## 4 Results and Discussion
### Simulation Results in the Rotating Reference Frame
In simulation cases 1 and 2, the IPC schemes with integral controllers plus the azimuth offset achieved a greater reduction in the DEL value of 30% compared to the CPC, whereas those same IPC schemes without the azimuth only achieved a reduction of approximately 15-20%. With proportional controllers in the IPC, the reduction in the DEL was 25%, and the inclusion of the azimuth offset did not improve this value. In simulation case 3, the two IPC schemes with integral controllers \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Control Scheme**} & \multicolumn{4}{c}{\(\overline{\text{DEL}}\)**(M) (MNm)**} & \multicolumn{4}{c}{\(\overline{\text{NAT}(\beta)\) (\%)}} & \multicolumn{4}{c}{\(\overline{\text{STD}(\text{Pg})}\) (MW)} & \multicolumn{4}{c}{\(\overline{\text{STD}(\text{w}_{\text{g}})}\) (tpm)} \\ \cline{2-13}  & **Case 1** & **Case 2** & **Case 3** & **Case 1** & **Case 2** & **Case 3** & **Case 1** & **Case 2** & **Case 3** & **Case 1** & **Case 2** & **Case 3** \\ \hline CPC & 23.67 & 25.62 & 29.68 & 4.91 & 4.38 & 4.07 & 0.46 & 0.60 & 0.80 & 0.23 & 0.30 & 0.40 \\ CPC + IPC\_P2 & 17.55 & 18.79 & 20.45 & 48.9 & 52.5 & 50.61 & 0.46 & 0.61 & 0.81 & 0.23 & 0.31 & 0.41 \\ CPC + IPC\_P2b & 17.50 & 18.71 & 19.72 & 50 & 52.3 & 51.57 & 0.46 & 0.61 & 0.81 & 0.23 & 0.31 & 0.41 \\ CPC + IPC\_I1 & 18.80 & 21.94 & 21.68 & 41.6 & 44.6 & 46.45 & 0.46 & 0.61 & 0.80 & 0.23 & 0.31 & 0.40 \\ CPC + IPC\_I1b & 16.60 & 17.25 & 17.51 & 38.8 & 43.4 & 49.45 & 0.46 & 0.60 & 0.81 & 0.23 & 0.30 & 0.41 \\ CPC + IPC\_I2 & 18.77 & 20.3 & 21.63 & 41.0 & 42.2 & 46.64 & 0.46 & 0.60 & 0.80 & 0.23 & 0.30 & 0.41 \\ CPC + IPC\_I2b & 16.66 & 17.18 & 17.47 & 39.6 & 43.8 & 49.47 & 0.46 & 0.61 & 0.81 & 0.23 & 0.30 & 0.41 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance indicators of variables in the rotating reference frame for the control schemes were calculated from the simulation data for each simulation case. The table shows the average DEL value of the OoP blade moment (\(\overline{\text{DEL}}\)(M)), the average normalized actuator travel of the pitch (\(\overline{\text{NAT}(\beta)}\)), the STD of the generated power, and the STD of the generator angular velocity. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Control Scheme**} & \multicolumn{4}{c}{\(\overline{\text{M}}_{\text{t}}\)**(MNm)**} & \multicolumn{4}{c}{\(\overline{\text{STD}}\)**(M) (MNm)**} & \multicolumn{4}{c}{\(\overline{\text{M}}_{\text{y}}\)**(MNm)**} & \multicolumn{4}{c}{\(\overline{\text{STD}}\)**(M) (MNm)**} \\ \cline{2-13}  & **Case 1** & **Case 2** & **Case 3** & **Case 1** & **Case 2** & **Case 3** & **Case 1** & **Case 2** & **Case 3** & **Case 1** & **Case 2** & **Case 3** \\ \hline CPC & 6.678 & 7.516 & 9.282 & 3.84 & 3.89 & 4.17 & 2.582 & 3.298 & 3.558 & 3.50 & 4.02 & 4.17 \\ CPC + IPC\_P2b & \(-\)0.208 & \(-\)0.252 & 0.118 & 2.86 & 3.15 & 3.62 & \(-\)0.294 & \(-\)0.067 & \(-\)0.207 & 2.73 & 3.22 & 3.55 \\ CPC + IPC\_P2b & \(-\)0.209 & \(-\)0.27 & 0.158 & 2.86 & 3.15 & 3.61 & \(-\)0.219 & 0.588 & 1.202 & 2.70 & 3.19 & 3.42 \\ CPC + IPC\_I1 & \(-\)0.015 & \(-\)0.038 & 0.024 & 3.37 & 4.53 & 4.36 & 0.039 & \(-\)0.072 & 0.100 & 3.46 & 4.61 & 3.97 \\ CPC + IPC\_I1b & \(-\)0.004 & \(-\)0.008 & \(-\)0.006 & 2.56 & 2.76 & 3.25 & \(-\)0.011 & \(-\)0.002 & \(-\)0.013 & 2.24 & 2.45 & 2.89 \\ CPC + IPC\_I2 & \(-\)0.06 & \(-\)0.032 & 0.018 & 3.30 & 3.52 & 3.83 & \(-\)0.015 & 0.247 & 0.188 & 3.91 & 4.84 & 4.43 \\ CPC + IPC\_I2b & \(-\)0.002 & \(-\)0.004 & \(-\)0.003 & 2.64 & 2.86 & 3.24 & \(-\)0.008 & \(-\)0.007 & \(-\)0.011 & 2.33 & 2.59 & 2.87 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The mean values and STD values of the non-rotating moments \(\text{M}_{\text{t}}\) and \(\text{M}_{\text{y}}\) were calculated from the simulation data for each simulation case. and azimuth offset achieved a DEL reduction of 40%. This reduction was only 27% for IPC schemes with integral controllers without azimuth offset and 32% for IPC schemes with proportional controllers.