Adaptive rejection of multiple sinusoids of unknown frequency

This tutorial paper is part of an invited session at the 2007 European Control Conference that was organized to review methodologies available for the adaptive rejection of unknown multiple narrowband disturbances. In the paper, two types of schemes are discussed. The first scheme is based on a magnitude phase-locked loop approach, where the magnitudes, frequencies, and phases of the sinusoidal components are estimated together in an integrated algorithm. The second scheme uses an indirect approach where a frequency estimator is combined with a control law for the rejection of disturbances of known frequency. The design of the discrete-time algorithms and their implementation are discussed in detail, and simulation results are presented to illustrate the application of the methodologies.