# Passive Vibration Control of a Semi-Submersible Floating Offshore Wind Turbine
## 4 Performance Verification and Analysis of the Optimized TMDs
Similar as standard deviation, the short-term DEL of a time-series can reflect, in some extent, the level of fluctuations departing from the mean value. Therefore, because \(\sigma_{\text{TTD}}\) is the objective function in optimizing the TMD parameters, it is well reasoned that the DELs can be reduced. As a whole, the main embodiment of TMD device in OC4-DeepCwind is to absorb the energy and mitigate the fatigue loads induced by moderate wind and wave conditions. According to the above discussion, TMD devices with 20,000 kg mass, 133,467 N/m spring coefficient and 9293 N/(m/s) damping coefficient are chosen for OC4-DeepCwind in practical application. The time-histories of platform pitch and roll and the tower base moments \(T_{\text{TB}}\) in the fore-aft and side-side directions are illustrated in Figure 8. The responses with and without TMD under the three load conditions are drawn in red and blue lines, respectively. The time domain results also verify the statistics. The platform motions nearly coincide with each other and the controlling performance can be observed in the tower base moments. Similar to the results of [PERSON] et al. (2012), the generated power time-histories of the 5 MW FOWT under 10 m/s and 18 m/s wind velocities indicate that the TMD devices have negligible interference on the electricity generation. As can be seen in Figure 9, the comparison between the power spectral density of uncontrolled responses and responses controlled by the selected TMD device displays the alleviating effects in frequency domain. Since the TMD is tuned near the wind turbine's fore-aft natural frequency \(f\approx\) 0.43 Hz, the control is generally most effective for tower base moment, which is critical in extending the service life of FOWT. In addition, to reveal the performance of TMD device on different kinds of floating foundations, the simulation results of OC3-Hywind, a spar type 5 MW FOWT, using the same environmental conditions from [11] are listed in Figure 9. Power spectral density of tower base moments under rated operation condition with and without TMD: (a) Side-side; and (b) Fore-aft. Table 8 to compare with the semi-submersible OC4-DeepCwind. The TMD device is also installed in the nacelle with \(m\) = 20,000 kg, \(k\) = 16,4231 N/m, \(d\) = 20,889 N/(m/s), which is similar to the 20,000 kg high stiffness TMD in this work. One of the noteworthy differences between spar and semi-submersible platform is their hydrostatic stiffness of pitch; in other words, the small angle stability of spar is worse than the semi-submersible. Encountering the same realistic loads, the pitch response of OC3-Hywind is supposed to be larger than OC4-DeepCwind. However, the response reduction ratios of the two type foundations manifest a similar variation tendency. For DEL of \(T_{\text{TB}}\) at rated and extreme wind speed, the control effects of TMD on OC4-DeepCwind are better than OC3-Hywind. At maximum operating wind speed, TMD on OC3-Hywind can mitigate more fatigue loads. Figure 8: Time-histories of response under three load conditions with and without TMD: (**a**) 10 m/s; (**b**) 18 m/s; and (**c**) 37 m/s.