In order to further increase the observation range and sensitivity of the Five-hundred-meter Aperture Spherical Telescope (FAST), an innovative design of the cable-driven fine-tuning platform (CDFP) is required to replace the existing bulky rigid mechanism to increase rotation capability and reduce weight for more powerful receivers. A key issue is to ensure its stability and anti-disturbance ability. In this paper, an intuitive illustration and analysis method is proposed on the anti-disturbance ability of cable-driven parallel robots (CDPRs), based on the Available Wrench Set (AWS). The approach decomposes the high-dimensional wrench space into the low-dimensional force space and the moment space, enabling the visualized analysis of the anti-disturbance performance and avoiding dimensional inconsistency. On this basis, auxiliary branches are introduced to enhance the anti-disturbance ability of CDPR. Anti-disturbance performance of the CDFP is analyzed, and simulation indicates that the anti-disturbance performance of the CDFP is improved by 186 %, and will greatly improve the observation capabilities of the FAST. This paper provides an efficient method for analyzing and improving the anti-disturbance ability of the CDPR.