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This study presents a modified model reference adaptive system speed estimator for induction motors (IMs) based on regulation of the instantaneous rotor magnetising reactive power, which does not use integration or stator resistance in the reference model. The proposed modifications allow analytical tuning and facilitate implementation of the estimator in a digital signal processor. The detuning of the estimator with respect to the rotor time constant is exploited as a source of information in a novel parallel identification mechanism for this parameter. The rotor time constant error is obtained by correlation of the high-frequency components of the speed estimator error and the torque producing current, thus enabling simultaneous estimation of the IM speed and the rotor time constant. The robustness and accuracy of the proposed schemes are verified experimentally.