Theoretical and experimental research on multi-modal vibration control of flexible beams via the multiple-input multiple-output decoupling control strategy

In this study, a multiple-input multiple-output decoupling control (MIMO-DC) strategy is proposed based on the linear active disturbance rejection control (LADRC) algorithm to suppress the multi-modal vibration of flexible beams. Firstly, the dynamic equation of flexible beams is established using the Euler-Bernoulli beam theory. Then, a virtual control vector is introduced to decouple the MIMO system. The effectiveness of the flexible beam model is verified by comparing it with the experimental frequency response. Finally, experimental studies are carried out to analyze the vibration suppression performance of three control forms in suppressing the vibration of flexible beams under first-order modal excitation, second-order modal excitation, multi-modal excitation, variable multi-modal excitation, and multi-modal excitation with random disturbance, respectively. The robustness of the MIMO-DC strategy against parameter perturbations is also studied. The results show that the proposed MIMO-DC strategy not only exhibits excellent control performance for various types of modal excitations but also has strong adaptability to variable multi-modal excitation and strong anti-disturbance ability. Furthermore, the strategy exhibits strong robustness against parameter perturbations.