Normal industrial PD control of Robot has two drawbacks: it needs joint velocity sensors, and it cannot guarantee zero steady-state error. In this paper we make two modifications to overcome these problems. High-gain observer is applied to estimate the joint velocities, and an RBF neural network is used to compensate gravity and friction. We give a new proof for high-gain observer, which explains a direct relation between observer gain and observer error. Based on Lyapunov-like analysis, we also prove the stability of the closed-loop system if the weights of RBF neural networks have certain learning rules and the observer is fast enough.
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Yu et al. (2006) studied this question.