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This paper presents a digital strategy to suppress magnetic- and cross-saturation effects in a sensorless predictive direct-torque-controlled synchronous reluctance machine (SynRM). In SynRMs, the angular position of the rotor can be estimated by using inductance variations due to geometrical effects of the rotor. However, magnetic- and cross-saturation effects lead to large errors on the estimated angular position, particularly when the magnetization level and torque load change. This error deteriorates the performance of the electrical drive when the estimated position of the rotor is used instead of the measured one in a sensorless control scheme. In this paper, it is shown how saturation effects can be readily alleviated by using a digitally implemented quadrature phase-locked loop observer, together with linear regression, so that easy digital implementation, stable operation, and null parametric dependence can be achieved. The experimental results at very low and zero speeds verify the effectiveness of the proposed sensorless control scheme.