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This paper proposes an adaptive flux observer (AFO) method of sensorless induction motor (IM) drives. The AFO gains are designed to ensure accurate estimated speed, especially at very low frequencies in the regenerating mode of operation. Stability analysis of AFO with the designed gains is presented using the Lyapunov theory. These gains are calculated to be adaptively dependent on the IM variables and parameters. The observer gains play a significant role on the stability and precision of AFO in the regenerating mode. The influence of the machine parameters mismatch on the AFO stability with zero feedback gains as well as the proposed feedback gains is provided. The sensitivity to stator resistance is also analyzed. The complete sensorless IM drive with the proposed AFO is executed by both MATLAB/Simulink program, and also in the laboratory. Analytical and experimental results under various working conditions are provided to prove the effectiveness of the proposed AFO, especially at very low stator frequencies.