Finite element based, Model Predictive Control of a one-link flexible manipulator

A new Model Predictive Control (MPC) method is developed and demonstrated on vibration suppression of a rotating beam. The physical system is modeled as an Euler-Bernoulli beam including the effect of a driving motor using Lagrange's equation associated with an assumed mode method. The experimental set-up consists of a DC motor to drive the beam to a desired angle; a strain gauge to sense the deformation of the flexible beam; four piezoceramic actuators for actively suppressing the undesired vibrations caused by the torque during the motion; and a signal conditioner to filter the noise of the signals. A multivariable MPC controller is designed to control both the angular rotation and the beam oscillation. In the standard MPC algorithm, the process behavior is represented by an empirical model that is identified from open loop test data. A finite element (FE) model of the system is incorporated in the MPC algorithm to predict the process dynamic behavior. The proposed methodology can accurately predict process behavior over a much wider range of operating conditions when compared to using the standard MPC and therefore will have a better capability to deal with nonlinearity. Numerical simulations and experiments were conducted and improved results were obtained in terms of level of vibration reduction. The control performance on the beam with tip mass has also been investigated.