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PDE Backstepping Boundary Observer Design with Application to Thermal Management of PCR Process in Lab-on-a-Chip Devices Open Access


Other title
PDE Backstepping
Thermal Management
Boundary Observer
Type of item
Degree grantor
University of Alberta
Author or creator
Banaei Khosroushahi, Reza
Supervisor and department
Marquez, Horacio J. (Electrical and Computer Engineering)
Examining committee member and department
Sepehri, Nariman (University of Manitoba)
Dubljevic, Stevan (Chemical and Material Engineering)
Tavakoli, Mahdi (Electrical and Computer Engineering)
Marquez, Horacio J. (Electrical and Computer Engineering)
Fair, Ivan (Electrical and Computer Engineering)
Zhao, Qing (Electrical and Computer Engineering)
Department of Electrical and Computer Engineering
Control Systems
Date accepted
Graduation date
Doctor of Philosophy
Degree level
In the past two decades, the idea of Lab-on-a-Chip (LOC) devices has received a growing attention from researchers. A Lab-on-a-Chip device can be thought of as a miniaturized biological microchip that integrates several functionalities such as sample pre-treatment, sample transportation, mixing, reaction, separation and detection. Among the important functionalities that have been successfully integrated into a Lab-on-a-Chip device is the Polymerase chain reaction (PCR) process which enables rapid and inexpensive genetic analysis. PCR process relies on a thermal cycling process of repeated heating and cooling to replicate the DNA to a sufficient amount for detection and analysis. However, the PCR process requires precise measurement and control of the reaction temperature that is a challenging problem especially in the miniaturized LOC environment. The challenges associated with the thermal control problem of a PCR process in the LOC environment fall into two categories: first, there is no direct measurement of the temperature inside the reaction chamber and second, the heat distribution equation governing the thermal dynamics inside the microchip naturally leads the modeling and control of the microchip into the distributed parameter systems framework. This thesis deals with the estimation of the temperature inside the PCR-LOC microchip. Our goal in this thesis has two folds: first to contribute to the backstepping theory for the PDE systems both in the observer design and controller design stages, and second to use this theory for our application, PCR-LOC microchip. PDE Backstepping boundary observer design and its successful implementation involve several challenges, including: -Solving the PDE equation for the kernel function of the integral transformation in the PDE backstepping design and all of the numerical issues that come along. -Simulation aspects of the coupled PDE system composed of the PDE observer and the original PDE system. -Verification aspects, i.e. how to ensure that calibration is correct and the PDE observer actually presents the temperature inside the chamber. This thesis presents a number of innovative approaches to exclusively deal with each of the aforementioned challenges. The successful implementation of the designed observer and a previously designed controller is also presented.
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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