Enhanced delayed resonator for complete single- and multiple-frequency vibration suppression: A hybrid feedforward-feedback control approach

Delayed resonator (DR) is an active vibration absorber capable of achieving complete vibration suppression at a specific frequency by distinctively incorporating appropriate time delays into the control loop. Existing works drive the DR mainly following the absorber-based feedback control laws. Alternatively, we here propose a hybrid control law that integrates both feedforward and feedback control, in which the feedforward control is based on excitation and the feedback one is based on the states of the primary structure instead of the absorber. A resulting key benefit is that system stability analysis can be significantly simplified thanks to the decoupling between the control parameters to be tuned and the characteristic equation. In addition to this, enhanced control performance over classical DRs is achieved in both cases of single- and multiple-frequency vibration suppression. Results show that the hybrid control law can extend the operable frequency band, expedite setting the transient process, and extend the antiresonance valley to suppress residual vibrations in steady states. Particularly, the alleviated stability issues in the multiple-frequency case allow the hybrid control law to fully leverage the strength of the delayed control in raising system order so that a single-mass absorber can yield multiple zero antiresonance points at multiple given frequencies. This work establishes a basic design and analysis framework for applying feedforward control to the DR and combining it with feedback control strategies to maximize control performance.