Feedback Delays for Vibration Mitigation and External Disturbance Rejection at the Microscale

This effort discusses the implementation of delayed-feedback algorithms as effective mechanisms for vibration mitigation at the microscale. A delayed velocity-feedback algorithm is considered and employed to mitigate the flexural vibrations of a microcantilever beam. The linear stability of the closed-loop unforced system is assessed to determine the gain-delay combinations wherein the fixed points of the system are locally-asymptotically stable. The method of multiple scales is then implemented to analyze the steady-state forced response of the closed-loop dynamics. Theoretical results demonstrate that inherent system delays can be easily augmented into a larger delay period that can be used to stabilize the system dynamics and enhance the damping characteristics of the response. The proposed concept is implemented experimentally on a microcantilever sensor. The feedback algorithm is shown to have excellent performance in mitigating the effects of external disturbances and periodic excitations