Rejection of periodic disturbances of unknown and time‐varying frequency

The paper reviews available methods for the rejection of periodic disturbances. Such disturbances are often encountered in active noise and vibration control, due to rotating machinery. The emphasis of the paper is on feedback control problems where reference sensors are not available. The case where the frequency of the disturbance is known is considered first. Two sets of algorithms are discussed: one based on the internal model principle of feedback control theory, and the second based on adaptive feedforward cancellation. An interesting observation is that algorithms originating from both approaches can be shown to be equivalent under certain conditions. When the frequency of the disturbance is unknown, an intuitive approach consists in combining a method for the rejection of disturbances of known frequency with a frequency estimator. Alternatively, one may seek to develop a stable adaptation mechanism so that the disturbance is cancelled asymptotically. While algorithms can be designed to adapt to plant and disturbance parameters, the most successful approaches use some limited plant information to adapt the magnitude, frequency, and phase parameters of the control signal. Applications are discussed throughout the paper. Copyright © 2004 John Wiley & Sons, Ltd.

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