CASPIAN JOURNAL
MANAGEMENT AND HIGH TECHNOLOGIES
Construction of Stability Domains for Non-Linear Dynamic Systems
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Read | Shapkarin Aleksey V., Prosandeev Anton V., Kullo Ivan G., Safonenko Viktor A. Construction of Stability Domains for Non-Linear Dynamic Systems // Caspian journal : management and high technologies. — 2013. — №1. — pp. 85-93. |
Shapkarin Aleksey V. - Ph.D. (Engineering), Associate Professor, National Research Nuclear University “MEPhI”, 31 Kashirskoe Shosse, Moscow, 115409, Russian Federation, prosandeev@bk.ru
Prosandeev Anton V. - Senior Lecturer, National Research Nuclear University “MEPhI”, 31 Kashirskoe Shosse, Moscow, 115409, Russian Federation, prosandeev@bk.ru
Kullo Ivan G. - Senior Lecturer, National Research Nuclear University “MEPhI”, 31 Kashirskoe Shosse, Moscow, 115409, Russian Federation, kivan.mail@gmail.com
Safonenko Viktor A. - Associate Professor, National Research Nuclear University, “MEPhI”, 31 Kashirskoe Shosse, Moscow, 115409, Russian Federation, vasafonenko@mephi.ru
The article considers the use of a harmonic balance approach to construct stability domains for nonlinear dynamic systems (NDSs). The critique relates that the approach relies on periodic solutions set forth by Goldfarb’s equation to vary the range of system gain within the stability domains’ boundaries. It adds that current literature has few examples of NDS analyses, having stable or unstable control objects. Consequently, the modified approach will adopt V.M. Popov’s criterion about the stability of the self-oscillatory process in a NDS containing a stable object to assess the NDS on hand (despite the fact that the considered approach contains unstable objects). Moreover, Simulink-based system models have been used, the paper indicates, to verify and more precisely define the theoretical boundaries of the stability domains. Finally, experiments have been conducted using the value-changing capability of input action, with the aim of integrating NDSs into a particular area of the stability domain.
Key words: harmonic balance method,non-linear dynamic systems,stability domains,self-oscillations,MATLAB,Simulink