Hybrid AC/DC microgrids that integrate photovoltaic

wind

battery and hydrogen energy systems are prone to DC-bus voltage fluctuations because of their low inertia and converter-based operation. This paper proposes a robust backstepping nonsingular fast terminal integral sliding mode controller that incorporates a virtual capacitor and a fractional-power reaching law to emulate synthetic inertia and improve transient damping. The controller coordinates energy exchange among distributed generation units and ensures precise DC-bus voltage regulation while managing bidirectional power transfer between AC and DC subgrids. An adaptive neuro-fuzzy inference system automatically tunes the controller gains in real time

and system stability is rigorously established through control Lyapunov functions. A detailed MATLAB/Simulink model

comprising PV

PMSG-based wind turbine

battery storage

electrolyser and PEM fuel cell

implements ANN-based MPPT to maximise renewable energy harvesting. The BNFTISMC is evaluated in three case studies against two benchmark controllers: the enhanced integral terminal SMC and the enhanced nonsingular terminal SMC. Under severe disturbances and varying load conditions

the proposed controller cuts overshoot by 75%–100%

reduces rise time by 58%–80% and completely eliminates mean absolute and mean squared errors. Processor-in-the-loop testing confirms zero steady-state error

whereas converter efficiency reaches 95.78% compared with 69.21% for the reference designs

demonstrating improved DC-bus voltage regulation

enhanced microgrid reliability and efficient real-time operation.