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This paper proposes the design method of adaptive rotor flux observer gain to improve stability at low speed and regenerating mode. The method is based on the stability analysis. The stability analysis utilizes the linearized model considering all systems including each control loop. Therefore the proposed method considers the effects of motor constants and control circuit constants. The stability analysis using the transfer function for rotor speed considers the arrangement of pole and zero and the steady state error. The rotor flux observer gain which improves the stability for each operating condition is clarified. Also this paper proposes the real time tuning method of observer gain. The validity of the proposed method is confirmed on the simulation using Matlab Simulink and experiment.