Passivity-Based Analysis for Partially Variable Nonlinear PID Controller for Robot Manipulators

Abstract

This paper presents a passivity-based analysis of a PID controller for robot manipulators where a theorem of interconnected passive systems is used to proof that the unique equilibrium of the system in closed loop is asymptotically stable in a global sense. The structure of the PID controller is formed by variable PD gains that improve system performance, allowing getting better transient responses, and a constant I gain. A controller with fixed gains is limited because it is not adaptable to new operation conditions. A system with variable PD gains and constant I gain is better because the gains are selected online and the integral gain avoid the necessity of calculate the gravity forces vector into the control law. As consequence variable PD gains and constant I gain make possible to obtain the most adequate torque output that get better response of the outputs. An evaluation in simulation to verify the theoretical results is realized