Design of Robust Digital Stabilizing Controller for Fourth-Order Boost DC–DC Converter: A Quantitative Feedback Theory Approach

Abstract

In this paper, we have proposed a quantitative feedback theory based robust digital voltage mode controller for a fourth-order boost dc-dc converter operating in continuous conduction mode. Discrete-time models of the converter are established for triangular trailing-edge modulation, which is then used in the compensator design. It is observed that an up-down glitch is present in the frequency response of control-to-output transfer functions of higher order dc-dc converters, and because of this, gain margin (GM) and phase margin (PM) alone are unable to give correct information about closed-loop stability. Therefore, in this paper, we have introduced a safety margin as an additional design specification, which along with GM and PM information reflects the actual stability of the higher order dc-dc converters. A simplification in loop-shaping approach is also proposed, which considerably reduces the time and effort involved in loop-shaping as compared to present trial-and-error-based approach and also results in a robust compensator of feasible order. Robustness of the designed controllers is analyzed in frequency and time domains through computer simulations and is then verified experimentally on a 28-V 30-W laboratory prototype converter. The experimental results are in line with the analytical design studies and demonstrate that the controller, which is directly designed through a discrete-time model, is more robust than an average model-based digitally redesigned controller.