Biased sinusoidal disturbance rejection with plant uncertainty via an adaptive third-order generalized integrator

In this paper a method to reject periodic biased disturbances of unknown frequency is presented. The entire set of unknown disturbance parameters is estimated via a third-order generalized integrator (TOGI). An interesting property of the method is that internal signals of TOGI are combined linearly to produce the control signal, resulting in a very simple algorithm. Only a single adaptive parameter permits to govern the system. It is shown that, within the assumptions of an averaging analysis, the adaptive system is stable and completely rejects the disturbance, even if a rough estimation of the plant is available. Bounds on the uncertainty of the plant are given in terms of the bounds on the input disturbance. Simulations demonstrate the properties of the algorithm in a variety of conditions.