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A mathematical model was developed, during which the voltage equations of the three-phase winding of a brushless DC motor with permanent magnets, the electromagnetic torque of a brushless DC motor, electromagnetic power, the induced emf of each winding, and the differential torque equation of the servo system were obtained. Based on the constructed mathematical model of the BLDC for a specific motor with given parameters, simulation modeling was carried out and the dependences of electromechanical quantities were obtained: angular velocity of the rotor, electromagnetic torque, stator phase current and rotor rotation angle on time. The simulation results confirmed the theoretical justification of the mathematical model. The resulting mathematical description of the BLDC can be used to build the architecture of a control unit based on a neural network controller.