Active Disturbance Rejection Control based on a simultaneous adaptive observer and a time varying parameter identifier

Design of adaptive observers has been an active field in the systems theory. Until know, most of the existing solutions use a class of regular form with a set of unknown parameters. A different scheme used an estimation of external perturbations that can be compensated by the adaptive gain associated to the observer. In this paper, the presence of external perturbations for a model defined by a chain of integrators is considered. The adaptive observer used an identifier to obtain the time varying parameters used by the observer. Simultaneously, an adaptive gain associated to the observer adjusts the observer trajectories to provide the convergence between the states of the uncertain nonlinear system and the ones associated to the estimator suggested in this paper. Once the states of the uncertain system were obtained, a simple feedback controller was able to reject actively the perturbations that affect the nonlinear system. A simple third order uncertain system was evaluated in a numerical simulation for proving the performance of this observer/identifier. The same system was controlled using the estimated trajectories provided by the observer.