Analysis of linearization limit conditions and automated synthesis of the output voltage regulator of a PWM-buck converter in MATLAB/SIMULINK
DOI:
https://doi.org/10.15588/1607-6761-2025-4-6Keywords:
buck converter, solar power plant converters, automated controller synthesis, converter transfer functions, MATLAB/SimulinkAbstract
Purpose. Determination of the transfer function of the output voltage regulation of buck converters as a function of the PWM duty cycle, determination of the constraints and conditions for convergence of transient processes in the linearized and pulsed model of the buck converter, as well as presentation of a method for automated calculation of PI and PID controller parameters using the Matlab/Simulink tool.
Methodology. Electrical theory, automatic control theory, analytical calculations in MathCad and simulation modeling in Matlab.
Findings. The results of the study of linearization and determination of the transfer function of the output voltage regulation of a step-down pulse converter (buck converter) as a function of the pulse duty cycle in pulse-width modulation are presented. The transfer function of a buck converter with PWM is determined and the limitations of this linearization are determined, namely, the condition for the adequacy of the linearized model of the buck converter is the limitation of the input signal value, i.e. the pulse duty cycle in PWM, less than 1. The method of automatic calculation of the parameters of P, PI, PD and PID controllers is presented according to the criterion of forming a transient process of a satisfactory form by using the “PID controller” block in Matlab/Simulink. The presented method of automatic calculation of the coefficients of controllers in the automatic control system (ACS) structures works exclusively with linearized models, and does not allow calculations for pulse and nonlinear models. For the defined linearized model and the corresponding transfer function of the buck converter, the PI coefficients of the output voltage regulator are determined. The results of the analytical calculation of the instantaneous function of the buck converter output voltage as part of the automated output voltage control system, which is obtained by inverse Laplace transformation of the inverse function of the automatic control system, are presented. The results of the modeling of the buck converter output voltage on the linearized model (transfer function) and the simulation model in Matlab/Simulink are also presented. The results of the analytical calculation and the two methods of computer modeling gave identical results, which indicates the adequacy of the linearization performed and the satisfaction of the method of automatic calculation of the regulator parameters according to the criterion of forming a transient process of a satisfactory form according to the parameters of the transient process time and the value of overshoot.
Originality The conditions for convergence of transient processes of the buck converter output voltage regulation in the structures of automatic control systems for linearized and pulsed models have been determined, which allows obtaining a real transient process of the desired form, which corresponds to the previous analytical calculation.
Practical value. The presented transfer functions and the method of automatic synthesis of PID parameters of the output voltage regulator of the buck converter in Matlab/Simulink can be used in the development of power semiconductor converters and allows to simplify the synthesis process of regulators in automatic control systems.
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