQuest.

Permalink

https://hdl.handle.net/2142/19127

Description

Title
Model-based control of spatially extended systems
Author(s)
Shermer, Russel Duane
Issue Date
1991
Doctoral Committee Chair(s)
Packard, Norman H.
Department of Study
Physics
Discipline
Physics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
  • Engineering, General
  • Physics, General
  • Engineering, System Science
Language
eng
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 Navier-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.
Type of Resource
text
Permalink
http://hdl.handle.net/2142/19127
Copyright and License Information
Copyright 1991 Shermer, Russel Duane

Owning Collections

Graduate Dissertations and Theses at Illinois PRIMARY
Graduate Theses and Dissertations at Illinois
Dissertations and Theses - Physics
Dissertations in Physics