**1.2 About mathematical models and linear stationary systems**

Reality is more complicated than any mathematical model. At the same time, strict solutions exist only in the area of linear stationary systems (LSS), which are described by linear differential equations with constant coefficients in the "left" part of the equations—the one that describes the control object itself—in our case, the electric drive. For such systems, you can highlight a number of important features:


Naturally, real electric drives can be identified by LSS with only very large approximations. In direct-current drives with independent excitation, these approximations are insignificant; they mostly relate to mechanical structures with stiffness and gaps. In asynchronous electric drives, the reduction to LSS is associated with much larger errors. The equations of a generalized AC motor, even with significant assumptions, can be reduced to linear equations with variable coefficients or to nonlinear control systems. For engineering calculations, the differences between these systems are very conditional. If variable coefficients depend on the same coordinates of the electric drive (rotational speed, stator current, etc.), the

*Nonlinear Dynamics of Asynchronous Electric Drive: Engineering Interpretation and Correction… DOI: http://dx.doi.org/10.5772/intechopen.88223*

system with variable coefficients should be considered rather nonlinear. Moreover, for a system with variable coefficients, transfer functions, stability criteria, and dynamic characteristics will not be as accurate and strict as for LSS.

Engineers need to solve the problem of whether to use rigorous calculation methods, reducing the actual system of the electric drive to LSS, very far from the original one, or describe the electric drive with a closer nonlinear system and use much less rigorous methods of calculation in its analysis. This work is aimed at finding a compromise of identification and calculation methods for asynchronous electric drives.
