Control of friction induced oscillation by displacement feedback with a second order filter

Abstract

The present work utilizes a displacement feedback control strategy to mitigate the friction driven stick-slip vibration of a mechanical system with single degree of freedom. The stick-slip vibration is primarily caused by the decrease in friction force due to the changes in velocity of the moving surface. This phenomenon, also known as Stribeck effect, can have a negative impact on the system's performance. A mass on a moving belt is considered as the primary system for stick-slip vibration. The dynamics of stick slip oscillation is represented by the polynomial model. Prior to being sent to the system, the displacement signal of the mass undergoes processing via a filter to effectively control the friction induced instability. Eigenvalue analysis of the linearized controlled system is carried out to obtain the boundary line at which the static equilibrium switches its stability. To conduct the nonlinear analysis, the method of averaging is utilized and the resulting outcomes are then verified through simulation results. The bifurcation analysis shows that the controller has the capability to eliminate undesired oscillations and stabilize the system. In order to optimize the filter parameters, the pole crossover method is utilized. The amplitude of the vibration is seen to be reduced significantly by applying the proposed control. Finally, theoretical study of the nonlinear behavior of the controlled system is carried out while taking into account the existence of time delay.