Friction compensation using adaptive nonlinear control with persistent excitation

Nonlinear dynamics and modelling uncertainties of a frictional force can cause instability in an adaptive friction compensation scheme. We propose an adaptive nonlinear controller where the persistent excitation in the desired trajectory enables stability of the closed-loop system when the friction force effects are due to static, Coulomb and viscous components, as well as for inertia and the Stribeck effects. The controller is shown to be robust to uncertainties due to frictional lag and frictional memory. Stable adaptation for the nonlinearly-occurring Stribeck parameter is achieved by exploiting convexity/concavity properties. An analytical framework is given to explain the effectiveness of dither in friction control problems.