Singular Perturbation Method for Boundary Value and Optimal Problems to Power Factor Correction Converter Application

Abstract

A linear discrete stable control system is considered. The Power Factor Correction (PFC) converter to allow independent control of current and voltage. It converter are fast and slow states to inheres sty present small parameters inductor and capacitor its computes stiffness and to include switching ripple effects. As an alternative a Singular Perturbation Method (SPM) is presented Boundary Value Problem (BVP) and Optimal Problem. It is applied to two state switching power converters to provide rigorous justification of\ the time scale separation. It is modeled as a one parameter singularly perturbed system. SPM consists of an outer series solution and one boundary layer correction (BLC) solution. A boundary layer correction is required to recover the initial conditions lost in the process of degeneration and to improve the solution. SPM is carried out up to second-order approximate solution for the PFC converter model for BVP and optimal control problems. The results are compared with the exact solution (between with and without parameters). The results substantiate the application.