A noisy behavior of the time-domain passivity controller during the period of low velocity is analyzed. Main reasons of the noisy behavior are investigated through a simulation with a one-DOF haptic interface model. It is shown that the POW is ineffective in dissipating the produced energy when the sign of the velocity, which is numerically calculated from the measured position, is suddenly changed, and when this velocity is zero. These cases happen during the period of low velocity due to the limited resolution of the position sensor. New methods, ignoring the produced energy from the velocity sign change, and holding the control force while the velocity is zero, are proposed for removing the noisy behavior. The feasibility of the developed methods is proved with both a simulation and a real experiment.