Fractional-Memory Super-Twisting Control for Wave-to-Wire Regulation of a Heaving Point Absorber Wave Energy Converter

Reliable wave-to-wire regulation of a heaving point-absorber wave energy converter (PAWEC) requires coordinated control of the coupled hydrodynamic, mechanical, electromagnetic, and grid-connected stages, while wave excitation and radiation memory introduce persistent disturbances into the conversion chain. This study develops a fractional-memory super-twisting sliding mode control (FOSTSMC) framework for grid-connected PAWEC regulation. A control-oriented wave-to-wire model combines Cummins-based heave dynamics, a reduced-order PTO–generator interface, a permanent magnet synchronous generator (PMSG), a DC link, and a grid-side converter (GSC). The physical plant remains integer order, while fractional dynamics are introduced only through a memory state in the feedback manifold. The super-twisting mechanism establishes finite-time reaching under bounded perturbation-rate conditions, followed by asymptotic tracking-error convergence governed by Mittag–Leffler-stable fractional-memory dynamics. FOSTSMC is compared with nonlinear adaptive backstepping control (NAB), conventional sliding mode control (SMC), and super-twisting sliding mode control (STSMC) under regular-wave excitation and a 100 s fixed-seed JONSWAP irregular-wave realization. The principal benefit of FOSTSMC is improved generator-speed disturbance regulation. Over the 20–100 s irregular-wave analysis interval, FOSTSMC reduces generator-speed root-mean-square error (RMSE) and mean absolute error (MAE) by approximately 29.5% and 59.7%, respectively, relative to STSMC. Electromagnetic-torque tracking and electrical-power responses remain broadly comparable among the four controllers, while grid-current harmonic performance depends on the operating condition. The results indicate that fractional-memory feedback can improve generator-speed regulation without requiring a fractional-order model of the physical PAWEC plant.