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There are usually noise problems when the position sensorless control of a synchronous reluctance motor (SynRM) is carried out by high-frequency (HF) signal injection method. Due to the special structure, the cross-saturation effect of the SynRM is particularly serious, resulting in reduced position observation accuracy. In this paper, a variable-angle random HF voltage injection strategy with cross-saturation effect compensation is proposed for position sensorless SynRM drives. Random number generation based on the chaotic mapping method is used to generate random HF voltage signals with different frequencies for injection; the current power spectral density (PSD) distribution is extended and the HF noise can be reduced. A control strategy based on variable-angle square-wave injection is proposed to suppress the cross-saturation effect. By measuring the position error curves of different loads off-line and polynomial fitting the curves, the position error is achieved by combining with the corresponding signal demodulation algorithm. The proposed method does not require additional hardware resources and can maintain high control accuracy and robustness. Finally, the effectiveness of the proposed sensorless control strategy is verified on a 3 kW SynRM experimental platform. [ABSTRACT FROM AUTHOR]