Model-based design of a wave-feedforward control strategy in floating wind turbines

Floating wind turbines rely on feedback-only control strategies to mitigate the effects of wave excitation. Improved power generation and lower fatigue loads can be achieved by including information about the incoming waves into the wind turbine controller. In this paper, a wave-feedforward control strategy is developed and implemented in a 10MW floating wind turbine. A linear model of the floating wind turbine is established and utilized to show how wave excitation affects the wind turbine rotor speed output, and that collective-pitch is an effective control input to reject the wave disturbance. Based on the 5 inversion of the same model, a feedforward controller is designed, and its performance is examined by means of linear analysis. A gain-scheduling algorithm is proposed to adapt the feedforward action as the wind speed changes. Non-linear time-domain simulations prove that the proposed feedforward control strategy is an effective way of reducing rotor speed oscillations and structural fatigue loads caused by waves.

model of the floating wind turbine, and numerical simulations are carried out in realistic environmental conditions to evaluate the benefits of the feedforward control strategy. Section 8 draws the conclusion and gives some recommendations for future work.

Definition of a reference floating wind turbine
This section defines the floating system that is considered in this study. The FOWT is formed by the DTU 10MW Bak et al. 50 (2013) wind turbine and the INNWIND.EU TripleSpar platform Azcona et al. (2017); . The characteristics of this FOWT concept are similar to those of the current commercial projects, and are publicly available.
The wind turbine is regulated with an industry-standard generator-speed controller. In below-rated winds the controller maximizes the extracted power by keeping the blade pitch angle θ constant and varying the generator torque Q G as a function of generator speed ω G squared: with k G = 1 2 ρπR 5 C p,max /τ 3 λ 3 opt , where ρ is the air density, R the rotor radius, and τ the transmission ratio. C p,max is the maximum power coefficient, which is achieved for zero pitch angle and the optimal tip-speed-ratio λ opt .
In above-rated winds, the controller regulates the extracted power to its rated value setting the generator torque to a constant value, equal to rated. Generator speed oscillations are directly reflected by the wind turbine power output. The rotor speed is regulated to its rated value ω G,r by the CPC, which reacts to the generator speed feedback as: where k P and k I are the proportional and integral gains, which are tuned following the model-based approach of Fontanella et al. (2018) to achieve the maximum damping for the platform pitch mode and for the drivetrain mode. A gain scheduling factor is introduced to adjust the PI controller gains as the wind speed varies. The generator-speed feedback controller constitutes the 65 baseline configuration against which the benefits of feedforward are assessed.

The control-design model
Feedforward control is a model-based control strategy and its development requires a linear model of the floating wind turbine.
The control-design model is derived based on linear first-principle equations of the most important physics of the FOWT, rather than from the linearization of a higher-order model. The main features of the model are recalled below, while a detailed 70 description is found in Fontanella et al. (2020). The structural dynamics builds on the theory of multibody systems. The model considers the FOWT components as rigid bodies: this simplification is deemed acceptable in a control-oriented model, as the bandwidth of an FOWT controller is usually lower than the flexible modes of the tower, blades and drivetrain. Moreover, the focus of the control-oriented model is 80 the coupled rotor-platform response induced by waves more than the dynamics of the flexible components.
Rotor aerodynamics are introduced in the model with a simplified approach. The aerodynamic model does not consider the single blade, but computes the integral rotor forces. This simplification is valid because the global dynamics of the FOWT is determined by the integral rotor loads, rather than the loads of the single blades Lemmer (ne Sandner). Only the rotor torque and thrust force are taken into account because they drive the global dynamics of the floating turbine: aerodynamic torque sets 85 the wind turbine power production and thrust force the motion of the floating platform. Torque and thrust are modeled by means of the quasi-steady approach, based on the derivatives of the torque and thrust curves of the wind turbine. The formulation of the control-oriented model enables the inclusion of the unsteady aerodynamic effects associated with the motion of the FOWT, which may have an influence on the dynamics of the platform modes. In this respect, a similar approach to the one presented in Bayati et al. (2017) could be used.

Frequency-dependent hydrodynamic loads
Hydrodynamic radiation and first-order-wave forces are modeled by means of linear-time-invariant parametric models.
The frequency-dependent radiation forces are approximated by a parametric model in state-space form, from the added mass and damping matrices of panel code pre-calculations. In this work, the frequency domain identification method of the MATLAB toolbox developed in Perez and Fossen (2009)

Input-output analysis
An input-output analysis is carried out to gain insight into the FOWT response to the available controls, generator torque and collective-pitch, and to the wave disturbance. The analysis answers the question of which is the best combinations of controls to 110 be used to reject the detrimental effects of waves. This information is used later on to support the synthesis of the feedforward control strategy. Moreover, the analysis gives a picture of the FOWT dynamics that may prove to be useful also for other purposes.
The analysis starts from the control-design model in a transfer function representation (3)

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The system has two outputs, rotor speed and tower-top motion, which are collected inŷ = [ω r , x tt ] T ; two control inputs, collective-pitch and generator torque, collected inû = [θ, Q g ] T ; and two disturbance inputs, the variation from average of the hub-height wind speed and the wave elevation,d = [v, η] T . The model of Eq. (3) is used to compute the deviation of the outputs from their steady-state value, because of a change in the control and disturbance inputs.
inputs and outputs are of the same importance. The scaled model is obtained by dividing any variable by its maximum expected (for the disturbances) or allowed (for the control inputs) change. The output, input and disturbance scaling matrices (D y , D u and D d respectively) are where ω 0 is the rated rotor speed, Q g,0 the rated generator torque, and U the mean wind speed. The scaled model is Given an input between 0 and 1, where 0 is no input and 1 is the maximum expected value, the outputs of the model of Eq.
(5) take a value between 0 and 1, where 0 is no output and 1 corresponds to the maximum expected or allowed value for the 130 output.

Control inputs
The model without disturbancesŷ =Ĝû is considered first. The transfer function matrixĜ has two couples of input and output directions, each with an associated gain. For any selected frequency, the directions and gains of matrixĜ are obtained from its singular value decomposition (SVD) Levine (1996) The column vectors of V = [v, v] are the input directions, the column vectors of U = [u, u] the output directions, and the respective singular values are along the diagonal of Σ = diag(σ, σ). When the input vectorû has the same direction of vector v, the outputŷ is along the direction u, the gain is equal to σ and it is the largest possible for that frequency. The input produces the most effect on the output, and the directions of v and u are named the strongest. Conversely, when the input is directed as 140 v, the gain is σ, and the input has the least effect on the output, which is along u. The directions of v and u are named the weakest.
The (1,1) element ofĜ is much larger than the (1,2) element, so the rotor speed is a lot more sensitive to a steady-state (i.e. 145 a very slow) change in collective-pitch, the first input, than in generator torque, the second input. Collective-pitch effects both rotor speed, the first output, and tower-top motion, the second output, in the same direction. If collective-pitch is increased, the rotor is slowed because of the decreased aerodynamic torque, and the nacelle moves upwind, because of the lower thrust force.
The plant model is decomposed into its SVD is increased. It takes a small collective-pitch action to move the nacelle, because the resulting rotor thrust variation excites the resonant response of the platform. Controlling rotor speed is hard. In the wave frequency range, the gain is decreased so it becomes more difficult to control the system, and rotor speed is easier to control than tower-top motion.
In summary, collective-pitch is the most effective control in above-rated winds. It effects both rotor speed and tower-top motion. In the frequency range where wave is active, collective-pitch becomes less effective, so it is harder to control the wind 170 turbine.

Disturbances
The wind and waves disturbances are here considered separately. The direction of a disturbance is whereĝ d is the appropriate column ofĜ d (the first for wind, the second for wave). The disturbance condition number is where σ(·) is the maximum singular value. The DCN measures the control effort required to reject a given disturbance, relative to rejecting a disturbance with the same magnitude but aligned with the strongest output direction (i.e. the direction where controls are effective the most) Skogestad and Postlethwaite (2005). The higher the DCN is, the harder it is to reject the disturbance with the available controls.

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The effects of the wind and waves disturbance in the frequency range up to 0.3 Hz is assessed in Fig. 2, for seven operating points of wind speed between 12 and 24 m/s. Wind turbulence acts directly on the rotor causing, first, a variation of the aerodynamic torque, which affects rotor speed. Wind turbulence also acts on the platform, through the rotor thrust, but this excitation mechanism is less effective than wave forcing. The wind disturbance is aligned to the rotor speed output direction.
Collective-pitch is very effective for controlling rotor speed, and rejecting the wave disturbance with collective-pitch does not 185 require a large effort. This is visualized by the DCN. Wave is aligned to tower-top motion, and partially shifts towards rotor speed for increasing frequency. Waves act on the platform, but also excite rotor speed. The platform motion caused by waves, turns out into a variation of the apparent wind speed, which affects rotor torque, and then speed. This mechanism of excitation is more effective above the platform pitch frequency, because most of the wave energy is concentrated here. The gain of waves is maximum at the platform modes frequencies, where wave excites the FOWT in resonance causing large motions, and in the 190 wave range. The wave disturbance is not aligned to the rotor speed output direction, and the DCN shows that it is very hard to counteract the wave disturbance by means of the wind turbine controls. To sum up, waves effect rotor speed, because waves drive the platform motion which result into an apparent wind speed at rotor. The wave excitation is stronger at the platform frequencies, where the FOWT is excited in resonance, and in the wave range, where it is concentrated most of the wave energy. Moreover, it is quite hard to counteract the wave disturbance by means 195 of the wind turbine controls. All this shows that new control strategies specific to FOWTs are needed to deal with waves.
The wave-feedforward control strategy leverages the knowledge of the FOWT dynamics to improve the performance of the traditional wind turbine controller with respect to the mitigation of the wave effects.

The wave-feedforward control strategy
The feedforward (FF) controller is designed to cancel the effect of the wave disturbance on rotor speed, end hence on the power 200 output of the wind turbine. The FF controller regulates rotor speed producing an additional collective-pitch request which is summed to the pitch signal of the existing generator-speed feedback (FB) controller. The FBFF control strategy is shown in 3. For wave-disturbance rejection, the reference signal r is zero and the closed-loop rotor speed output ω is where, G s is the collective-pitch to rotor-speed plant, G d the wave disturbance model, K fb the FB controller, K ff the FF 205 controller, η the wave disturbance. In the model-inverse approach, the FF controller K ff is designed to cancel the effect of η on ω, thus the transfer function of the controller is K ff is the transfer function between the input wave elevation measurement and the collective-pitch command. In general, G s , G d , and K ff , depend on the wind turbine operating condition and so, on the mean wind speed.

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The transfer function of the FF controller obtained based on Eq. (13), which was evaluated for different wind conditions, is shown in Fig. 4. There is a significant difference between the generic shape assumed by K ff in below-rated and aboverated conditions. The amplitude is increased in below-rated winds because collective-pitch is not effective for controlling rotor speed. There, a variation of the collective-pitch produces a smaller variation of rotor torque than in above-rated winds. For this reason, it is decided to confine the action of the FF controller to the above-rated region: when the mean pitch angle falls below https://doi.org/10.5194/wes-2021-9 Preprint. Discussion started: 1 March 2021 c Author(s) 2021. CC BY 4.0 License.
The above-rated controller K ff has a peak at the platform pitch natural frequency which is not present in below-rated winds.
In above-rated winds, the platform pitch mode damping is decreased and the wave excitation leads to a large response at this frequency. This causes significant oscillations of the tower-top, with consequently large variations of the apparent wind speed.
A high control effort is therefore required to balance the wind fluctuations.

Disturbance rejection analysis
Considering the FBFF controller of Fig. 3, and the closed-loop disturbance response of Eq. (12), the FB, the FF and the FBFF sensitivity function is defined respectively as behavior of the wind turbine with U i = 12, 13, . . . , 24 m/s and U = 16 m/s.
The disturbance-rejection function is derived from the sensitivity function and it directly relates the wave disturbance to the closed-loop rotor speed. For the FB and the FBFF controllers it is defined respectively as The disturbance-rejection function of the FB and FBFF controllers at 16 m/s wind speed is shown in Fig. 5   The disturbance-rejection function of the FBFF controller is computed for different above-rated wind speeds U i with U i = 12, 13, . . . , 24 m/s and S fbff (U i ) already obtained in Eq. (15). The magnitude of T fbff (U i ) is shown in Fig. 5. The disturbance-rejection function, and so the performance of the FBFF controller, is sensitive to the mean wind speed. This is due to the rotor aerodynamics which changes for different operating conditions. The benefit of the additional FF controller is 245 maximum at 16 m/s, the operating point considered for model inversion, lower elsewhere, and minimum in 12 m/s wind.

Gain scheduling
The wave disturbance effect on the FOWT is sensitive to the mean wind speed. To have the maximum possible reduction of the wave disturbance, the FF controller needs to take into account how the FOWT dynamics are modified with the operating condition.

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Based on the procedure introduced above, a linear model of the FOWT is computed for several above-rated wind speeds and, by means of Eq. (13), an FF controller is obtained for each of them. The transfer function of the FF controllers is shown in Fig. 6. From visual inspection of the figure, it is evident that the effort required to cancel the wave disturbance is maximum in near-rated winds and decreases in high winds. If the FF controller obtained from the 16 m/s model is used at any wind speed, the FF action would be less-than-ideal for wind speeds between rated and 16 m/s, and higher-than-ideal for greater wind 255 speeds, leading to a decreased performance as highlighted by the disturbance rejection analysis of Fig. 5. as the scheduling variable. The gain-scheduling law is obtained fitting a quadratic function to the DC-gain of the K ff (jω) computed for different above-rated winds. The scheduled FF controller is where p 2 , p 1 , p 0 are the coefficients of the quadratic best-fit function, β is collective-pitch, and K ff (U ) is the FF controller for 16 m/s wind speed.

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In Fig. 6, the scheduled FF controllers K ff (β) = c ff (β)K ff (U ) are compared to the model-inversion FF controllers obtained from the evaluation of Eq. (13) for different above-rated wind speeds. The scheduled controller is a good approximation of the ideal case. The proposed scheduling strategy leaves the phase of K ff (jω) unchanged, but this is acceptable since the phase does not change much with wind speed. The disturbance rejection function of the FBFF controller with scheduling is obtained by replacing K ff (U ) with K ff (β) in 270 Eq. (15) and Eq. (17) and it is shown in Fig. 7. The disturbance rejection in the wave frequency range is lower for any wind speed, as the controller action is adjusted based on the wind turbine operating condition.
The FF controller for implementation is obtained as in Eq. (18). The order of the transfer function K ff (U ) is too high for practical usage: a reduced-order approximation is utilized in place of the original transfer function. The low-pass filtered collective-pitch angle measurement is used for scheduling.

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6 Wave measurement and prediction The transfer function of the FF controller has an intrinsic delay of t d . A suitable wave elevation measurement is required to compensate the intrinsic delay of the FF controller: it is required to know the wave t d before it arrives at the platform. The wave prediction is obtained from a measurement of the surface elevation in a point at a distance l upstream the platform. The measurement is propagated downstream in space and forward in time. The wave elevation in two points along the wave propagation direction is related by the frequency response function where k is the wave number, and, for gravity waves on deep-water, k ≈ ω 2 /g.
The frequency response function that relates the upstream wave measurement to the wave prediction at the FOWT is For a given distance l and a preview time of t d , H(jω) behaves as a pure negative-delay operator only for ω > gt d /l = ω t .
The wave spectral components with a frequency greater than ω t are successfully predicted. Prediction of the wave components with a lower frequency is not possible, because the wave arrives at the platform location in a time lower than the preview time t d . It is possible to predict the lower-frequency harmonics by measuring the wave elevation far upstream the FOWT or by decreasing the preview time.  Several technologies are available to measure the surface elevation. Some examples are wave-rider buoy, radar, airborne or satellite. The radar technology is particularly attractive because it scans a large area, it detects waves far from its location (up to 4 km) and it is capable of fully autonomous operation. The X-band radar, commonly used by ships for navigation, received a lot of attention as a remote wave sensor. Images of the wave field are obtained from the radar as radar beams are reflected and 300 shadowed by the crests of the wave fronts. An example of this technology is the wave monitoring system WaMoS II presented in Ziemer and Dittmer (1994) and at the base of the real-time wave-prediction system developed within the On board Wave and Motion Estimator (OWME) Reichert et al. (2010). In Naaijen and Wijaya (2014) a methodology based on 2D-FFT is proposed to obtain a directional phase-resolved prediction of the wave elevation from radar data (additional information about the directional energy spectrum is required, e.g. from a wave buoy). A similar measurement could be used in wave-FF control.

Results
The wave-FF control strategy is evaluated by means of numerical simulations in the servo-aero-hydro-elastic code FAST Jonkman and Marshall (2005). The FAST model has 7 DOFs: platform motions (surge, sway, heave, roll, pitch and yaw) and the rotor rotation. The drivetrain is rigid as well as the tower and blades. The hydrodynamic model is based on linear potential flow theory with viscous effects. The radiation and the first-order wave forces are computed prior to the simulation based on 310 the same WAMIT data that are used to build the control-design model. The calculation of the frequency-dependent radiation loads is based on the convolution integral of the retardation functions matrix. Second-order wave loads are modeled by means of Newman's approximation Newman (1974).
The wave-FF control strategy considered for the verification is displayed in Fig. 9. Three cases are considered: a baseline case with only FB control, the FBFF control without gain scheduling, and the FBFF control with gain scheduling. In the 315 simulations, an ideal upstream wave measurement is used and the accuracy of the wave measurement system (e.g. radar) is not taken into account. Results are therefore indicative of the upper performance limit of wave-FF control.

Thrust force ( , )
Collective pitch action Turbulent wind Upstream wave measurement Wave at wind turbine Preview time Figure 9. Schematics of the wave-feedforward control strategy. Wave excite the floating platform and generate a varying apparent wind speed for the rotor. The oscillating wind results into rotor speed fluctuations which are only partially rejected by the standard feedback controller.
The feedforward action is based on the wave elevation measured upstream the wind turbine. This measurement is used to obtain a preview of the wave elevation at the floating platform, which is the input of the controller. The resulting collective-pitch action, which is summed to the pitch request from the feedback controller, counteracts the wave disturbance, modifying the aerodynamic torque and the rotor thrust force.

The environmental conditions
The floating wind turbine is subjected to three realistic turbulent wind and irregular wave combinations (see table 1), representative of an offshore site with moderate-severity met-ocean conditions. The reference site is part of the Gulf of Maine (North 320 Atlantic ocean), about 25 km southwest of Monhegan Island and 65 km east of Portland, and the mean water depth is 130 m. Three above-rated winds were selected and, for any of them, the wave was defined from the Pierson-Moskowitz spectrum.
The significant-heigh H s and peak-period T p were selected as the most probable combination of values for any assigned wind speed. For wind, a power-law profile with exponent 0.14 is assumed, turbulence is modeled according to the Kaimal spectrum and turbulence intensity is selected for each wind speed based on the IEC-61400, considering a wind turbine of class IC. Wind 325 and waves are aligned to the zero-degree direction. The wave prediction algorithm presented in section 6 is tested in the met-ocean conditions corresponding to the 16 m/s mean wind speed case of table 1. The wave elevation is sampled every 0.1 s at distance of 200 m upstream the FOWT. The wave elevation at platform location is computed based on the last 1000 samples and a preview time of 7.5 s is requested. The wave elevation preview is compared to the wave at platform in Fig. 10. The overall quality of the estimate is good. The PSD of the two signals reveals that the largest error is introduced in the low-frequency harmonics. The error is due to the intrinsic 335 characteristics of the transfer function on which the wave prediction algorithm is based. For the present case, the transfer functions correctly predicts the wave harmonics above a threshold frequency of 0.058 Hz.

Steady wind
The effect of the FF control strategy is first demonstrated considering a steady wind without shear. With this assumption, the wave is the only disturbance acting on the FOWT. Sample time series of the rotor speed and blade pitch command for a 22 340 m/s wind speed case are shown in Fig. 11. The amplitude of rotor speed oscillations caused by the wave disturbance is reduced with FBFF control with respect to the FB case, and this is achieved at the expense of an increased pitch activity. The pitch effort required by the scheduled FBFF is less than without scheduling for a comparable disturbance rejection performance.

Turbulent wind
The FBFF control is evaluated in more realistic power production conditions.

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Sample time series of rotor speed and blade pitch angle for the 22 m/s case are shown in Fig. 12. As visible looking at the FB case, the largest fraction of rotor speed oscillations is set by wind turbulence. This is in agreement with the MIMO disturbance  analysis of section 4. The FF control reduces the part of rotor speed oscillations caused by waves, but it does not compensate for the effect of wind turbulence. The pitch actuation is increased with any FBFF compared to the FB case.
The power spectral density (PSD) of the rotor speed and pitch-angle-command time series of Fig. 12 is shown in Fig. 13. The   The FF control is designed to reduce the wave disturbance effect on rotor speed. However, it is expected it affects also the structural loads for the different wind turbine components and the motion of floating platform. The fatigue loads are studied 355 in terms of damage-equivalent loads (DEL), which are calculated by means of Rainflow counting with an equivalent load frequency of 1 Hz and a Whöler exponent of 10 for the steal components (shaft, tower and mooring line) and 3 for the blades.
The DEL percentage variation that is achieved with FBFF compared to FB is computed as where DEL FB and DEL FBFF are the 1 Hz damage equivalent loads for the FB and the FBFF.

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The DEL the FOWT components and the standard deviation of platform motions, rotor speed and blade pitch is examined in Fig. 14 for the three load cases. Only the case of FBFF with scheduling is considered. Reducing rotor speed oscillations also results into a lower fatigue damage for the wind turbine shaft and tower; platform motions are slightly increased and this is reflected into the mooring line loading. Figure 14. The damage equivalent load (DEL) and standard deviation (σ) with FBFF for three above-rated power production conditions. A negative ∆ means a reduction with respect to feedback-only control. LSS stands for low-speed shaft, OoP for out-of-plane, TT for tower-top and TB for tower-base.

Conclusions
This paper investigated a model-inversion feedforward control strategy for the mitigation of wave disturbance in floating offshore wind turbines. A linear control-design model is utilized to carry out an MIMO analysis of the floating wind turbine.
Collective-pitch is more effective than generator torque for rotor speed control in above-rated winds. Above the platform natural frequencies, wave equally affects rotor and platform motions, with a strength comparable to wind speed. Based on 370 linear analysis, a model-inversion feedforward controller is designed for canceling the wave-induced rotor speed (and generator power) oscillations using collective-pitch. The feedforward controller is added to an industry-standard feedback controller. The performance improvement is demonstrated by means of linear analysis. A gain-scheduling algorithm is devised to improve 20 https://doi.org/10.5194/wes-2021-9 Preprint. Discussion started: 1 March 2021 c Author(s) 2021. CC BY 4.0 License. the controller performance by adapting the feedforward action as the wind turbine operating condition changes. The control strategy is finally verified by means of time-domain simulations in a non-linear aero-servo-hydro-elastic model. It is found that 375 feedforward control can reduce the standard deviation of rotor speed up to 2%. It also has a positive side effect on the damageequivalent load of several wind turbine components: the shaft torsion is reduced of 15%, the tower-base fore-aft bending of 5%. Platform motions are however slightly increased and this is reflected into the mooring line loads.
The following suggestions should be considered in future work about wave-based control in floating wind turbines: the proposed feedforward controller is linear and compensates only for first-order wave loads. Recent numerical and 380 experimental studies proved that second-order wave loads have a noticeable effect on the response of the floating wind turbine Roald et al. (2013). Thus, a first research suggestion is to investigate non-linear controllers and to include secondorder hydrodynamics in the controller design; in the control-design model, rotor aerodynamics are modeled based on the quasi-steady theory. Thus, the controller obtained from the model does not account for unsteady aerodynamic effects, which may be significant for the response 385 in the upper wave-frequency range Mancini et al. (2020). It is therefore suggested to develop a control-oriented model of the unsteady rotor aerodynamics and to include it in the control-design model, so to investigate how unsteadiness affects the response of the controlled FOWT.
in the case at hand, the feedforward controller is designed to regulate rotor speed, and the reduction of fatigue loads is obtained as a positive side effect. As it has been shown, a large part of rotor speed oscillations is caused by wind 390 turbulence; the wave disturbance drives platform motions and, consequently, it is cause of increased tower fatigue loads.
It is therefore advisable to use the wave information to control the platform motions and use another controller, that also includes the wind measurement, to reduce rotor speed and power fluctuations; the wave prediction model may find application in several control-related tasks, which are not envisioned here. Waves drive the rigid-body motion of the floating platform, which in turn is likely to have an effect on the wind turbine wake.

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Wave prediction may be included in future floating wind farm control strategies; single-input single-output feedback controllers remain the default choice in floating wind turbines and advanced controllers are still far from reaching commercial projects. Tighter relationships between industry and academia are advisable to promote the adoption of advanced control strategies.
Author contributions. AF and MA developed the wave feedforward control methodology in all its aspects. MB and JWvW supervised the 400 research activity mentoring AF and MA. Finally, AF prepared the manuscript of this article with contribution from all co-authors.
Competing interests. The authors declare that they have no conflict of interest.