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Applications of nonautonomous infinite-dimensional systems control theory for parabolic PDEs Open Access

Descriptions

Other title
Subject/Keyword
Czochralski
lithium
infinite
dimensional
battery
regulation
diffusion
estimation
system
reaction
numerical
pde
convection
control
nonautonomous
optimal
state
parabolic
thermal
ion
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Ng, James C
Supervisor and department
Dubljevic, Stevan (Chemical and Materials Engineering)
Shah, Sirish L. (Chemical and Materials Engineering)
Examining committee member and department
Jovanovic, Mihailo R. (Electrical and Computer Engineering)
Marquez, Horacio J. (Electrical and Computer Engineering)
Li, Zukui (Chemical and Materials Engineering)
Forbes, J. Fraser (Chemical and Materials Engineering)
Department
Department of Chemical and Materials Engineering
Specialization
Process Control
Date accepted
2013-07-11T13:40:27Z
Graduation date
2013-11
Degree
Doctor of Philosophy
Degree level
Doctoral
Abstract
Parabolic partial differential equations (PDEs) are used as models of transport-reaction phenomena in a variety of different industrial chemical and materials engineering processes, and can yield precise descriptions of process variables with complex temporal and spatially dependent system dynamics. In many cases, the process dynamics are also affected by time-dependent features of the system which arise from the underlying physical characteristics of the process or the methods utilized in the formation and treatment of materials which may result in phase transitions, deformations or a combination of these behaviours. The dynamical analysis of these processes provides a fundamental basis for development of model based control strategies through a number of approaches including from within the framework of infinite-dimensional systems control theory. However, each class of transport-reaction system presents its own unique challenges and requires the development of new strategies within the existing framework. The focus of this thesis is the systematic treatment and realization of the feedback control design for two general classes of problems. The first class deals with the optimal boundary control problem for unstable parabolic PDEs with nonautonomous and nonhomogeneous infinite-dimensional system representation, and is considered within the context of a lithium-ion battery thermal regulation problem. The key challenges addressed include the time-dependence of system parameters, system instability, the restriction of the input along a portion of the battery domain boundary, the observer based optimal boundary control design, and the realization of the outback feedback control problem based on state measurement and interpolation methods. The second class of problems is the optimal distributed and boundary control of parabolic PDEs on time-varying spatial domains with nonautonomous infinite-dimensional system representation. The key challenges addressed include the development of an appropriate function space setting to handle the time-dependence of the spatial domain, the formulation of the infinite-dimensional system representation of the PDE control problem within this function space setting, and the realization of the optimal distributed and boundary control problems within the context of the Czochralski crystal temperature stabilization problem.
Language
English
DOI
doi:10.7939/R3QT11
Rights
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
Citation for previous publication
Ng J, Dubljevic S. (2013). Boundary control synthesis for a lithium-ion battery thermal regulation problem. AIChE Journal.  http://dx.doi.org/10.1002/aic.14183Ng
J, Aksikas I, Dubljevic S. (2013). Control of parabolic PDEs with time-varying spatial domain: Czochralski crystal growth process. International Journal of Control.  http://dx.doi.org/10.1080/00207179.2013.786187Ng
J, Dubljevic S. (2011). Optimal control of convection-diffusion process with time-varying spatial domain: Czochralski crystal growth. Journal of Process Control.  http://dx.doi.org/10.1016/j.jprocont.2011.07.017Ng
J, Dubljevic S. (2012). Optimal boundary control of a diffusion-convectionreaction PDE model with time-dependent spatial domain: Czochralski crystal growth process. Chemical Engineering Science.  http://dx.doi.org/10.1016/j.ces.2011.06.050

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