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In order to improve the observation accuracy of rotor positions in the sensorless control of permanent magnet synchronous motors and to simplify the parameter adjustment process, this paper proposes an improved finite-time adaptive super-twisting sliding mode observer. First, a linear gain term is introduced into the conventional super-twisting sliding mode observer model as a way of improving the identification accuracy of the observer. Then, for the multi-parameter variable problem in the traditional observer model, a rotational speed variable function design is presented, which simplifies the multi-variables into a single adaptive variable. This reduces the complexity of the observer model while further improving the observation accuracy and stability of the improved observer algorithm (which is verified using Lyapunov's stability theory). A new back EMF filter and an adaptive phase-locked loop are then used to improve the model's speed tracking capability. Finally, through simulation and experimental tests, the improved algorithm's ability to quickly observe changes in rotor position and speed, as well as its fast convergence, small jitter and high accuracy characteristics, are verified. [ABSTRACT FROM AUTHOR]