Cascade Control System Design and Stability Analysis for a DC–DC Boost Converter with Proportional Integral and Sliding Mode Controllers and Using Singular Perturbation Theory

Abstract

This paper deals with the controller design and closed-loop asymptotic stability analysis of a DC-DC boost converter based on the singular perturbation theory. Due to the nature of two-time scales with fast and slow dynamics in this converter, the cascade control structure is used to control it. This control system has two control loops: an outer loop to regulate the output voltage based on a proportional-integral (PI) controller and an inner loop to regulate the inductor current based on a sliding mode controller. These controllers within each of the loops are designed based on the perturbation theory to satisfy the constraints considered for the converter operation and to guarantee the asymptotic stability of the closed-loop system over a wide range of the converter initial state conditions. The numerical results show that with a proper selection of the outer loop PI controller parameters, the asymptotic stability and optimal performance of the closed-loop system are satisfied. Moreover, the robustness of the proposed control method is shown by the numerical experiments under step parameter uncertainties and disturbances.