H<inf>∞</inf> and state-feedback controllers for vibration suppression in a single-link flexible robot

Abstract

The demand on more efficient structures has increased the use of lightweight flexible structures in industrial applications. The main objective of this work is to suppress vibration at the free end of a single-link rotational robot subjected to fast movements. The control architecture is made up of two independent control loops; the first loop is employed to control the position of the hub and the second loop is used to attenuate the vibration of the arm. The position control of the hub is achieved through a proportional integral derivative (PID) controller with feedforward gains. The active vibration control (AVC) is achieved implementing two different controllers. An observer-based state-feedback controller and an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> suboptimal controller. These are used to damp the first resonance frequency of the system. A pair of piezoelectric patches is used as actuator. The system is considered as a cantilevered beam, and its model is obtained using black box system identification techniques. The inertial force induced by the movement is considered for the second loop as a transient disturbance at the measure point. The arm with a payload is subjected to different joint trajectories, which excites the free vibration mode of the arm at the end of the movement. Experimental results show the effectiveness of the observer-based state-feedback controller and suboptimal H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> controllers for the rejection of this unwanted vibration. The controllers are capable of suppressing the disturbance in a short period of time.