Sensorless Speed Control of PMSM in the Low-Speed Region Using a Runge–Kutta Model-Based Nonlinear Gradient Observer

High-performance operation of permanent magnet synchronous motors (PMSMs) strongly depends on the reliable availability of rotor position and speed information. Although this information is commonly obtained using physical position sensors, such sensors increase system cost and structural complexity and may reduce long-term reliability, particularly in demanding operating environments. In this study, a model-based, discrete-time, nonlinear gradient observer is adapted for the sensorless estimation of rotor speed and position in PMSMs. The developed Runge–Kutta model-based gradient observer (RKGO) utilizes stator voltage inputs and measured stator currents within a mathematical motor model to estimate the system states. In contrast to conventional sensorless estimation approaches, the adopted observer framework exploits discretization-based gradient dynamics to enhance numerical robustness and convergence behavior under nonlinear operating conditions. The observer design specifically targets stable and accurate state estimation in discrete-time implementations, with a particular focus on low-speed operating conditions. The performance of the adapted method is experimentally evaluated under low-speed operating conditions, including transient and steady-state operation. Real-time implementation is carried out on a dSPACE DS1104 control platform, including loaded acceleration scenarios to assess practical robustness. In addition, a comparative analysis with the Extended Kalman Filter (EKF) and the Runge–Kutta Extended Kalman Filter (RKEKF) is conducted at 60 rad/s under identical experimental conditions. Experimental results show that the RKGO method achieves accurate steady-state speed and position estimation with acceptable transient performance. The findings demonstrate that RKGO can be considered a viable alternative for low-speed sensorless PMSM drive applications.