Global Stability of a Saturated Nonlinear PID Controller for Robot Manipulators

This paper presents a simple and global stable nonlinear proportional-integral-derivative (N-PID) controller incorporated with a new saturated function design. The new class of saturated function is derived from quasi-natural potential function to shape the position and velocity errors. The coordinate of the saturated function is either in joint space or in Cartesian space, and the function is adjustable by changing the function parameters. The new controller formulation differs from traditional SP-ID control in that a nonlinear velocity (D-) control term is added. The global asymptotic stability of the controlled system is analyzed. Experiments performed on a two-link robot manipulator demonstrate the improved performance of the proposed nonlinear PID controller.