Lyapunov-based Proportional-Integral Controller Design with Guaranteed Region of Convergence for dc-dc Power Converters

Abstract

In this paper, Lyapunov stability of dc-dc power converters controlled with proportional-integral (PI) controllers is investigated. The class of dc-dc converters with discrete-time bilinear averaged dynamic model is considered. An integral action on the output voltage is introduced for robust output regulation in case of model parameter uncertainties and external disturbances. An algorithmic method, using sum of squares programming, is introduced to calculate a candidate Lyapunov function, and the coefficients of P and PI controllers are calculated to guarantee a decrease in the Lyapunov function in each time step while input constraints are fulfilled. The controller design method is iterated in order to improve the region of convergence of the state trajectories. The resulting controller designs are evaluated through simulations of detailed switching models for a boost and a cuk converter.