# Adaptive Pitch Controller of a Large-Scale Wind Turbine Using Multi-Objective Optimization
## 4 Proposed Design Evaluation
### Simulation with Stochastic Wind Speed Profile  
The second simulation was performed using a more realistic wind speed profile with the following characteristics: a mean value of 17 m/s, a turbulent component with standard deviation of 10%, and a sine component with amplitude of 1 m/s and period of 100 s. Figure 13 shows the simulation results using this wind speed profile. The corresponding performance indices are collected in Table 6, where a comparative quantitative summary analysis of the three GSC tuning solutions (satisfactory, optimal \(\text{IAE}_{\text{avg}}\), and optimal \(\text{CVR}_{\text{xt}}\) solutions) is shown in comparison with the baseline control for stochastic wind speeds. Regarding the results in this second simulation, similar conclusions can be obtained: the designed GSC tuned with satisfactory solution obtains a better \(\text{CVR}_{\text{xt}}\) index value, reducing it by 41% in comparison to that of the BSC. With respect to the \(\text{IAE}_{\text{avg}}\) index value, the designed controller reduces this index by 92.9% compared to BSC. Figure 14 shows the spider diagrams obtained from the simulations performed with stochastic wind. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Control/Indices** & \(\text{IAE}_{\text{avg}}\) & \(\text{CVR}_{\text{x}_{\text{t}}}\) & \(\text{CVR}_{\beta}\) & \(\text{CVR}_{\text{Mfa}}\) & \(\text{CVR}_{\text{Mss}}\) \\ \hline
**BSC** & 4.66\(\cdot\)10\({}^{4}\) & 15.59 & 138.37 & 2.68\(\cdot\)10\({}^{6}\) & 4.52\(\cdot\)10\({}^{5}\) \\
**Satisfactory GSC** & 3.28\(\cdot\)10\({}^{3}\) & 9.20 & 253.10 & 1.58\(\cdot\)10\({}^{6}\) & 4.36\(\cdot\)10\({}^{5}\) \\
**Optimal \(\text{IAE}_{\text{avg}}\) GSC** & 3.09\(\cdot\)10\({}^{3}\) & 9.78 & 258.35 & 1.89\(\cdot\)10\({}^{6}\) & 4.40\(\cdot\)10\({}^{5}\) \\
**Optimal \(\text{CVR}_{\text{xt}}\) GSC** & 4.87\(\cdot\)10\({}^{3}\) & 8.88 & 233.59 & 1.45\(\cdot\)10\({}^{6}\) & 4.33\(\cdot\)10\({}^{5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Performance indices for stochastic change wind speed profiles. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**Standardized in Baseline Control**} \\ \hline
**Controller/Indices** & \(\text{IAE}_{\text{avg}}\) & \(\text{CVR}_{\text{x}_{\text{t}}}\) & \(\text{CVR}_{\beta}\) & \(\text{CVR}_{\text{Mfa}}\) & \(\text{CVR}_{\text{Mss}}\) \\ \hline
**Satisfactory GSC** & \(-93.3\%\) & \(-42.3\%\) & 28.3\% & \(-37.7\%\) & \(-43.6\%\) \\
**Optimal \(\text{IAE}_{\text{avg}}\) GSC** & \(-93.9\%\) & \(-33.9\%\) & 20.4\% & \(-30.4\%\) & \(-35.4\%\) \\
**Optimal \(\text{CVR}_{\text{xt}}\) GSC** & \(-88.2\%\) & \(-46.1\%\) & 29.7\% & \(-41.3\%\) & \(-46.8\%\) \\ \hline \hline \multicolumn{4}{c}{**Standardized in Satisfaction GSC**} \\ \hline
**Controller/Indices** & \(\text{IAE}_{\text{avg}}\) & \(\text{CVR}_{\text{x}_{\text{t}}}\) & \(\text{CVR}_{\beta}\) & \(\text{CVR}_{\text{Mfa}}\) & \(\text{CVR}_{\text{Mss}}\) \\ \hline
**Optimal \(\text{IAE}_{\text{avg}}\) GSC** & \(-9.8\%\) & \(+14.5\%\) & \(-6.2\%\) & \(+11.8\%\) & \(+14.7\%\) \\
**Optimal \(\text{CVR}_{\text{xt}}\) GSC** & \(+75.1\%\) & \(-6.6\%\) & \(+1.1\%\) & \(-5.8\%\) & \(-5.6\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Performance indices from Table 4 standardized to baseline control and satisfactory gain scheduling controller (GSC). Figure 12: Spider diagrams for first simulation. In a similar way to the results obtained for step wind, the results for stochastic wind show that a relevant improvement with respect to the base controller is achieved in the indices \(\text{IAE}_{\text{avg}}\), \(\text{CVR}_{\text{xt}}\), and \(\text{CVR}_{\text{Mfa}}\) for the three GSC designed. However, the same does not happen for the index \(\text{CVR}_{\text{MSs}}\), which is hardly improved, since the objective functions designed for tuning the GSC did not consider this type of structural tower load. Figure 14: Spider diagrams obtained with stochastic wind. Figure 13: Simulation responses for second simulation.