On the efficacy of an active absorber with internal state feedback for controlling self-excited oscillations

An active absorber, utilizing the state feedback of the absorber mass, is proposed for controlling the self-excited vibration of a single degree-of-freedom extended Rayleigh oscillator. The control strategy renders the design standalone. The process of optimizing the control gains is discussed. The analysis reveals that by selecting a suitably high value of the absorber frequency, the overall damping of the system can be made as high as the critical damping irrespective of the amount of negative linear damping present in the primary self-excited system. It is shown that a higher value of the absorber frequency is profitable in almost all respects related to the performance as well as the robustness of the system under parametric uncertainty. The nonlinear analysis of the system reveals that the proposed absorber can control the amplitude of oscillation even in case detuning (up to some limit) of the absorber frequency from its nominal value. The region of global stability increases with the increase in the value of the absorber frequency. However some aspects, like higher absorber deflection, reduced lower bound of the admissible detuning and the lower range of the tolerance on the mass ratio limit using a very high value of absorber frequency. The results of numerical simulations confirm the analytical results.