Control design for floating wind turbines

Hegazy, Amr; Naaijen, Peter; van Wingerden, Jan-Willem

doi:https://doi.org/10.5194/wes-2025-68

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https://doi.org/10.5194/wes-2025-68

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30 Apr 2025

| 30 Apr 2025

Status: this preprint is currently under review for the journal WES.

Control design for floating wind turbines

Amr Hegazy, Peter Naaijen, and Jan-Willem van Wingerden

Abstract. While the feedback control of onshore wind turbines is well-established, applying the same controllers to floating offshore wind turbines causes the turbines to become unstable. Such instability is attributed to the coupling between the fore-aft motion and the wind turbine controller, which makes the wind turbine negatively damped. The non-minimum phase zeros existing in the transfer function from the blade pitch to the generator speed impose a fundamental limitation on the closed-loop bandwidth, posing a challenge to the operation of the floating turbines. This paper gives an overview of the control strategies and their tuning techniques employed for floating wind turbines in the presence of the negative damping instability. It discusses the different available strategies. Moreover, we propose a new controller that can alleviate the adverse effects of the negative damping while preserving the standard proportional-integral control structure. Contrary to the multi-inputmulti-output controllers that have been proposed, the proposed controller is more robust since it does not require additional signals of the floating platform, which makes controllers often sensitive to unmodelled dynamics. The controller is compared against the previously proposed controllers using the non-linear simulation tool, OpenFAST. The proposed controller excels in regulating generator speed, surpassing other controllers in performance. Additionally, it effectively mitigates the platform pitch in addition to the tower and blade loads. However, achieving a balance between power quality, actuator usage, and structural loading presents inherent trade-offs that need to be carefully addressed.

Received: 13 Apr 2025 – Discussion started: 30 Apr 2025

Competing interests: At least one of the (co-)authors is a member of the editorial board of Wind Energy Science.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this preprint. The responsibility to include appropriate place names lies with the authors.

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Amr Hegazy, Peter Naaijen, and Jan-Willem van Wingerden

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RC1:
'Comment on wes-2025-68', Anonymous Referee #1, 20 May 2025 reply
General comments
Dear Authors,
I was invited by the Associate Editor to review your article, which I have read carefully. I would like to share my feedback below.
The stabilization of floating wind turbines at above-rated wind speeds, through the development of control strategies that overcome the limitations of conventional approaches used in bottom-fixed turbines, is a classical topic in this research field. The article addresses this issue, offering a discussion of existing strategies and proposing a new control architecture and tuning methodology. Overall, the topic is of interest and relevance to the floating wind turbine control community, and the manuscript deserves consideration for publication. However, several aspects require revision.
In particular, the second part of the article, where the SIMO and MIMO controllers are described and the results presented, is generally written better and it is more coherent than the first part, which introduces the problem, derives the model, and discusses the detuning strategy. Sometimes, the first part is inaccurate and has unclear statements. I strongly recommend a thorough revision of this section, considering the comments below.
Another concern I have is about to the writing style, especially in the first half of the paper. While I cannot verify whether AI tools were used, some sentences seem to be written very well but lack clarity or technical accuracy. I use such tools myself to improve clarity, and they can be helpful when used carefully. However, in your manuscript, a few sentences appear artificial and not precise. I have pointed out some of these under Specific Comments, but I ask you to revise the text thoroughly to ensure that all sentences are meaningful and technically sound.
Lastly, a major issue concerns the tuning of the controllers. Proper tuning is very important when comparing different control architectures, as a poorly tuned controller may perform worse even if its structure is theoretically sound. While the manuscript explains general tuning procedures, it is often unclear how the actual tuning was performed: which gains were used in the simulations, which hyperparameters were fixed to compute the gains, and what rationale was applied? Please provide more details in this regard.

Specific comments
Abstract: "feedback control”: Specify the type, e.g., generator speed or power control.

Abstract: "applying the same … unstable”: Clarify that only the pitch-to-feather scheme typically induces instability; other feedback control strategies exist that maintain stability in floating wind turbines.

Abstract: "fore-aft motion”: Specify this is the nacelle fore-aft motion.

Abstract: "more robust”: Define what is meant by "robustness". Robust to what (e.g., model uncertainties, disturbances)?

Lines 18–19: Remove “this is not … know that” and “no wonder … wind energy”. These are unnecessary and informal.

Lines 20–26: Consider whether this section is necessary. Is the article relevance limited to the EU context?

Lines 37–38: The phrase "while modifications … to reducing the LCOE” is vague. Co-design of turbine and platform may reduce LCOE. Please clarify the mechanism you’re referring to.

Line 80 and following: Including physical units is not necessary. Models can use different units.

Line 87: "and a non-linear function f(x) = 0”. Unclear connection with the surrounding text.

Line 98: Instead of "remains constant … and assumption errors”, state clearly that the control strategy assumes accurate knowledge of kg.

Line 113: "Notice that the terms irrelevant to the control problem”. Please specify which terms are considered irrelevant and why.

Line 131: The definition of above-rated operation is incorrect. Rated wind speed is the minimum at which rated power is produced. All higher wind speeds are above-rated.

Line 133: "The steady-state … generator speed variations”. This appears inaccurate. In above-rated conditions, pitch is increased to limit aerodynamic torque. Clarify.

Line 135: "The objective is to achieve … differential diminishes”. Unclear. Please rephrase for clarity.

Line 138: "capturing the critical dynamics”. Specify what these critical dynamics are. Are you referring to adding platform pitch to drivetrain dynamics? State clearly which degrees of freedom are included and which are not, along with your rationale.

Line 149: "omitting radiation damping … frequency-dependent coefficients”. This choice is questionable. Why are some terms relevant only in certain scenarios? Clarify.

Line 181: "clearly shows … via the term”. Why is this term important?

Line 192: "is of the main interest”. Justify why this is the main interest.

Line 205: "quasi-static … wind speed”. Define quasi-static equilibrium more precisely. What does it mean that system variables are “balanced”?

Line 208: "modifies the force direction”. Unclear. What force? How is the direction modified?

Line 229: “the pitch angle … are negative”. I think you are mixing gradients and steady state values. The derivatives of thrust and aerodynamic torque wrt blade pitch are negative. As the wind speed increases, the blade pitch is drecreased to have constant aerodynamic torque (hence to balance the increase it would have because of wind speed). The increase in blade pitch doesn't yield constant thrust but thrust decreases.

Line 293: "this approach”. Please clarify which approach is being referred to.

Line 299: The explanation regarding gain tuning and stability is not clear. Rephrase.

Line 313: "a range of … xi_c”. Define these parameters explicitly.

Line 321: The effects of omega_c and xi_c on bandwidth and stability are difficult to interpret without definitions. Please clarify.

Line 326: What is omega_p and how does it differ from omega_c? Define all parameters clearly.

Line 336: "regularisation terms”. Briefly explain what regularization is used for in this context.

Lines 371, 377: "blade pitch damping” ???

Line 400: "should this objective … it will be unstable”. Unclear. Explain what the objective is and why instability would result.

Line 463: "It was learnt … band-pass filter”. Why is it feasible to retain the PI controller and what is the role of the band-pass filter?

Line 468: "an inverted notch”. Clarify the purpose of using an inverted notch filter.

Line 519: "to compensate for … aerodynamic damping”. Rephrase for clarity. What is being compensated, and how?

Line 522: "appears to be doing slightly better”. Specify the performance metric used for this comparison.

Line 549: "generator torque actuator”. This is misleading. There is no dedicated actuator. The generator torque is actively regulated.

Line 568: "torque feedback”. If you mean dynamic generator torque control, please state so clearly. It doesn’t appear that feedback from generator torque is used.

Line 580: "wave forces”. Are wave forces used as a control input? If so, how are they measured in practice?

Line 605: "simulation failure”. Generalize this to relate it to operational stability or reliability concerns in real turbines.

Technical corrections
Line 42: Remove “peak to peak”.

Line 80: Remove “(kg.m2)” and similar notations. The dot is not conventionally used.

Line 121: Replace “lie in the vicinity of” with “include”.

Line 122: Replace “there” with “the”.

Line 129: Replace “pitch” with “platform pitch”; replace “full load” with “above-rated wind speed regime”.

Line 272: Remove “a point that is elaborated further in this section”. It’s redundant.

Line 277: Replace “triggered by” with “associated with”; replace “causing” with “causes”.

Line 320: Consider replacing “failure” with “instability” if that’s what you meant.

Line 325: Replace “:” with “,”.

Lines 367–368: Replace “actuators” with “actuation”.

Figure 15: Adjust the line style for β to improve readability.

Figure 15 caption: Explain which transfer function the Bode plot represents.

Figure 16, magnitude: I think one dot is missing. Figure 16, phase: one vertical line is hard to see.

Line 510: Replace “how impressive of a difference” with “the significant impact”.

Line 531: Remove repeated citation. Only cite once unless needed.

Figure 17: Reduce line thickness to avoid covering differences.

Line 547: Replace “dramatic” with “large”.

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Citation: https://doi.org/10.5194/wes-2025-68-RC1
RC2:
'Comment on wes-2025-68', Anonymous Referee #2, 21 May 2025 reply
The paper consists of two parts, where the first part summarizes the state-of-the-art of floating wind turbine control, and the second part elaborates on an extension of existing controllers, as well as the development of a new SIMO controller. The results show that the rotor speed tracking performance, as well as platform motion differs among the controllers with a clear benefit of the more advanced controllers.

The paper provides a good summary of the state-of-the-art, even though there are multiple other papers already providing such summaries. The new controller is interesting, but requires a clearer description of the control structure and design methods.
The following items should be reconsidered:
Clarify the turbine model used (which platform, rating etc)

Clarify the site conditions assumed, i.e. wave height, period, wind shear, TI

Clarify the controller architecture and changes of existing controllers from the literature

Tabulate used controller gains for reproducibility of results

Clarify structure of new SIMO controller, especially why the plant is changed. I expected only K to change, not the plant

Discuss sensitivity to sea state: Often controllers perform well in benign sea states but fail in harsher conditions. It should be proven that the controllers don't amplify first-order wave motions

Improve comparability of the results: Some controllers use a lot of generator torque actuation, while others don't

Further comments in the pdf attached

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Citation: https://doi.org/10.5194/wes-2025-68-RC2
RC3:
'Comment on wes-2025-68', Anonymous Referee #3, 02 Jun 2025 reply
In this WES-2025-68 paper, the authors review a number of methods for controlling floating wind turbines and propose one new single-input multiple-output (SIMO) controller that uses generator speed feedback to both the generator torque and collective blade pitch inputs to the wind turbine. They outline a conversion of the SIMO to a SISO control structure to simplify the controller design. Results show potential advantages, as well as drawbacks, of this SIMO controller.

I have interest in the control of floating wind turbines and recently reviewed the special October 2024 issue of the IEEE Control Systems Magazine (CSM). The authors of this WES-2025-68 indeed cite one of the papers (Stockhouse and Pao, CSM, 2024)¹ in the IEEE CSM special issue. However, the authors of WES-2025-68 do not cite the more major tutorial paper in the CSM special issue (Stockhouse et al., CSM, 2024)². Because of the common first author to both of these IEEE CSM papers, I will refer to (Stockhouse et al., CSM, 2024) as the “main CSM tutorial paper” and the (Stockhouse and Pao, CSM, 2024) paper as the “CSM MIMO paper” for better clarity in this review of WES-2025-68.

The authors of WES-2025-68 refer to their paper as a tutorial, e.g. on page 3, line 65, they state “This paper provides a tutorial on the design of closed-loop controllers for FOWTs …” and indeed they go into some detail in reviewing the various controllers. Given that they cite a different paper in the same special IEEE CSM issue, it is surprising that they don’t cite the main tutorial paper in this CSM special issue. It would be useful for the authors of WES-2025-68 to explain why they believe another (very similar) tutorial paper is needed so soon after the 30-page October 2024 tutorial paper in the IEEE CSM.

Unfortunately, I found the amount of overlap and similarity of WES-2025-68 with both the main CSM tutorial and the CSM MIMO papers quite disturbing. Here are some similarities that seem to go beyond just coincidence:

Figure 1 of WES-2025-68 looks quite similar (even in style) with Figure 3 of the CSM MIMO paper. Of course, I do expect that authors may have similar wind turbine diagrams; and I only noted this particular similarity after having marked many of the other similarities enumerated below.

Figure 3 of WES-2025-68 is quite similar to Figure 2 of the main CSM tutorial paper. The numerical values are not exactly the same, as the floating wind turbines considered are different in the two papers.

The particular architectures reviewed in WES-2025-68, as illustrated in its Figures 4, 9, and 11, are special cases of Figure 2 in the CSM MIMO paper and are also separately discussed in the CSM MIMO paper. A summary discussion is also provided in the main CSM tutorial paper (e.g. Figure S12).

Looking in detail at the text, I continue to find several surprising overlaps that make me quite uncomfortable:

Lines 54 to 59 of Page 2 in WES-2025-68 read: “A multi-loop feedback system evaluation requires a Multi-Input, Multi-Output (MIMO) transfer function representation. Those multi-loop FOWT control strategies in the literature often employ a compartmentalised feedback design, where individual control channels are separately tuned to achieve improved dynamic responses of a specific output. While this segmented tuning methodology remains widespread, inter-loop dynamic coupling inherent in MIMO architectures generates cross-channel interference phenomena, whereby localised parameter adjustment in a single control loop perturbs the closed-loop response characteristics of adjacent feedback channels.”

A similar paragraph in the right-hand column on page 64 (in the special issue) of the previously published 2024 CSM MIMO paper reads: “Many multiloop FOWT control design approaches in the literature use single-loop closure, where each loop is designed in isolation with simplifying assumptions, typically to target improvement of a single-output behavior. For example, the common constant-power control loop is designed to decrease the dependence of generator power variations on generator speed variations, but it also has the side effect of reducing the natural stability of the FOWT system. Tuning each loop in isolation is common practice, although coupling between multiple loops means that tuning of one loop most often induces changes in the behavior targeted by another, and a tradeoff is necessary to satisfy multiple performance objectives.”

Equation (14) of WES-2025-68 is the same as Equation (14) in the main CSM tutorial paper, except the orders of the states and inputs have been changed. Similarly, Table 1 in WES-2025-68 is the same as Table 1 in the main CSM tutorial paper, except with some different symbols and notation used. While control-oriented models may end up being of similar forms, it is quite uncanny how the presentation of the model in WES-2025-68 is also so similar to that in the previously published main CSM tutorial paper.

The discussion and analysis of the condition for non-minimum phase zeros on pages 9-12 of WES-2025-68 are similar to both the main CSM tutorial paper (pages 40-42 of the CSM special issue) and the CSM MIMO paper (page 67, which references the main CSM tutorial paper). All of these analyses are based on previous work, especially that of (Fischer, 2013)³.

The stability margin discussion on pages 14-16 of WES-2025-68 is very similar to the Robust Controller Tuning section in the CSM MIMO paper (page 69). In particular, the contour plots on page 15 of WES-2025-68 are very similar to those in Figures S1 and S2 in the CSM MIMO paper, again with different specific numerical results because different floating wind turbines are considered in these papers.

The authors of WES-2025-68 have added an additional term in their cost function (Equation (24)) to directly address control effort (control saturation), while the authors of the CSM MIMO paper discuss “constraining or regularizing the controller gains in the tuning optimization” to mitigate controller saturation (page 75).

Section 3.3.1 in WES-2025-68 is very similar to the Blade-Pitch Platform Damping section of the CSM MIMO paper (pages 73-74 in the CSM special issue). Given the overlaps that I was noticing, I also looked up the Stockhouse et al., Wind Energy, 2024 paper⁴ (which I will refer to as the WE paper) and note that this Section 3.3.1 of WES-2025-68 has similar ideas as Section 3.1.2 in the WE paper. In particular, the idea of tuning the “strength” of k_{beta} via a xi_{beta} parameter that varies from 0 to 1 already appeared in the WE paper with the alpha_{beta} parameter in Equation (18) in the WE paper. While perhaps the authors of WES-2025-68 are meaning to review this MISO control structure from past papers, they do not cite either the CSM MIMO paper or the WE paper in Section 3.3.1 in WES-2025-68. They do cite (Jonkman, 2008; van der Veen et al., 2012) early in Section 3.3.1, but the tunable “strength” of k_{beta} does not appear in either of these much earlier papers.

Similarly, Section 3.3.2 in WES-2025-68 is very similar to the Parallel Compensation section of the CSM MIMO paper (pages 74-75), including the tunable xi_{tau_g} parameter (which is alpha_{comp} in the CSM MIMO paper and alpha_{tau} in the WE paper).

Lines 573-577 on page 30 of WES-2025-68 state: “Based on these findings, the authors recommend an adaptive approach, where different proposed controllers are alternated depending on environmental conditions and control objectives. For example, at certain times, the turbine operator may prioritise minimising generator speed oscillations and activate the corresponding controller. At other times, the focus may shift to reducing structural loading, necessitating a different control strategy. Since no single controller can simultaneously optimise all objectives—some of which may be conflicting—dynamic selection based on operational priorities is advised.”

The conclusion of the CSM MIMO paper (page 79) states: “Four multiloop FOWT-control approaches have been analyzed and compared to a stable single-loop baseline controller. The simulation performance of these controllers shows the tradeoffs in designing a multiloop controller. Wind energy producers must balance instantaneous power-regulation demanded by grid operators while ensuring operational safety and component longevity for the lifetime of a wind farm. Multiloop control designs can schedule the usage and combination of multiple control loops at different points of the operating region to garner performance benefits, while mitigating drawbacks of each control strategy. The control approaches taken in this work are intended to serve as a basis for the intuitive understanding of the impact of structured multiloop control on FOWT system dynamics.”

Section 3.3.3 may be the key section that appears to be new in WES-2025-68, and is based on the authors’ earlier 2023 IFAC World Congress paper⁵. So a question is whether such a full-length paper is warranted for the contribution in Section 3.3.3, and perhaps the addition of a control effort term to the objective function used in the optimization.

While I do realize that accessing the IEEE Control Systems Magazine requires a subscription or membership in the IEEE Control Systems Society, whereas the Wind Energy Science journal is an open-access journal, many major universities with multiple engineering departments have institutional subscriptions to IEEE Xplore that include the IEEE Control Systems Magazine. Further, many control systems researchers are indeed members of the IEEE Control Systems Society. A question is then: what are the rules for overlapping material and ideas with already-published papers, possibly in journals that require a subscription? Do the above similarities give others pause, or am I an outlier in finding this amount of overlap disturbing? My own opinion is that newly submitted manuscripts should not have substantial overlap with previously published papers, regardless of whether they are open-access or not.

I spent quite some time on this review, but really wanted to be as careful as possible in forming this opinion before writing all of this up. I found that the October 2024 IEEE CSM special issue is largely based on a special so-called “tutorial session” at the 2023 American Control Conference (ACC), and earlier versions of both the CSM MIMO and main CSM tutorial papers were published at the 2023 ACC (and also available via IEEE Xplore), so many of these ideas were already published in 2023.

¹ CSM MIMO paper: Stockhouse, D. and Pao, L. Y.: Multiloop Control of Floating Wind Turbines: Tradeoffs in performance and stability, IEEE Control Systems Magazine, 44, 63–80, https://doi.org/10.1109/MCS.2024.3432340, 2024.

² main CSM tutorial paper: Stockhouse, D., Phadnis, M., Henry, A., Abbas, N. J., Sinner, M., Pusch, M., and Pao, L. Y.: A Tutorial on the Control of Floating Offshore Wind Turbines: Stability Challenges and Opportunities for Power Capture, IEEE Control Systems Magazine, 44, 28–57, https://doi.org/10.1109/MCS.2024.3433208, 2024.

³ Fischer, B.: “Reducing rotor speed variations of floating wind turbines by compensation of non-minimum phase zeros,” IET Renewable Power Gen- er., vol. 7, no. 4, pp. 413–419, 2013, doi: 10.1049/iet-rpg.2012.0263.

⁴ WE paper: Stockhouse, D., Pusch, M., Damiani, R., Sirnivas, S., and Pao, L.: Robust multi-loop control of a floating wind turbine, Wind Energy, 27, 1205–1228, https://doi.org/https://doi.org/10.1002/we.2864, 2024.

⁵ Hegazy, A., Naaijen, P., and van Wingerden, J. W.: A novel control architecture for floating offshore wind turbines, IFAC 22nd World Congress, 2023.

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Citation: https://doi.org/10.5194/wes-2025-68-RC3

Amr Hegazy, Peter Naaijen, and Jan-Willem van Wingerden

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Short summary

Floating wind turbines face stability issues when traditional onshore control methods are used, due to their motion at sea. This research reviews existing control strategies and introduces a new controller that improves stability without needing extra sensors. Simulations show it outperforms others in maintaining performance and reducing structural stress. The study highlights key trade-offs and the need for smarter, tailored control in offshore wind energy.


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