To overcome poor error suppression performance and low control accuracy in the polishing robot-driven branch chain control system, this paper proposes an improved active disturbance rejection control (ADRC) from the design of the derived nonlinear function. Subsequently, the tracking differentiator (TD), extended state observer (ESO) and nonlinear state error feedback (SEF) are designed in the ADRC, and the driven branch’s ADRC servo-control system is established based on the permanent magnet synchronous motor (PMSM) with each driven branch. Meantime, by establishing first-order and second-order ADRC, current-loop control, and speed-and-position-loop control are realized, respectively. Finally, this study analysed differences in the speed and motor rotor error performance between the proportional-integral-derivative (PID)control and ADRC control strategy by using Simulink. Furthermore, an experiment platform, including hardware and software, is built to validate some inclusions. The results show that the ADRC not only realises high-precision trajectory tracking control but also ensures the rapid response performance of the system.