Multistable Dynamics of a Control System with Unipolar Pulse-Width Modulation
https://doi.org/10.17586/0021-3454-2024-67-3-220-229
Abstract
The dynamics of a non-smooth mapping with a large number of switching manifolds, which describes the behavior of a unipolar pulse-width control system for the energy supply of a heating installation (furnace) for growing sapphire single crystals, is studied. Such a mapping is shown to demonstrate a special type of multistability, when several nested attractive closed invariant curves corresponding to stable two-frequency oscillations coexist in the phase space of the dynamic system. Results of the research are important for creating new methods of predicting, detecting, and suppressing irregular oscillations and catastrophic phenomena that arise when parameters vary and are exposed to interference, as well as for designing pulsed automatic control systems with specified dynamic properties and predictable dynamics.
Keywords
multistability,
border collision bifurcations,
non-smooth continuous mapping,
quasi-periodic saddle-node bifurcation,
closed invariant curve,
two-frequency oscillations
Supporting agencies: The work was supported by the Ministry of Science and Higher Education of the Russian Federation, the program of strategic academic leadership “Priority-2030”, grants No. 1.71.23 P, 1.7.21/S-2, and Osh State University, grant No. 14-22.
About the Authors
Zh. T. Zhusubaliyev
Southwest State University, Department of Computer Science; International Scientific Laboratory for Dynamics of Non-Smooth Systems
Russian Federation
Russian Federation
Zhanybai T. Zhusubaliyev — Dr. Sci., Professor,
Kursk.
A. Z. Abdirasulov
Osh State University, IT Academy
Kyrgyzstan
Kyrgyzstan
Aitibek Z. Abdirasulov - Director,
Osh.
U. A. Sopuev
Osh State University, Faculty of Mathematics and Information Technology
Kyrgyzstan
Kyrgyzstan
Ulanbek A. Sopuev — PhD, Associate Professor, Dean,
Osh.
E. A. Kolomiets
Southwest State University, Department of Computer Science, International Scientific Laboratory for Dynamics of Non-Smooth Systems
Russian Federation
Russian Federation
Elena A. Kolomiets — PhD, Senior Lecturer,
Kursk.
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Review
For citations:
Zhusubaliyev Zh.T., Abdirasulov A.Z., Sopuev U.A., Kolomiets E.A. Multistable Dynamics of a Control System with Unipolar Pulse-Width Modulation. Journal of Instrument Engineering. 2024;67(3):220-229. (In Russ.) https://doi.org/10.17586/0021-3454-2024-67-3-220-229
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