**1.1 About asynchronous electric drives**

Asynchronous electric motors (AEM) are the most common electromechanical converters in the industry. Invented more than 150 years ago, they very quickly became integral elements in all technical systems due to their manufacturability, low price, good weight, and size characteristics. At the same time, for more than

100 years, they have been used in mechanisms with virtually no control over the speed of rotation or the mechanical moment developed. Only in the 1980s of the twentieth century, that is, 100 years after the invention, with the start of production of powerful controlled semiconductor switches, it became possible to effectively control the stator frequency and, along with it, almost any AED coordinates. There was a very interesting situation. The principles of frequency control were developed at the beginning of the twentieth century, but not having a wide practical application, they largely remained a theory. Developed in the 1970s, the principles of "transvector" control were immediately recognized as "reducing" the AED to a DC drive, that is, practically to a linear stationary system. The use of AED with frequency converters in a wide practice has encountered a number of problems. It turned out that AEDs are a substantially nonlinear link and the existing control methods (scalar control (SC), space vector control (SVC)) do not remedy this situation too much. At present, the following situation is "generally accepted": scalar control preserves the nonlinearity of the AED, but is not intended for dynamic mechanisms and does not require dynamic analysis, and vector control reduces the AED to a DC drive; therefore, complex nonlinear methods are not applied to anything. Everything is complicated by the fact that both linear and nonlinear equations of electromechanical complexes are only an approximation to real technical systems.

system with variable coefficients should be considered rather nonlinear. Moreover, for a system with variable coefficients, transfer functions, stability criteria, and

*Nonlinear Dynamics of Asynchronous Electric Drive: Engineering Interpretation and Correction…*

Linear stationary systems, which we will further call simply linear, have one big advantage over reality. These equations have exact solutions. But nonlinear equations are either very difficult to solve or not at all. But this is not the biggest problem in the interaction of linear and nonlinear systems. Linear cybernetic systems, and electric drives in particular, have processes whose quality—stability, transient time, and the magnitude of the static and dynamic errors of the drive—do not depend on the input "master" signals and on external influences and disturbances, since they are determined only by parameters of the control system itself. Thus, such system is predictable. To identify it, it is not necessary to test it with signals of different magnitudes and rates; it should not allow unexpected operating modes and all the more emergency ones. In addition, it is quite simply adjusted by regulators and feedbacks. For nonlinear control systems, all these are just dreams and desires. Systems behave differently at different speeds and under different loads, stable at nominal speed, and they become oscillatory at low speeds, etc. But probably the biggest problem is that they cannot be adjusted by the usual methods—PI and PID regulators behave completely unpredictable. Paraphrasing the classic, one can say: "All linear systems are the same, and nonlinear ones are each nonlinear in their own way." From the foregoing, it is clear that any engineer would prefer to deal with linear control systems and electric drives, or at least with the systems closer to linear with those tasks and disturbances that this system is experiencing. Nonlinear components can be very different—inevitable "imperfections," restrictions, dead zones, backlashes, etc. But there are also "fundamental" nonlinearities in electric drives; this is the *moment formation*—the operation of multiplying two variable functions current and magnetic flux. In asynchronous motors, these are periodic functions; as a result, this drive even has a mechanical characteristic that is strictly nonlinear. It is obvious and follows from the Kloss formula and the equivalent scheme, in which there is an element, dependent on slip. Those nonlinearities of asynchronous electric drives are known, but adjusting them with simple means (*IR*, compensation) does not work. The electric drives becomes ineffective. To overcome this, a special "vector" control is applied, which also turns out to lead to new nonlinearities and problems, including unexpected ones. In this way, to bring an automatic system closer to a linear one is to make it predictable, adjustable, reliable, and efficient. In the proposed paper, some methods of such an approximation are given. We called them linearization methods. Usually, this term is called the simplification of the original nonlinear equations of the system. But we left this term unchanged. In our opinion, this term reflects too well the goals and results of this work to replace it with another. In modern high-tech industrial mechanisms, electric actuators play a very important role. The quality of technical complexes and their competitiveness depend on their ability to "fend off" disturbances, for example, change in air

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.

dynamic characteristics will not be as accurate and strict as for LSS.

**2.1 Asynchronous electric drives and linear stationary systems**

**2. Problem statement**

*DOI: http://dx.doi.org/10.5772/intechopen.88223*

**171**
