Scholarly Communications Project

Distributed Parameter Control of Thermal Fluids

by

Diana Rubio

PhD Dissertation submitted to the Faculty of the Virginia Tech in partial fulfillment of the requirements for the degree of

Doctor of Philosophy

in

Mathematics

Approved

John A. Burns, Chair
Terry L. Herdman
Eugene M. Cliff
Tao Lin
Jeffrey T. Borggaard

April 21, 1997
Blacksburg, Virginia

Abstract

We consider the problem of controlling a thermal convection flow by feedback. The system is governed by the Boussinesq approximation of the coupled set of Navier-Stokes and heat equations. The control is applied through Dirichlet boundary conditions. We concentrate on a two-dimensional mode and use a semidiscrete Galerkin scheme for numerical computations. We construct both a linear control and a non-linear quadratic control and apply them to the full non-linear model. First, we test these controllers on a one-mode approximation. The convergence of the numerical scheme is analyzed. We also consider LQR control for a two-dimensional heat equation.

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