## 1 Introduction  
The main overall goal of structural control is to reduce fatigue so that large structures, such as wind turbines (WTs), have longer service lives and require less maintenance. In particular, tuned mass dampers (TMDs) are a widely used structural control system in several disciplines, highlighting its extensive use in civil engineering applications. TMDs have been implemented in a variety of configurations on both onshore and offshore wind turbines, demonstrating their effectiveness in reducing vibrations caused by internal (e.g., pitch control of the blades) and external disturbances (e.g., wind, waves) [1, 2]. Tuned mass dampers (TMDs) are structural control devices consisting of springs, dampers, and masses that move longitudinally and/or laterally, exerting forces to reduce structural vibrations. TMDs are commonly classified as passive, semi-active, or active, depending on whether their parameters are fixed, varied according to a predefined schedule, or adaptively adjusted. The parameters of passive TMDs remain constant. Semi-active TMDs are essentially adjustable passive TMDs that automatically re-tune their parameters through adjustment mechanisms, staying optimally tuned to their target frequencies. Due to this continuous in situ re-tuning (via adjustments in stiffness and/or damping), semi-active TMDs exhibit robust performance even when the dynamics (and thus the natural frequencies) of the target structures change. An active tuned mass damper (ATMD) integrates a controllable element, such as a linear actuator, into a passive TMD. Structural vibrations are continuously monitored to generate damping forces that reduce the vibrations. ATMs require external power, but since an active TMD is essentially a passive TMD with an added actuator, part of the vibration suppression is accomplished by the passive component, minimizing the power demand. In an active TMD, parameter adaptation occurs continuously, while in a semi-active TMD, the parameter adjustments follow a gain scheduling scheme. Despite their apparent simplicity, TMDs have proven to be highly effective in reducing wind-induced oscillations in civil structures such as bridges, tall buildings, and wind turbines [3]. Common passive control devices researched for wind energy converters include tuned mass dampers (TMDs), ball vibration absorbers (BVAs), tuned liquid dampers (TLDs), rolling ball dampers (RBDs), tuned inerters, and tuned liquid column dampers (TLCDs). TMD parameter tuning is a crucial task, as is the case in any control system. Several different techniques can be used to adjust these parameters, specifically spring stiffness and damping values. Typically, these parameters are fixed (passive TMDs), but it may be advantageous to adjust them based on internal variables or external disturbances (semi-active or active TMDs), where stiffness and/or damping can be modified during operation [4]. The main advantage of semi-active control over passive control is its adaptability to external changes and disturbances. Passive TMDs are tuned to the natural frequencies of the structure under specific environmental conditions. For instance, in the case of a floating offshore wind turbine, the optimized TMD settings differ between scenarios with significant wave heights or calm seas. On the other hand, semi-active control enables the TMD parameters to adapt to both situations. The most commonly used techniques for tuning TMD parameters include frequency tuning, surface plots, and metaheuristic methods such as genetic algorithms (GAs). Among these, the surface plot approach is often disregarded due to its computational cost and time requirements. Frequency adjustment is efficient for certain applications, but its limitations have led to the widespread adoption of evolutionary optimization techniques like GA [3]. In this paper, the authors propose and compare passive and semi-active structural control methodologies for an NREL 5 MW floating offshore wind turbine (FOWT) [5]. This barge-type floating device is mounted on an ITI platform.