Adaptive harmonic steady-state disturbance rejection with frequency tracking

The paper is concerned with the rejection of sinusoidal disturbances of unknown frequency acting at the output of unknown plants. Disturbance rejection is based on an adaptive harmonic steady-state (ADHSS) algorithm combined with a magnitude/phase locked-loop (MPLL) frequency estimator. The paper shows that when the MPLL is integrated with the ADHSS algorithm, the two components work together in such a way that the control input does not prevent frequency tracking by the MPLL and so that the order of the ADHSS can be reduced. Thus, the addition of the MPLL allows disturbances of unknown frequency to be considered without significantly increasing the complexity of the original ADHSS. From the theory of averaging, it is found that the system has a two-dimensional equilibrium surface such that the disturbance is exactly cancelled. A subset of the surface is proved to be locally stable. Active noise control experiments demonstrate the performance of the algorithm.