# A Study on \(H_{\infty}\)-Fuzzy Controller for a Non-Linear Wind Turbine with Uncertainty
## 4 Controller Validation  
### Dynamic Simulations  
In order to validate results, the proposed \(H_{\infty}\)-fuzzy controller was implemented for the target 40 W wind turbine, and dynamic simulations were performed using Bladed. Also, the results were compared with the results of two different control algorithms, including the PI controller using reference bias control and the LQR based on fuzzy logic controller [20,23]. To account for uncertainty and nonlinearity effects, Gaussian sensor noise was applied to generator speed, generator torque, generator power, and blade pitch angle, respectively. Figure 5 shows time series data for the dynamic simulation results to which Gaussian sensor noise is applied. In order to consider the non-linear effect of a control system on wind speed over a wide range, dynamic simulation was performed for 100 s under wind conditions with turbulence intensity of about 10% and mean wind speeds of 4 m/s and 8 m/s. As shown in Figure 5a, the three controllers showed almost the same control operation impact. This is because the control gains and weights were tuned in such a way that all three controllers commonly prioritized maximum power point tracking (MPPT) control in regions where the wind speed is lower than the rated wind speed (i.e., in this region, all the kinetic energy of the wind turbine should be used for power production.). In addition, a thrust transient occurred during significant wind speed changes at approximately 48 s and 82 s, revealing differences in the responses of the three controllers. While both the LQR controller and the \(H_{\infty}\) controller assigned a high weight to the torque state variable to prioritize MPPT torque control, it was observed that they still utilized nacelle acceleration state variables and fuzzy control to stabilize the rotor thrust force. Consequently, this led to a reduction in the thrust transient. Also, in the case of pitch control, all three controllers maintained  
Figure 5: Results from simulations of the target wind turbine for the PI controller (black solid lines), the LQR controller (red dotted lines), and the \(H_{\infty}\) controller (green dashed lines). The left-hand plot (**a**) shows the results below the rated wind speed region (mean 4.0 m/s). The right-hand plot (**b**) shows the results for the above-rated wind speed region (mean 8.0 m/s). a fine-pitch angle capable of producing maximum power. In contrast, the difference in motion between the three controllers is more pronounced, as shown in Figure 5b. Since this operating region is one where the wind speed is higher than the rated wind speed, the generator torque is controlled to be maintained at the rated torque via reference bias control. In addition, the pitch angle maintains the rotor speed and power at a rated value, even when the wind speed changes (i.e., it is free from the MPPT set point), and the remaining kinetic energy can be used to reduce the fluctuation of the rotor speed or the fatigue load. As a result, compared to PI controllers that simply control rotor speed, the LQR and \(H_{\infty}\) controllers that modulate multiple state variables was able to reduce the fluctuation of the rotor speed, power, and thrust load. In addition, it was found that the \(H_{\infty}\) controller with loop shaping applied in the frequency domain could further improve the control performance compared to the LQR controller by utilizing pitch control to a greater extent. In this study, the performance indicators for confirming control performance were selected as the mean and standard deviation of the rotor speed, power, a rain flow cycle counting-based damage equivalent load (DEL) of thrust load. The reason for these choices is that each controller's set-point follow-up performance, toughness performance, and load reduction performance can be directly checked.