Рассматривается система управления непосредственным понижающим преобразователем напряжения на основе метода направления на цель. Приводится математическая модель системы в форме стробоскопического отображения. Построены карты динамических режимов и диаграммы относительного размаха колебаний, позволяющие оценить нелинейные динамические свойства системы. Приводится функциональная схема экспериментальной установки, позволяющей проводить исследования нелинейной динамики замкнутых импульсных систем автоматического управления с различными видами широтно-им-пульсной модуляции. Показана эффективность метода направления на цель при управлении нелинейной динамикой как при численном моделировании, так и при экспериментальном исследовании.
The main purpose of the research is experimental study of nonlinear dynamics of a buck converter with the control system based on target-oriented control which allows eliminating undesirable dynamic modes. Target-oriented control is a relatively new nonlinear dynamics control method and until now the possibility of its application for nonlinear dynamics control of switching power converters has been given only a theoretical estimation. In order to accomplish the mentioned purpose, the study of nonlinear dynamics behavior of the considered system using a mathematical simulation is required. Thereafter, the results of the study should be experimentally verified. The systems of the considered class are described by piecewise-smooth mathematical models in terms of differential equations with discontinuous right-hand side. This paper presents a mathematical model of the automatic control system based on target-oriented control in its stroboscopic maps. The transition to stroboscopic maps is implemented by solving a primal system of differential equations. Dynamic modes maps and voltage ripple relative swing amplitude diagrams have been calculated using the given mathematical model. They allow estimating a certain dynamic mode damages in relation to the output voltage parasitic oscillation amplitude. This paper also presents a functional description of the experimental circuit for study of nonlinear dynamics behavior of a closed-loop control system with different pulse-width modulation types. The peculiarity of the experimental circuit is the control system based on high-performance ARM core microcontroller, allowing the method feasibility estimation and using up-to-date hardware components. One-parameter bifurcation diagrams were calculated using both the mathematical model and the experimental circuit. A comparative study of the theoretical and experimental bifurcation diagrams has been carried out. The efficiency of nonlinear dynamics of target-oriented control for a buck converter has been proved. The given results have been quoted for the first time. They can be used for development the automatic control systems for a broad range of switching power converters types.
The authors declare that there are no conflicts of interest present.