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This paper presents a control strategy for velocity tracking in mechanical systems with unknown constant disturbance, using only the sign information of the tracking error. The behavior of the closed-loop system including the error convergence is analyzed via relay feedback system theory and nonsmooth Lyapunov argument. Additionally, it is shown that an arbitrary nonlinearity can be allowed as long as it is smooth and positive. The proposed control strategy is applied to the so-called dynamic ramp loading/unloading scheme in computer disk drives, which requires an additional servo action that must take place before the existing digital servo system comes into play. The application illustrates that the proposed strategy provides this problem with a feedback control solution more cost-effective than any other conventional solution. Simulation is conducted to verify the theoretical performance and further to predict the practical performance under nonideal implementation. Also provided are experimental results based on the actual implementation, which demonstrate the practical efficacy of the proposed strategy.