Simple relay non-linear PD control for faster and high-precision motion systems with friction

This study addresses the problem of robust faster and high-precision positioning of uncertain one-degree-of-freedom mechanical systems with friction. A very simple relay non-linear proportional–derivative (PD) controller is proposed. Global asymptotic positioning stability is proven by Lyapunov's direct method invoking Barbalat's lemma. The appealing features of the proposed control are that it is fairly easy to construct with simple intuitive structure and without reference to modelling parameter and the ability to ensure global asymptotic positioning stability featuring faster transient and higher steady-state precision. Simulations and experiments demonstrate the effectiveness and improved performance of the proposed approach.