Proper Orthogonal Decomposition for Reduced Order Control of Partial Differential Equations

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, 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.

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

2000

Author dc:creator

• Atwell, Jeanne A.

Chair dc:contributor.committeechair

• King, Belinda B.

Committee members dc:contributor.committeemember

• Rogers, Robert C.
• Herdman, Terry L.
• Cliff, Eugene M.
• Burns, John A.
• Borggaard, Jeffrey T.

• Stabilized Finite Elements
• Burgers' Equation
• Heat Equation
• Proper Orthogonal Decomposition
• Reduced Order Feedback Control

Statement dc:rights

• In Copyright

Licence dc:rights.uri

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

Dc Identifier Other

etd-04192000-17360039

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/26985