Numerical modeling of step-down pulse dc-dc voltage converters regulated by digital feedback


Аuthors

Tarasov D. Y.1*, Sukhomlino G. L.1**, Mikhailov V. V.2***

1. Bauman Moscow State Technical University, MSTU, 5, bldg. 1, 2-nd Baumanskaya str., Moscow, 105005, Russia
2. Leonov Moscow Region University of Technology, Korolev, Moscow Region, Russia

*e-mail: tarasovdu@bmstu.ru
**e-mail: sukhomlinov@bmstu.ru
***e-mail: mo_techuniv@mosreg.ru

Abstract

In the introductory part of the article, it is noted that in the research works of design organizations related to the development of regulated step-down pulse DC-DC voltage converters, approaches based on the use of such powerful software complexes as MATLAB/Simulink have been widely used. At the same time, the direction associated with the development of simpler computing tools remains in demand, which can be relied on not only when conducting specific computational studies of the designated converters, but also to confirm the reliability of the results obtained on the basis of these software packages. The purpose of the article is to describe two computational models designed to solve problems of dynamics of a step-down pulse DC-DC voltage converter controlled by digital (proportional, integral and differential) feedback. One of the models performing frequency analysis is designed to calculate the stability of the regulated converter in question. Another model based on the numerical integration method is focused on the study of transient and steady-state modes in the operation of the same converter. The main content of the article is devoted to the description of the designated two computational models. The calculation scheme of a step-down pulse converter is presented here and the corresponding (based on an approximate "continuous" calculation model) dynamics problem is formulated in the form of a system of two first-order differential equations (with respect to the current i in the throttle and the voltage UН of the load). It is indicated that an important requirement for this type of converter is its ability to reliably maintain the required value of the load voltage, which can be provided by including a feedback link in the circuit of operation of such a converter. It is assumed that the control system of the converter under discussion is based on the use of a digital PID controller in the feedback structure (which has the capabilities to implement proportional, integral and differential communication). A linear differential equation describing the functioning of the feedback link is written. Based on the obtained relations, a linear differential equation is formulated that establishes the relationship between the control parameter at the input and output of the open loop of the control system under consideration. An algorithm for calculating the frequency characteristics of such an open loop is presented. (Based on their analysis, a conclusion is made about the stability of the closed-loop control system). A system of linear differential equations describing the dynamics of the controlled (feedback) step-down converter is also formulated. An algorithm for the numerical solution of this type of dynamics problem based on the use of an implicit Euler scheme is presented. Examples of the application of the proposed two computational models to the study of the dynamics of a specific controlled step-down converter are given. The final part of the article contains conclusions on the research performed. A brief description of the two proposed computational models is given here. It is also indicated that the reliability of the results obtained using these computational models is confirmed by practical coincidence with the results of computer modeling and physical experiment available in the literature.

Keywords:

step-down pulse DC-DC voltage converter, feedback, frequency analysis, implicit Euler scheme of numerical integration

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