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Infinite-Dimensional LQ Control for Combined Lumped and Distributed Parameter Systems Open Access


Other title
Hyperbolic PDE
Coupled PDE-Algebraic Equations
Linear Quadratic
Optimal Control
Infinite-Dimensional Systems
Distributed Parameter Systems
Coupled PDE-ODE
Type of item
Degree grantor
University of Alberta
Author or creator
Alizadeh Moghadam, Amir
Supervisor and department
Forbes, J. Fraser (Department of Chemical and Materials Engineering)
Dubljevic, Stevan (Department of Chemical and Materials Engineering)
Examining committee member and department
Zhao, Qing (Department of Electrical and Computer Engineering)
Forbes, J. Fraser (Department of Chemical and Materials Engineering)
Dubljevic, Stevan (Department of Chemical and Materials Engineering)
Dochain, Denis (Université Catholique de Louvain)
Hayes, Robert E. (Department of Chemical and Materials Engineering)
Department of Chemical and Materials Engineering
Chemical Engineering
Date accepted
Graduation date
Doctor of Philosophy
Degree level
Transport-reaction processes are extensively present in chemical engineering practice. Typically, these processes involve phase equilibria and/or are combined with well-mixed processes. Examples include counter-current two-phase contactors, interconnected CSTR-PFR systems and distillation columns. These processes belong to the class of distributed parameter systems and their mathematical description involves combinations of partial differential equations (PDEs) , ordinary differential equations (ODEs) and algebraic equations. The commonly used techniques for controlling such distributed parameter systems involve approximation of the PDEs with a set of ODEs and applying standard control methods for lumped parameter systems. It is recognized that such approximate methods may result in significant errors in the analysis and control synthesis for distributed parameter systems. Therefore, the accurate analysis and control synthesis for these systems require the development of methods based on the infinite-dimensional control system theories. The thesis focuses on the development of infinite-dimensional linear quadratic (LQ) control for distributed parameter systems described by combinations of hyperbolic PDEs, ODEs and algebraic equations. In order to solve the optimal control problem, the dynamical properties of the systems considered, including C0-semigroup generation, exponential stabilizability and exponential detectability, are explored. These properties provide guarantees of the existence and uniqueness of the solution to the optimal control problem. The technique used to design the LQ controller is based on solving an operator Riccati equation (ORE). This is achieved through finding the equivalent matrix Riccati equation, which can be solved numerically by using proposed algorithms. Several numerical simulation studies, including an interconnected CSTR-PFR process, a continuous counter-current adsorption process of two interacting components in a moving-bed adsorber and a catalytic distillation process, are performed to demonstrate the theoretical results.
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
Alizadeh Moghadam, Amir (2013). Boundary optimal (LQ) control of coupled hyperbolic PDEs and ODEs. Automatica.Alizadeh Moghadam, Amir (2012). Infinite-dimensional LQ optimal control of a dimethyl ether (DME) catalytic distillation column. Journal of Process Control.Alizadeh Moghadam, Amir (2012). Optimal LQ-control of a PDAE model of a catalytic distillation process. Proceedings of the 8th IFAC Symposium on Advanced Control of Chemical Processes.Alizadeh Moghadam, Amir (2011). Distributed optimal control of a dimethyl ether (DME) catalytic distillation column. Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference.Alizadeh Moghadam, Amir (2011). LQR control of an infinite-dimensional time-varying CSTR-PFR system. Proceedings of the 18th IFAC World Congress.Alizadeh Moghadam, Amir (2010). LQ control of coupled hyperbolic PDEs and ODEs: Application to a CSTR-PFR system. Proceedings of the 9th International Symposium on Dynamics and Control of Process Systems.Alizadeh Moghadam, Amir (2010). LQ-optimal control for a class of time-varying coupled PDEs-ODEs system. Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems.

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