In this article, we introduce the development of a robust control adaptive system for an induction motor drives and fuzzy logic adapter to the rotor time constant estimation is proposed. We develop and combine the model reference adaptive system (MRAS) method with fuzzy logic approach to achieve our objectives. Two main objectives are covered; the first aim is to study and develop a speed control of the induction machine using the MRAS to estimate the rotor time constant, the second one is to study and develop an intelligent adaptation method based on the fuzzy logic algorithms, keeping the same performance. A robust vector control of induction motor drives scheme is proposed taking into consideration the compensation of the rotor time constant inverse variation. The new presented approach improves the performances of the MRAS compared to the usual methods. Finally, the validity of the proposed control is demonstrated by a series of computer simulations and the obtained results show that the designed control system can achieve satisfactory performances and to the adaptability of the rotor time constant variation. Index Terms --Asynchronous machine, adaptive control, fuzzy systems, estimation of the rotor time constant, model reference adaptive system (MRAS).