Extended delayed resonators - Design and experimental verification

The key contribution of the paper is in the modification of the well-known delayed resonator concept for vibration suppression using both delayed and non-delayed acceleration feedback control laws together. We further improve the classical resonator setting with lumped delay introducing a distributed delay structure into the control law. It is known that the operable frequency ranges for the delayed resonators are relatively narrow, taking into account both the stability and implementation constraints. As the key result of this paper, in order to widen the operable frequency range, the resonator's feedback is extended by including a non-delayed part to adjust virtually the mass and thus the natural frequency of the active absorber. The proposed extension takes into consideration also the existence of feedback delay and filters to reduce the measurement noise, and retain the simplicity of active controlled resonator tuning against excitations with time varying frequencies. The properties and performance of the resulting algorithms are compared with the delay free PI (proportional and integral) feedback control law. It is shown that the delay-based resonators are easier to implement and can better deal with the measurement noise compared to PI. Spectral theory of retarded and neutral time delay systems are applied to perform a thorough analysis of the resonators. The key theoretical results are validated on a laboratory set-up with voice-coil magnetic shakers.