In this paper, we provide an answer to the longstanding question of designing global asymptotically stable proportional-integral-derivative (PID) regulators for uncertain robotic manipulators. Our main contribution is to establish the global asymptotic stability of the controlled system with the commonly-used PID controller by using Lyapunov's direct method and LaSalle's invariance principle. Furthermore, an improved nonlinear proportional-integral plus derivative (NPI-D) controller is proposed to fast the transient. Simulations performed on a planar two degrees-of-freedom (DOF) robot manipulator demonstrate the improved performance of the proposed NPI-D controller over the commonly-used PID controller.
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Su et al. (2007) studied this question.
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