Switching-based rejection of an unknown harmonic disturbance in uncertain stable linear systems under measurement noise

We consider the problem of rejection of a sinusoidal disturbance of unknown frequency, phase and magnitude acting on an uncertain internally stable SISO linear system. We present a solution that extends our previous work on adaptive feedforward control of uncertain systems by disposing of the need to know the frequency of the harmonic disturbance. The proposed methodology reposes upon a switching-based combination of an adaptive feedforward control algorithm and a deadbeat frequency estimator. The method accounts for the presence of bounded sensor noise as well as imprecise frequency estimation; it is shown that the regulation error is bounded by a function of the norm of the noise that depends on the choice of the controller and the estimator gains.