| 14 Aug 2026
Fixed Frame Control-Oriented Modeling and Characterization of Asymmetric Wind Disturbances for Advanced Individual Pitch Control Design
Abstract. The development of advanced load reduction strategies is becoming increasingly important for modern wind turbines, making it essential to incorporate both the dynamics and the characteristics of the wind disturbances responsible for structural loading into the control design process. In this context, this work proposes a control-oriented framework that combines the modeling and characterization of asymmetric wind disturbances. Starting from a linearized model with distributed horizontal wind inputs, the inflow is reduced to three equivalent disturbances in a fixed reference frame through a sensitivity-based aggregation of the wind field. The methodology is validated on the IEA 15 MW Reference Wind Turbine, including all relevant aeroelastic degrees of freedom, through turbulent OpenFAST simulations. The results demonstrate accurate reconstruction of open-loop time-domain responses and prediction of closed-loop output spectra, enabling control design to be directly focused on the disturbances to be rejected while reducing the reliance on computationally expensive aeroelastic simulations.
General Comments
This work derives and validates a control-oriented framework for asymmetric wind disturbances, intended for use in IPC controller design. The relevance of the contribution is made very clear, and I personally welcome this line of work, as it could improve the process of IPC controller design when using the MBC transformation. However, in its current form I recommend major revisions before publication in Wind Energy Science for two main reasons. First, the derivation of the methodology is not yet clear enough, which makes it difficult to follow the underlying steps, assumptions, and limitations. Second, I believe the paper would become substantially stronger if the authors applied their own proposed methodology to design the IPC controllers used in the validation. I will elaborate both points below, followed by more specific comments.
The derivation of the method
When trying to reproduce the derivation from Eq. 10 to Eq. 13, I arrive at a different result for Eq. 13, which in the frequency domain results in:
$\delta W_{d}^{eq}(s) = \frac{\sum_{n=1}^{N} G_{y,d}^{n}(s)\,\delta u_{d}^{n}(s)}{\sum_{n=1}^N G_{y,d}^{n}(s)}$
I suspect the authors have assumed $G_{y,d}^{n}(s) = G_{y,d}^{n}(0)$, which indeed results in the same definition of the equivalent disturbance as in Eq. 13. If so, please note that this is not consistent with the definition announced in Eq. 11.
I would like to ask the authors to either correct the derivation or state the underlying assumption explicitly, together with their justification and limitations. Since dynamic amplification can be significant in wind turbine blades, I would be curious to see whether the validation results improve further if the equivalent disturbance were computed without the steady-state assumption. In addition, would it be possible to add a plot similar to Figure 5, comparing the equivalent disturbance with and without this assumption, perhaps for different output weightings as well?
A minor thing about the derivation is the consistency of symbols. Symbols seem to switch between lower and upper case while referring to the same quantity. In addition, I think it would help the reader if a single, consistent symbol were used for quantities related to the wind disturbance (rather than both u and w).
IPC tuning procedure
Having tuned simple IPC controllers myself, I have wondered whether there might be a better way to choose, for example, the crossover frequency, so I am glad to see this contribution. I think the paper would benefit from a section where the proposed method is also applied to IPC controller design. While I think that applying it using quantitative feedback theory or H-infinity would be outside the scope of this paper, and is indeed a nice future work, I do think that showing some loop gains and doing some manual loop shaping using this method would greatly improve the completeness of this work.
This point is reinforced by the fact that the design of the two IPC controllers used for validation is not discussed in the paper. The gains and controller structure are not motivated, whereas the method introduced in this paper would offer a natural way to justify their design.
Minor points
There are a few more minor points that I would like to make.
The authors do not include the azimuth offset in the reverse MBC transformation. While this is by no means mandatory, it does conflict with certain claims made in the text. Without the azimuth offset, the tilt and yaw channels remain coupled, which prevents the use of simple linear control laws, since a MIMO controller would then be required. This seems to conflict with the statement on line 130. Related to this, Fig. 9 shows that IPC1, which gives the strongest attenuation, does not only attenuates the loads, it also shifts the peak of the loads to a different frequency. This is a typical result of omitting the azimuth offset. See for example Fig. 16 in Mulders, Sebastiaan Paul, Atindriyo Kusumo Pamososuryo, Gianmarco Emilio Disario, and Jan Willem van Wingerden, "Analysis and Optimal Individual Pitch Control Decoupling by Inclusion of an Azimuth Offset in the Multiblade Coordinate Transformation," Wind Energy, 2019, https://doi.org/10.1002/we.2289.
I think it would help to add some discussion and motivation around the output weighting of the equivalent disturbance. If I am designing an IPC controller for the out-of-plane loads, for example, why would I use an output weighting based on a different output? Is this simply because a single output weighting is used across all outputs of the plant, which then introduces some inaccuracy? This point is relevant to both section 3.2 and section 4.2.2. Related to this, I would suggest turning Fig. 6 into a frequency-domain plot, similar to Fig. 5, which would give more insight into the differences one might expect between the different output weightings.
Specific Comments
Line 96-97: This could perhaps be phrased more precisely. Could the authors add that the models are averaged in the fixed reference frame to obtain models suited for conventional control design.
Paragraph starting on line 260: Could the authors elaborate what the reader is meant to take away from this result?
Line 305: Is there a particular reason to assess the controllers with both the R^2 and NRMSE measures? If so, could you add those insights to the paper? Are both measures showing the same underlying result and reinforce each other or do we also get additional information by including both?
Line 331: Could the authors add what the expected difference is between these controllers?
Line 349: Is standard deviation the most suitable metric here? Two quite different signals can have the same standard deviation. I do not think this is actually a problem in your case, since Fig. 9 shows good agreement, but would R^2 and/or NRMSE not be a more informative metric than standard deviation?
Line 370: Section 5 could be structured somewhat more clearly, as it currently moves back and forth between contribution and validation between the paragraphs.
Technical corrections
Line 40: Should 'the' be removed?
Line 130: Should 'low-frequency' be 'steady-state'?
Line 158: On first reading, it is not very clear what "the resulting state-space model" refers to.
Line 191: It might be nice to elaborate on "the transfer function" (from what to what).
Line 195: "being G(0)..." could be reformulated to "where G(0)..." to be consistent with the rest of the text.
Line 225: Should "are" be "is"?
Line 259: Should "from" be "using"?
Line 271: "frecuency" -> "frequency".