Stick-slip and convergence of feedback-controlled systems with Coulomb friction

TL;DR

This paper analyzes the stick-slip behavior and convergence properties of feedback-controlled systems with Coulomb friction, revealing that only asymptotic convergence with multiple cycles is achievable, supported by theoretical proofs and numerical examples.

Contribution

It provides a closed-form description of the stiction region and proves global attractivity and the inevitability of stick-slip cycles in such systems.

Findings

The stiction region is always reachable and globally attractive.

Only asymptotic convergence is possible, with multiple stick-slip cycles.

Numerical results support the theoretical analysis.

Abstract

An analysis of stick-slip behavior and convergence of trajectories in the feedback-controlled motion systems with discontinuous Coulomb friction is provided. A closed-form parameter-dependent stiction region, around an invariant equilibrium set, is proved to be always reachable and globally attractive. It is shown that only asymptotic convergence can be achieved, with at least one but mostly an infinite number of consecutive stick-slip cycles, independent of the initial conditions. Theoretical developments are supported by a number of numerical results with dedicated convergence examples.