## 1 Introduction  
The limited natural resources and the environmental impacts associated with conventional energy sources represent major challenges for global strategic efforts towards sustainable development. Consequently, considerable efforts have been made in several countries to reorient their energy policies towards renewable energy sources, including wind, solar, bioenergy, and ocean wave energy [1]. Among these alternatives, wind power occupies a crucial position, given that its worldwide electricity production is growing continuously [2]. The potential for stronger, more reliable winds at high altitudes, along with the height limitations of conventional turbines [3], led to the development of a new type of wind-harvesting energy technology known as airborne wind energy (AWE) as an alternative to traditional wind turbines. This technology produces electricity using tethered flying devices (flexible kites or aircraft) instead of towered turbines [4]. Two primary concepts are currently under development: pumped-mode and drag-mode systems [5]. The pumping mode technology involves the tethered wing generating power by reeling out a cable from a ground winch linked to an electric generator. Once the maximum length of the tether has been reached, the wing is retracted using some of the energy generated during the first phase. On the other hand, drag-mode systems use turbines mounted on the tether's wings to generate electricity, which is then transmitted to the ground station via the tether. AWE is an emerging wind power technology that has been investigated by industry and academia over the past decade [6]. Several studies and demonstrations have been carried out, addressing the aerodynamic aspects [7; 8; 9], flight path control [10; 11; 12; 13; 14], speed control of the generator [3; 15], and DC-link voltage control [16; 17]. The conversion system architecture usually comprises a synchronous machine (SM) connected to the grid via two full-power, two-level pulse width modulation (PWM) converters linked by a DC-link. This configuration is commonly used in wind energy conversion systems in order to control the permanent magnet synchronous machine (PMSM) and enable bidirectional power exchange with the grid. Additionally, it ensures adherence to grid code compliance requirements [18]. Even though this new technology operates in comparatively less turbulent atmospheric conditions than traditional wind generators, the complex aerodynamic characteristics of these systems pose significant challenges for the accurate modeling of their behavior. In particular, due to the dynamic interaction between the kite's trajectory and variations in wind speed, the optimal rotational speed in traction phases is generally time- and space-dependent [19]. During this phase, the instantaneous optimal reeling speed is one-third of the wind speed component along the tether direction [20; 21]. This leads to periodic variations in the speed reference in maximum power point tracking (MPPT) control. Moreover, in the transition phases, the machine speed has to be reversed to retract the kite or to start a new generation phase. The system must therefore achieve stable and fast transitions to guarantee maximum efficiency. Because of these challenges, the use of advanced control techniques is inevitable. Previous work in [22] used a proportional-integral (PI) controller to regulate the rotational speed in a grid-connected closed-orbit power generation system; however, its robust performance has not been thoroughly investigated. In [23], the challenge of periodic variations in shaft speed and torque has been highlighted in the context of MPPT control for a tidal underwater kite system. The generator speed has been regulated through a PI control loop with active damping. Nevertheless, the tracking performance was found to be poor, particularly during high-speed kite movements.