## 7 Conclusions and Future Works  
In this study, different structural control strategies for FOWT were proposed. First, a simplified model of a floating wind turbine was developed using the Euler-Lagrange approach. The validity of this model was confirmed by comparing it with data from the high-fidelity simulation software OpenFAST, which captures the non-linear dynamics of the wind turbine. Simulations conducted with the simplified model enabled the authors to assess the impact of installing a TMD in the turbine nacelle and to verify its effectiveness in mitigating vibrations. After validating the effect of the passive TMD, its parameters were further optimized using Genetic Algorithms, resulting in an improvement over the performance of the reference TMD.  
An initial approach to semi-active control based on the amplitude of vibrations demonstrated the effectiveness of this technique in addressing some of the limitations of passive control. The ability to adapt the TMD parameters to the real-time conditions of the turbine had a significant positive impact on vibration mitigation. This concept was further extended by developing a semi-active control strategy that adjusts the TMD parameters based on the turbine's pitch rotation frequency. A frequency response analysis of the system highlighted the critical role frequency plays when disturbances are present.  
The development of a real-time frequency detection algorithm, utilizing the Short-Time Fourier Transform (STFT), proved effective in identifying the vibration frequency of the turbine under external disturbances. The implementation of frequency-based semi-active control confirmed its potential for reducing vibrations induced by variable-frequency disturbances, such as waves. Additionally, the importance of proper TMD tuning was highlighted, both for passive and semi-active control strategies, as the effectiveness of the results heavily depended on optimal parameter selection.  
In summary, TMDs have proven to be effective structural control devices for mitigating vibrations appearing in FONTs. However, their performance relies heavily on optimal tuning methods to improve the stability of the structure under varying conditions and initial perturbations.  
The results here presented suggest exploring additional degrees of freedom and accounting for certain nonlinearities of the TMDs, such as physical stops. Future research will focus on evaluating alternative metaheuristic techniques for optimizing the tuning parameters of the TMD in these control strategies. Furthermore, the authors plan to validate this approach using a scaled-down prototype.  
Another promising direction for further research would be to investigate potential practical implementation of these devices. As a matter of fact, existing industrial applications of structural control solutions make use of sensors capable of detecting vibrations or resonances in the structure. These sensors transmit signals to an active damping system, which creates counteracting forces to suppress undesired vibrations. Typically, this is achieved using actuators, such as hydraulic or electromagnetic devices that apply forces to the structure to counterbalance the effects of the vibrations.  
Conceptualization, M.S. and M.T.-R.; methodology, J.E.S.-G.; software, A.R.; validation, M.S., J.E.S.-G. and A.R.; investigation, A.R.; writing--original draft preparation, A.R. and M.S.; writing--review and editing, M.T.-R., J.E.S.-G. and M.S.; funding acquisition, M.S. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This work was partially supported by the Spanish Ministry of Science, Innovation and Universities under MCI/AEI/FEDER Project no. PID20201-123543 OB-C21.  
**Data Availability Statement:** The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding authors.  
**Conflicts of Interest:** The authors declare no conflicts of interest.