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Model Predictive Control of Dissipative Distributed Parameter Systems Open Access


Other title
Model Predictive Control
Input/state constraints
Distributed parameter systems
Type of item
Degree grantor
University of Alberta
Author or creator
Liu, Liu
Supervisor and department
Stevan Dubljevic (Chemical and Materials Engineering)
Biao Huang (Chemical and Materials Engineering)
Examining committee member and department
Stevan Dubljevic (Chemical and Materials Engineering)
Biao Huang (Chemical and Materials Engineering)
Jinfeng Liu (Chemical and Materials Engineering)
Department of Chemical and Materials Engineering
Process Control
Date accepted
Graduation date
Master of Science
Degree level
Distributed parameter systems (DPSs) are distinguished by the fact that the states, controls, and outputs may depend on spatial position. The certain class of dissipative DPSs includes many underlying chemical and mechanical spatiotemporal phenomena such as chemical reactions, convection and diffusion, flexible structures and certain wave propagation problems, all of which can be described by partial differential equations (PDEs). In the past decade, considerable work has concentrated on the construction of a general framework of reduced-order control synthesis for PDEs systems arising from the modeling of DPSs on the basis of low-order ODEs models which are derived by spectral decomposition schemes. Among those control synthesis, model predictive control (MPC) is a popular and widely used method because of its ability to account for input and state constraints. However, these works did not address completely the problem of state constraints in the predictive controller design for either the PDE systems with non-self-adjoint operators or the PDE system describing flexible structures. Furthermore, almost all the existing MPC designs for DPSs are developed in an implicit form and implemented in an on-line way, which leads to the numerically-determined control actions and relatively large computational effort. This thesis presents a MPC scheme for the parabolic PDE system where a convective term is included in the operator to describe the convective heat and mass transfer which makes the operator non-self-adjoint as well as a MPC scheme for the flexible structural system described by a fourth-order PDE, and an explicit/multi-parametric MPC scheme for dissipative PDE systems. First, a MPC scheme which accounts for the input and state constraints is proposed for the parabolic PDEs system describing the axial dispersion chemical reactor. Subsequently, an approach is proposed to approximate the infinite-dimensional representation of Euler-Bernoulli beam system by a reduced-order finite-dimensional model, and the proposed MPC scheme is implemented on the reduced-order beam system. Following this, an explicit MPC scheme, which is solved off-line, is proposed to stabilize the certain class of dissipative PDE systems as well as guarantee the input and state constraints.
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.
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