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Structured and unstructured uncertainties are the main obstacles in the development of advanced controllers for high-accuracy tracking control of hydraulic servo systems. For the structured uncertainties, nonlinear adaptive control can be employed to achieve asymptotic tracking performance. But modeling errors, such as nonlinear frictions, always exist in physical hydraulic systems and degrade the tracking accuracy. In this paper, a robust integral of the sign of the error controller and an adaptive controller are synthesized via backstepping method for motion control of a hydraulic rotary actuator. In addition, an experimental internal leakage model of the actuator is built for precise model compensation. The proposed controller accounts for not only the structured uncertainties (i.e., parametric uncertainties), but also the unstructured uncertainties (i.e., nonlinear frictions). Furthermore, the controller theoretically guarantees asymptotic tracking performance in the presence of various uncertainties, which is very important for high-accuracy tracking control of hydraulic servo systems. Extensive comparative experimental results are obtained to verify the high-accuracy tracking performance of the proposed control strategy.