Adaptive feed-forward friction compensation through developing an asymmetrical dynamic friction model

This article presents an adaptive feed-forward method to compensate for the dynamic friction in the machine tool systems so that the tracking errors of the machine axes can be reduced. To achieve this aim, a dynamic friction model is firstly established by constructing a continuous and differentiable two-segmented arc tangent curve to characterize the asymmetrical and nonlinear static friction phenomenon in relation to the positive and negative velocity ranges of the machine axes. Subsequently, a new feed-forward method is proposed to compensate for the friction by constructing an adaptive controller with three advantages, i.e. no need of velocity and acceleration measurement, large adaptive rate and high steady-state accuracy. During the model establishment, a discontinuous projection mapping in the learning process is constructed. Especially, the stability of the adaptive controller is strictly proved by theoretical derivation. Besides, a new two-step adaptive method is formulated to analytically calculate the unobservable parameter z. Finally, both simulations and experiments confirm that the proposed compensation method can reach to lower tracking errors, especially in the velocity reversal area, by comparing with the existing approaches.