Frequency-Adaptive Observer for Sensorless Control of PMSM Based on a Generalized BEMF Observer Model

The sensorless control method based on back electromotive force (BEMF) observers has garnered significant attention in the field of medium- to high-speed permanent magnet synchronous motor (PMSM) drives. However, traditional BEMF observers, due to their low-pass characteristics, struggle to handle DC errors caused by factors such as measurement inaccuracies and inverter nonlinearity, leading to degraded sensorless control performance. Moreover, some advanced methods are constrained by specific design frameworks, resulting in complex observer structures that are not conducive to practical implementation. Therefore, in this paper, a simple and flexible inverse design method for the observer based on a generalized BEMF observer model is first proposed. Subsequently, the method is employed with the gradient descent algorithm to develop a frequency-adaptive observer (FAO), which can completely eliminate DC errors. The proposed observer exhibits zero phase lag and amplitude attenuation at the fundamental frequency of the PMSM, with the fundamental frequency information provided by the frequency-adaptive rule. Compared to other observers, the proposed observer has a simpler structure and is easier to implement. Furthermore, a small-signal model of the FAO is established through linearization to facilitate parameter tuning, and its stability is analyzed based on Lyapunov theory. Finally, comparative experiments are conducted on a 1.5 kW PMSM platform, where the proposed FAO is compared with other observers, validating its effectiveness and feasibility.