# A Study on \(H_{\infty}\)-Fuzzy Controller for a Non-Linear Wind Turbine with Uncertainty
## 6 Conclusions  
In this study, an \(H_{\infty}\)-fuzzy control algorithm was proposed in order to control wind turbines for the purpose of considering their uncertainties and nonlinearities. In order to validate the performance of the proposed controller via simulation and experimentation, a 40 W wind turbine capable of wind tunnel testing was used as a control target.  
Using a commercial aero-elastic code known as Bladed, the performances of the conventional PI, LQR controllers and the proposed \(H_{\infty}\) controllers were compared in two turbulent wind conditions in an environment reflective of perturbation and sensor noise effects. The simulation showed that the rotor speed deviation was reduced by 31.0%. Additionally, the power deviation was reduced by 15.9%, compared with the LQR-fuzzy control algorithm, which had better performance than the conventional PI. To validate the performance of the control algorithm in more real situations, the target wind turbine was applied to wind tunnel experiments. As a result, the rotor speed deviation and power deviation were reduced by 39.9% and 32.0%, respectively, and the fatigue load based on the thrust force was reduced by 2.4% compared with the LQR fuzzy control algorithm.  
Through additional control performance validation, it was confirmed that the proposed \(H_{\infty}\)-fuzzy control algorithm reduced the transient response in the rated wind speed region compared with the previously studied pitch-\(H_{\infty}\) control algorithm. In addition, through experiments on the blade pitch actuator failure situation of one blade, the proposed \(H_{\infty}\)-fuzzy control algorithm showed its improved robustness and adaptation compared with the LQR fuzzy control algorithm, and the regulating performance and load reduction performance were well maintained. In conclusion, \(H_{\infty}\)-fuzzy study can be used to improve the robustness and adaptation of the control systems of wind turbines having uncertainties and nonlinearities.  
Figure 9: Control performance in blade failure situations for the LQR controller (black solid lines) and the \(H_{\infty}\) controller (red solid lines).  
In this study, a wind tunnel test using a wind turbine scaled model was conducted to experimentally validate the performance of the proposed control algorithm. Future research should subject the proposed control algorithm to additional field tests in order to validate the control performance in the actual wind turbine operation situation. In addition, the study will be conducted on the application of the proposed control algorithms in floating wind turbines with higher potential nonlinearity and uncertainty effects, e.g., assessing hydrodynamics in terms of waves and currents effects.  
Conceptualization, T.J. and Y.S.; methodology, T.J.; software, T.J.; supervision, I.P.; validation, T.J. and Y.S.; writing--original draft preparation, T.J. and Y.S.; writing--review and editing, I.P. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry and Energy (MOTIE) of the Republic of Korea (No. 2020303002070).  
Not applicable.  
The authors declare no conflict of interest.