Narrowband disturbance rejection using adaptive feedback algorithms

Two adaptive algorithms that reject narrowband disturbances of unknown frequency are compared. The first is based on an adaptive implementation of the internal model principle. The second is based on a phase-locked loop structure and generates a signal whose magnitude and phase match those of the disturbance. The adaptive internal model principle algorithm provides global stability under ideal conditions, tracks reference inputs, and can stabilize unstable plants. However, the algorithm suffers from convergence and robustness problems in simulations and does not appear to be well-suited to high-order systems or systems with unknown time delays, two situations that are typically encountered in active noise control applications. The algorithm based on the phase-locked loop concept has better convergence and robustness properties and can be applied to a broad range of stable systems. Some prior information is required about the magnitude and frequency of the disturbance and about the frequency response of the plant, however. A real-time implementation of the phase-locked loop scheme in an active noise control task provides a 25 dB reduction of a sinusoidal tone of unknown frequency.