Controlling the bifurcation in friction induced vibrations using delayed feedback

We analyse the control of friction induced vibrations using linear time-delayed displacement feedback applied in a direction normal to the friction force. Linear analysis reveals that the steady state looses stability via a Hopf bifurcation. The nature of the bifurcation is either subcritical or supercritical depending on the choice of control parameters. Hence, with a linear delayed feedback we are able to both stabilize the system by completely quenching the vibrations as well as control the nature of the bifurcation which is important for cases with partial quenching.