The mathematical model for calculation of frequency response of a push-pull DC-DC converter with a PI-regulator

Abstract

Background: The analysis of the frequency response of pulse-width converters is necessary at the stage of their design in order to ensure their stability. The most accurate results can be achieved using nonlinear dynamic mathematical models of these systems. At present, obtaining of frequency response data of pulse-width converters is carried out using the models created in the existing software that uses numerical methods for solving systems of differential equations to calculate electromagnetic processes, which leads to the accumulation of errors in the calculation of time dependencies, and also requires significant computation time to obtain the result. Therefore, the development of a mathematical model that eliminates these downsides is a relevant task.

Objective: Development of a nonlinear dynamic mathematical model of a DC/DC converter with a closed automatic control system with feedback on the output voltage when exposed to measuring signals from a frequency response analyzer.

Methods: The methods of mathematical modeling of electronic circuits and the theory of differential equations were used. The frequency response data were calculated using a program written using the C++ language. The results obtained using the proposed mathematical model were also compared with the results obtained using the model in the MATLAB/Simulink and using analytical expressions.

Results: A mathematical description of electromagnetic processes in a push-pull bridge DC/DC converter on the interval of invariance of the structure of the power section in analytical form is given. Nonlinear transcendental equations are also given, allowing to calculate the moments of switching the circuit valves. The frequency response data were calculated using the proposed mathematical model and a comparative analysis was carried out with the frequency response data obtained using other methods and the correctness of the developed model was confirmed. Thus, it is shown that the calculation speed increased more than five times compared to the calculation carried out using the MATLAB/Simulink model.

Conclusions: The results obtained in this work make it possible to conduct large-scale studies of the frequency response of push-pull DC-DC converters at an acceptable calculation speed. The calculation program based on the developed model can be implemented in any high-level language, as well as in the built-in MATLAB language.

Keywords

push-pull DC/DC converter / closed-loop control system / nonlinear dynamic model / frequency response / frequency response analyzer

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