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In the realm of sensorless control for a permanent magnet synchronous motor (PMSM), the flux observer algorithm is widely recognized. However, the estimation accuracy of rotor position is adversely impacted by the interference from DC bias and high-order harmonics. To address these issues, an advanced flux observation method, second-order generalized integrator flux observer extend (SOGIFO-X), is introduced in this paper. The study begins with a theoretical analysis to establish the relationship between flux observation error and rotor position error. The SOGIFO-X method, developed in this study, is compared with traditional methods such as the Low Pass Filter (LPF) and second-order generalized integrator flux observer (SOGIFO), employing mathematical rigor and Bode plot analysis. The emphasis is on the methodology and the general performance improvements SOGIFO-X offers over conventional methods. Simulations and experiments were conducted to assess the impact of SOGIFO-X on the steady-state and dynamic performances of sensorless control. Findings indicate that SOGIFO-X demonstrates significant enhancements in terms of reducing the reduced flux observation error, contributing to the advancement of position estimation accuracy and sensorless motor control technology. [ABSTRACT FROM AUTHOR]