Maximum Torque per Ampere Control of PMSMs Using Real-Time Numerical Optimization

This paper proposes a novel online maximum torque per ampere (MTPA) control method for permanent magnet synchronous motors (PMSMs), addressing nonlinearities such as magnetic saturation and cross-coupling effects. A flux linkage based nonlinear PMSM model is developed to improve torque control under dynamic conditions. The proposed gradient projection descent (GPD) method is introduced as a computationally efficient solution specifically tailored for real-time applications. It is evaluated alongside the Levenberg-Marquardt algorithm (LMA), renowned for its high accuracy and rapid convergence. Compared with LMA method, the proposed GPD method achieves an optimal balance between computational efficiency and control accuracy, making it suitable for embedded systems with limited resources. Notably, the method can support online experimental characterization and online parameter estimation techniques to capture real operating conditions, such as temperature and load variations, providing a significant advantage for dynamic PMSM applications. Extensive simulations and experimental validations using a 1.3 kW interior PMSM prototype and a TMS320F28375S control platform demonstrate the effectiveness of the proposed methods. Results demonstrate that GPD ensures real-time feasibility while maintaining acceptable levels of torque accuracy. These findings highlight the potential of GPD as a practical solution for high-performance motor control applications, especially in resource-limited embedded systems, with future work planned to explore online characterization and estimation for enhanced adaptability.