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This paper deals with the full-order flux observer design for speed-sensorless induction motor drives. An unstable region encountered in the regenerating mode at low speeds is well known. To remedy the problem, a modified speed-adaptation law is proposed. Instead of using only the current estimation error perpendicular to the estimated flux, the parallel component is also exploited in the regenerating mode. Using current estimation error loci in steady state, a linearized model, simulations, and experiments, it is shown that the observer using the proposed speed-adaptation law does not have the unstable region. It is also shown that the effect of erroneous parameter estimates on the accuracy of the observer is comparatively small.