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Low‐order optimal regulation of parabolic PDEs with time‐dependent domain
Author(s) -
Izadi Mojtaba,
Dubljevic Stevan
Publication year - 2015
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.14664
Subject(s) - partial differential equation , control theory (sociology) , observer (physics) , mathematics , distributed parameter system , eigenfunction , parabolic partial differential equation , galerkin method , discrete time and continuous time , transformation (genetics) , boundary (topology) , controller (irrigation) , tracking (education) , domain (mathematical analysis) , time domain , boundary value problem , finite element method , mathematical analysis , computer science , engineering , control (management) , eigenvalues and eigenvectors , physics , pedagogy , chemistry , structural engineering , biology , psychology , biochemistry , quantum mechanics , agronomy , computer vision , statistics , gene , artificial intelligence
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