2022/05/19 by Michael Ruderman, Leonid Fridman, Ruderman, Michael +1
Engineering · #Control and Stability of Dynamical Systems #Dynamics and Control of Mechanical Systems #FOS: Electrical engineering #Iterative Learning Control Systems #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2205.09352
openalex publication_date 2022/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Standard problem of one-degree-of-freedom mechanical systems with Coulomb friction is revised for a relay-based feedback stabilization. It is recalled that such a system with Coulomb friction is asymptotically stabilizable via a relay-based output feedback, as formerly shown 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. This is in the sense of stable limit cycles, in addition to chattering caused by the actuator dynamics. The numerical examples and an experimental case study accompany the provided analysis.