An indirect adaptive scheme for attenuation of multiple narrow-band disturbances: stability analysis

In this paper, a stability proof for an indirect adaptive control method used for the attenuation of multiple unknown time varying narrow-band disturbances is presented. The method is based on the real time estimation of the frequency of the unknown narrow-band disturbances using adaptive notch filters (ANF) followed by the design of a controller using adjustable band-stop filters (BSF) for the appropriate shaping of the output sensitivity function. An Youla-Kučera parametrization of the controller is used for reducing the computation load. Sufficient conditions for stability of the full scheme are stated and a stability proof is given. Finally, an experimental comparison with a direct adaptive method based on the internal model principle (IMP) is shown.