## 1 Introduction  
Currently, global warming and climate change are major concerns that are driving efforts to reduce greenhouse gas emissions. Since energy generation accounts for approximately 30% of these emissions, wind energy has been a key renewable energy source from the outset [1]. In 2021, wind power capacity worldwide reached 837 GW, with the USA, China, India, Germany, and Spain representing 72% of it. However, the International Energy Agency forecasts that by 2030, wind power capacity needs to reach 3200 GW to limit the temperature increase to 1.5 degC [2]. In 2021, the EU introduced a plan to lower net greenhouse gas emissions by 2030 by at least 55%. The arrangement incorporates more investment in clean energy, and by 2030, onshore and offshore wind power is expected to produce 25% of the EU's renewable energy [3]. The main new developments in wind energy technology have involved increasing the size of wind turbines, which has increased energy generation and energy efficiency but has created challenges for maintenance and operation. To make this expansion economically affordable and competitive, the operation of wind turbines must be more efficient. Currently, new wind turbines are becoming larger and more flexible. Consequently, reducing their fatigue loadings to extend their lifetime has become particularly important. If the structural loads of wind turbines are not relieved, their overall performance may deteriorate or premature failure may occur. Therefore, it is important to understand how structural stresses affect wind turbine output and equipment life. Various deflection modes of towers, rotors, blades, and vibrations of turbine drive trains are the most typical phenomena and can result in different types of structural stresses [1]. From a control viewpoint, the service life of wind turbines can be extended by reducing various structural loads. Currently, wind turbines with three rotor blades and variable speed and variable blade pitch (VS-VP) on a horizontal axis are the most common. This study focuses on the full-load region, where it is essential to minimize the negative effects of high wind speeds to prevent system damage. Traditionally, wind turbines operating in this region use collective pitch control (CPC) for speed control. However, most modern wind turbines now have independent pitch control (IPC) mechanisms for each blade. IPC can provide advantages because it can help decrease the stress on the rotor blades, hubs, and tower structures without having significant effects on the generated power. There are two types of blade fatigue loads: in-plane and out-of-plane. These loads primarily arise at integer multiples of the turbine's rotational speed (n-P) [4]. As illustrated in Figure 1a [5], these components have different directions: The out-of-plane (OoP) component is aligned in the direction perpendicular to the plane of rotation, whereas the in-plane component is aligned in the direction tangential to it. Sensors installed on each blade can measure the bending moment. Nevertheless, as shown in Figure 1b [6], where the OoP moment at the root of the i-th blade is referred to as M\({}_{\text{yi}}\), the respective rotating coordinate frame of each blade affects these measurements. Most research on IPC uses the azimuth-dependent multi-blade coordinate (MBC) transform, which converts the blade rotating moments into two components in a non-rotating reference system [7]. In this frame, a multivariable controller in IPC is implemented to decrease these two moment components. Although decoupling between these components is expected, in practical scenarios, there is still coupling in the resulting transformed system [4; 8]. Some authors have shown that the decoupling of the fixed-frame multivariable system can be improved by using an azimuth offset as an extra parameter in the reverse MBC transformation. In [7], by introducing an azimuth offset in the MBC transformation, the coupling for the 1P harmonic was minimized, which led to advantages in pitch performance and blade fatigue load reduction.