Robust error based noncollocated output tracking control for a heat equation Abstract   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 noncollocated 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 infinitedimensional extended state observer in terms of tracking error only which gives an estimation of both states of the frozen plant and exosystem. An observerbased 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.

Adaptive boundary observer design for linear hyperbolic systems; Application to estimation in heat exchangers Abstract   In this work, we consider the estimation of temperature along the pipes of concentric heat exchanger tubes in which CO2 is the working fluid. The transport phenomenon is modeled using (2x2) linear hyperbolic partial differential equations, with one rightward equation for the hot flow and one leftward equation for the cold flow. Both flows exchange energy through the wall interface, which physically induces a coupling between the two dynamics. Our objective is to estimate the temperature distribution along the flows from measurements at the tubes boundaries only. In this framework, we propose an adaptive boundary observer that can estimate not only the full state of the system, but also unknown indomain parameters. The design is based on transforming the error system via a finitedimensional backsteppinglike transformation into a desired filterbased system, for which standard backstepping observer techniques and adaptation laws can be used. The theoretical results are evaluated against the temperature measurements taken from a CO2 refrigeration apparatus built at CERN, Switzerland.