Friction compensation in a controlled one-link robot using a reduced-order observer

In this paper, friction compensation in a controlled one-link robot is studied. Since friction is generally velocity dependent and controlled mechanical systems are often equipped with position sensors only, friction compensation requires some form of velocity estimation. Here, the velocity estimate is provided by a reduced-order observer. The friction is modeled by a set-valued velocity map including an exponential Stribeck curve. For the resulting discontinuous closed-loop dynamics, both the case of exact friction compensation and nonexact friction compensation are investigated. For the case of exact friction compensation, design rules in terms of controller and observer parameter settings, guaranteeing global exponential stability of the set-point are proposed. If the proposed design rules are not fulfilled, the system can exhibit a nonzero steady-state error and limit cycling. Moreover, in the case of nonexact friction compensation, it is shown that undercompensation leads to the existence of an equilibrium set and overcompensation leads to limit cycling. These results are obtained both numerically and experimentally.