Motor Simulation Model Based on Mathematical Modeling of Permanent Magnet Synchronous Motors

Permanent Magnet Synchronous Motors (PMSMs) are widely used in modern industrial applications due to their high operational efficiency and precise control characteristics, making them the preferred choice for many drive systems. To achieve accurate control of PMSMs, it is essential to first establish their mathematical model and then build simulation models based on this foundation for performance analysis and control strategy validation.

### Mathematical Model of PMSM The mathematical model of PMSM is typically constructed based on voltage and flux linkage equations in the d-q coordinate system. This model incorporates the motor's electromagnetic characteristics, including stator winding resistance, inductance, and the magnetic field distribution of permanent magnets. Through coordinate transformations (such as Park transformation), three-phase AC variables are converted into DC quantities in a synchronous rotating reference frame, simplifying control system design. Implementation note: The Park transformation can be implemented using trigonometric functions to convert three-phase quantities (a, b, c) to d-q coordinates, typically requiring rotor position information for accurate synchronization.

### Simulation Model Construction Based on the mathematical model, simulation tools like MATLAB/Simulink can be used to build PMSM simulation models. The model typically includes these key modules: Motor Core Model: Implements relationships between voltage, current, and torque, simulating electromagnetic and mechanical dynamic characteristics. Space Vector PWM (SVPWM): Generates PWM signals for inverter control to drive motor operation. Dual-loop Control Structure: Typically includes current loop (inner loop) and speed loop (outer loop) for regulating motor torque and speed respectively. Code implementation: The SVPWM algorithm involves sector identification and vector time calculation, often implemented using comparison operations and timing functions to generate appropriate switching sequences.

### Application of PI Controllers in Dual-loop Control In PMSM control strategies, PI controllers are widely adopted due to their simplicity and robustness. Current Loop (Inner Loop): By regulating d-axis and q-axis currents, achieves rapid torque response and improves system dynamic performance. Speed Loop (Outer Loop): Based on the error between target speed and actual speed, the PI controller outputs q-axis current reference values, enabling smooth motor operation and suppressing speed fluctuations. Algorithm explanation: The PI controller implementation typically involves discrete-time difference equations: output = Kp×error + Ki×Σerror, where integral term accumulation requires anti-windup protection in practical implementations.

Through proper tuning of PI controller parameters, system dynamic response can be optimized, overshoot reduced, and stability improved, ultimately achieving high-precision speed control of PMSMs.

This simulation approach based on mathematical modeling and PI dual-loop control not only provides theoretical foundation for practical motor system debugging but also establishes groundwork for research on more complex control strategies such as adaptive control and predictive control.