Flexible appendages carried by large flexible spacecraft are prone to low-frequency vibrations in the space environment, which affect attitude stability through structural coupling. This paper proposes a modal identification method by mapping acceleration signals into the modal space. Furthermore, a fuzzy adaptive control approach, integrating the identification results with Particle Swarm Optimization (PSO), is employed for low-frequency vibration suppression in flexible spacecraft. Simulation results demonstrate that the proposed identification method effectively reduces the impact of mode aliasing on identification, with all identification errors remaining below 2%. The control method significantly attenuates modal vibrations, achieving reductions of up to 70% in the first-mode vibration amplitude and 50% in the second-mode vibration amplitude. Moreover, a 65% improvement in system response speed is achieved.