This paper presents the theoretical proof for the closed-loop asymptotic stability of a DC-DC buck converter based on singular perturbation theory. Due to the two-time scales structure of this converter with fast and slow dynamics, a cascade control structure is used to More
This paper presents the theoretical proof for the closed-loop asymptotic stability of a DC-DC buck converter based on singular perturbation theory. Due to the two-time scales structure of this converter with fast and slow dynamics, a cascade control structure is used to control it. This controller has two control loops: an outer loop to control the output voltage based on the proportional-integral control and an inner loop to control the inductor current based on the sliding mode control. The controllers in the loops are designed based on perturbation theory to meet the constraints of the converter and ensure the asymptotic stability of the closed-loop system over a wide range of initial conditions. For validation, the proposed control design method is simulated for a typical buck converter in the MATLAB-SIMULINK environment. The simulation results show that by properly selecting the PI controller coefficients in the outer loop, the problem requirements are met, and the asymptotic stability of the closed-loop system is guaranteed in a wide range of the converter initial conditions. Furthermore, the system robustness against load uncertainty and input disturbances as well as the voltage reference tracking are evaluated, and the proposed structure is compared with a PI-PI structure.
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