Position Control of a Single-link Flexible Robot

Abstract

In this chapter fractional-order control is applied to accurate positioning of the tip of a single-link lightweight flexible manipulator. This kind of robot exhibits the advantage of being very lightweight. But they present a drawback in that vibrations appear in the structure when they move that prevent precise positioning of the end effector. Moreover, these vibrations may substantially change their amplitudes and frequencies when the tip payload changes, which is quite usual in robotics. The control of this kind of mechanical structure is nowadays a very challenging and attractive research area. These robots have found application in the aerospace and building construction industries, among others. This chapter develops a fractional-order controller that removes the structural vibrations and is robust to payload changes. The proposed control system is based on Bode’s ideal transfer function described in Section 2.3.4. Properties of this transfer function are used to design a controller with the interesting feature that the overshoot of the controlled robot is independent of the tip mass. This allows a constant safety zone to be delimited for any given placement task of the arm, independently of the load carried, thereby making it easier to plan collision avoidance. Other considerations about noise and motor saturation issues are also presented throughout the chapter.