To achieve the ultra-spectral detection of atmospheric trace gases in both nadir and limb, the time-modulated Fourier transform spectrometer was used to obtain the spectral information, and the optical path scanning speed stability satisfied greater or equal to 99.5%. In this paper, a control system of the translational scanning interferometer was investigated and the system principle diagram was presented. Considering the long-range optical path distance (OPD) and high scanning speed stability requirements, a interferometer control system of the translational optical path scanning was applied, and the schematic diagram of the scanning implementation was given. As the fluctuation of scanning speed caused by frictions, mechanical vibrations and other disturbances, its influence on the interference signal intensity and inversion spectrum was theoretically analyzed. The motion of OPD scanning and the interference have a characteristic of periodicity, this paper proposed a plug-in repetitive controller, which has an excellent in suppressing periodic disturbances, and implements uniform scanning. MATLAB numerical simulation and experimental verification were carried out for the control strategy, the results indicate that the plug-in repetitive controller can improve the speed stability periodically. When the angular mirror moves at 10.625 mm/s, the final displacement error is about ±0.000 25 mm, and the velocity error is about ±0.000 4 mm/s, which meet the performance requirements.