Spectral Design and Experimental Validation of Noncollocated Vibration Suppression by a Delayed Resonator and Time-Delay Controller

A generally applicable spectral design to realize noncollocated vibration suppression performed primarily by a delayed resonator (DR) is presented. The vibration suppression is achieved by direct assignment of imaginary axis zeros of the receptance, i.e., the transfer function between the periodic disturbance force and the target's displacement. To increase the stability margin and to widen the range of frequencies which can be suppressed, the noncollocated vibration absorption by a DR is supplemented by a stabilizing controller tuned by spectral optimization. A unifying aspect of the resonator and the controller is that both use time-delayed output feedback where both the gains and delays are used as controller parameters. Another important aspect of the proposed method is that it can be applied to a system of general structure, where possibly paths exist between the entry point of the disturbance force and the noncollocated absorber that bypass the suppression target, thereby precluding the existence of a resonating substructure. The proposed method has been experimentally validated on a multi-degree of freedom (DOF) experimental setup actuated by voice coils.