The time-modulated Fourier transform spectrometer realizes spectrum detection by scanning the optical path of the corner mirror. During the scanning process, the servo system is required to have high-precision and low-speed characteristics. Aiming at the fluctuation of scanning speed caused by spatial micro-vibration during scanning, a closed-loop model reference adaptive control algorithm based on feedforward is studied. The permanent magnet synchronous linear motor is used to drive the angle mirror to move back and forth along the guide rail to achieve large optical path and high-precision scanning with the maximum optical path difference of ± 34cm, the speed stability ≥ 99%.