Centralized and decentralized adaptive harmonic control for sinusoidal disturbance rejection

This paper presents two new algorithms for rejection of known-frequency sinusoidal disturbances that act on a completely unknown, multi-input multi-output, asymptotically stable, linear time-invariant system. The first algorithm is centralized adaptive harmonic control (AHC), which does not impose any structural constraints on the input–output channels of the controller. The second algorithm is decentralized AHC, which imposes the constraint that each local control is computed using only local sensor measurements. These new control methods are data-driven, adaptive algorithms that do not rely on any information regarding the system. It is also worth noting that all control computations are performed using discrete Fourier transform data. The stability and closed-loop performance with each algorithm are analyzed. The main analytic results show that each algorithm asymptotically rejects sinusoidal disturbances. Illustrative numerical simulations and active noise control experiments demonstrate the effectiveness of centralized and decentralized AHC.