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Micromachines
Volume 11
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10.3390/mi11090834
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Article

Single-Switching Reachable Operation Points in a DC-DC Buck Converter: An Approximation from Time Optimal Control

by
Ilya Dikariev
1,*,
Fabiola Angulo
2 and
David Angulo-Garcia
3
1
Department of Optimization, Campus Cottbus, Institute of Mathematics, Brandenburg University of Technology, Platz der Deutschen Einheit 1, 03046 Cottbus, Germany
2
Departamento de Ingeniería Eléctrica, Electrónica y Computación—Bloque Q, Campus La Nubia, Facultad de Ingeniería y Arquitectura, Universidad Nacional de Colombia—Sede Manizales, Manizales 170003, Colombia
3
Grupo de Modelado Computacional—Dinámica y Complejidad de Sistemas, Instituto de Matemáticas Aplicadas, Universidad de Cartagena, Carrera 6 # 36-100, Cartagena de Indias 130001, Colombia
*
Author to whom correspondence should be addressed.
Micromachines 2020, 11(9), 834; https://doi.org/10.3390/mi11090834
Submission received: 4 July 2020 / Revised: 19 August 2020 / Accepted: 29 August 2020 / Published: 31 August 2020
(This article belongs to the Special Issue Power Electronics and Sensors)
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Abstract

In this paper, we study the time optimal control problem in a DC-DC buck converter in the underdamped oscillatory regime. In particular, we derive analytic expressions for the admissible regions in the state space, satisfying the condition that every point within the region is reachable in optimal time with a single switching action. We then make use of the general result to establish the minimum and maximum variation allowed to the load in two predefined design set-ups that fulfills the time optimal single switching criteria. Finally, we make use of numerical simulations to show the performance of the proposed control under changes in the reference voltage and load resistance.
Keywords: DC-DC synchronous buck converter; time optimal control; pontryagin maximum principle; control synthesis DC-DC synchronous buck converter; time optimal control; pontryagin maximum principle; control synthesis

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MDPI and ACS Style

Dikariev, I.; Angulo, F.; Angulo-Garcia, D. Single-Switching Reachable Operation Points in a DC-DC Buck Converter: An Approximation from Time Optimal Control. Micromachines 2020, 11, 834. https://doi.org/10.3390/mi11090834

AMA Style

Dikariev I, Angulo F, Angulo-Garcia D. Single-Switching Reachable Operation Points in a DC-DC Buck Converter: An Approximation from Time Optimal Control. Micromachines. 2020; 11(9):834. https://doi.org/10.3390/mi11090834

Chicago/Turabian Style

Dikariev, Ilya, Fabiola Angulo, and David Angulo-Garcia. 2020. "Single-Switching Reachable Operation Points in a DC-DC Buck Converter: An Approximation from Time Optimal Control" Micromachines 11, no. 9: 834. https://doi.org/10.3390/mi11090834

APA Style

Dikariev, I., Angulo, F., & Angulo-Garcia, D. (2020). Single-Switching Reachable Operation Points in a DC-DC Buck Converter: An Approximation from Time Optimal Control. Micromachines, 11(9), 834. https://doi.org/10.3390/mi11090834

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