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In general, DC-DC converter is a highly nonlinear system. More than one decade ago, many researchers have approved that DC-DC converters are experiencing bifurcation and chaotic oscillations. In this paper, both DC-DC Buck and Boost converters are been studied and analyzed. The study showed that such DC-DC converters are experiencing a nonlinear be...
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Considering that the state equations of peak current-mode (PCM) controlled buck light-emitting diode (LED) driver with proportion-integration (PI) compensator are third-order singular matrices with maximum rank 2, it is not invertible and may lead to non-convergent problem under certain circuit parameters. Therefore, an improved discrete-time modeling is performed by substituting state variables of power stage circuit for PI compensator equivalently in this paper. Based on this modeling, the stability of PCM controlled buck LED driver is investigated by analyzing bifurcation diagram and the maximum Lyapunov exponent spectrum, while the conduction-mode boundary and stability boundary are deduced which indicate the operation regions of the system intuitively, providing design guidelines for LED driver. Experimental results are further presented to verify the theoretical analysis.
Relevance of the research is defined by the necessity to increase the efficiency of converters for the needs of renewable energy. The strict and conflicting requirements are often imposed to the control algorithms of DC voltage converters used in solar and wind power. The theory of deterministic chaos may be one of the ways of solving the problem of improving the algorithms. The aim of the research is to study and develop the control systems for DC-DC converters which allows working both in periodic mode and in deterministic chaos mode; to develop a physical model of DC-DC converter including the control system operating in deterministic chaos mode; make the voltage feedback circuit for stabilizing the output voltage at the given level. Research method: a review of patent and literature on the topic. The mathematical and experimental methods of investigation of the DC-DC converters were used. The method of mathematical modeling is based on preparation of electrical systems equations solution. The method of experimental research is based on the study of the output graphs, taken from the physical model of the DC-DC converters. Results. The authors have developed the physical model of the DC-DC converter with the control system operating in the deterministic chaos mode. The results show that the method of controlling the DC-DC converters with the help of deterministic chaos reduces electromagnetic interference, and improves significantly energy efficiency. The results obtained in the study can be used both at the stage of designing the power supplies in this class, and for further research and development of new control systems, including the control by deterministic chaos.
The discrete mapping model of current-mode controlled buck converter with constant current load, taking account of composite output capacitors (parallel connection of two different types of capacitor branches, i.e. electrolytic capacitors and ceramic capacitors), is established. Based on the model, dynamical effects of varying output capacitance and equivalent series resistance (ESR) are investigated by bifurcation behaviours. The period of low-frequency oscillation among coexisting fast-slow scale instability is derived by exploring the loci of eigenvalues, while the operating regions are estimated. Time-domain simulation and experimental waveforms are provided for verification of the theoretical analysis, indicating the existences of subharmonic oscillation and coexisting fast-slow scale instability in the converter with variation of output capacitance and ESR. Research results reveal that the low-frequency oscillation can be eventually eliminated due to a relatively large (or small) ESR and the capacitance in the same branch presents to identical tendency of dynamical effects on the converter. Moreover, the interaction effects between two parallel capacitor branches are demonstrated. It illustrates that the low-frequency oscillation can be removed with smaller (or larger) ESR or capacitance in one branch of the composite output capacitors while larger (or smaller) ESR or capacitance in the other branch.
