A new approach to design a finite-time extended state observer: Uncertain robotic manipulators application

In this article, a new approach to design a finite-time extended state observer (FT-ESO) for a class of uncertain nonlinear systems is proposed based on a novel coordinate transformation. First, a time-varying extended state observer (ESO) is designed to make the estimation error uniformly bounded. In this regard, the dynamic of the estimation error is transformed into a linear system with a generalized disturbance term as its input. Then, the time-varying gains of the ESO are designed to stabilize the system and consequently, to converge the estimation error to the neighborhood of zero and to remain uniformly bounded as t -> t(0) + T. In this article, without any knowledge about the disturbance, and uncertainties, a fault-tolerant FT-ESO is designed. Simulation results demonstrate the effectiveness of the proposed finite-time ESO for serial robotic manipulators with any number of links, in the presence of disturbances and an unknown fault.