State-Space Approach to Modeling and Ripple Reduction in AC–DC Converters

Abstract

This brief develops a systematic state-space approach to the modeling of boost type ac-dc converters and reduction of output ripples. The bridge rectifier voltage is modeled as a periodic disturbance whose harmonics have given frequencies but uncertain phases and magnitudes. These types of disturbances are described as the output of an external autonomous linear system, called an exogenous system, with uncertain initial conditions. The exogenous system is integrated with the boost converter as a whole system in state-space description. The whole system is a nonlinear system whose differential equation has a bilinear term, which is handled by an inclusion. Via a recently developed Lyapunov framework, the problem of ripple reduction is converted into a numerically efficient optimization problem, which involves linear matrix inequalities. The resulting feedback law is a simple linear state-feedback. Experimental results validate the effectiveness of the theoretical approach and design method.