Modeling and Analysis of Caputo–Fabrizio Definition-Based Fractional-Order Boost Converter with Inductive Loads

Abstract

This paper proposes a modeling and analysis method for a Caputo–Fabrizio (C-F) definition-based fractional-order Boost converter with fractional-order inductive loads. The proposed method analyzes the system characteristics of a fractional-order circuit with three state variables. Firstly, this paper constructs a large signal model of a fractional-order Boost converter by taking advantage of the state space averaging method, providing accurate analytical solutions for the quiescent operating point and the ripple parameters of the circuit with three state variables. Secondly, this paper constructs a small signal model of the C-F definition-based fractional-order Boost converter by small signal linearization, providing the transfer function of the fractional-order system with three state variables. Finally, this paper conducts circuit-oriented simulation experiments where the steady-state parameters and the transfer function of the circuit are obtained, and then the effect of the order of capacitor, induced inductor, and load inductor on the quiescent operating point and ripple parameters is analyzed. The experimental results show that the simulation results are consistent with those obtained by the proposed mathematical model and that the three fractional orders in the fractional model with three state variables have a significant impact on the DC component and steady-state characteristics of the fractional-order Boost converter. In conclusion, the proposed mathematical model can more comprehensively analyze the system characteristics of the C-F definition-based fractional-order Boost converter with fractional-order inductive loads, benefiting the circuit design of Boost converters.

Application Study of Fractional Modelling and Analysis Methods for Piecewise-Smooth Fractional-Order Circuit Systems: An Efficiency Analysis Oriented Case for Dickson Type Switched-Capacitor Converters

“…By reviewing the key works in related fields, one can find that research on linear, continuous, and commensurate systems is relatively common, and the most widely used models are some first or second order transfer functions, or in the form of linear fractional-order differential equations, since a wide variety of practical systems can be approximated by them, and they are easy to be analyzed for engineering applications [5]. However, there are still a wide range of objects in the real world that do not operate in continuous and linear ways, for instance, those nonlinear cases.…”