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- Title
Low-order optimal regulation of parabolic PDEs with time-dependent domain.
- Authors
Izadi, Mojtaba; Dubljevic, Stevan
- Abstract
Observer and optimal boundary control design for the objective of output tracking of a linear distributed parameter system given by a two-dimensional (2-D) parabolic partial differential equation with time-varying domain is realized in this work. The transformation of boundary actuation to distributed control setting allows to represent the system's model in a standard evolutionary form. By exploring dynamical model evolution and generating data, a set of time-varying empirical eigenfunctions that capture the dominant dynamics of the distributed system is found. This basis is used in Galerkin's method to accurately represent the distributed system as a finite-dimensional plant in terms of a linear time-varying system. This reduced-order model enables synthesis of a linear optimal output tracking controller, as well as design of a state observer. Finally, numerical results are prepared for the optimal output tracking of a 2-D model of the temperature distribution in Czochralski crystal growth process which has nontrivial geometry. © 2014 American Institute of Chemical Engineers AIChE J, 61: 494-502, 2015
- Subjects
PARTIAL differential equations; TIME-varying systems; GALERKIN methods; CALCULATIONS &; mathematical techniques in atomic physics; NUMERICAL analysis; CRYSTAL growth
- Publication
AIChE Journal, 2015, Vol 61, Issue 2, p494
- ISSN
0001-1541
- Publication type
Article
- DOI
10.1002/aic.14664