Adaptive Harmonic Steady-State Disturbance Rejection with Frequency Tracking

This 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 harmonic steady‐state method assumes that the plant can be approximated by its steady‐state frequency response. For high‐order plants such as those encountered in active noise and vibration control (ANVC), this assumption greatly reduces the number of parameters and enables online estimation of the plant response using simple algorithms. 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. After analyzing the reduced‐order ADHSS in the ideal case, the equations describing the complete system are considered. The theory of averaging is used to gain insight into the steady‐state behavior of the algorithm. It is found that the system has a two‐dimensional equilibrium surface such that the disturbance is cancelled exactly. A subset of the surface is proved to be locally stable. Extensive active noise control experiments demonstrate the performance of the algorithm, even when disturbance and plant parameters are changing.