Switching-based regulation of uncertain stable linear systems affected by an unknown harmonic disturbance

The problem of rejection of a sinusoidal disturbance with unknown frequency acting on an unknown single-input-single-output stable linear system is addressed in this paper. We present a new hybrid approach that does not require knowledge of the frequency response of the transfer function over the range of frequencies of interest. The proposed controller reposes upon a switching strategy within a family of linear controllers based on the adaptive feedforward / internal model control methodology. A dead-beat frequency estimation method is integrated in the controller. The method also accounts for the presence of bounded sensor noise as well as imprecise frequency estimation. It is shown that, within a finite number of switchings, the regulation error is ultimately bounded by a function of the norm of the noise that depends on the choice of the controller and the estimator gains.