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In the paper there are presented results of method for rotor time constant adaptation with application of artificial neural network. The method employs the model reference adaptive system (MRAS). The adaptation algorithm is designed according to the Popov's criterion for hyperstability. The method is based on application of current model and voltage model of rotor flux in MRAS. The estimation of rotor time constant for adaptive model of MRAS is realized by the help of PI-controller. In next part of the paper there is described a replacement of adaptation algorithm in MRAS by the help of artificial neural network. The estimated rotor time constant is necessary for so-called current model. The current model is used in the vector control of the induction motor and serves for the determination of the quantities for the transformation from stationary reference frame into reference frame, which is oriented on the rotor flux space vector. Simulations have been performed in the Matlab-Simulink. The control algorithms are implemented using TMS320C2812 DSP. At the end of the paper some simulation and experimental results are provided to demonstrate the effectiveness of proposed method.