Robust control of the delayed resonator vibration absorber

A recent active vibration absorption scheme, the delayed resonator (DR), is considered. This method uses a very simple delayed partial state feedback control law. This simple but unconventional control invites some challenging practical problems, among which is the highlight of this paper: automatic tuning of the absorber despite parametric uncertainties in the absorber model. A frequency domain technique to achieve this objective is presented. It is based on gradient analysis of a frequency transfer function. It is shown that the routine can be implemented in real-time due to its simplicity and recurrent nature. The theoretical findings are also experimentally verified on an oscillating beam. Excellent vibration suppression is obtained not only under excitations with fixed frequency but also for those of sweep frequency type.