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The sensorless controlled brushless DC motor with trapezoidal back EMF has been studied. Since the detected position information on the sensorless rotor has some uncertainty, the brushless DC motor cannot be driven with a maximum torque. To investigate the nature of torque in the sensorless controlled brushless DC motor, the torque characteristics as a function of commutation delay (or commutation timing error) have been analysed. It shows that the generation torque is influenced by the commutation delay and has a single maximum point. This maximum point is changed by the rotating speed and load conditions. Therefore, it needs to be adjusted at every operating point. However, if the operating condition is varied continuously, the sensorless controlled brushless DC motor cannot be driven with a maximum torque at every operating point. In the paper, an iterative learning algorithm and a fuzzy logic controller are employed to drive the brushless DC motor with maximum torque. To show the effectiveness of the proposed control scheme, the change of the torque-current ratio is shown in various operating points through computer simulations and real experiments. It is well demonstrated from these results that the proposed drive method provides desirable performance by the sensorless controlled brushless DC motor with trapezoidal back EMF.