For the problem of that the permanent magnet linear synchronous motor(PMLSM) is prone to be affected by uncertain factors such as parameter perturbation, load disturbance, etc., which affects its displacement tracking control accuracy, a dynamic surface backstepping sliding mode control method is proposed based on the nonlinear disturbance observer(NDO) and the extreme learning machine(ELM). Firstly, the NDO is developed to dynamically observe the mismatched uncertainty in the system model, and the displacement tracking controllers for the PMLSM are presented by combining backstepping control with dynamic surface control and sliding mode control, which improves the anti-interference ability of the system, and avoids the ``differential explosion'' problem during using the conventional backstepping control. Then, ELM neural networks are used to approximate the matched uncertainties in the system model, and the estimated values of the outputs are introduced into the designed dynamic surface backstepping sliding mode controllers for compensation. Furthermore, the artificial fish-frog jump hybrid algorithm is adopted to optimize the main parameters of the designed controllers, which improves the convergence speed and stability accuracy of the system. Finally, the proposed control method is compared with other control methods, and the simulation results verify the effectiveness of the proposed control method.