**Abstract**

The results of theoretical and practical research studies most widely used in the industry of variable frequency drives (VFD) are presented in this manuscript. Such objects are characterized by dynamic nonlinearities that are difficult to take into account in the mathematical description for the development of control algorithms. Accounting for these nonlinearities leads to equations that are very problematic to solve. Therefore, the equations of the mathematical model on which the vector control system is based are compiled with the assumption of the sinusoidality of the processes occurring in the control object. Comparative results of the analysis of dynamic of VFD with two types of sensorless control, vector and scalar, show the problems that these assumptions lead to.. For identification of nonlinearities, dynamic formulas of transfer functions of torque generator in VFD are proposed, taking into account slip and stator voltage frequency The nonlinear transfer functions obtained in this work made it possible to substantiate structural solutions that linearize the VFD and substantially increase their efficiency. The use of dynamic feedback on the stator current allowed to significantly increase the dynamics and efficiency of a more stable scalar control.

**Keywords:** electric motors, asynchronous electric motors, nonlinear control systems, rotor and stator currents, spectral composition, stability criterion, linearization of a nonlinear system, mathematical modeling, nonlinear transfer functions
