Time-delayed absorber for controlling friction-driven vibration

The efficacy of an active absorber based on the time-delayed displacement difference feedback in controlling friction-driven vibrations is discussed. Mainly two types of absorbers are considered: the tuned absorber having the natural frequency same as that of the primary system and the high-frequency absorber with the natural frequency higher than that of the primary system. The local stability analysis clearly demonstrates that the static equilibrium can be locally stabilized by appropriately selecting the control gain and the time-delay. The regions of stability are delineated in the plane of the control parameters. The robustness analysis is performed to help select the control parameters for the best performance. A method of optimizing the robustness of the system is presented. The influences of the absorber parameters on the degree of stability and the robustness are discussed. Numerical simulations of the system demonstrate that proper choices of the control parameters can also attain the global stability of the system. Numerical simulations reveal that apart from the globally stable static equilibrium or the coexisting locally stable static equilibrium with the stationary limit cycle vibrations, unbounded motions are also possible for some parameter values. Thus, care should be exercised in selecting the absorber parameters.