## 3 Proposed Methodology
### Control System Scheme  
The control system proposed in this study is shown in Figure 2. It has two control blocks: a CPC and an IPC. The control signals of these blocks are combined to provide the total pitch command signal \(\beta_{1}\) for each pitch actuator. As in the full load region, the wind turbine is designed to generate power at the rated power output and the generator torque \(T_{g}\) is set to its nominal value \(T_{g,rated}\). Therefore, the generated power (\(P_{g}\)) depends only on the generator speed \(\omega_{g}\) according to Equation (5) [24]. If the wind turbine rotation speed is regulated to its rated value \(\omega_{g,rated}\), then the power generated can be maintained at the rated value. The CPC generates the same pitch signal \(\beta_{\text{CPC}}\) for all blades to maintain this speed at its rated value and rejects changes in wind speed \(\
u\). \[P_{g,rated}=T_{g,rated}\cdot\omega_{g,rated} \tag{5}\]  
This study does not consider the CPC tuning procedure. We use a pre-designed CPC PI controller that is reimplemented in Simulink based on the reference open-source controller (ROSCO) implementation. We use the tuning parameters presented in [25], which are adjusted by gain scheduling based on the CPC pitch signal. \begin{table}
\begin{tabular}{c c} \hline
**Property** & **Value** \\ \hline Power rating & 15 MW \\ Rotor orientation, configuration & Upwind, 3 blades \\ Cut-in, rated rotor speed & 5 rpm, 7.56 rpm \\ Cut-in, rated, cut-out wind speed & 3 m/s, 10.59 m/s, 25 m/s \\ Drivertrain & Low speed, direct drive \\ Rated generator torque & 19,786,767.5 Nm \\ Electrical generator efficiency & 95.756\% \\ Rotor, hub diameter, hub height & 240 m, 7.94 m, 150 m \\ Rotor nacelle assembly mass & 1,070,000 kg \\ Tower mass & 860,000 kg \\ Blade pitch angle limits & 0-90 deg \\ Pitch slew-rate limits & 2 deg/s \\ Generator torque slew-rate limits & 4,500,000 Nm/s \\ \hline \end{tabular}
\end{table} 
Table 1: IEA 15 MW RTW properties. This work focuses on the design of the IPC block, whose main goal is to reduce blade loads. The proposed IPCs are combined with the pre-designed CPC to run the simulations. The considered IPC scheme is shown in Figure 3. It consists of the MBC transformation for 1P harmonic reduction; a multi-loop control with two controllers, \(\mathrm{C_{t}(s)}\) and \(\mathrm{C_{y}(s)}\); and the reverse MBC transformation, which can incorporate the azimuth offset \(\psi_{0}\). From the OoP blade moments (\(\mathrm{M_{1}}\), \(\mathrm{M_{2}}\), and \(\mathrm{M_{3}}\)) measured in the rotating frame, the tilt and yaw moments \(\mathrm{M_{t}}\) and \(\mathrm{M_{y}}\) in the non-rotating frame are computed using the MBC transform. A decentralized control scheme with two controllers provides the tilt and yaw pitch signals (\(\beta_{1}\) and \(\beta_{y}\)) to reduce the tilt and yaw moments, respectively. The calculated non-rotating tilt and yaw pitch signals are then transformed into the three different blade pitch angles in the rotating frame using the reverse MBC transform. The decoupling between the pitch and yaw axes can be improved by using the azimuth offset, which can help achieve a greater reduction in the periodic blade loads compared with the IPC schemes without offset (\(\psi_{0}=0^{\circ}\)). Finally, the IPC signal \(\beta_{\mathrm{IPCI}}\) and the CPC value \(\beta_{\mathrm{CPC}}\) are added to obtain the total command pitch angle for each blade. In this study, we design and compare six different cases of IPC according to the complexity (the number of degrees of freedom to be tuned) and the type of controller in  
Figure 3: General scheme of the IPC with the azimuth offset in the reverse MBC transform and a decentralized control composed of the controllers \(\mathrm{C_{t}(s)}\) and \(\mathrm{C_{y}(s)}\). The forward MBC transformation \(\mathrm{T(\psi)}\) transforms the 1P harmonics of the OoP blade load moments to a fixed reference system. Then, a decentralized control loop reduces the computed tilt- and yaw-axis moments.