# A Study on \(H_{\infty}\)-Fuzzy Controller for a Non-Linear Wind Turbine with Uncertainty
## 5 Discussion  
In order to further validate the performance of the proposed controllers, two additional experiments were performed. One compared the performances of the proposed \(H_{\infty}\)-fuzzy controller and the pitch \(H_{\infty}\) controller in the previous study [17]. The sought to demonstrate the performance of the proposed controller under special conditions, such as during the pitch actuator failure of one blade. The difference between the proposed \(H_{\infty}\)-fuzzy controller and the pitch \(H_{\infty}\) controller discussed in the previous study lies in the scope of application of the \(H_{\infty}\) controller. The pitch-\(H_{\infty}\) only contributes pitch control. Conversely, the proposed \(H_{\infty}\)-fuzzy \(H_{\infty}\) control theory is applied to both blade pitch and torque control, but also helps to improve both uncertainty and non-linear characteristics using fuzzy logic. Therefore, in order to assess the operation of pitch control and torque control together, an additional wind tunnel experiment was conducted to compare the two controller operations in the rated wind speed region. Also, wind tunnel experiments \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Operating** \\ **Region** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Wind Turbine** \\ **Controller** \\ \end{tabular} } & \multicolumn{4}{c}{**Control Performance in Wind Tunnel Experiments**} \\ \cline{3-6}  & & & **Mean** & & **Std. Dev.** & **DEL** \\ \cline{3-6}  & & \(\Omega_{\tau}\) **(rpm)** & **P (W)** & \(\Omega_{\tau}\) **(rpm)** & **P (W)** & \(\mathbf{F_{f}}\) **(N)** \\ \hline \multirow{4}{*}{\
\begin{tabular}{c} Below-Rated \\ Region \\ \end{tabular} } & PI (A) & \(524.240\) & \(18.595\) & \(20.289\) & \(1.760\) & \(3.464\) \\  & LQR (B) & \(528.132\) & \(18.428\) & \(20.131\) & \(1.812\) & \(3.282\) \\  & \(H_{\infty}\) **(C)** & \(527.759\) & \(18.404\) & \(19.940\) & \(1.794\) & \(3.275\) \\ \cline{2-6}  & \((\mathrm{B-A})/\mathrm{A}\) (\%) & \(0.742\) & \(-0.898\) & \(-0.779\) & \(2.955\) & \(-5.254\) \\  & \((\mathrm{C-A})/\mathrm{A}\) (\%) & \(0.671\) & \(-1.027\) & \(-1.720\) & \(1.932\) & \(-5.456\) \\ \hline \multirow{4}{*}{
\begin{tabular}{c} Above-Rated \\ Region \\ \end{tabular} } & PI (D) & \(678.087\) & \(39.749\) & \(29.900\) & \(2.494\) & \(11.330\) \\  & LQR (E) & \(677.839\) & \(39.947\) & \(21.113\) & \(1.706\) & \(9.112\) \\ \cline{1-1}  & \(H_{\infty}\) **(F)** & \(678.856\) & \(39.714\) & \(12.683\) & \(1.160\) & \(8.896\) \\ \cline{1-1} \cline{2-6}  & \((\mathrm{E-D})/\mathrm{D}\) (\%) & \(-0.037\) & \(0.498\) & \(-29.388\) & \(-31.596\) & \(-19.576\) \\ \cline{1-1}  & \((\mathrm{F-D})/\mathrm{D}\) (\%) & \(0.113\) & \(-0.088\) & \(-57.582\) & \(-53.488\) & \(-21.483\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Quantitative results from wind tunnel experiments of the target wind turbine for the PI, LQR, and \(H_{\infty}\) controllers. were conducted on the failure condition of the blade pitch actuator of one-blade failure situations in order to assess the expectation that the proposed \(H_{\infty}\) controller would have excellent regulating and robustness performances compared to previously studied fuzzy logic-based LQR controllers [20]. Figure 8 shows the results of wind tunnel experiments for further validation of the performance of the proposed \(H_{\infty}\) control algorithm. As shown in Figure 8a, these procedures involve pitch and torque control being alternately turned on in the rated wind speed region, resulting in a transient response occurring frequently. This can be seen through frequent intersections of pitch and torque control strategies and a partial increase in vibration peaks of thrust. These features were observed in both controllers. However, it was confirmed that the proposed control algorithm showed better regulating performance compared with the pitch-\(H_{\infty}\) control algorithm.