Model Predictive Control of Vibration in a Two Flexible Link Manipulator — Part I

Abstract

A model predictive controller (MPC) in the form of dynamic matrix control (DMC) is implemented for attenuating in-plane vibrations of a two flexible link planar manipulator. The rotation of the joints and inertia effect of both the joints and links induce vibration. Piezoelectric actuators, mounted in a bimorph configuration, provide the control actions to reduce vibrations. Implementation of this control scheme is shown to provide appreciable attenuation of vibration over the uncontrolled case, increasing the damping ratio for the first and second link by a factor of 5.99 and 3.40, respectively. DMC control is further shown to reduce the mean amplitude of dominant vibrations from the uncontrolled case by 90.0% and 87.4%, respectively, for the first and second links. Furthermore, for the two link setup, this control is shown to outperform the more conventional ProportionalIntegral-Derivative (PID) control and is sufficiently robust to handle an unknown payload.