CASPIAN JOURNAL
MANAGEMENT AND HIGH TECHNOLOGIES
Periodic Fluctuations in Nonlinear Continuous-Discrete Systems: Analysis of Stability
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Read | Chuvykin Boris V., Dolgova Irina A., Yeremenko Alexey V. Periodic Fluctuations in Nonlinear Continuous-Discrete Systems: Analysis of Stability // Caspian journal : management and high technologies. — 2013. — №1. — pp. 26-31. |
Chuvykin Boris V. - D.Sc. (Engineering), Professor, Penza State University, 40 Krasnaya St., Penza, 440026, Russian Federation, phone 8 (8412) 36-82-38, e-mail: irina-penza@mail.ru, chuvykin_bv@mail.ru
Dolgova Irina A. - Ph.D. (Engineering), Associate Professor, Penza State University, 40 Krasnaya St., Penza, 440026, Russian Federation, phone 8 (8412) 36-82-38, e-mail: irina-penza@mail.ru, chuvykin_bv@mail.ru
Yeremenko Alexey V. - Ph.D. (Engineering), Associate Professor, Penza State University, 40 Krasnaya St., Penza, 440026, Russian Federation, phone 8 (8412) 36-82-38, e-mail: irina-penza@mail.ru, chuvykin_bv@mail.ru
The article discusses the challenge of using a nonlinear continuous-discrete (NCD) system to determine the causes of its periodic fluctuations. The NCD system would contain a third-order sigma-delta modulator, a key element in the structure of a high-precision sigma-delta analog-to-digital converter. The presence of periodic fluctuations in continuous-discrete systems, the critique relates, is a necessary condition for stable modulator functioning and high-precision analog-to-digital conversion. The document presents a method of computer simulation that establishes the boundary values for feedback coefficients of the sigma-delta modulator whenever chaotic fluctuations for mode transition occur. The method is based on an analysis of the integrator input/output in the phase plane and of the output signals from the third-order sigma-delta modulator. It enables the user to obtain quantitative estimates of the latter device’s sensitivity to variation-coefficient-value feedback from the boundary values, which corresponds to a steady availability state for periodic fluctuations. The commentary notes that a Simulink-model is used by the third-order sigma-delta modulator, which includes direct-channel analog integrators and provides covered-pulse feedback. Finally, the blueprint presents the quantitative results of the simulation and a graphical illustration of the NCD system’s transition from periodic to chaotic fluctuations.
Key words: nonlinear continuous-discrete systems,sigma-delta ADC,sigma-delta modulator,periodic fluctuations,chaotic fluctuations,phase plane,spectral analysis,stability