The Chinese Giant Solar Telescope (CGST) is the next generation solar telescope of China with diameter of 8 meter. The unique feature of CGST is that its primary is a ring, which facilitates the polarization detection and thermal control. In its present design and development phase, two primary mirror patterns are considered. For one thing, the primary mirror is expected to construct with mosaic mirror with 24 trapezoidal (or petal) segments, for another thing, a monolithic mirror is also a candidate for its primary mirror. Both of them depend on active control technique to maintain the optical quality of the ring mirror. As a solar telescope, the working conditions of the CGST are quite different from those of the stellar telescopes. To avoid the image deterioration due to the mirror seeing and dome seeing, especially in the case of the concentration of flux in a solar telescope, large aperture solar projects prefer to adopt open telescopes and open domes. In this circumstance, higher wind loads act on the primary mirror directly, which will cause position errors and figure errors of the primary with matters worse than those of the current 10-meter stellar telescopes with dome protect. Therefore, it gives new challenges to the active control capability, telescope structure design, and wind shielding design. In this paper, the study progress of active control of CGST for its mosaic and monolithic mirror are presented, and the wind effects on such two primary mirrors are also investigated.