Construction of an enhanced 2-DOF finite element model for precise control of flexible beam vibration

This study deals with constructing an enhanced two-degree-of-freedom finite element-based model for a cantilever flexible beam (FB) with a dynamic solution near the actual beam under various loadings. This model is obtained by adding a complementary term to the simple discrete model, initially developed with one element for the FB, to upgrade its content toward the actual beam. The complementary term that compensates for the model mismatching is online calculated by minimizing the estimation error defined as the difference between the end-point position of the actual beam measured by the sensor and the position obtained for the enhanced model. The experimental responses of the constructed model in both time and frequency domains are in a good agreement with the actual beam within the structure of an open-loop system. Accordingly, an optimization-based controller using the proposed model is designed to reduce the beam vibration. The accuracy of the closed-loop control system is evaluated through Adams–MATLAB co-simulations. The results reveal that the proposed model-updating algorithm remarkably enhances the accuracy of the nominal model in the presence of un-modeled dynamics and parametric uncertainties. Also, comparative results indicate that the proposed control system has a superior performance in suppressing the beam vibrations.