Enrichment of Approximated Flexible Beam Model for Constrained Control of Vibration Suppression

For flexible beams, the application of distributed models with infinite degrees of freedom is complicated to precise control of vibration. Also, the approximated models bring uncertainties that negatively affect the controller performance. This paper aims to enhance the content of an assumed mode model of a cantilever beam by using the measurement information. A new estimation method is developed to estimate the uncertainty of the approximated model by minimizing the output estimation error at the current time. Experimentally tests are conducted to show the performance of the proposed estimation method compared with an extended state observer. Accordingly, a novel controller is developed using the estimated model to reduce the vibration of beam considering the control input limitations. The stability of the constrained second-order control system is mathematically analyzed, and its performance is evaluated through a co-simulation environment via Adams-MATLAB. The obtained results demonstrate that the suggested estimation scheme remarkably improves the accuracy of the approximated beam model. Consequently, the controller that uses the model uncertainty and disturbance information has a great efficiency in suppressing the vibrations of the beam.