PDE Modeling of a Microfluidic Thermal Process for Genetic Analysis Application - Reza Banaei Khosroushahi; Horacio J. Marquez; Jose Martinez-Quijada; Christopher J. Backhouse (Journal of Applied Mathematics)
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.