Robust stabilization for friction-induced vibration with parameter uncertainties

Friction-induced vibration (FIV) is considered one of the principal causes of noise generated in mechanical systems. Furthermore, in practical cases, FIV is influenced by a great number of parameters which vary prodigiously. Nonetheless, the conventional passive structure modification remedy is verified to be of low flexibility under changeable conditions. In this paper, a robust state feedback control is proposed for stabilizing FIV with uncertain mass, damping, stiffness and friction coefficient. The eigenvalues of the system are first assigned using linear quadratic regulator (LQR) with the minimization of the quadratic cost function. Subsequently, the robust position of the eigenvalues of the system is obtained by finding the minimum norm of the sensitivities of poles to variations of uncertain parameters. Consequently, the robustness of this suggested control strategy is guaranteed. The simulation results demonstrate that the presented control method is more robust at stabilizing the FIV than the original LQR method.