Algebraic estimation and active disturbance rejection in the control of flat systems

This paper proposes a feedback method for the control of uncertain systems with unknown external disturbances, which includes an algebraic estimator and relies on the Active Disturbance Rejection Control (ADRC) approach. The proposed estimator considers a generalized disturbance in order to deal with systems which may simultaneously present time varying parameters, external disturbances, un-modeled dynamics, and process noise. The on-line estimated disturbance is obtained by means of differential algebraic methods and it is used as the major part of an on-line feedback cancellation scheme aiming at linearization and uncertainty suppression. The algebraic estimator proposed in the paper makes unnecessary the use of classical extended state observers, which are widely used in ADRC. The speed of response and reliability of the proposed algebraic disturbance estimator-based control scheme was experimentally tested on three laboratory systems, including a system of directly-coupled DC motors, a roto-magnet system, and a disc and beam system, showing that the experimental results are in excellent agreement with the predictions of the theory.