## 3 Proposed Methodology
### Control System Scheme
By using the reverse MBC transform, these control signals are converted to the rotating frame to obtain the final IPC signals \(\beta_{\mathrm{IPCI}}\). The gains of the decentralized controllers and the azimuth offset are adapted by scheduled values according to the mean value of the filtered moments of the three blades. Figure 2: IPC + CPC control scheme for the above-rated region. The CPC supplies a common pitch command angle for the blades to control the rotational speed of the generator at its rated value. The IPC computes an individual action for each blade to decrease the blade moments. Both control actions are combined to provide the total command signals for each pitch actuator of the wind turbine [14]. the IPC scheme (proportional or integral control). When \(C_{t}(s)\) and \(C_{y}(s)\) are proportional (P) controllers, they are equal to unity and \(k_{t}\) and \(k_{y}\) are proportional gains; when they are integral (I) controllers, \(C_{t}(s)=C_{y}(s)=1/s\) and \(k_{t}\) and \(k_{y}\) are integral gains. In addition, IPC schemes can include the azimuth offset \(\psi_{o}\) and can force the gains to have the same value. By combining these three factors (P or I controllers, gains with identical or different values, and including the azimuth offset or not), six cases are proposed for evaluation; the two cases with identical gains and P controllers are not considered. The six proposed cases are the following:  
* Control 1 (IPC_P2): The IPC comprises two different P controllers, and no azimuth offset is tuned. Therefore, \(C_{t}(s)=C_{y}(s)=1\), \(k_{t}\
eq k_{y}\), and \(\psi_{o}=0^{\circ}\). There are only two parameters to be tuned: the controller gains. * Control 2 (IPC_P2\(\psi\)): The IPC comprises two different P controllers and includes the azimuth offset. Therefore, \(C_{t}(s)=C_{y}(s)=1\) and \(k_{t}\
eq k_{y}\). There are three parameters to be tuned: the controller gains \(k_{t}\) and \(k_{y}\) and the azimuth offset \(\psi_{o}\). * Control 3 (IPC_I1): The IPC is composed of two identical I controllers because they are forced to have the same gain; no azimuth offset is tuned. Therefore, \(C_{t}(s)=C_{y}(s)=1/s\), \(k_{t}=k_{y}\), and \(\psi_{o}=0^{\circ}\). There is only one parameter to be tuned: the common controller gain. * Control 4 (IPC_I1\(\psi\)): The IPC is composed of two identical I controllers and includes the azimuth offset. Therefore, \(C_{t}(s)=C_{y}(s)=1/s\) and \(k_{t}=k_{y}\). There are two parameters to be tuned: the common controller gain and the azimuth offset \(\psi_{o}\). * Control 5 (IPC_I2): The IPC comprises two different I controllers, and no azimuth offset is tuned. Therefore, \(C_{t}(s)=C_{y}(s)=1/s\), \(k_{t}\
eq k_{y}\), and \(\psi_{o}=0^{\circ}\). There are two tuning parameters: the controller gains. * Control 6 (IPC_I2b): The IPC comprises two different I controllers and includes the azimuth offset. Therefore, \(C_{t}(s)=C_{y}(s)=1/s\) and \(k_{t}\
eq k_{y}\). There are three parameters to be tuned: the controller gains and the azimuth offset \(\psi_{o}\). Variations in wind speed modify the wind turbine operating point and, consequently, the control performance is affected. In this work, an adaptive control based on gain-scheduled IPC is proposed for the control system to perform properly under different wind conditions. To create a gain adaptive control system for the IPC that can adjust to changes in wind speed, the controller is tuned for the five operating points based on the previously determined wind conditions. Nevertheless, the wind speed is not used as the scheduling variable; instead, as a novelty of this work, we propose using the mean value \(\overline{M}\) of the filtered moments of the blades as the scheduling variable. In the above-rated region, this mean moment practically depends only on the mean wind speed, and the higher the wind speed, the lower the mean moment of the blades. Table 2 shows this relationship for the five operation points in the IEA 15 MW wind turbine.