A Globally Asymptotically Stable Nonlinear PID Regulator with Fuzzy Self-tuned PD Gains, for Robot Manipulators

A well known control strategy is the PID regulator for robots manipulators which ensures semiglobal asymptotic stability for symmetric positive definite (Proportional, Integral and Derivative) fixed gain matrices. In this paper we show that global asymptotic stability of the closed loop system is reached for a class of PD variable gain matrices depending on position errors. This scheme with PD variable gains increases the potential of the PID control to improve the performance of the transient response and to handle practical constraints in actual robots, such as limited torque capabilities for joints and actuators. To the best of the author's knowledge, our proposal of a Nonlinear PID Regulator with PD variable gains for robot manipulators is the first one with a global asymptotic stability proof without needing of the gravity compensation. In this work the PD variable gains are self tuned via fuzzy techniques. Some experiments are carried out to illustrate the performance of the proposed controller.