Robust asymptotic observer of motion states with nonlinear friction

This paper revisits the previously proposed linear asymptotic observer of the motion state variables with nonlinear friction and provides a robust design suitable for both, transient presliding and steady-state sliding phases of the relative motion. The class of motion systems with the only measurable output displacement is considered. The reduced-order Luenberger type observer is designed based on the obtained simplified state-space representation with a time-varying system matrix. The resulted observation error dynamics proves to be robust and appropriate for all variations of the system matrix, which are due to the nonlinear spatially varying friction. A specially designed tribological setup to accurately monitor the relative motion between two contacting friction surfaces is used to collect the experimental data of the deceleration trajectories when excited by a series of impulses. The performance of the state estimation using the proposed observer is shown based on the collected experimental data.