# Robust Control Examples Applied to a Wind Turbine Simulated Model
## 4 Simulations and Comparisons
### Performance Verification and Comparisons  
The evaluation of the performances of the data-driven and model-based control strategies considered in this paper has been evaluated also on the basis of the following performance metrics, borrowed and modified from the fault diagnosis framework [40]:  
* False Tracking Rate (FTR): the ratio between the total number of wrongly reference tracking and the number of simulations; \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Control** & **Partial Load** & **Full Load** & **Delay Time** & **Settling Time** & **Max. Overshoot** \\
**Strategy** & **NSSE**\% & **NSSE**\% & **T\({}_{\mathbf{d}}\)** & **T\({}_{\mathbf{a}}\)** & **S\%** \\ \hline Baseline governors & 48.23\% & 21.75\% & 0.91 s & 2.5 s & 23\% \\ Fuzzy controllers & 37.19\% & 17.94\% & 0.04 s & 0.34 s & 8\% \\ Adaptive controllers & 24.52\% & 13.72\% & 0.02 s & 0.18 s & 4\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Monte Carlo analysis for the considered control schemes. * Missed Tracking Rate (MTR): the ratio between the total number of missed reference tracking and the number of simulations;
* Correct Tracking Rate (CTR): the ratio between the number of correct reference tracking and the number of simulations;
* Mean Tracking Delay (MTD): the delay time between the reference tracking and the reference timing. With reference to the indices above, note that the CTR index is complementary to MTR, since they refer to the tracking capabilities in the presence of uncertainty and disturbance. In contrast, the FTR index describes the tracking performance achieved only by the control designs, without considering any errors or anomalies occurring in the system. On the other hand, the MTD index considers the average delay occurring during the tracking of the reference signals. Also in this case, a proper Monte Carlo analysis has been performed in order to compute these performance metrics and to test the robustness of the considered control schemes. A set of 1000 Monte Carlo runs has been performed, during which realistic wind turbine uncertainties have been considered as described in Table 5. Moreover, in addition to the considered fuzzy and adaptive strategies, the performance metrics of other control schemes are analyzed. The first alternative approach considered here uses a Support Vector machine based on a Gaussian Kernel (GKSV) originally developed in [42] and it was exploited here for control purpose. The scheme defines a vector of features for each working condition of the wind turbine, which contains relevant signals obtained directly from measurements, filtered measurements or their combinations. These vectors are subsequently projected onto the kernel of the Support Vector Machine (SVM), which provides suitable control sequences for all of the defined working conditions. The second scheme consists in an Estimation-Based (EB) solution shown in [43]. In particular, a bank of observers is designed to estimate the control signals that have to feed the controlled process. These observers were designed on the basis of a system linear model. The third method relying on Up-Down Counters (UDC) was addressed in [44]. These tools, are commonly used in the aerospace framework, and they provide a different approach to the decision logic usually applied to the control. Indeed, the design of the control signals involves discrete-time dynamics and is not simply a function of the plant working conditions. The fourth approach refers to Combined Observer and Kalman (COK) filter methods [45]. It relies on an observer used as a control signal residual generator, when the wind speed is considered a disturbance. This observer was designed to decouple the disturbance and simultaneously achieve optimal reference tracking in a statistical sense. Finally, the fifth method is a General Fault Model (GFM) scheme, which is a method of automatic design [46]. The design strategy consists of three main steps. In the first step, a large set of potential controllers is designed.