-axis subsystems are firstly transformed into two linear subsystems by using feedback linearization technique, then, integral terminal sliding mode controller and finite-time controller are designed respectively. The proof of finite time stability are given for the PMSM closed-loop system. Compared with the corresponding asymptotical stability control method, the proposed controller can make the system output track the desired speed reference signal in finite time and obtain a better dynamic response and anti-disturbance performance. Meanwhile, considering the large chattering phenomenon caused by high switching gains, a composite integral terminal sliding mode control method based on disturbance observer is proposed to reduce chattering phenomenon. Through disturbance estimation based feed-forward compensation, the composite integral terminal sliding mode controller may take a smaller value for the switching gain without sacrificing disturbance rejection performance. Experimental results are provided to show the superiority of proposed control method.