Efficiency of Applying the Nyquist and V.M. Popov Criteria for Stability Analysis of Linearized Automatic Control Systems in Electromechanics and Power Engineering

Vladimir Kodkin, Alexander Anikin () and Ekaterina Kuznetsova
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Vladimir Kodkin: Department of Electric Drive, Mechatronics and Electromechanics, South Ural State University, 454080 Chelyabinsk, Russia
Alexander Anikin: Department of Electric Drive, Mechatronics and Electromechanics, South Ural State University, 454080 Chelyabinsk, Russia
Ekaterina Kuznetsova: Department of Electric Drive, Mechatronics and Electromechanics, South Ural State University, 454080 Chelyabinsk, Russia

Energies, 2023, vol. 16, issue 2, 1-18

Abstract: It is well known that all real automatic control systems (ACS) are significantly nonlinear systems. Along with this, in engineering analysis the simplifications of their mathematic description, that is, linearization, are inevitable. These simplifications naturally introduce errors into engineering calculations. For the most complicated calculation of stability conditions, these errors can be very significant, since they lead to not only incorrect forecast of the ACS condition but also to the operating inability of the designed ACS. Most often, engineers simplify nonlinear structures in their calculations. In other words, they linearize these structures according to one of the numerous approaches which have been developed over 100 years. Calculation methods for linear ACS, in particular the Nyquist criterion, can be applied to the already linearized structure for the calculation of ACS stability condition. In this article, the authors suppose that for electromechanical and power ACS it would be more effective to widely use the absolute stability criterions or hyperstability which were developed when solving the “Aizerman problem” by V.M. Popov in the 1960s of the 20th century. This solution is not used as widely as the Nyquist criterion despite its outstanding qualities. In this article, the assumption was made that it is effective to apply the stability criterion of nonlinear ACS for the linearized models of nonlinear systems. Otherwise speaking, it is effective to use the criterion of V.M. Popov and its interpretation according to the logarithmic frequency characteristics of the ACS proposed earlier by the authors of the article. The authors provide simple and illustrative examples and give the results of the simulation.

Keywords: discreteness; frequency response; automatic control system; PID controller; variable structure system with sliding processes (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2023
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