Combined identification and rejection of periodic disturbances in the presence of plant uncertainty

Abstract The paper proposes an algorithm for the rejection of periodic disturbances of unknown frequency. The frequencies of the components of the disturbance are estimated using an orthogonal signals generator based on second-order generalized integrators. A novel feature of the algorithm is that internal signals of the frequency estimator are combined linearly to produce the control signal, resulting in a very simple algorithm. For a sinusoidal disturbance, the entire scheme is governed by a single adaptive parameter. It is shown that, within the assumptions of an averaging analysis, the adaptive system is globally stable and completely rejects the disturbance, even in the presence of plant uncertainty. Bounds on the uncertainty can be computed a priori based on bounds on the disturbance frequency. Simulations demonstrate the properties of the algorithm in a variety of conditions.