Fractional Order Pole Placement for a buck converter based on commensurable transfer function

Abstract

In this work, a novel methodology for tuning fractional order controller, so-called fractional order pole placement (FOPP) is proposed. The proposed methodology extends classical (integer order) pole placement technique, using commensurable transfer functions for representing fractional order controllers and placing the fractional dominant poles within an extended stability region based on three terms fractional transfer functions. The designed fractional order controller can be digitally implemented by using the Oustaloup integer approximation of the fractional order dynamics with Hankel model reduction. The proposed FOPP is used to design fractional order controllers for a DC/DC buck converter. The experimental tests include comparisons between the proposed FOPP and other tuning methodologies for integer and fractional order controllers for the DC/DC buck converter that is subject to load, parametric, and load variations. Integral indices are computed to aid the assessment of the control strategies with respect to the robustness, performance specification compliance, and control effort. The results show that the proposed method outperforms the other approaches when occurs the variations.

Keywords: Commensurable Order Transfer Functions; DC/DC power converter; Fractional Order Pole Placement; Fractional order control; Fractional order three terms transfer function; Pseudo damping factor.