Frequency Criterion for the Existence of Sliding Processes in Control Systems with an Arbitrary Variable Structure

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

Mathematics, 2024, vol. 12, issue 6, 1-20

Abstract: The article proposes a criterion for the existence of sliding processes according to the frequency characteristics of the control device and the control object. It is shown that the conditions for the existence of slip are equivalent to the conditions for the absolute stability of equivalent circuits of the original systems with a variable structure. This approach is proposed by the authors as an alternative to the method of phase trajectories and state space equations used by other researchers. Frequency criteria make it possible to formulate several practical engineering provisions that are very important for the implementation of this control method in real electric drives. The main conclusions are confirmed by simulation of both processes in systems with a variable structure and in equivalent circuits.

Keywords: control systems with variable structure (VSS); sliding modes (SM); slow and fast movements; perfect glide; phase trajectories; control object (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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