Design of a PD Position Control based on the Lyapunov Theory for a Robot Manipulator Flexible-Link

Abstract

We propose the design of a PD position control for a one link flexible manipulator. This paper is based in development the scheme control using the theory Lyapunov, where the existence, unicity and asymptotic behavior of the equilibrium point is defined inside workspace of the robot manipulator, furthermore we are presenting a detailed mathematical development based in the dynamics of the robot, we proved that finding a K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> and K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">v</sub> constants such as the controller converge to unique solutions. The workspace of the robot manipulator is defined in the x-y plane, with rotational joints under gravity force. The mathematical model considers the link as beam the Euler-Bernoulli. The Lagrange-Euler equation have been used to obtained generalized equation of movement and the method Assumed-Modes for modelling the transversal deformation of the beam in any point and to identify the position of the end-effector.