The solar panels on spacecraft and space robots have rotating double flexible beam structures. When they were slewing or affected by external disturbance, the resulting vibration will influence the positioning accuracy and stability of the system. The backlash nonlinearity of the speed reducer will influence the dynamic characteristics of the rotating double flexible beams structure. This will increase the control degree of difficulty. In light of this, a multivariable nonlinear T-S fuzzy(NTS) control algorithm was investingated. The controller use the decoupling design technique and sub-control strategy based on properly designed T-S fuzzy rules. Therefore, the low amplitude vibration near the equilibrium point could be eliminated effectively. The experimental platform of the rotating double flexible beams driven by an alternating current(AC) servo motor with a planetary reduction gear was designed and established. Piezoelectric sensors were used to acquire the vibration signal of double flexible beams. Piezoelectric actuators and an AC servo motor were used to attenuate the vibrations. The experimental results demonstrate that the investigated NTS algorithm shows good performance in suppressing both the large amplitude and lower amplitude vibrations of the system, as compared with a proportional and derivative(PD) controller.