Observer of Nonlinear Friction Dynamics for Motion Control

Abstract

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 Luenbergertype 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 spatiallyvarying 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.

Analysis of Linear Feedback Position Control in Presence of Presliding Friction

“…However, no pre-sliding friction range with a consequent residual 'creeping' response, due to the integral control action, has been explicitly addressed. Another possible way to compensate for the presliding friction is to observe explicitly the corresponding presliding state(s) and to inject this (these) into the control signal, as proposed in (11) (12) and recently in (13) . The problem of position settling performance in presence of the nonlinear friction has been also addressed in (14) .…”

Full- and reduced-order model of hydraulic cylinder for motion control

“…For more details on varying kinetic friction and its impact on the motion control we refer to e.g. [10], [11].…”

Impulse-based hybrid motion control

“…assuming infinite accelerations of the moving mass. Since a real system acceleration is bounded and with an actuation force dynamics, (18) represents rather the lower gain boundary, below which the state trajectory cannot, even theoretically, reach zero equilibrium after an impulsive control execution. For determining the upper gain boundary one can show that in case of α = m|ẋ 0 |, the jump map yields the state "successor" x + = −x(t 0 ), here theoretically as well i.e.…”