High-performance permanent magnet synchronous motor (PMSM) servo systems are widely adopted in precision motion control applications; however, conventional cascaded PI/PID architectures suffer from performance degradation under large reference transients, parameter uncertainties, and actuator saturation constraints. These limitations often manifest as overshoot, prolonged settling time, and integral windup, which significantly restrict the achievable dynamic performance and robustness of industrial servo drives. To address these challenges, this paper proposes a hierarchical model predictive control (MPC)-inspired servo framework based on Dynamic Matrix Control (DMC) for PMSM position tracking systems. The proposed approach establishes a reduced-order discrete-time predictive model derived from the step-response representation of the speed subsystem, enabling computationally efficient non-parametric prediction without requiring explicit full-state system identification. On this basis, a three-layer cascaded control architecture is developed, consisting of an outer-loop proportional-derivative (PD) position controller, a middle-layer DMC-based velocity predictive optimizer, and an inner-loop current regulation stage. To further enhance practical applicability, multi-rate sampling coordination is introduced to decouple electrical and mechanical dynamics, allowing high-frequency current regulation and low-frequency predictive optimization to coexist within a unified control framework. In addition, explicit hard constraints on current magnitude and variation rate are embedded into the DMC optimization problem, together with an anti-windup feedback correction mechanism to mitigate performance degradation under actuator saturation. A reference trajectory smoothing strategy is also incorporated to improve transient behavior and suppress aggressive control actions. Simulation results based on MATLAB/Simulink demonstrate that the proposed method achieves zero-overshoot position tracking, significantly reduced settling time, and enhanced disturbance rejection capability compared with conventional cascaded PI control schemes. Moreover, under sudden load disturbances, the proposed controller exhibits superior dynamic stiffness and faster recovery performance while maintaining bounded current profiles and improved electrical safety. These results validate the effectiveness of the proposed DMC-based hierarchical control framework for high-performance PMSM servo applications with stringent real-time and constraint requirements.