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Based on the LuGre friction model, a sliding mode adaptive controller is presented to compensate for the friction in the servo system. The terminal switching function is selected as the sliding mode surface, which can make the error of the system converge to the equilibrium point in finite time. The main analytical result is a stability theorem for the proposed controller which can achieve asymptotical stability of the closed-loop system. Furthermore, the transient performance of the system is analytically quantified. To support the theoretical concepts, the authors present dynamic simulations for the proposed control scheme.