The Five-hundred-meter Aperture Spherical radio Telescope (FAST) is currently under construction at a Karst
depression in the Guizhou province of China. The active reflector of the telescope is composed of 4395 triangular panels
laid on a cable-net structure. The aperture of the spherical surface is 500 meters, with open angle of about 110~120
degrees. Acting as the nodes of the reflector, the joint of these panels are adjusted by 2235 down-tie cables drawn by
actuators. The RMS error of the parabola reflector is expected to be 5mm.
To form the parabola shape of the reflector, for each of the actuators, a minimal working stroke of 950mm is required,
with maximal speed of 1.6mm/s at the load of 50kN. Considering the elastic deformation of the down-tie cable and other
factors, a positioning error within 0.25mm is required for the actuators.
In this paper, the base formula for the motion of a general actuator at a typical observation time is studied analytically.
The results are used to estimate the control error of the actuators and the pointing error of the whole reflector. Based on
the designed error budgets, a statistical method is employed to estimate the overall surface error of the parabola reflector.
The overall surface error is a comprehensive result of the panel design error, panel fabrication error, thermal deformation
error, panel wind load induced error, cable-net error, installation error, measurement and control error etc. The results
may be used as a reference in the measurement and control of the active reflector when in operation.