The rotating double flexible beam structure driven by a planetary reducer with gear backlash is a multiple-input multiple-output (MIMO) system of strong coupling and nonlinear characteristics． In order to solve the
vibration control problem in this system，a hierarchical fuzzy control algorithm on the basis of the MIMO system is proposed． In the algorithm，first，the hierarchical structure is introduced into the fuzzy controller，and the system running state of the rotating double flexible beam is divided into different zones． Then，the experimental platform of the rotating double flexible piezoelectric beam driven by a planetary reducer is established，and piezoelectric actuators and an alternating current (AC) servo motor are used to attenuate the vibrations of the double flexible beam structure，so as to verify the proposed algorithm by experiments． The results demonstrate that，in comparison with the proportional and derivative (PD) controller，the proposed algorithm can suppress both the large amplitude vibrations and the small amplitude vibrations of the structure more quickly．