Mathematical Model of Permanent Magnet Synchronous Motor

The mathematical model of permanent magnet synchronous motors (PMSM) holds significant importance in motor control applications, where its accuracy directly impacts the performance of control algorithms. Implementing the model using S-functions in Simulink enables high-precision simulation verification, providing a robust platform for control system development.

The PMSM mathematical model typically consists of three fundamental equations: voltage equations, flux linkage equations, and motion equations. The voltage equations describe the relationship between stator voltage and current, involving d-axis and q-axis components. The flux linkage equations express the coupling effect between the magnetic field generated by permanent magnets and the armature reaction field. The motion equation connects electromagnetic torque with mechanical motion, incorporating parameters such as load torque and moment of inertia.

When implementing these equations in S-functions, discretization processing is required while considering sampling time effects. The key advantage of S-functions lies in their flexibility for custom algorithm development while maintaining efficient interaction with other Simulink blocks. Through proper configuration of input and output ports, real-time observation of dynamic responses for critical variables like current and rotational speed becomes achievable. The implementation typically involves defining derivatives in continuous mode or update methods in discrete mode, with careful handling of state variables for numerical stability.

During experimental verification phases, simulation results must be compared with measured data, with particular focus on steady-state performance and dynamic response characteristics. A correct mathematical model should accurately reflect the motor's nonlinear characteristics, such as magnetic saturation effects and cogging torque. Furthermore, parameter identification proves crucial, including stator resistance, inductance, and permanent magnet flux linkage values. This often involves employing parameter estimation algorithms like least squares methods or recursive identification techniques.

In summary, the S-function-based PMSM model provides a reliable platform for control strategy design and system optimization. The validity of this approach has been thoroughly verified through experiments, making it suitable for various high-performance drive scenarios including electric vehicle propulsion and industrial servo systems.