Adaptive Compensation of Nonlinear Friction in Mechanical Systems Without Velocity Measurement

TL;DR

This paper introduces a globally convergent adaptive control method that compensates for nonlinear friction in mechanical systems without requiring velocity measurements, using an innovative observer approach.

Contribution

It presents the first globally convergent solution for friction compensation without velocity measurement, employing an immersion and invariance-based adaptive observer.

Findings

Effective friction compensation demonstrated in simulations

Works with static, Coulomb, and LuGre friction models

No velocity measurement needed for control accuracy

Abstract

Friction is an unavoidable phenomenon that exists in all mechanical systems incorporating parts with relative motion. It is well-known that friction is a serious impediment for precise servo control, hence the interest to devise a procedure to compensate for it -- a subject that has been studied by many researchers for many years. The vast majority of friction compensation schemes reported in the literature rely on the availability of velocity measurements, an information that is hard to obtain. A second limitation of the existing procedures is that they rely on mathematical models of friction that contain several unknown parameters, some of them entering nonlinearly in the dynamic equations. In this paper we propose a globally convergent tracking controller for a mechanical system perturbed by static and Coulomb friction, which is a reliable mathematical model of the friction phenomenon, that does not rely one measurement of velocity. The key component is an immersion and invariance-based adaptive speed observer, used for the friction compensation. To the best of our knowledge, this is the first globally convergent solution to this challenging problem. We also present simulation results of the application of our observer for systems affected by friction, which is described by the more advanced LuGre model.