Analysis of relay-based feedback compensation of Coulomb friction

Abstract

Standard problem of one-degree-of-freedom mechanical systems with Coulomb friction is revised for a relay-based feedback stabilization. It is recalled that a system with Coulomb friction is asymptotically stabilizable via a relay-based output feedback, as formerly demonstrated in [1]. Assuming an upper bounded Coulomb friction disturbance, a time-optimal gain of the relay-based feedback control is found by minimizing the derivative of the Lyapunov function proposed in [2] for the twisting algorithm. Furthermore, changing from the discontinuous Coulomb friction to a more physical discontinuity-free one, which implies a transient presliding phase at motion reversals, we analyze the residual steady-state oscillations, in the sense of stable limit cycles, in addition to chattering caused the by the actuator dynamics. The numerical examples and an experimental case study accompany the provided analysis.