Robust adaptive compensation of periodic disturbances with unknown frequency

Single-input, single-output known stable linear systems with no zeros on the imaginary axis are considered. They are affected by disturbances which are matched by the control input. An indirect adaptive output feedback compensator is designed to attenuate the effects of continuous periodic disturbances with unknown frequency. The compensator contains an adaptive internal model which rejects a fixed number of harmonics in the Fourier series expansion of the periodic disturbance. It also contains an independent frequency estimator whose estimation error converges into an arbitrarily small neighborhood of the origin, provided that a design parameter is chosen to be sufficiently large. The adaptive compensator ensures the global exponential convergence of the closed-loop error signals to a neighborhood of the origin, whose size depends on the higher order harmonics which are neglected by the adaptive internal model.