Abstract
In this paper, we suggest a method for estimating the parameters of periodic motions and also a frequency-domain criterion of their stability for nonlinear time-invariant homogeneous (identical) multivariable automatic control systems with structurally identical subsystems. This method can be used to simply determine the parameters of periodic motions and their stability in the class of systems mentioned above based on the structural decomposition and the method of harmonic linearization. The results are confirmed by mathematical modeling.
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REFERENCES
O. S. Sobolev, Research Methods for Linear Multiply Connected Systems (Energoatomizdat, Moscow, 1985) [in Russian].
B. T. Polyak and Ya. Z. Tsypkin, “Stability and robust stability of similar systems,” Avtom. Telemekh., No. 11, 91–104 (1996).
B. N. Petrov, B. A. Cherkasov, B. G. Il’yasov, and G. G. Kulikov, “Frequency analysis and synthesis of multidimensional automatic control systems,” Dokl. Akad. Nauk SSSR 247, 304–307 (1979).
B. G. Il’yasov and Yu. S. Kabal’nov, “A study of the stability of the same type of multiply connected automatic control systems with holonomic connections between subsystems,” Avtom. Telemekh., No. 8, 82–90 (1995).
B. G. Il’yasov, G. A. Saitova, and E. A. Khalikova, “Analyzing stability margins of homogeneous MIMO control systems,” J. Comput. Syst. Sci. Int. 48, 502 (2009).
B. G. Il’yasov and G. A. Saitova, “A systems approach to studying multiconnected automated control systems based on frequency methods,” Autom. Remote Control 74, 456 (2013).
B. G. Il’yasov and G. A. Saitova, “Stability analysis of dynamic systems in the polynomial vector-matrix representation,” J. Comput. Syst. Sci. Int. 57, 171 (2018).
B. G. Il’yasov, G. A. Saitova, and E. V. Denisova, “Analysis of periodic motions in non-linear, homogeneous, multiply connected automatic control systems (MCACS),” Mekhatron., Avtomatiz., Upravl., No. 7, 29–34 (2001).
B. G. Il’yasov, R. A. Munasypov, G. A. Saitova, et al., “Analysis of periodic motions in multiply connected systems with fuzzy regulators in separate subsystems,” Mekhatron., Avtomatiz., Upravl., No. 8, 24–29 (2004).
S. N. Vasil’ev, B. G. Il’yasov, M. N. Krasil’shchikov, et al., Control Problems of Complex Dynamic Objects of Aviation and Space Technology, Ed. by S. N. Vasil’ev (Mashinostroenie, Moscow, 2015) [in Russian].
Funding
This work was supported by the Russian Foundation for Basic Research, project nos. 18-08-00702 A and 17-48-020956 r_a.
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Translated by A. Mazurov
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Il’yasov, B.G., Saitova, G.A. A Study of Periodic Motions in Homogeneous Nonlinear Multivariable Systems Written in the Polynomial Vector-Matrix Representation. J. Comput. Syst. Sci. Int. 59, 1–7 (2020). https://doi.org/10.1134/S1064230719060078
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DOI: https://doi.org/10.1134/S1064230719060078