Robust error based non-collocated output tracking control for a heat equation

In this paper, an output tracking problem for a heat equation is considered, where all possible disturbances produced from an exosystem and a systematic uncertainty are considered and the performance output is non-collocated with control. The objective is twofold: to look at how the internal model principle works for the output tracking of PDEs: and to see how to design a robust tracking error feedback control for PDEs. To this purpose, we first select a frozen case with specially selected frozen coefficients of the disturbances. For this frozen system, we design a feedforward control by solving simply regulator equation and an infinite-dimensional extended state observer in terms of tracking error only which gives an estimation of both states of the frozen plant and exosystem. An observer-based tracking error feedback control is then designed for the frozen system, which is shown to be in line with the internal model principle. As a result, the system is shown to be robust to system uncertainty and disturbances in all channels. The numerical simulations validate the results. (C) 2020 Elsevier Ltd. All rights reserved.