<title>Rejection of disturbances with a large sinusoidal component of unknown frequency</title>

Abstract

An important application of smart materials and structures is the control of periodic disturbances or vibration in environments such as aircrafts and helicopters. In these cases, the source of the noise is a rotating machine, so that a large component of the disturbance is periodic. While it is often possible to take measurements on the machine that is the source of the periodic disturbance, concerns of reliability and maintainability sometimes make such measurements undesirable, if not impossible. Then, the problem is to attenuate a periodic disturbance whose frequency is unknown. An adaptive algorithm is presented in this paper for periodic disturbance attenuation, using the concept of a phase-locked loop. For simplicity, the disturbance is assumed to be sinusoidal. An approximate analysis is performed and the results are found useful to select the design parameters. Simulations are presented that demonstrate the ability of the algorithm to reject sinusoidal disturbances with unknown frequency, and to follow signals with slowly varying magnitude and frequency. The effect of measurement noise and of additional disturbances is also analyzed. The results provide numerical measures of the parameter variations and of the loss of performance in the presence of noise.