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A speed control of sensorless induction motor (IM) drives at zero and very low frequencies is designed in this paper. A new adaptive sliding mode observer (SMO) to estimate the stator current, rotor flux, and rotor speed is proposed. To improve the robustness and accuracy of an adaptive SMO during very low frequency operation, the sliding mode flux observer uses independent gains of the correction terms. The gains of current and rotor flux SMOs are designed using Lyapunov stability theory to guarantee the stability and fast convergence of the estimated variables. A Lyapunov function candidate utilizing the error of rotor fluxes and speed estimation error is synthesized for speed estimation. Detailed simulations and experiments are given showing the operation of the sensorless speed control at very low frequency. The results prove the accuracy and robustness of the proposed adaptive SMO. Also, comparison results with the state-of-the-art methods prove that the proposed method shows excellent transient and steady-state speed estimation, particularly at very low and zero frequency operations. [ABSTRACT FROM PUBLISHER]