A new approach for Lyapunov-based adaptive friction compensation

In this paper, an approach for constructing a nonlinear estimator for adaptive compensation of the Coulomb friction in mechanical control systems is proposed where the Coulomb friction coefficient is unknown but its variation with time is bounded. The design is based on Lyapunov technique and attempts to compensate the frictional force by estimating the Coulomb friction coefficient. It is shown that asymptotic stability of the error dynamics is guaranteed. The major contribution of this paper is an adaptive control law for friction compensation in the system in which the variation of the Coulomb coefficient with time has not any specified frequency. The simulation results confirm the advantages of the proposed approach against the previous methods for a simple single-mass system.