Generalized Adaptive Delayed Resonator Design for Complete Vibration Suppression With Force-Tuning Inaccuracies

Delayed resonator (DR) is an active vibration absorber that can enable complete vibration suppression through proper tuning of the actuation forces based on delayed (past) system states. However, the tuning requires exact knowledge of system parameters, thus causing residual vibrations which are sensitive to parametric inaccuracies/uncertainties. To eliminate such residual vibrations, we generalize an adaptation strategy to online correct the parameters of a classical control law by equating the effects of the force output at the vibration frequency to the alteration of the absorber’s stiffness and damping, thereby accommodating the inaccurate estimations in all parameters involved in the tuning process. Furthermore, the equivalent model also allows the resulting adaptive DR to compensate for the inaccurate realization of the control parameters arising from the inaccurate hardware parameters. Simulations and experiments both verify the effectiveness and the efficacy of the general adaptation strategy, which significantly reduces the accuracy requirement for system parameter identifications and modeling for tuning DRs to achieve complete vibration suppression, while maintaining the simplicity of the delayed control logic.