Temperature control of functionally graded plates using a feedforward–feedback controller based on the inverse solution and proportional-derivative controller

As a first endeavor, an approach for the two- and three-dimensional temperature control of functionally graded (FG) plates by using the inverse solution and the proportional-differential (PD) controller is provided. For this purpose, firstly, having the desired temperatures at different locations and times, heat fluxes at the boundaries of the plates are estimated by inverse solution techniques offline. Then, the estimated heat fluxes as feedforward control inputs are combined with a PD controller to introduce a hybrid feedforward–feedback control input to the FG domain in the presence of disturbance and noise. In order to show the efficiency and accuracy of the proposed (inverse + PD) controller in two- and three-dimensional domains, different distinct examples, which include different boundary conditions, material properties and disturbance sources are presented. It is shown that the presented approach can adjust heat fluxes for control of the temperature accurately; also, the PD controller gains do not need to be re-adjusted for different problems.