A Sliding-mode Based Smooth Adaptive Robust Controller for Friction Compensation

In this paper, a new approach employing both adaptive and robust methodologies is proposed for stick—slip friction compensation for tracking control of a one degree-of-freedom DC-motor system. It is well known that the major components of friction are Coulomb force, viscous force, exponential force (used to model the downward bend of friction at low velocity) and position-dependent force. Viscous force is linear and Coulomb force is linear in parameter; thus, these two forces can be compensated for by adaptive feedforward cancellation. Meanwhile, the latter two forces, which are neither linear nor linear in parameters, can only be partially compensated for by adaptive feedforward cancellation. Therefore, a robust compensator with an embedded adaptive law to ‘learn’ the upper bounding function on-line is proposed to compensate the uncancelled exponential and position-dependent friction. Lyapunov’s direct method is utilized to prove the globally asymptotic stability of the servo-system under the proposed friction compensation method. Numerical simulations are presented as illustrations. ( 1998 John Wiley & Sons, Ltd.