the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 21 Nov 2025
Wind speed estimation using second-order sliding-mode observers: simulation and experimental validation on a floating offshore wind turbine
Abstract. Wind speed estimation is crucial for the control and performance optimization of floating offshore wind turbines (FOWTs). This paper introduces a robust estimation framework based on second-order sliding-mode observers (SOSMOs), developed in both constant-gain and adaptive versions. The observers are developed using a reduced-order dynamic model and validated in the OpenFAST simulation environment when all degrees of freedom are activated. Their performances are compared with the continuous-discrete extended Kalman filter (CD-EKF) used in the reference open-source controller (ROSCO). The proposed approach is assessed under stochastic wind/wave conditions through OpenFAST simulations and further validated experimentally using a scaled software-in-the-loop (SIL) setup. Simulation results indicate that the proposed observers perform comparably to the CD-EKF in terms of estimation accuracy, while offering robustness, simpler implementation, and reduced computational complexity.
- Preprint
(4513 KB) - Metadata XML
- BibTeX
- EndNote
Status: open (until 19 Dec 2025)
- RC1: 'Comment on wes-2025-206', Anonymous Referee #1, 03 Dec 2025 reply
-
RC2: 'Comment on wes-2025-206', Anonymous Referee #2, 09 Dec 2025
reply
*General comments*
The article is overall well-written and structured. It is commendable to have a theoretical study of the observer as well as an experimental evaluation. Addressing the three turbine operational regimes is also of interest. A few elements could be improved and a few parts would benefit from more details as suggested below. In particular, more details on the tuning of the observers would be welcome so that the community can more easily reproduce and compare results. The prospect of connecting the observers with a control strategy in the future is interesting and would nicely complement this work.
*Specific comments*
- Throughout the document, "wind speed" is mentioned as-is when it is (most likely) free-wind speed (a.k.a. free-flow wind speed) that the authors want to estimate. Given that turbines have an induction zone with altered wind properties, it should be specified in the introduction (and abstract, possibly title too) that this study addresses *free* wind throughout.
- line 43: motion not only distorts the lines of sight but also the apparent wind speed because of the lidar translation.
- 90: specify motivation for proposing a 2nd-order observer instead of first-order one.
- 142: specify that omega is replaced by lambda and its expression from (4).
- 179: delta(t) having no influence on observability: is it a strong assumption? Can its validity be checked somehow? Consider elaborating on this.
- 186: lambda is now lambda(omega,v), consider aligning and stabilizing your notation across equations.
- 188-189: consider reformulating or correcting the first sentence.
- 197-198: several steps are skipped from "det(...) not equal to 0" to "partial derivative of y-dot wrt v not equal to zero", which may confuse readers. Agree with (15).
- 216: "double integrator": consider introducing this choice with more justification.
- 216: "supertwisting": if that name can help get a better understanding, consider explaining it.
- 221: "Assumptions 1-4": shouldn't this be 1-3 instead?
- 227: Proof of Theorem 1 is central to the theoretical study, yet difficult to understand because too concise in my opinion. It is unclear how the delta(t) term comes back into play to ensure the claimed robustness, especially because this term was set to zero in several steps of the reasoning. It would benefit from further development, perhaps in an appendix.
- Eq. (31)-(32): specify the variables to tune and initialize, along with guidance on selecting appropriate values, so the community can reproduce and compare results.
- 271: it should be mentioned that the simulation result is in zone (III) and that other regimes are covered in the experimental section.
- 276: is there vertical shear in the TurbSim wind? More details on the model fidelity would be appreciated. Same for the hydrodynamic part.
- 307: lower cost: this is supported by metrics given later in 4.2 so this statement comes too early. Consider moving it.
- 311: "under varying wind scenarios": what are these? Only one main scenario appears in 4.1.
- Overall comment on section 4: to capture the inherent stochastic aspect of (simulated) wind and assess sensivitiy to model fidelity, more scenarios would need to be run, possibly using other wind generation models. This would illustrate how SOSMO and ASOSMO compare to CD-EKF and provide a statistical view of the performance. The authors could consider a separate publication focused solely on simulation results to achieve these purposes. Section 4 is valuable but would benefit from more content. More generally, it raises the question of whether Section 4 has an added value and if Section 5 might suffice on its own, thereby freeing space for more details in other sections.
- Section 5: a diagram alongside Fig.10 would help clarify which parts are experimental and which are simulated, especially since the observer is in SIL but also a part of the turbine response is provided through OpenFAST. Additionally, it would be useful to indicate the differences between this setup and one where only the observer is in SIL/HIL (i.e. without the turbine response provided by a model.
- Sections 4-5: clarify why the figures show rotor speed estimations while the observers are described as using rotor speed measurements as input (therefore not requiring estimation).
- 321: thrust generation by the fans and the connection with OpenFAST could be better explained, possibly with a diagram.
- Fig 11: ASOSMO exhibits what appears to be a transient response in [0;50] s. Are performance metrics calculated excluding the transients (for all algorithms)?
- 357-358: while no covariance matrix tuning is necessary, consider adding details on the tuning of the observers for a fair comparison.
- 362-363: "system stability and reduced fatigue loads" is this implicitly about a feedfoward control strategy? Can the proposed estimation strategy provide a prediction of free wind speed in the next seconds?*Technical corrections*
Suggested modifications: (square brackets for insertion, double dash for removal)
- 100: "a software-in-the-loop [setup] located in LHEEA lab"
- 117: "such as Betz's law" > "reported by Betz's law"
- 127: "taking into account -for- blade"
- 134: "control vector [u]"
- 139: "unknown[, which] gives"
- 188: "-It is why- However, the previous"
- 204: "-one- transformation"
- 214: "cannot"
- 249: -phenomenon-
- 254: "large enough"
- Sections 4-5: consider making figures that use the full width of the pages and possibly with increased height.
- 303: "-The- both"
- 306: "the findings -demonstrate- illustrate the efficacy"
- 354: "-validated- evaluated"--
Citation: https://doi.org/10.5194/wes-2025-206-RC2
Viewed
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 152 | 37 | 10 | 199 | 12 | 12 |
- HTML: 152
- PDF: 37
- XML: 10
- Total: 199
- BibTeX: 12
- EndNote: 12
Viewed (geographical distribution)
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
Review of Preprint wes-2025-206.
The paper proposes a novel second order sliding mode observer (SOSMO) for wind estimation on floating off shore wind turbines. Two methods are introduced and compared with the extended Kalman filter (CD-EKF) available in ROSCO. Simulation studies with FAST and Turbsim show that the SOSMO observers can produce wind estimates with smaller RMS error than those from CD-EKF. The results are further validated on a FOWT in laboratory-scale software in the loop experiments. Three wind profiles are considered and in each case the SOSMO observers again achieve smaller RMS errors than CD-EKF.
The paper is clearly written and the motivation is clear. Some comments:
The reference for Lidar (Jena and Rajendran, 2015) is now rather dated. The use of Lidar for WTC has been extensively investigated and was the subject of the IEA Wind Task 32. The authors are recommended to view their publications on the utility of Lidar for turbine control, available from https://zenodo.org/communities/ieawindtask32/about and use these to provide a more contemporary assessment on the utility of Lidar for WTC.
The discussion of computation time is too brief, what does runtime refer to? The computation for the convergence time for each algorithm needs to be shown, to enable comparisons of their suitability for real-time control implementation.
In the SIL experiments, the wind speed error is v - \hat v, but I didn’t see an explanation of how the actual wind speed v was obtained.
The use of rotor speed to estimate wind speed has been investigated for quite some time, see for example the survey in Soltani, et al Estimation of Rotor Effective Wind Speed: A Comparison, TCST 2013 https://doi.org/10.1109/TCST.2013.2260751 Due to their highly stochastic nature, all wind estimates requires low pass filtering before they can be used for control purposes. Indeed, it is clear from Figure 11-13 that all three estimation methods filter the wind. The important question is how well they preserve the portion of the spectrum that is useful for control, and RMS error may not be a good measure for this.
Ultimately, the real test of a wind speed estimate is its utility for WTC, and this aspect of REWs has been extensively investigated in several recent papers, notably Guo, F. et al Evaluation of lidar-assisted wind turbine control under various turbulence characteristics, WES 2023 https://doi.org/10.5194/wes-8-149-2023 and the cited WES paper by Moldenhauer 2025. These papers discussed many features of wind estimation and filtering for their implementation within control methodologies. The wind estimation methods were then combined with novel control methodologies to deliver improved WTC control for turbine fatigue load reduction.
Overall, the study is interesting and well presented, but the contribution is rather limited in scope and insufficient for a strong journal like WES. In its present form, it would be well suited to a conference presentation like WESC or Torque. If the authors wish to extend their work, they may consider combining SOSMO wind estimation with WTC methods (possibly combining it with Lidar) and demonstrating improvements in some aspects of turbine control performance.