Abstract: Estimate of the joint angular velocity of robot is preferable with two methods, i.e. the most popular model-free high-gain observer and the simplest LPP numerical difference method. Two PD controllers based on high-gain observer and on LPP numerical difference are given differently. In robot simulation, the tracking error and estimated error of the scheme of high-gain observer-based PD control are shown and compared with those of the same PD controller using numerical difference method. The results show that if the encoder can give very accurate measurement for joint position, the performance of robot using LPP numerical difference method is better than that using high-gain observer and vice versa.