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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 767853, 12 pages
http://dx.doi.org/10.1155/2013/767853
Research Article

PDE Modeling of a Microfluidic Thermal Process for Genetic Analysis Application

1Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada T6G 2V4
2Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada N2L 3G1

Received 12 July 2013; Accepted 29 August 2013

Academic Editor: Zhiwei Gao

Copyright © 2013 Reza Banaei Khosroushahi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper details the infinite dimensional dynamics of a prototype microfluidic thermal process that is used for genetic analysis purposes. Highly effective infinite dimensional dynamics, in addition to collocated sensor and actuator architecture, require the development of a precise control framework to meet the very tight performance requirements of this system, which are not fully attainable through conventional lumped modeling and controller design approaches. The general partial differential equations describing the dynamics of the system are separated into steady-state and transient parts which are derived for a carefully chosen three-dimensional axisymmetric model. These equations are solved analytically, and the results are verified using an experimentally verified precise finite element method (FEM) model. The final combined result is a framework for designing a precise tracking controller applicable to the selected lab-on-a-chip device.