Real-Time Implementation of Hammerstein Models for Temperature Estimation in Permanent-Magnet Synchronous Motors

Accurate real-time temperature estimation of permanent-magnet synchronous motors is essential to prevent overheating and ensure reliable operation. To this end, electric and thermal models are often used due to their low computational burden. However, parameter estimation for these models is challenging and error-prone. Though less sensitive to errors, data-driven techniques demand numerous parameters and are difficult to implement in real time. Additionally, considerations for translating models from double to single precision are often overlooked. This paper presents a numerical stability analysis and a real-time implementation of Hammerstein models initialized with a lumped-parameter thermal network to estimate the temperature in the windings and magnets of an out-runner permanent-magnet synchronous motor. The numerical stability of the Hammerstein model was evaluated to assess the feasibility of converting its coefficients from double to single precision by computing the condition number and eigenvalues of the state-transition matrix in the Hammerstein model’s linear block. A balanced state-space realization was used to reduce the condition number and avoid truncation errors when converting parameters to single precision. The model was implemented via a processor-in-the-loop simulation on an inverter-grade 32-bit microcontroller using MATLAB-Simulink, where the execution time and CPU utilization were computed. Results show that balancing the Hammerstein linear block improves the condition number of the state-transition matrix below 1.75, with an execution time under 200 µs and CPU utilization below 0.04%.