Abstract：Permanent magnet synchronous motor（PMSM）sensorless control systems based on the back electromotive force（BEMF）model exhibit excellent performance in medium-to-high speed ranges. They generally consist of a BEMF observer and a rotor information extractor. The linear extended state observer（LESO）is widely adopted for its simple structure, fast convergence, and low model dependency. However, owing to inverter nonlinearities and current sensor drift, the estimated BEMF inevitably contains interference such as DC bias. Since the LESO has a low-pass characteristic and the BEMF is a sinusoidal signal that varies with speed, amplitude, and phase deviation, DC bias errors arise during estimation. The traditional phase-locked loop（PLL）employs a fixed-gain PI controller, which introduces tracking errors proportional to acceleration under dynamic conditions. Moreover, repeated experiments are required to determine PI parameters, complicating parameter tuning. Therefore, this paper proposes a PMSM sensorless control method based on a frequency-adaptive linear extended state observer（FA-LESO）and an improved finite-position-set phase-locked loop（FPS-PLL). Firstly, the limitations of existing LESO schemes are analyzed. Unlike conventional local frequency compensation strategies, the proposed method employs a second-order generalized integrator（SOGI）to extract signals at specific frequencies and reconstruct the internal disturbance model of the LESO. An FA-LESO with band-pass characteristics is designed to enable unbiased extraction at the center frequency while rapidly attenuating out-of-band components. When the center frequency equals the motor speed, the observer achieves frequency-adaptive, lag-free estimation of the fundamental BEMF signal. Secondly, based on the model-predictive principle, a novel equivalent-voltage error is designed to form a cost function, and the FPS-PLL is improved using the secant method. The new cost function has one single convergence point per iteration, effectively overcoming false convergence caused by conventional cost functions within the angular error range. Moreover, the secant iteration avoids the derivative computation required by the Newton method and the initial-value preprocessing, thereby reducing computational cost and eliminating the need for parameter tuning. Finally, the proposed method is validated on a PMSM test platform using a Links-RT hardware-in-the-loop simulator. Results show that:（1）The FA-LESO achieves frequency-adaptive, lag-free estimation of BEMF signals at different frequencies. Compared with conventional schemes, the BEMF delay is reduced by 40% and 92% at 1 000 r/min and 2 000 r/min, respectively. With its band-pass characteristics, it effectively suppresses high-frequency noise and minimizes the impact of DC errors on position estimation accuracy.（2）The improved FPS-PLL has one convergence point per iteration and attains a theoretical accuracy of 3.52×10-6 rad within five iterations. Compared with the traditional PLL, the proposed method exhibits better dynamic response and requires no parameter tuning.
郭默冉, 赵希梅. 基于FA-LESO与改进有限位置集PLL的PMSM无位置传感器控制[J]. 电工技术学报, 2026, 41(16): 5439-5450.
Guo Moran, Zhao Ximei. PMSM Sensorless Control Based on Frequency-Adaptive Linear Extended State Observer and Improved Finite Position Set PLL. Transactions of China Electrotechnical Society, 2026, 41(16): 5439-5450.
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2026, Vol. 41 
