Modeling and analysis of fractional order Buck converter using Caputo–Fabrizio derivative

The capacitors and inductors in actual circuits often fail to exhibit the ideal integer-order characteristics, so as the circuits containing these types of electronic components. The errors can be compensated by introducing the concept of fractional calculus. The Caputo–Fabrizio​ fractional derivative, which fixes the defect of the singularity problem in Caputo derivative, has been proposed in recent years. This work uses Caputo–Fabrizio fractional derivative to model the fractional Buck converter working in continuous conduction mode and to deduce its analytical solutions by Laplace transformation and its inverse transformation. The analytical solution of the output voltage is obtained and the waveform of the output voltage is simulated. The correctness of the model is verified and the impact of the fractional order on the dynamic performance of the Buck converter is analyzed. The steady-state average output voltage of the open-loop fractional Buck converter is also calculated.