Model Predictive Control of Vibration in a Two Flexible Link Manipulator — Part 2

Abstract

A finite element based model predictive controller (FEMPC) is developed and practically implemented for attenuating in-plane vibration of a two flexible link planar manipulator. This FEMPC structure is based on that used in dynamic matrix control (DMC), with the exception that a finite element (FE) model replaces how the predictions are formulated. A linear FE model is developed for each individual link, which is used with the current measured strain and control actions, to predict the response of each link. These predictions are carried out at each time step to address the geometric non-linearities associated with the orientation of the second link and those associated with friction, backlash and compliance of the geared motors. Furthermore, the use of FE modelling enables the control structure to be formulated based on known properties of the system, eliminating the need for open loop testing. The resulting FEMPC scheme is shown to outperform DMC and is capable of providing substantial attenuation of vibration, reducing the mean amplitude of dominant vibration by 92.5% and 15.6%, for the first and second links, respectively.