Adaptive suppression of vibrations - a repetitive control approach

TLDR: The aim of this paper is to present an adaptive solution to suppression of vibrations that has its roots in repetitive control based on models of isolated frequencies rather than the commonly used delay model.

Abstract: The aim of this paper is to present an adaptive solution to suppression of vibrations. Adaptation is appropriate whenever the fundamental frequency is unknown or drifting, e.g., when the vibration is caused by a rotational machine with unknown rotational speed. The approach presented here has its roots in repetitive control based on models of isolated frequencies rather than the commonly used delay model. The relationship between different modeled frequencies is fixed by the model structure, and the fundamental frequency is obtained by gradient descent or Newton's method. To show the feasibility of this approach, it was used to reduce the vibrations on a lever that were caused by a motor with imbalance in its rotation. As an actuator, a standard loudspeaker was used, and the vibration was sensed by an accelerometer.