## 1 Introduction
In [9], the authors extended previous work and demonstrated the impact and importance of incorporating an azimuth offset to reduce higher periodic harmonics. Some studies have combined MBC conversion and control techniques, such as linear quadratic Gaussian control [4], model predictive control [10], and the H\({}_{\infty}\) technique [8]. Computational intelligence methods, such as artificial neural networks, fuzzy logic, genetic algorithms, particle swarm optimization, decision-making techniques, and statistical methods, are gaining popularity as alternatives to wind turbine control problems. These methods can help improve the performance, reliability, and efficiency of wind turbines by optimizing their control systems, reducing maintenance costs, and increasing their lifespan [11; 12]. In [13], Bayesian optimization is used to tune the gains of decentralized integral control and azimuth offset in an IPC scheme to reduce blade fatigue at 1P and 2P loads. The authors demonstrated that their scheme with the azimuth offset outperformed the same scheme without the azimuth offset and the same integral gains. In our previous work [14], we optimized both schemes according to the same cost function and demonstrated that including the azimuth offset provided a reduction of approximately 10% in blade fatigue load and pitch signal effort compared with the optimized IPC scheme without offset. All of these previous studies on IPC force the elements of decentralized control to be pure integral controllers with the same gain. This may be a limitation in achieving better IPC performance that has not yet been addressed. This work analyzes different simple IPC schemes where the decentralized controllers can have integral or proportional action with different gains. Furthermore, they may include the azimuth offset to improve the IPC response. To perform a fair comparison, all of the parameters of the different schemes are optimized with Gas to minimize fatigue on the OoP blade loads according to the DEL [15]. The proposed schemes are applied to the International Energy Agency (IEA) 15 MW reference wind turbine (RWT), which is simulated with OpenFAST v3.5 and MATLAB/Simulink R2022b software. The IPCs are designed to adaptively adjust their gain as a function of wind speed in the nominal region due to the system's nonlinearity. The results of all of the schemes are compared with those of a classic baseline CPC PI-controlled turbine without IPC. It is shown that the IPC schemes with integral controllers plus the azimuth offset outperform the other schemes, achieving the greatest reduction in the DEL value of the OoP blade moments using the lowest pitch signal activity. The IPC schemes with proportional controllers exhibit similar performance to the IPC schemes with integral controllers without the azimuth offset. Using different gains in the IPC controllers does not provide advantages compared with the respective IPC schemes with identical decentralized controllers. The main novelties of this work compared to the available literature are as follows:  
* In closely related previous research [14], IPC schemes with two identical pure integral controllers with and without the azimuth offset were compared. In this work, a study in more detail is performed for simple IPC schemes optimized to minimize the fatigue blade load. Specifically, we check the influence of using integral or proportional controllers, tuning them with different gains and including or not including the azimuth offset in the reverse MBC transform. The improvements that can be achieved considering these features are analyzed qualitatively and quantitatively. * The IPC schemes are implemented as adaptive blocks where the controller gains are scheduled according to the mean value of the measured filtered blade moments instead of the wind speed in the above-rated region. * Most of the research papers published so far on OpenFAST have concentrated on the 5 MW NREL turbine.