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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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SUMMARYThis paper is concerned with PID control of rigid robots equipped with brushless DC (BLDC) motors when the electric dynamics of these actuators is taken into account. We show that an adaptive PID controller yields global stability and global convergence to the desired link positions. Moreover, we also show that virtually the PID part of the controller suffices to achieve the reported global results. We present a theoretical justification for the torque control strategy, commonly used in practice to control BLDC motors. Our controller does not require the exact knowledge of neither robot nor actuator parameters.