A Comparative Study of Discretization Methods for Model Predictive Current Control of Permanent Magnet Synchronous Motors

This study presents a systematic comparative analysis of nine stator current discretization methods within the Model Predictive Current Control (MPCC) framework for Permanent Magnet Synchronous Motors (PMSMs). These methods have generally been examined individually or in limited combinations in previous research, and this holistic and comprehensive comparison constitutes the core contribution of this work by addressing a significant gap in the existing literature. The investigated MPCC methods—Forward Euler (FE), Backward Euler (BE), Midpoint Euler (ME), Fourth-Order Runge–Kutta (RK4), Runge–Kutta Ralston (RKR), Taylor Series (TS), Verlet Integration (VI), Crank–Nicolson (CN), and Adams–Bashforth (AB)—are comprehensively evaluated for their dynamic performance, including speed tracking, torque response, settling time, rise time, overshoot, and Total Harmonic Distortion (THD). Additionally, these analysis results are benchmarked against conventional Proportional–Integral–Derivative (PID) and Field-Oriented Control (FOC) methods. In terms of key performance indicators, the MPCC–RKR method proved optimal for speed tracking under no-load conditions, achieving the lowest overshoot, specifically ranging from 0.097% to 1.450%. Conversely, MPCC–ME and MPCC–CN demonstrated superior transient performance under sudden-load conditions (1.7 Nm), yielding the smallest torque deviations, fastest settling times. Specifically, MPCC-ME recorded the lowest overshoot (1.512%) at the 7 s load step, while MPCC-CN performed best at 9 s (1.220%) and 11 s (1.577%). Among the predictive schemes, the MPCC–RKR method achieved the highest current quality with a minimum THD of 3.69% at nominal speed. Finally, it has been confirmed through the applied statistical analysis techniques that the performance differences among the discretization methods are significant. The comparative analysis examines both the dynamic performance of the methods and the fundamental trade-off between accuracy and computational burden in MPCC design. Simple single-step explicit methods (FE, ME, RKR, VI, AB) offer low computational cost and are well suited for high–sampling-frequency real-time applications, especially with sufficiently small sampling times, whereas more complex multi-step or implicit methods (BE, RK4, TS, CN) may increase the processor load despite their potential gains in accuracy and stability. This study provides practical, evidence-based guidelines for selecting an optimal discretization method by balancing accuracy and dynamic performance requirements for PMSM applications.