The control effect of the interferometer moving mirror affects the performance of the Fourier spectrometer, and previous studies have shown that the double swing arm interferometer has better stability than the classic Michelson interferometer. However, due to the limitations of the manufacturing process and other factors, it is difficult to completely rely on the hardware to eliminate the problem that tilt will increase the control error of moving mirror. Therefore, this paper attempts to achieve the requirement that the control error of the interferometer moving mirror should not exceed 2% when the environmental parameters change from the perspective of the control method. Based on the analysis of the moving mirror controller, a software and hardware platform is built in this work, realizing the acquisition and communication of control signals on the hardware and the periodic swing of the moving mirror on the software. In the constant speed stage of periodic swing, the classic proportional-integral-differential (PID) control and fuzzy PID control are used in the controller respectively, and the test and data sampling are carried out under different conditions of horizontal and tilt. The test results show that compared with the classic PID control, the fuzzy PID control has better control effect for the moving mirror when system parameters change, with the error within 0.7% and an average error of 0.15% in horizontal condition, and the error within 1% and an average error of 0.29% in tilt condition. The control method proposed in this work provides a reference for the application and expansion of Fourier spectrometer in complex environments.