Reference for citation: Zhusubaliyev Zh. Т., Abdirasulov А. Z., Sopuev U. А., Kolomiets Е. А. Multistable dynamics of a control system with unipolar pulse-width modulation. Journal of Instrument Engineering. 2024. Vol. 67, N 3. P. 220—229 (in Russian). DOI: 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

Acknowledgement: 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.

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