To address the vibration challenges in flexible thin plate structures like solar panels on spacecraft, this study investigates a translational flexible hinged plate system. A binocular vision-based measurement and control experimental platform is developed. This platform employs the binocular stereo vision technique for vibration detection, and introduces a self-recurrent wavelet neural network controller (SRWNNC) to mitigate vibration. The system's binocular vision is precisely calibrated. Utilizing the principles of disparity and advanced image processing algorithms, it calculates the three-dimensional coordinates of specific markers to capture vibration signals. A finite element model of the system is constructed, facilitating the identification of system model parameters. Following this, the SRWNNC is trained within a simulation environment using the identified model parameters, aiming for effective vibration control in the experimental system. Experiments and simulations are conducted on the system, focusing on both fixed base and translational trajectory movements, to evaluate the effectiveness of binocular vision in vibration detection and the SRWNNC in active vibration suppression. The findings confirm that the binocular vision sensor achieves a high accuracy less than 0.1 mm in detecting vibrations, and the SRWNNC outperforms traditional large gain PD controllers in damping vibrations, thus validating the efficiency and accuracy of the proposed vibration detection and suppression methods.