# A Study on \(H_{\infty}\)-Fuzzy Controller for a Non-Linear Wind Turbine with Uncertainty
## 4 Controller Validation
### Wind Tunnel Experiments  
To validate the performance of the proposed \(H_{\infty}\) controller, a wind tunnel test was performed at a large wind tunnel test center in Joellanam-do, Republic of Korea (length \(\times\) width \(\times\) height: 40 \(\times\) 12 \(\times\) 2.5 m). Figure 6 shows the view of the target wind turbine and the overall configuration of the wind tunnel facility. The turbulence intensity in the wind tunnel test was about 10%, which is the maximum achievable in the wind tunnels using wedges and bar structures. The PI, LQR, and \(H_{\infty}\) controllers were tested under the same wind conditions as those used in dynamic simulation (i.e., mean 4.0 m/s and mean 8.0 m/s). The target-scaled wind turbine was controlled using [PERSON]'s programmable logic controller (PLC), where the proposed control algorithms were \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{3}{*}{\begin{tabular}{c} **Operating** \\ **Region** \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} **Wind Turbine** \\ **Controller** \\ \end{tabular} } & \multicolumn{3}{c}{**Mean**} & \multicolumn{3}{c}{**Std. Dev.**} & \multicolumn{1}{c}{**DEL**} \\ \cline{3-6}  & & \(\Omega_{\sigma}\) **(rpm)** & **P (W)** & \(\Omega_{\sigma}\) **(rpm)** & **P (W)** & \(\mathbf{F_{r}}\) **(N)** \\ \hline \multirow{3}{*}{\
\begin{tabular}{c} Below-Rated \\ Region \\ \end{tabular} } & PI (A) & 541.024 & 20.476 & 38.772 & 4.294 & 8.496 \\  & LQR (B) & 540.947 & 20.494 & 38.457 & 4.353 & 8.247 \\  & \(H_{\infty}\) (C) & 540.376 & 20.474 & 37.944 & 4.306 & 8.222 \\ \cline{2-6}  & \(\mathrm{(B-A)/A}\) (\%) & \(-\)0.014 & 0.088 & \(-\)0.812 & 1.374 & \(-\)2.931 \\  & \(\mathrm{(C-A)/A}\) (\%) & \(-\)0.120 & \(-\)0.010 & \(-\)2.136 & 0.279 & \(-\)3.225 \\ \hline \multirow{3}{*}{
\begin{tabular}{c} Above-Rated \\ Region \\ \end{tabular} } & PI (D) & 677.719 & 39.696 & 17.875 & 0.998 & 22.852 \\  & LQR (E) & 677.941 & 39.709 & 9.770 & 0.471 & 19.832 \\ \cline{1-1}  & \(H_{\infty}\) (F) & 678.503 & 39.742 & 6.738 & 0.396 & 19.644 \\ \cline{1-1} \cline{2-6}  & \(\mathrm{(E-D)/D}\) (\%) & 0.033 & 0.033 & \(-\)45.343 & \(-\)52.806 & \(-\)13.215 \\ \cline{1-1}  & \(\mathrm{(F-D)/D}\) (\%) & 0.116 & 0.116 & \(-\)62.305 & \(-\)60.321 & \(-\)14.038 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Quantitative results from simulations of the target wind turbine for the PI, LQR, and \(H_{\infty}\) controllers. implemented. In addition, a nacelle accelerometer was installed to measure acceleration at the nacelle and estimate the thrust force. The signal from the accelerometer was sampled and acquired using a data-acquisition board. The pitch system of the target wind turbine was designed to enable individual pitch control (IPC) using three pitch motors individually whenever needed. Figure 7 shows time series data from wind tunnel experiment results performed for 100 s. Like the dynamic simulation results, the PI, LQR, and \(H_{\infty}\) controllers were applied to the controller, and each performance was compared. Unlike the simulation, electrical noise transmitted from the sensor was observed in the wind tunnel experiment data, and the turbulent wind for each experiment could not be the same. As such, there was a slight difference in the time series of wind data. Figure 6: View of the target wind turbine and configuration of the wind tunnel environments. Figure 7: Results from wind tunnel experiments of the target wind turbine for the PI controller (black solid lines), the LQR controller (red dotted lines), and the \(H_{\infty}\) controller (green dashed lines). The left-hand plot (**a**) shows the results below the rated wind speed region (mean 4.0 m/s). The right-hand plot (**b**) shows the results for the above-rated wind speed region (mean 8.0 m/s). Figure 7a shows that the results of MPPT control by three different controllers in the below-rated wind speed region are similar to dynamic simulation results in overall operation.