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In this paper, we present a semiglobal asymptotic stability analysis via Lyapunov theory for a new proportionalintegral-derivative (PID) controller control scheme, proposed in this work, which is based on a fuzzy system for tuning the PID gains for robot manipulators. PID controller is a well-known set point control strategy for industrial manipulators which ensures semiglobal asymptotic stability for fixed symmetric positive definite (proportional, integral, and derivative) gain matrices. We show that semiglobal asymptotic stability attribute also holds for a class of gain matrices depending on the manipulator states. This feature increases the potential of the PID control scheme to improve the performance of the transient response and handle practical constraints in actual robots such as presence of actuators with limited torque capabilities. We illustrate this potential by means of a fuzzy self-tuning algorithm to select the proportional, integral, and derivative gains according to the actual state of a robotic manipulator. To the best of the authors' knowledge, our proposal of a fuzzy self-tuning PID regulator for robot manipulators is the first one with a semiglobal asymptotic stability proof. Real-time experimental results on a two-degree-of-freedom robot arm show the usefulness of the proposed approach.

One of the simplest and natural appealing motion control strategies for robot manipulators is the PD control with feedforward compensation. Although successful experimental tests of this control scheme have been published since the beginning of the eighties, the proof of global asymptotic stability has remained unattended until now. The contribution of this paper is to prove that global asymptotic stability can be guaranteed provided that the proportional and derivative gains are adequately selected. The performance of the PD control with feedforward compensation evaluated on a two degrees-of-freedom direct-drive arm appears as fine as the classical model-based computed torque control scheme.

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The joint position regulation problem for robot manipulators under a standard saturated proportional-integral differential (PID) compensator is studied in this brief. The main result states the existence of PID control gains yielding semiglobal asymptotic stability if the control torque bounds are larger than gravitational torques. Energy shaping plus damping injection methods, as well as singular perturbation analysis, are used to establish stability conditions to achieve regulation at any desired position. Some experiments are carried out to illustrate the stability results.

This paper proposes a saturated nonlinear PID regulator for industrial robot manipulators. Our controller considers the natural saturation problem given by the output of the control computer, the saturation phenomena of the internal PI velocity controller in the servo driver, and the actuator torque constraints of the robot manipulator. An approach based on the singular perturbations method is used to analyze the exponential stability of the closed-loop system. Experimental essays show the feasibility of the proposed controller. Furthermore, the theoretical results justify why the classical PID used in industrial robots preserves its exponential stability despite the saturation effects of the electronic control devices and the actuator torque constraints.

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