Proper orthogonal decomposition for reduced order modeling: 2D heat flow
Author
Efe, M. Ö.
Özbay, Hitay
Date
2003-06Source Title
Proceedings of 2003 IEEE Conference on Control Applications, CCA 2003
Publisher
IEEE
Pages
1273 - 1277
Language
English
Type
Conference PaperItem Usage Stats
155
views
views
195
downloads
downloads
Abstract
Modeling issues of infinite dimensional systems is studied in this paper. Although the modeling problem has been solved to some extent, use of decomposition techniques still pose several difficulties. A prime one of this is the amount of data to be processed. Method of snapshots integrated with POD is a remedy. The second difficulty is the fact that the decomposition followed by a projection yields an autonomous set of finite dimensional ODEs that is not useful for developing a concise understanding of the input operator of the system. A numerical approach to handle this issue is presented in this paper. As the example, we study 2D heat flow problem. The results obtained confirm the theoretical claims of the paper and emphasize that the technique presented here is not only applicable to infinite dimensional linear systems but also to nonlinear ones.
Keywords
Boundary conditionsHeat transfer
Mathematical models
Mathematical operators
Ordinary differential equations
Two dimensional
Finite dimensional ordinary differential equations
Heat flow
Proper orthogonal decomposition
Reduced order modeling
Control system synthesis