A compound control method based on adaptive high-order fast non-singular terminal sliding mode control (AHONFTSMC) and sliding mode disturbance observer is investigated in this paper, so as to shorten the response time of speed tracking, and improve the perturbation resistance of torque pulsation in permanent magnet synchronous motors. Firstly, considering the contradictory requirement of achieving both rapid response and mitigating severe jitter in traditional non-singular terminal sliding mode control (NFTSMC), an adaptive parameter technique is proposed to enhance the system's dynamic response. AHONFTSMC not only ensures the system's good tracking performance, but also effectively reduces the jitter in the control output. Secondly, a nonlinear disturbance observer is established to further improve the system response accuracy, so as to observe the disturbance differentials in the system, and perform feedforward compensation on the controller. The stability and convergence of the designed compound controller are demonstrated through the application of Lyapunov theory. The experimental results demonstrate notable improvements in the motor controlled by AHONFTSMC, especially compared to sliding mode control (SMC) and NFTSMC methods. Specifically, compared to SMC and NFTSMC, the time required to reach the rated speed is reduced by 68.6%, 15.6% respectively. The speed overshoot is reduced by 22 and 3% respectively. Compared to the non-adaptive HONFTSMC method, the time required to reach the rated speed is reduced by 7.3%. Furthermore, AHONFTSMC ensures stable changes in electromagnetic torque, effectively reducing the occurrence of chattering. These findings confirm that the proposed control strategy significantly enhances the accuracy of system control and improves the overall dynamic performance of the system.