Unknown Input Observer with sliding mode disturbance estimator for the Diffusion PDE

In this note an Unknown Input Observer and a disturbance estimator are proposed for a class of distributed parameter systems. The 1D diffusion equation subject to an uncertain exogenous input is dealt with, and point-wise measurements are considered. The observer/estimator design is carried out by making reference to a finite dimensional modal decomposition of the solution. A combined state and output transformation is applied to the resulting finite dimensional approximation, yielding a special form for the transformed system that allows the implementation of a linear observer for reconstructing the system state and a sliding mode observer for reconstructing the unknown input. Numerical simulations show the applicability of the suggested approach to the considered class of PDEs.