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The main purpose of this paper is to apply the fuzzy based general regression neural network (FGRNN) to the speed control of an induction motor. A general regression neural network (GRNN) is adopted to estimate the motor speed and thus provide a sensorless speed estimator system. The performance of the proposed FGRNN speed controller is evaluated for a wide range of operating conditions for the induction motor. These include startup and parameter variations. The obtained results show that the GRNN provides a very satisfactory speed estimation under the abovementioned operation conditions and also the sensorless FGRNN speed controller can achieve very robust and satisfactory performance and could be used to get the desired performance levels. The response time is also very fast despite the fact that the control strategy is based on bounded rationality. To evaluate the usefulness of the proposed method, we compare the response of this method with the PID controller. The simulation results show that our method has better control performance than the PID controller.