Global stability of PD+ controller with velocity estimation

Abstract

This paper addresses the demonstration of global asymptotic convergence for the PD+ compensator. The proposed strategy is developed for a Robotic Manipulator process, which is a typical Electro-Mechanical System (when only the joint positions are available to be measured). It is well known that in the case of robot manipulators, the optical incremental encoders are widely used to monitor joints positions information, however, joints velocities can only be measured by processing the position data (by filtering or by state estimation). The proposed feedback strategy is based on nonlinear state estimation with a Luenberger-like observer. The main result is based on the knowledge of the system dynamics for the design of a nonlinear observer in order to conclude with Global Asymptotic Convergence of the system trajectories by using a particular Lyapunov function.