Vibration Control of a Flexible Beam Using Model Predictive Control

Model predictive control is applied to suppress the vibration of a flexible link with piezoelectric actuators and strain gage transducer. The state-space dynamic model of the system was derived by using finite element method and experimental modal test. On the basis of the model, model predictive controller is designed taking into account the uncertain disturbance and measurement noise. The discrete prediction model is derived from the state-space equation of the system, and the future output is obtained from the model. The uncertain external disturbance and measurement noise are white noise signal, the Kalman filter estimator is designed to estimate the state variables of the system. A standard quadratic programming optimization problem is formed where the performance index function minimizes a quadratic performance function that trades off controller performance and control effort. The constraints are the control input voltage and its change rate. Finally, the optimization problem is solved to obtain the optimal control output. A MIMO control system is built using dSPACE DS1103 platform, and experimental tests are performed. The performances of the controller are verified experimentally. The results of experiment show the effectiveness of the controller.