Set-point control of motion systems with uncertain set-valued stribeck friction

In this paper, we present a control architecture for the set-point stabilization of motion systems subject to set-valued friction, including a velocity-weakening (Stribeck) effect. The proposed controller consists of a switching PID term and a term that robustly compensates for the Stribeck effect. It is shown that the controller asymptotically stabilizes the set-point, and a particular design of the integrator part of the PID controller term allows for faster convergence when overshoot occurs, compared to a conventional integrator. Moreover, this controller is shown to be robust for unknown static friction, and an uncertain contribution of the Stribeck effect. The working principle of the controller is illustrated by means of a numerical example.