# Adaptive Pitch Controller of a Large-Scale Wind Turbine Using Multi-Objective Optimization
## 5 Conclusions  
A wind turbine adaptive control structure operating on the pitch variable in the nominal zone is developed in this work. The proposed control strategy is based on the following control loops: the first loop to maintain the generator speed at its nominal value reducing the fluctuations and consequently keeping the generated power constant through a gain scheduling PI controller with adaptive feedforward control, and the second loop to reduce the tower fore-aft displacements through an active tower damping control (ATDC). The gain scheduling PI controller with adaptive feedforward regulates the turbine speed by actuating on the pitch angle, and the ATDC generates an extra pitch control component proportional to the tower fore-aft velocity reducing the structural fatigue of the tower. The tuning procedure of the PI controller parameters with fore-aft control and feed-forward compensation is treated as an optimization problem with two objectives using multi-objective genetic algorithm: minimizing structural loads and keeping constant the nominal generator speed. The computed Pareto curves of the trade-off between tower fore-aft fatigue load and deviation of the generator speed for different operation points demonstrate a potential tool for seeking possible solutions in tuning controllers for wind turbines. The average ranking of the MCDM methods SAW, TOSIS, and VIKOR is selected as satisfactory solution. The proposed controller tuned with the satisfactory solution parameters is evaluated with different wind conditions (step and stochastic wind profiles) and compared with a classic adaptive baseline controller as well as with the same controller tuned with each one \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{6}{c}{**Standardized in Baseline Control**} \\ \hline
**Controller/Indices** & **IAE\({}_{\text{avg}}\)** & **CVR\({}_{\text{x}_{\text{t}}}\)** & **CVR\({}_{\text{\beta}}\)** & **CVR\({}_{\text{Mfa}}\)** & **CVR\({}_{\text{Mss}}\)** \\ \hline
**Satisfactory GSC** & \(-92.9\%\) & \(-41\%\) & \(82.9\%\) & \(-41.1\%\) & \(-3.6\%\) \\
**Optimal IAE\({}_{\text{avg}}\) GSC** & \(-93.3\%\) & \(-37.3\%\) & \(86.7\%\) & \(-29.4\%\) & \(-2.7\%\) \\
**Optimal CVR\({}_{\text{xt}}\) GSC** & \(-89.5\%\) & \(-43\%\) & \(68.8\%\) & \(-45.9\%\) & \(-4.5\%\) \\ \hline \hline \multicolumn{6}{c}{**Standardized in Satisfactory GSC**} \\ \hline
**Controller/Indices** & **IAE\({}_{\text{avg}}\)** & **CVR\({}_{\text{x}_{\text{t}}}\)** & **CVR\({}_{\text{\beta}}\)** & **CVR\({}_{\text{Mfa}}\)** & **CVR\({}_{\text{Mss}}\)** \\ \hline
**Optimal IAE\({}_{\text{avg}}\) GSC** & \(-5.8\%\) & \(+6.3\%\) & \(+2.1\%\) & \(+19.9\%\) & \(\approx\)0\% \\
**Optimal CVR\({}_{\text{xt}}\) GSC** & \(+48.5\%\) & \(-3.5\%\) & \(-7.7\%\) & \(-8.2\%\) & \(\approx\)0\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Performance indices from Table 6 standardized to baseline control and satisfactory GSC. of the two other optimal solutions (minimum fore-aft tower displacements and minimum generator speed deviations). Comparing the qualitative and quantitative results for both wind patterns between the satisfactory and baseline controller, it is important to highlight that the improvement of the \(\text{IAE}_{\text{avg}}\), \(\text{CVR}_{\text{xt}}\), and \(\text{CVR}_{\text{Mfa}}\) indices fully compensates for the increase in the \(\text{CVR}_{\beta}\) index. The simulation and spider diagrams results show a significant performance improvement of the proposed controller tuned with the satisfactory solution parameters in comparison to those of the baseline controller for both step and stochastic wind profiles. An improvement in the reference tracking of the generator speed and in the mitigation of the tower fore-aft oscillations has been achieved for both wind conditions. With respect to the other two optimal solutions, the satisfactory solution reaches a good balance between the two objectives to minimize with negligible effect on the \(\text{CVR}_{\beta}\) index.