## 4 Results and Discussion
### Optimization Results  
Table 3 shows the tuning parameters obtained after optimization of the six proposed IPC schemes for the five operation points in the above-rated region, which are discussed and collected in Table 2. The mean DEL values of the OoP blade moments are also shown. The DEL values obtained for the CPC without any IPC are listed, as well as those for the baseline case. A graphical representation of these data is shown in Figure 6, which shows the IPC gains, azimuth offset, and mean DEL values with respect to the mean wind speed. From these data, the following points can be stated:  
* The IPC schemes with integral controllers plus the azimuth offset (IPC_I1\(\psi\) and IPC_I2\(\psi\)) achieved the largest reductions in the mean DEL value at all operating points evaluated. The average reduction was 41% with respect to the CPC case. The third best scheme was the IPC with P controllers and the azimuth offset (IPC_P2\(\psi\)), which showed an average reduction of 35% in the mean DEL value.
* The IPC schemes with integral action and without the azimuth offset showed the lowest gains and the lowest DEL reductions--only 30% on average. Including the azimuth offset in these schemes allowed the optimal designs to achieve higher gains.
* The two IPC schemes with integral controllers and the azimuth offset (IPC_I1\(\psi\) and IPC_I2\(\psi\)) had practically the same azimuth offset values \(\psi_{\rm o}\) at each operation point. In the IPC scheme with proportional controllers plus the azimuth offset (IPC_P2\(\psi\)), the values of \(\psi_{\rm o}\) were practically zero at all operation points except at 20 m/s. Even so, there did not seem to be much effect on the results when it was set to zero. This is because the integral action adds phase delay, whereas the proportional action does not.
* On the contrary, if we compare the IPC cases with integral controllers, the inclusion of the azimuth offset allowed an increase in the average DEL reduction of the OoP blade moments of about 10% more compared to the same scheme without the offset. Schemes IPC_I1 and IPC_I2 had an average DEL reduction of approximately 30%, but their respective cases with the azimuth offset (IPC_I1\(\psi\) and IPC_I2\(\psi\)) had an average reduction of 41%.
* Of the two best IPC schemes (IPC_I1\(\psi\) and IPC_I2\(\psi\)), the IPC_I1\(\psi\) case could be considered the most advisable, because, having achieved similar results, it had only two parameters to adjust. It does not seem worthwhile to let the integral gains be different (case IPCI2_\(\psi\)) since it does not provide significant improvements and requires the three parameters to be tuned. Furthermore, it was observed that the gains of both \(k_{\rm t}\) and \(k_{\rm y}\) were practically the same at several operating points.  
Figure 6: Graphical representation of the optimization results shown in Table 3: controller gains \(\rm k_{t}\) and \(\rm k_{y}\), azimuth offset, and mean DEL value of the OoP blade moments with respect to the five mean wind speeds considered in the nominal region. The units of \(\rm k_{t}\) and \(\rm k_{y}\) gains are in deg/(MNm) for the IPC_P2 and IPC_P2b cases.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Control Scheme**} & \multicolumn{6}{c}{**Wind Speed (m/s)**} \\ \cline{2-7}  & & **14** & **16** & **18** & **20** & **22** \\ \hline CPC & DEL(M) (MNm) & 24.07 & 23.08 & 25.06 & 30.8 &