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Adaptive estimation of friction forces with differential filter

In this article, we design adaptive observers to estimate the non-linear friction model when the output is the position. First, an adaptive observer is designed to estimate the viscous friction force with full-states measurements. In the case of position measurements, the velocity measurement is replaced to the estimate by using the adaptive differential filter. Secondly, the dynamic friction force is estimated by a fuzzy adaptive observer with position measurements. Finally, simulation results for the proposed observers are presented.