**6. Conclusions**

This paper discussed the robust design and intelligent tuning of super twisting-based second order sliding mode (STA-SOSM) controllers for the DC-link voltage loop of a DFIGbased wind energy conversion system. An adaptive fuzzy extended state observer (ESO) is firstly proposed to estimate the external disturbance of the controlled system. Such a proposed fuzzy gains-scheduling mechanism is performed to adaptively tune the bandwidth of the ESO during the occurrence of disturbances. Such a hybrid control law based on a TEO-tuned SOSM controller and adaptive extended state observer showed high superiority and robustness under grid disturbances and model uncertainties as well as in terms of closed-loop time-domain performance and chattering issue reduction. The simulation results as well as the conducted comparisons proved that the proposed algorithm gives the best THD values for the stator and rotor current with 0.26% and 0.28%, respectively. Moreover, the time-domain performance indices were better than those with the reported methods, such as TEO-tuned PI controller, TEO-tuned STA-SOSM controller, and STA-SOSM controller-based linear observer, which had the minimal value of overshoot with 1.81% for the DC-link voltage response. This clearly highlights the effectiveness of the proposed intelligent and adaptive fuzzy-based control approach for the DC-link voltage dynamics.

The current research work is restricted by supposing that the wind speed is fixed. Moreover, the proposed approach investigated a low voltage dip condition. Stability enhancement of the DFIG system under the previous concerns will be deeply investigated in future work. This will be implemented through interactions among DFIGs with various control methods, such as adaptive gain SOSM controllers and sensor-less control methods. Indeed, these methods deserve attention because they solve the difficulty of estimating the disturbance upper bounds for WECSs.

**Author Contributions:** Conceptualization, M.M.A. and S.B.; methodology, M.M.A., S.B. and M.N.I.; software, M.M.A.; validation, H.R. and S.B.; formal analysis, M.N.I. and S.B.; investigation, H.R. and S.B.; resources, M.M.A., S.B. and H.R.; data curation, M.M.A.; writing—original draft preparation, M.M.A.; writing—review and editing, H.R. and S.B.; visualization, H.R. and M.N.I.; supervision, H.R. and S.B.; project administration, M.N.I. and S.B.; funding acquisition, M.N.I. and H.R. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable.

**Data Availability Statement:** No new data were created or analyzed in this study.

**Conflicts of Interest:** The authors declare no conflict of interest.
