Feedback control of temperature distribution in a thick rectangular functionally graded plate

In this paper, a method for distributed control of temperature distribution in a thick rectangular functionally graded plate is proposed. In this way, the linear nonhomogenous conduction which its governing dynamics is a linear partial differential equation (PDE) with spatially varying coefficients is considered and actively controlled. For this purpose, firstly, this PDE is converted into a set of ordinary differential equations (ODEs) using the modified wavenumber methodology. This apporach is based on the combination of the fast Fourier transform (FFT) and finite difference techniques. Secondly, in order to stabilize each of these ODEs, linear optimal state feedback controller is utilized by minimizing a predefined performance index. The proposed controller is modified by adding a feedforward term to have a good tracking performance for the proposed method. The designed control inputs which are in the Fourier domain, are transfers to physical domain using the inverse Fast Fourier transform (IFFT). In order to solve the linear nonhomogenous conduction heat equation, a combination of finite difference and Runge-Kutta methodologies is implemented. Simulation studies show the performance of the proposed method, for example the smaller settling time, overshoot and also steady-state error.