This paper demonstrates that the Coulomb friction, the most difficult part of friction to be compensated because of its discontinuity with respect to the velocity, can be precisely compensated without either its mathematical model or a velocity measurement, as commonly required in the literature. Instead, the necessary information needed in the friction compensation is obtained in real time from an implicit extended observer in the context of a common proportional-derivative motion control system, using the proposed linear reference compensation scheme. The robustness of this particular observer design to the time-delay uncertainty resulting from the model reduction is thoroughly investigated, which illustrates the extent to which a high bandwidth can be employed to achieve the favorable dynamic performance such that the limitation on the bandwidth of the original extended state observer (ESO) can be effectively eliminated. Finally, numerical examples are provided to validate the proposed method.

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