Boundary control of temperature distribution in a thick rectangular FGM plate (cubic block)

In this paper an analytical method and a PDE-based solution to control temperature distribution in FGM thick plates is introduced. For the rectangular FGM thick plate under consideration, it is assumed that material properties such as thermal conductivity, density, and specific heat capacity are constant in length and width(x, y direction) but they vary in thickness direction of the plate; and the governing heat conduction equation of the thick 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, it will be shown how to obtain boundary heat flux required for producing a desired distribution of Td(x,y,z).