The Shanghai Soft X-ray Free-Electron Laser Facility is the first X-ray coherent light source in China and it is currently under construction. Polarization controlled X-ray light sources have been applied in many fields. This article presents the polarization controlled design based on the design indicators and actual operating parameters of SXFEL. High-quality circularly polarized X-rays with a circular deflection of more than 99.5% and a pulse energy of 186.4 μJ is obtained by using two-stage EPU simulation at the downstream of the plane undulator section. We also conclude that the bunch energy jitter of the device has little effect on the output performance of the scheme. After that, the difference between the emitted light energy jitter of the EPU and the plane undulator under different noise models is further compared. Theoretically, the suppression effect of reverse taper in the EPU structure on the jitter is analyzed, and the analysis results are in good agreement with the simulation results. In addition, by adjusting the two EPU to different polarization directions, and adding a set of fast correction magnet structures, the additional simulation has realized rapid switching between different polarization directions of circular polarization(10Hz magnitude) Besides, the pulse energy and circular deflection of the two circularly polarized beams have reached the design indicators, and met the requirements of the bunch energy jitter. The intensity of the fast correction magnet required by this solution is quite small, which is low for both the cost and difficulty of manufacturing. The idea of using a fast correction magnet to change the trajectory of the electron beam in the undulator can also be used to switch FEL between other different operating modes(it is easy to achieve especially at low repetition rates).