To meet the stringent requirements of high-speed positioning and dynamic response performance in the field of precision manufacturing, a long-stroke magnetically levitated planar actuator design and control method is proposed, based on a two-dimensional Halbach permanent magnet array and a printed circuit board (PCB) coil array. A dynamic model of the actuator is established using a harmonic model of the magnetic field distribution, enabling an in-depth analysis of the coupling effects between magnetic forces and torques during translational and rotational motions. The study reveals the nonlinear dynamic characteristics of the system and introduces a nonlinear model predictive control (NMPC) strategy to address these complexities. By optimizing control inputs, the proposed method achieves high-precision trajectory tracking along complex paths. The results demonstrate that this approach offers superior tracking accuracy, strong robustness, and fast dynamic response, providing both theoretical insights and technical references for the application of high-speed motion stages in precision manufacturing.