Impulsive Control of Mechanical Motion Systems with Uncertain Friction

In this paper, we consider the robust set-point stabilisation problem for motion systems subject to friction. Robustness aspects are particularly relevant in practice, where uncertainties in the friction model are unavoidable. We propose an impulsive feedback control design that robustly stabilises the set-point for a class of position-, velocity- and time-dependent friction laws with uncertainty. Moreover, it is shown that this control strategy guarantees the finite-time convergence to the set-point which is a favourable characteristic of the resulting closed loop from a transient performance perspective. The results are illustrated by means of an example.