High-gain proportional-integral-derivative (PID) position control involves some risk of unsafe behaviors in cases of abnormal events, such as unexpected environment contacts and temporary power failures. This paper proposes a new position-control method that is as accurate as conventional PID control during normal operation, but is capable of slow, overdamped resuming motion without overshoots from large positional errors that result in actuator-force saturation. The proposed method, which we call proxy-based sliding mode control (PSMC), is an alternative approximation of a simplest type of sliding mode control (SMC), and also is an extension of the PID control. The validity of the proposed method is demonstrated through stability analysis and experimental results.