Time-Domain Analysis of Fractional Electrical Circuit Containing Two Ladder Elements

The paper is devoted to the theoretical and experimental analysis of an electric circuit consisting of two elements that are described by fractional derivatives of different orders. These elements are designed and performed as RC ladders with properly selected values of resistances and capacitances. Different orders of differentiation lead to the state-space system model, in which each state variable has a different order of fractional derivative. Solutions for such models are presented for three cases of derivative operators: Classical (first-order differentiation), Caputo definition, and Conformable Fractional Derivative (CFD). Using theoretical models, the step responses of the fractional electrical circuit were computed and compared with the measurements of a real electrical system.

Automated summary

This paper focuses on the theoretical and experimental analysis of an electric circuit with two elements described by fractional derivatives of different orders. The study shows that solutions for different derivative operators result in varying step responses for the circuit. By comparing the theoretical models with measurements of a real electrical system, it is evident that there are discrepancies between them.