## 1 Introduction  
As one of the clean and renewable energy resources, wind energy has been harvested extensively worldwide. In contrast with onshore wind turbines, offshore wind turbines are generally located in a better wind environment that has a higher wind speed and lower turbulence intensity than on land; there is also no need to worry about noise caused by offshore wind turbines because they are away from the coast. Thus, the offshore wind turbine is one of the wind engineering research hotspots. However, compared with onshore or fixed-bottom offshore wind turbines, floating offshore wind turbines generally vibrate more violently when under the coupling impact of wind and wave. Their surge movement amplitudes commonly exceed 10 m when under extreme environmental conditions, potentially resulting in the wind turbine overtopping and mooring system damage. The excessive vibrations of floating offshore wind turbines also significantly increase their cost ([PERSON] and [PERSON] [1] found that offshore wind turbines generally cost two to three times more than that of onshore or fixed-bottom offshore wind turbines). Therefore, it would be valuable to find out how to effectively reduce the structural displacements of the floating offshore wind turbine (floating offshore wind turbine is simply called offshore wind turbine in the following sections). A blade pitch control system was first found to be helpful for wind turbine vibration control. [PERSON] et al. [2] proposed a novel electrical-hydraulic blade pitch control system, which consisted of a hydraulic pump, hydraulic motor, and pitch control gear. That pitch control system could help the wind turbine harvest wind energy as much as possible, and it could also reduce wind turbine vibration by tuning the blade pitch angle. Next, [PERSON] et al. [3] presented an adaptive super-twisting generator controller based on an integral blade pitch control strategy for floating offshore wind turbines; their numerical results showed that their developed pitch angle controller could be applied to tune wind turbine rotor speed and to control floating wind turbine platform vibration. [PERSON] et al. [4] then utilized an adaptive sliding mode pitch angle controller to tune blade pitch angle. Their control strategies were effective in reducing wind turbine vibration. Although pitch angle control can reduce significant wind load on the floating offshore wind turbine and can increase wind turbine energy output, wave load can hardly be reduced. Further, frequently tuning blade pitch angle will obviously reduce blade lifetime resulting in additional blade maintenance cost. Next, some researchers applied a tuned mass damper (TMD) in the floating offshore wind turbine nacelle to control wind turbine vibration. [PERSON] et al. [5] installed a TMD in the wind turbine nacelle. The TMD's structural parameters were optimized through parametric analysis. Their numerical results implied that a TMD could passively control wind turbine vibration, and tower top and nacelle movements could be significantly reduced by 10%. [PERSON] et al. [6] also applied a TMD in a wind turbine nacelle, and they developed a simulation tool called HAWC2-TMD to numerically simulate the wind interaction of the wind turbine with a TMD. They reached the same conclusion that wind turbine vibration could be controlled by applying a TMD in the nacelle. Innovatively, [PERSON] et al. [7] used a radial basis function neural network to predict TMD performance, and utilized a genetic algorithm to globally and systematically optimize the TMD structural parameters. They also investigated the effects of upstream wind turbine wake on downstream wind turbine TMD optimization. They concluded that upstream wind turbine wake effects on downstream TMD optimization should be considered when wind turbine spacing is approximately twice that of rotor diameter. Subsequently, [PERSON] et al. [8] applied a rotational inertia double-tuned mass damper (RIDTMD) in the wind turbine nacelle.