Approximation and Control of the Boussinesq Equations with Application to Control of Energy Efficient Building Systems

In this thesis we present theoretical and numerical results for a feedback control problem defined by a thermal fluid. The problem is motivated by recent interest in designing and controlling energy efficient building systems. In particular, we show that it is possible to locally exponentially stabilize the nonlinear Boussinesq Equations by applying Neumann/Robin type boundary control on a bounded and connected domain. The feedback controller is obtained by solving a Linear Quadratic Regulator problem for the linearized Boussinesq equations. Applying classical results for semilinear equations where the linear term generates an analytic semigroup, we establish that this Riccati-based optimal boundary feedback control provides a local stabilizing controller for the full nonlinear Boussinesq equations. In addition, we present a finite element Galerkin approximation. Finally, we provide numerical results based on standard Taylor-Hood elements to illustrate the theory.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2012

Author dc:creator

• Hu, Weiwei

Chair dc:contributor.committeechair

• Burns, John A.

Committee members dc:contributor.committeemember

• Cliff, Eugene M.
• Zietsman, Lizette
• Ball, Joseph A.
• Borggaard, Jeffrey T.

• Taylor-Hood Elements
• Analytic Semigroup
• Algebraic Riccati Equation
• LQR Control
• Boundary Feedback Control
• Boussinesq Equations

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-06192012-174604

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/38664