Leverrier´s algorithm based modeling of higher-order dc-dc converters

It is observed that many researchers are working in developing new breed of dc-dc converters for various applications. For analysis and controller design, physical system is needed to be modeled into either transfer function form or state space form. However, researches are using conventional approach for obtaining transfer function from state space form. But this approach is troublesome when the order of the system is higher and physical variables are involved. Therefore, in this paper, a simple analytical approach is presented to determine small signal transfer functions of higher-order dc-dc converters. This approach is based on Leverrier´s algorithm, which is used to calculate resolvent matrix of the linearized state-space model obtained from state-space averaging (SSA) modeling technique. This Leverrier´s algorithm is although well-known in control literature but not familiar in dc-dc converter modeling applications. In order to show the application of this approach, control-to-output and input-to-output transfer functions of fourth-order Cuk converter are obtained.