In this study, a composite control algorithm was developed for controlling the turntable speed of a circumferential scanning imaging system (ICSIS) driven by a permanent magnet synchronous motor (PMSM) to obtain stable high-resolution images. Based on the load characteristics of the turntable and the mathematical model of the PMSM, a single-sampling rate control system model, comprising the mechanical parameter uncertainty and fast-changing torque disturbance, was established. The fast nonsingular terminal sliding mode (FNTSM) control and an extended high-gain observer were used in designing the speed-tracking controller. The maximum torque current ratio control was determined through another FNTSM control. Finally, the performance of the speed tracking control based on the above composite algorithm was analyzed and verified. The experimental results show that when the turntable speed is set to 120 or 240 r/min, the speed tracking error is less than 0.1%. Compared with the proportional-integral control, FNTSM control, and linear sliding mode control+observer, the governing system with the proposed algorithm was characterized by no overshooting, stronger anti-disturbance, and higher speed-tracking precision, which enabled the ICSIS to capture clear and stable circumferential images.