PID Controllers for Robots Equipped with Brushed DC-Motors Revisited

In this note we are concerned with controller design for robot manipulators equipped with brushed DC-motors in the case when the electric dynamics of these actuators is not neglected. We present, for the first time, stability proofs which show that PD control with desired gravity compensation and the classical PID controller presented previously in the literature under the assumption that no actuator dynamics exists can also be designed in this case. In the case of the classical PID controller we show that design can be done without the exact knowledge of neither robot nor actuator parameters. We present, for the first time, a theoretical justification for use of torque control, a strategy commonly used in industrial practice to control brushed DC-motors.