Interplay between integral feedback and discontinuous Coulomb friction: novel sliding-mode based solution for old control engine

Abstract

Stick-slip behavior, known as a noticeable phenomenon in control practice and studied for a long time, is often caused by using integral action in feedback control systems with Coulomb friction. The convergence of such closed-loop dynamics to a set reference point is not trivial and requires a coherent distinction of motion trajectories between alternating sticking and slipping phases. A novel solution to analyze the convergence of feedback-controlled systems with Coulomb friction was proposed in § based on standard first-order sliding modes. Such an approach can describe, in a closed manner, the entering in and escape from the sticking phases, assuming the simplest but also most common Coulomb friction law with discontinuity at zero-velocity crossing. The talk will also focus on the largest invariant set of equilibrium points around zero equilibrium and demonstrate possible convergence scenarios, showing an unavoidable emergence of stick-slip cycles. Several numerical examples as well as the published motivating experimental observations of different researchers will accompany the presented analysis. 

§ M. Ruderman. Stick-slip and convergence of feedback-controlled systems with Coulomb friction. Asian Journal of Control, in print, 2021.

Biosketch

Michael Ruderman (michael.ruderman [at] uia.no) earned his Dr.-Ing. degree in electrical engineering from TU University Dortmund, Germany, in 2012. He is a full professor at the University of Agder, Grimstad, Norway, teaching control theory in M.S. degree and Ph.D. degree programs. He serves on various IEEE editorial boards and technical committees. He was the general chair of the 16th IEEE International Workshop on Advanced Motion Control, in 2020, and he chaired the IEEE Industrial Electronics Society Technical Committee on Motion Control, in 2018–2019 and 2020–2021. He is a Senior Member of IEEE.