Delayed feedback for controlling the nature of bifurcations in friction-induced vibrations

We analyse the control of friction-induced vibrations using time-delayed displacement feedback. We have used the exponential model for the drooping characteristics of the friction force for which the bifurcation is subcritical in nature. With an appropriate choice of the control parameters we have managed to change the nature of the bifurcation to supercritical along with increasing the stability boundaries. A nonlinear controller is required when the control force is applied in a direction parallel to the friction force. In contrast, a linear time-delayed displacement feedback applied in a direction normal to the friction force achieves our dual objective of controlling the nature of the bifurcation as well as quenching the vibrations. We also consider a dynamic friction model (the LuGre model) and observe that the qualitative change in the nature of the bifurcation is independent of the complexity considered in modeling the friction force.

► We control the nature of bifurcation associated with friction-induced vibrations.
► Time-delayed feedback control has been used.
► Linear controller normal to the contact surface is found to be sufficient.
► Results are robust with respect to the friction model used for the study.