Delayed Resonator With Hybrid Multiple-Delayed Control for Enhanced Complete Vibration Suppression

Delayed resonator (DR) is an active vibration absorber that can enable complete vibration suppression of a force-excited primary structure at a given frequency by manipulating the loop delay. This work introduces a hybrid multiple-delayed control law to actuate the DR by incorporating the delayed states of the primary structure in addition to absorber states. The key benefit of this control law is its complete compliance with the tuning mechanism of the conventional absorber-based control parameters, thus simplifying implementation. Improved vibration suppression is sought in three aspects: first, Shortened settling time of transient process; second, widened operable low-frequency band; and third, enhanced robustness against residual vibrations. Based on spectral analysis, stability analysis, and frequency response analysis, selection rules of the two newly introduced control parameters related to the primary structure, including a gain plus a delay, are established to maximize control performance. The resulting significantly enhanced vibration suppression is justified by comparisons with classical DRs.