Controlling mode-coupling instability in friction-induced vibration by acceleration feedback

•Acceleration feedback is used to control friction-induced mode-coupling instability.•The linear stability analysis of the controlled system is carried out.•Optimization of control parameters is performed by pole-crossover design.•Robustness of the control is studied.•Averaging method is used to study the dynamics of nonlinear system.•Bifurcation analysis of the nonlinear system is done in AUTO.