Floating wind turbines rely on feedback-only control strategies to mitigate the negative effects of wave excitation. Improved power generation and lower fatigue loads can be achieved by including information about incoming waves in the turbine controller. In this paper, a wave-feedforward control strategy is developed and implemented in a 10 MW floating wind turbine. A linear model of the floating wind turbine is established and utilized to understand how wave excitation affects rotor speed and so power, as well as to show that collective pitch is suitable for reducing the effects of wave excitation. A feedforward controller is designed based on the inversion of the linear model, and a gain-scheduling algorithm is proposed to adapt the feedforward action as wind speed changes. The performance of the novel wave-feedforward controller is examined first by means of linear analysis and then with non-linear time-domain simulations in FAST. This paper proves that including some information about incoming waves in the turbine controller can play a crucial role in improving power quality and the turbine fatigue life. In particular, the proposed wave-feedforward control strategy achieves this goal complementing the industry-standard feedback pitch controller. Together with the wave-feedforward control strategy, this paper provides some insights about the response of floating wind turbines to collective-pitch control and waves, which could be useful in future control-design studies.

Floating offshore wind turbines (FOWTs) are currently operated without any real-time information about ocean conditions. Industry-standard controllers are feedback (FB) only: the wind turbine controller reacts to the external disturbance of wind and waves as this occurs. One possibility for improving the current floating wind technology is to include real-time information about the marine environment in the turbine controller and to design new control logics based on that.

Concerning wind turbulence, feedforward (FF) control has recently drawn the attention of the research community, as it can effectively reduce fatigue loads and improve power production. Research has been mainly driven by improvements in the lidar (light detection and ranging) technology that enables measurement of the wind field upstream of the wind turbine.
One of the first studies about lidar-assisted control was carried out by

Wave disturbance is responsible for a considerable fraction of dynamic excitation experienced by an FOWT.
This was first shown in the work of

Applying the same idea behind wind-FF control to waves is therefore an attractive perspective, but the idea is largely unexplored.

The present paper further develops the concept of wave FF exploiting tools of model-based control. The wave-FF control strategy is enabled by an integrated model of the FOWT that captures its most relevant physics. Hence, this work proves the effectiveness of multidisciplinary analysis as a means to advance the current floating wind technology.

All the reasoning is made with reference to a floating wind turbine, but it is deemed valid for any FOWT. The floating wind turbine of reference is based on an open-source concept and is defined in Sect. 2. The idea is to use tools of multivariable systems control to gain insight about the effects of waves on the FOWT response and assess which is the best control input (generator torque or collective pitch) to mitigate them. Then, this knowledge is leveraged to design a feedforward controller that reduces power fluctuations caused by waves. A control-oriented linear model of the FOWT is required first for the multivariable analysis and later for the synthesis of the feedforward controller. The control-oriented linear model is briefly introduced in Sect. 3. Section 4 deals with the input–output analysis. The feedforward controller is designed in Sect. 5. Again, linear analysis is utilized to assess the controller performance, which is shown to be highly dependent on the wind turbine operating point. Hence, a gain-scheduling law is introduced to have the maximum performance in any wind condition. The wave-feedforward controller requires as input a preview of the incoming waves, which is obtained based on the algorithm presented in Sect. 6. In Sect. 7, the feedforward controller and the wave prediction algorithm are implemented in a non-linear, medium-fidelity 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.

This section defines the floating system that is considered in this study.
The FOWT is formed by the DTU 10 MW

The floating 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

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.
Rotor speed is regulated to its rated value

The wave-FF control strategy we want to develop is model-based, 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 description is reported in the article of

The structural dynamics builds on the theory of multibody systems. The model considers the FOWT components 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 the coupled rotor–platform response induced by waves more than the dynamics of the flexible components.

Rotor aerodynamics are introduced into 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 FOWT global dynamics is determined by the integral rotor loads, rather than by the loads of the single blades.
This assumption is reasonable for a reduced-order model of the FOWT, as noticed by

Hydrodynamic radiation and first-order wave forces are modeled by means of linear-time-invariant parametric models.

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 by

Also the first-order wave excitation is introduced into the model with a parametric model in state-space form, which connects the wave elevation to the wave forces.
This choice allows having the wave elevation, rather than wave forces, as input to the model.
The wave excitation model is obtained based on the wave-force coefficients, which are usually computed at discrete frequencies through a panel code (e.g.,

An input–output analysis is carried out to gain insight into the FOWT response to the available controls, generator torque and collective pitch, and the wave disturbance. The analysis answers the question of which is the best combination of controls to reject the negative effects of waves. This information is used later to support the synthesis of the wave-FF control strategy. Moreover, the analysis gives a picture of the FOWT dynamics that may prove to be also useful for other purposes.

The analysis starts from the control-design model in a transfer function representation:

To facilitate the interpretation of input–output analysis results, the model of Eq. (

The model without disturbances

The steady-state (i.e., zero-frequency) plant model of the FOWT in a 16 m/s wind is

The SVD of the plant model

Singular value decomposition of the floating wind turbine plant for several above-rated operating points (grey, arrows for increasing wind), and for the 16 m/s wind case (black). Values for the zero-frequency case are displayed by the marks

In summary, collective pitch is the most effective control in above-rated winds. It has an effect on both rotor speed and tower-top motion. In the frequency range where the wave is active, collective pitch becomes less effective, so it is harder to control the wind turbine.

The wind and waves disturbances are here considered separately.
The direction of a disturbance is

The effect of wind and wave disturbance in the frequency range up to 0.3 Hz is assessed in Fig.

The direction with respect to the rotor speed output direction, the singular value (gain), and the disturbance condition number (DCN) associated with wind and waves. Grey lines correspond to the above-rated operating points (arrows for increasing wind), and the black line corresponds to the one of 16 m/s wind speed. The vertical dashed lines are the frequency of the platform surge and pitch modes; the frequency range where waves are active is enclosed by the vertical dotted lines.

To sum up, waves effect rotor speed because waves drive the platform motion which result in an apparent wind speed at the rotor. The wave excitation is stronger at the platform frequencies, where the FOWT is excited in resonance, and above the platform pitch frequency.
Moreover, it is quite hard to counteract the wave disturbance by means of controls available in the wind turbine.

The wave-FF controller cancels the oscillations of rotor speed and hence of the turbine power output that are caused by waves. The additional collective-pitch command it produces is summed to the pitch signal of the existing generator-speed FB controller and counteracts the variation in aerodynamic torque caused by the platform motion induced by waves.
The FBFF control strategy is shown in Fig.

Block diagram of the feedback–feedforward controller.

For wave disturbance rejection, the reference signal

The FF controller transfer function obtained from Eq. (

The feedforward controller transfer function

The control-synthesis procedure described above is valid for any platform typology.
When a different platform is considered, the disturbance model changes, because forcing produced by waves depends on the platform geometry and the way waves interact with it.
The FF transfer function

Considering the FBFF controller of Fig.

The sensitivity function of the feedback (FB) controller for onshore and offshore tuning and of the feedback–feedforward (FBFF) in 16 m/s wind is compared to the typical PSD of wind and waves (magnitude has been rescaled to ease the comparison with sensitivity functions). The vertical dashed lines are the frequency of the platform surge and pitch modes; the dotted lines mark the bandwidth of the FB controller with onshore and offshore gains.

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

Disturbance rejection function of the feedback–feedforward controller in above-rated winds. The feedback controller (FB) in 16 m/s wind is reported for comparison. The vertical dashed lines are the frequency of the platform surge and pitch modes, whereas the frequency range where waves are active is enclosed by the vertical dotted lines.

The FOWT dynamics (i.e., the response for a given input) depends on the mean wind speed. The turbine is more sensitive to variations in blade-pitch angle in high winds, and this is visualized in the input–output analysis of Fig.

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. (

The scheduled feedforward controllers

Figure

In Fig.

The disturbance rejection function of the FBFF controller with scheduling is obtained by replacing

Disturbance rejection of the FBFF controller with (black) and without (grey) scheduling, for several above-rated operating conditions. The vertical dashed lines are the frequency of the platform surge and pitch modes; the frequency range where waves are active is enclosed by the vertical dotted lines.

The FF controller for implementation is obtained as in Eq. (

The transfer function of the FF controller has an intrinsic delay of

The wave elevation at two points along the wave propagation direction is related by the frequency response function:

For a given distance

For real-time control purposes, the wave prediction model of Eq. (

Scheme of the wave prediction algorithm.

Several technologies are available to measure the surface elevation.
Some examples are wave-rider buoy, radar, or airborne or satellite technology.
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, has 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 shadowed by the crests of the wave fronts. An example of this technology is the wave monitoring system WaMoS II introduced by

The wave-FF control strategy is evaluated by means of numerical simulations in the servo-aero-hydro-elastic code FAST

The wave-FF control strategy considered for the verification is displayed in Fig.

Schematics of the wave-feedforward control strategy. Waves excite the floating platform and generate a varying apparent wind speed for the rotor. The oscillating wind results in rotor speed fluctuations which are only partially rejected by the standard feedback controller. The feedforward action is based on the wave elevation measured upstream of 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.

Three realistic turbulent wind and irregular wave combinations (see Table

Metocean conditions considered for the verification of the wave-FF control strategy.

The wave prediction algorithm presented in Sect.

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 m/s wind speed case are shown in Fig.

Time series of the rotor speed

The FBFF control is evaluated in more realistic power production conditions. Turbulent wind fields were generated in TurbSim

Sample time series of rotor speed and blade-pitch angle for the 22 m/s case are shown in Fig.

Time series of rotor speed

Power spectral density (PSD) of rotor speed and pitch angle command is computed from the aggregated time series of the six seeds relative to the same operating condition. Results for the 22 m/s case are reported in Fig.

Power spectral density of rotor speed

Wave FF is designed to reduce the effects of wave disturbance and improve rotor speed regulation.
However, it is expected to also affect the structural loads for the turbine components.
Fatigue loads for each operating condition are evaluated in terms of damage-equivalent loads (DELs) computed with MLife

Damage equivalent load (DEL) and standard deviation (

This paper investigated a model-inversion feedforward control strategy for mitigation of wave excitation 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 controlling rotor speed in above-rated winds. Above the platform natural frequencies, wave equally affects rotor and platform motions, with the same strength of wind turbulence. Based on 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, and the performance improvement is demonstrated by means of linear analysis. A gain-scheduling algorithm is devised to improve 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 feedforward control can reduce the standard deviation of rotor speed by up to 2 %. It also has a positive side effect on the fatigue loads of several wind turbine components: the shaft torsion is reduced by up to 16 % and the tower-base fore-aft bending by up to 5 %. Platform motions are slightly increased, and this is reflected in the mooring line loads. The blade-pitch actuator usage is increased. Wave-FF control improves the dynamic response of the floating turbine without requiring the replacement of the industry-standard feedback controller. A wave measurement and forecast system must be implemented, but this is feasible to obtain with technologies already used in the maritime industry. The extra cost of the wave measurement system and fatigue of the blade-pitch actuators are likely to be offset by the lower cost of the turbine generator and tower, which can be redesigned in light of the reduced overspeed and fatigue loads respectively.

The following suggestions should be considered in future work about wave-based and wave-feedforward control in floating wind turbines:

The wave-feedforward controller is sensitive to the accuracy of wave elevation prediction and to the fidelity of the wave-disturbance model. The focus of this work is about development of the wave-feedforward control strategy and did not address the topic of uncertainties.
In the present work, uncertainties in the wave measurement are only due to the preview algorithm and, as it is shown, the prediction error is small. Larger errors are expected when using a realistic measurement of upstream waves.
Model uncertainties are mostly related to identification of the wave-excitation model. The model we consider here has been assessed against a medium-fidelity model in a previous work

The proposed feedforward controller is linear and compensates only for first-order wave loads. Recent numerical and experimental studies, for example the one of

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 in the upper wave frequency range

In the case at hand, the feedforward controller is designed to regulate rotor speed, and the reduction in tower loads is obtained as a positive side effect. A large fraction of tower loads is caused by waves, so it is advisable to use wave information to reduce tower fatigue loads.

The wave prediction model may find application in several control-related tasks that are not envisioned here. Waves drive the rigid-body motion of the floating turbine, and this is likely to affect the turbine wake

Single-input single-output feedback controllers remain the default choice in floating wind turbines, and advanced controllers are still far from being used in commercial projects. Tighter relationships between industry and academia are advisable to promote the adoption of advanced control strategies.

MATLAB codes and simulation results of this article can be obtained by contacting the authors.

AF and MA developed the wave-feedforward control methodology in all its aspects. MB and JWvW supervised the research activity, mentoring AF and MA. Finally, AF prepared the manuscript of this article with contributions from all co-authors.

The authors declare that they have no conflict of interest.

This paper was edited by Amir R. Nejad and reviewed by Farid Khazaeli Moghadam and one anonymous referee.