Model predictive control of piezo-actuated structures using reduced order models

A model predictive control method for a flexible structure consisting of two beams, equipped with macro fiber composite (MFC) patches as piezoelectric actuators is presented. Adjacent beams are connected at the tip by an elastic string. The equations of motion are derived by the evaluation of the extended Hamilton's principle. Spatially dependent parameters are considered, due to different material characteristics of the carrier beams and the MFC patches. The spatially dependent variable is approximated using Galerkin's method, leading to the state space representation of the beam structure by means of ordinary differential equations (ODEs). In order to avoid approximation errors, a high order approximation of the distributed-parameter system is required. With a model order reduction a small system describing approximately the same dynamics is obtained. A model predictive controller is designed, analyzed and evaluated in a simulation and at the experimental set-up. For the real-time capability of the model predictive controller a move blocking method by downsampling the prediction horizon is presented.