A New Approach to Active Noise and Vibration Control—Part I: The Known Frequency Case

This paper presents a new approach to rejection of complex-valued sinusoidal disturbances acting at the output of a discrete-time stable linear plant with unknown dynamics. It is assumed that the frequency of the sinusoidal disturbance is known, and that the output signal is contaminated with wideband measurement noise. The disturbance rejection control rule is first derived and analyzed for a nominal plant model, different from the true model. Then a special adaptation mechanism is added, which is capable of compensating modeling biases (errors in both magnitude and phase) so that, under Gaussian assumptions, the closed-loop system can converge in mean to the optimal solution.