Adaptive Harmonic Control for Rejection of Sinusoidal Disturbances Acting on an Unknown System

We present a sampled-data adaptive harmonic control algorithm that rejects sinusoids with known frequencies that act on a completely unknown asymptotically stable linear time-invariant system. We analyze the stability and closed-loop performance for systems with at least as many controls as performance measurements. We show that the closed-loop system is uniformly Lyapunov stable and the adaptive controller asymptotically rejects the disturbances. We present numerical simulations comparing the new sampled-data adaptive controller with an existing sinusoidal disturbance rejection approach (i.e., higher harmonic control). We also present results from an active disturbance rejection experiment in an acoustic environment. These experimental results demonstrate the practical effectiveness of the adaptive harmonic controller.