Friction compensation using adaptive non-linear control with persistent excitation

TLDR: In this article, an adaptive non-linear friction compensation scheme for a friction model is presented, which captures problematic friction effects such as Stribeck effect, hysteresis, stick-slip limit cycling, pre-sliding displacement and rising static friction.

Abstract: Non-linear frictional dynamics reduce the tracking performance of machine control systems involving high-precision, low-velocity tasks. We present an adaptive non-linear friction compensation scheme for a friction model, which captures problematic friction effects such as Stribeck effect, hysteresis, stick-slip limit cycling, pre-sliding displacement and rising static friction. We show that without robust adaptation, frictional dynamics and other modelling uncertainties can cause an adaptive friction compensation scheme to become unstable. We extend robust adaptive theory to include a new type of error model with a non-linear regression vector and Lipschitz disturbances. By using persistent excitation in the desired trajectory, our controller achieves stable adaptation for friction force effects due to static, Coulomb and viscous components, as well as for inertia and the Stribeck effects, while remaining robust to perturbations in friction force due to frictional lag and frictional memory. Although the S...