This paper investigates a novel anti-disturbance speed tracking control problem for permanent magnet synchronous motor (PMSM) systems with unknown mismatched disturbances. In order to realise the rejection and compensation for load torque, a cascaded PMSM system is constructed by using a coordinate transformation such that the load disturbances become matched with respect to the virtual control input. By combining disturbance observer with proportional-integral feedback control structure, a composite speed controller is proposed on this basis to ensure the PMSM system stability, and convergence of the tracking error of angular velocity to zero. The favourable observation performance for the load torque and its derivative can also be achieved simultaneously. Meanwhile, the L1 performance index is used to further optimise the robustness of the PMSM system. Finally, the effectiveness of the proposed control scheme is verified by simulations for the PMSM system with monotonous disturbances and harmonic disturbances respectively.