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

• Author / Creator

  Banaei Khosroushahi, Reza

• 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.

• Subjects / Keywords

  • Thermal Management
  • Boundary Observer
  • PDE Backstepping

• Graduation date

  Fall 2013

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/R3BK16Z07

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.