Title page for ETD etd-04192000-17360039

Type of Document Dissertation
Author Atwell, Jeanne A.
URN etd-04192000-17360039
Title Proper Orthogonal Decomposition for Reduced Order Control of Partial Differential Equations
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
King, Belinda B. Committee Chair
Borggaard, Jeffrey T. Committee Member
Burns, John A. Committee Member
Cliff, Eugene M. Committee Member
Herdman, Terry L. Committee Member
Rogers, Robert C. Committee Member
  • Stabilized Finite Elements
  • Burgers' Equation
  • Heat Equation
  • Proper Orthogonal Decomposition
  • Reduced Order Feedback Control
Date of Defense 2000-04-10
Availability unrestricted
Numerical models of PDE systems can involve

very large matrix equations, but

feedback controllers for these systems must be computable

in real time to be implemented on physical systems.

Classical control design methods produce

controllers of the same order as the numerical models.

Therefore, emph{reduced} order control design is vital for practical

controllers. The main contribution of this research is a method

of control order reduction

that uses a newly developed low order basis. The low order basis

is obtained

by applying Proper Orthogonal Decomposition (POD) to a set of

functional gains, and is referred to as the functional gain

POD basis.

Low order controllers resulting from the

functional gain POD basis

are compared with low order controllers resulting from

more commonly used time snapshot POD bases, with the two dimensional

heat equation as a test problem. The functional gain

POD basis avoids subjective criteria associated

with the time snapshot POD basis and provides

an equally effective low order controller with larger stability

radii. An efficient and effective methodology is introduced for

using a low order basis in reduced order compensator design. This

method combines

"design-then-reduce" and "reduce-then-design" philosophies.

The desirable qualities of the resulting

reduced order compensator are verified by application

to Burgers' equation in numerical experiments.

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