Adaptive Fractional-Order Fuzzy Sliding Mode Control for Grid-Connected PV Flyback Inverters Under Dynamic Uncertainties

Abstract

This paper proposes an adaptive fractional-order fuzzy sliding mode control strategy for grid-connected photovoltaic current-source flyback inverters. The converter is modeled as a control-affine system in the decoupling-capacitor voltage and the transformer magnetizing current, so that the regulated state and the control coupling follow directly from the circuit charge and volt–second balances, and the residual arising from the control-affine representation is bounded explicitly rather than neglected. A non-local sliding manifold built on a Riemann–Liouville fractional integral is combined with a fuzzy switching-gain modulator synthesized on a fractional phase plane, the modulator being constructed so that the lower bound required by the Lyapunov argument holds by construction over the entire phase plane rather than being assumed. Chattering is attenuated by a boundary-layer saturation whose width appears explicitly in the stability certificate, and parameter drift is precluded by a projection operator combined with leakage. The stability analysis is conducted entirely in the fractional domain: the composition of the Caputo derivative with the manifold integral is established, and the resulting Lyapunov argument yields uniform ultimate boundedness of the sliding variable and the parameter estimation error, together with an explicit bound on the residual tracking error obtained from the input-to-state gain of the manifold. Simulation results across various harsh dynamic scenarios validate the efficiency of the proposed scheme. Quantitatively, relative to a Modulus-Optimum-tuned linear PI benchmark, the proposed approach achieves up to a 4% increase in output power, a 3% gain in overall efficiency, reduced steady-state error, and a 17% reduction in control energy, while satisfying a duty-cycle budget condition that keeps the commanded input within its admissible range in all tested scenarios.