Zero–Average Dynamics Technique Applied to the Buck–Boost Converter: Results on Periodicity, Bifurcations, and Chaotic Behavior

Diego A. Londoño Patiño (), Simeón Casanova Trujillo () and Fredy E. Hoyos
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Diego A. Londoño Patiño: Grupo de Investigación Cálculo Científico y Modelamiento Matemático, Universidad Nacional de Colombia, Sede Manizales, Manizales 170003, Colombia
Simeón Casanova Trujillo: Grupo de Investigación Cálculo Científico y Modelamiento Matemático, Universidad Nacional de Colombia, Sede Manizales, Manizales 170003, Colombia
Fredy E. Hoyos: Facultad de Minas, Departamento de Energía Eléctrica y Automática, Universidad Nacional de Colombia, Sede Medellín, Carrera 80 No. 65-223, Robledo, Medellín 050041, Colombia

Energies, 2025, vol. 18, issue 8, 1-35

Abstract: This study addresses chaos control in a Buck–Boost converter using ZAD technique and FPIC. The system analysis identified 1-periodic orbits and observed the occurrence of flip bifurcations, indicating chaotic behavior characterized by sensitivity to initial conditions. To mitigate these instabilities, FPIC was successfully applied, stabilizing periodic orbits and significantly reducing chaos in the system. Numerical simulations verified the presence of chaos, confirmed by positive Lyapunov exponents, and demonstrated the effectiveness of the applied control methods. Steady-state and transient responses of the open-loop model and experimental system were evaluated, showing a strong correlation between them. Under varying load conditions, the numerical model accurately predicted the converter’s real dynamics, validating the proposed approach. Additionally, closed-loop control with ZAD exhibited robust performance, maintaining stable inductor current even during abrupt load changes, thus achieving effective control in non-minimum phase systems. This work contributes to the design of robust control strategies for power converters, optimizing their stability and dynamic response in applications that require precise management of power under variable conditions. Finally, a comparison was made between the performance of the Buck–Boost converter controlled with ZAD and the one controlled by PID. It was observed that both controllers effectively regulate the current, with a steady-state error of less than 1%. However, the system controlled with ZAD maintains a fixed switching frequency, whereas the PID-controlled system lacks a fixed switching frequency and operates with a very high PWM frequency. This high frequency in the PID-controlled system presents a disadvantage, as it leads to issues such as chattering, duty cycle saturation, and consequently, overheating of the MOSFET.

Keywords: dynamic system; power converter; system stability; bifurcations; ZAD technique; Lyapunov exponents; closed-loop control; load variation response (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2025
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