Time-delayed feedback control of friction-induced instability

Time-delayed feedback control of different types of friction-induced instabilities is discussed. Mainly, three well-known mechanisms of friction-induced instabilities are considered: (1) Stribeck instability governed by velocity-weakening characteristics of friction force, (2) mode-coupling instability, and (3) sprag-slip instability. Control force is constructed utilizing the delayed difference of a single measurable state (displacement here) as proposed by Pyragas. Regions of local stability of the equilibrium are constructed in the plane of control parameters (gain and delay). Global stability regions are also constructed for the Stribeck type instability. A comprehensive methodology for selecting the control parameters is discussed. Analytical results are substantiated by direct numerical simulation.