# Robust Control Examples Applied to a Wind Turbine Simulated Model
## 3 Data-Driven and Model-Based Control Designs
### Model-Based Adaptive Control Scheme
The complete block scheme is shown in Figure 6.  
Note that, the adaptive control scheme represented in Figure 6 will replace the baseline wind turbine controller recalled in Section 2 and depicted in Figure 4. In this way, the adaptive controller should be able to manage possible uncertainty affecting the wind turbine system, thus allowing one to improve the performance of the baseline wind turbine control described in Section 2. Note that an important point concerns the stability issue when the switching of the controllers is considered, and it can be solved as bumpless transfer for adaptive control. In more detail, in the adaptive control setting, the controller output can have undesired transients (bumps), if a current on-line controller and a new controller to be switched have different outputs at the switching instant. To attenuate these bumps associated with controller switching, which could lead to stability problems,  
Figure 6: Diagram of the adaptive control strategy. a variety of bumpless transfer methods have been suggested. As in this case, the plant is not precisely known at the outset, and the goal of adaptive control is to change the controllers to improve performance as plant data begins to reveal some information about the plant. Thus, in adaptive switching control an exact plant is generally unavailable at the time of switching. Moreover, in the adaptive application considered in this work where the true plant model may only be poorly known at controller switching times, it may be preferable to employ a bumpless transfer technique that does not depend on a precise knowledge of the true plant model. Therefore, the bumpless transfer method presented in [34; 35] based on the slow decomposition of the controller is considered. It consists of a method that can be implemented without precise knowledge of the true plant at switching times. In particular, by appropriately re-initializing the states of the controller modes at switching times, this method ensures that not only will the controller output be continuous, but also that it avoid fast transient bumps after switching. Another key aspect concerns the possible non-minimum phase behavior of the considered wind turbine. In this case, the self-tuning design procedure represented by Equations (39) and (40) would lead to poor performances. However, it is worth noting that according to Section 2, there are two possible regions of turbine operation, namely the high and low wind speed regions. High-speed operation is frequently bounded by the speed limit of the machine. Conversely, regulation in the low-speed region is usually not restricted by speed constraints. However, the system has possible non-minimum phase dynamics in this low-speed region. Moreover, this behavior in the low-speed region can be observed for very low tip-speed-ratio, i.e., when \(\lambda\) is near to zero. However, as presented by the paper in Section 4, the condition \(\lambda\approx 0\) is always not satisfied, also for low wind speed. Therefore, the benchmark under consideration can present non-minimum features only for working conditions different from the ones considered in Section 2. However, alternative design methodologies that take into account time delay behavior can be found, e.g., in [36]. Considering again Equation (46), the Taylor approximation of a time delay transfer function leads to verify that an inverse response time constant \(T_{o}^{inv}\) (negative numerator time constant in Equation (46)) may be approximated as a time delay:  
\[(-T_{o}^{inv}\,w+1)\approx e^{-T_{o}^{inv}\,w} \tag{41}\]  
This represents the deteriorating effect of an inverse response similar to that of a time delay.