For all its simplicity, local proportional and derivative (PD) control remains an effective and popular tool in robot manipulation. The analysis of such a control system has usually been based on the assumption that the PD algorithm is implemented continuously. This article explores the issue of digital high-gain PD control on robot manipulators from the viewpoint of singular perturbation. It is shown that the fast subsystem becomes unstable when the gains are high enough, due to the effect of sample-and-hold. The stability is related to the feedback gains, the length of sampling period, the computation time, and the eigenvalues of the mass matrix. With reasonable approximations, simple and explicit stability criteria are derived. It is also shown that when the gains reach the critical values, chattering in the control signal occurs, similar to what happens in a variable structure system with sliding mode. Since the eigenvalues of the mass matrix vary with robot positions, the system stability and control chattering are also affected by the trajectory that the robot is planned to follow.
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