In the aerospace field, the rigid-flexible coupled structure is widely used due to its high structural efficiency. However, the existence of the rigid-flexible coupling effect poses a significant challenge to active vibration control. To address this issue, this paper takes the three-flexible beam coupling system as the research object and conducts active vibration control research. During the investigation, first, a vibration measurement and control platform for a three-flexible beam coupling system was established, and piezoelectric sensors and actuators were used to detect and suppress the vibration signals. Based on this, vibration measurement and control algorithm design were carried out. Subsequently, the system dynamics model was established by combining the finite element method with the Hamilton variational principle. The main modal shapes of the system’s free vibration in the simulation environment were determined, and the modal coordinates were introduced to obtain the state space equations of the system. At the same time, considering the uncertainty of model parameters, wavelet analysis and jump spider optimization algorithm were used to accurately identify the parameters of the system state space equations. In addition, considering the nonlinearity and parameter uncertainty of the system, a fuzzy logic controller based on Gaussian membership function was designed to suppress the vibration of the flexible beams. Simulated and experimental results show that, within the same control saturation voltage period, the fuzzy logic controller performs better than the large-gain PD (Proportional and Derivative) control in suppressing the vibration of the three-flexible beam coupling system. It can suppress the large-amplitude vibration quickly while suppressing the small-amplitude vibration at a faster speed, effectively shortening the time for the system to reach a stable state and significantly improving the vibration control effect. In summary, the fuzzy logic controller based on Gaussian membership function designed in this paper overcomes the nonlinearity and parameter uncertainty in the vibration control of rigid-flexible coupling structures, and shows stronger adaptability and higher control efficiency than the traditional large-gain PD control.