Boundary control of temperature distribution in a rectangular FGM plate

In this paper an analytical method and a PDE-based solution to control temperature distribution in FGM plates is introduced. For the rectangular FGM plate under consideration, it is assumed that the material properties such as thermal conductivity, density, and specific heat capacity, vary in the width direction (y); and the governing heat conduction equation of the plate is a second-order partial differential equation. Since there has been little control synthesis work for PDE-based systems as compared to the abundance of control design techniques available for ordinary differential equations (ODEs), most of the proposed control approaches for continuous domain rely on discretizing the PDE model into a set of ODEs. Using Lyapunov's theorem, we will show that with applying controlled heat flux through the boundary of the domain, the temperature distribution of the plate will approach to the desired distribution of T_d(x,y). Finally, numerical methods are used to analyze transient heat transfer as distributed temperature T(x,y,t) converge to desired one af T_d(x,y).