General Comments

Overall, I find this paper to be a very interesting exploration of helical wake improvements using remote sensing measurements. The analysis given is rigorous, with a LiDAR data processing pipeline implemented, and combination of numerous advanced wind turbine control developments such as a helix frame transformation for analyzing the hub position and H-infinity control synthesis.

The analysis provided in this paper is strong. However, there are a few points that could be elaborated/explored further. When analyzing the data in Figure 13, power increases in the downstream wind turbine are highlighted, the “All” section of the bar plot is not mentioned. When looking at this column, there is a 0.4% power increase overall, with an 8-14% increase in blade loads. These load increases relative to the overall power increase are very concerning, and should be addressed in some way to not leave the reader wondering. In addition, no error bars are provided, raising additional concerns since an error margin of >0.4% could be somewhat reasonable.

Overall, there is no inherent problem in Figure 13; rather, there should be more text elaborating the data it is present. This could be done through more body text in the results section, or through more descriptive captions. Throughout the paper, the captions for figures are sparse, leaving a lot of abbreviations and annotations ambiguous. For example, Table 3 does not explicitly define what "WT_i" or “Greedy” mean. The meaning of these terms can be assumed based on context, but adding an additional sentence to the caption could help disambiguate these terms.

The idea of using closed-loop control to improve hub wake positioning in shear and turbulent conditions is compelling, but its actual success in industry seems somewhat dubious when comparing the increase in blade loads with the increase in power production. While it would be outside the scope of this paper to do a complete techno-economic analysis on the net benefit despite increased loads, this downside should be discussed in more detail. Even open-loop helical wake generation increases blade loads due to individual blade pitching at each revolution. Therefore, a modest discussion of why closed-loop helical wake generation should be used with or in the place of other methods such as wake steering would increase the impact of this paper. Such a discussion could be placed right before (5) Conclusion.

The Methods used in this paper are very well presented and thorough. For example, the MBC transform and LiDAR modelling methods were very well established. However, there was a lack of discussion of the Internal Model Identification. It is not established clearly why the authors decided to use system identification instead of an analytical physical derivation, or even gray box modeling of unknown system parameters. A brief elaboration on why this design choice was made would be insightful for the reader.

Also, there could be more discussion on how the nonminimum phase zero is limiting the system performance. It seems like the system bandwidth reduction was chosen due to work done in Skogestad and Postlethwaite (2005). However, it is not made clear where the nonminimum phase zero is coming from (e.g., from actuator limitations, or from the helix generation dynamics themselves). This is a very important point to establish, since the nonminimum phase zero is preventing any improvements in hub vortex tracking in turbulent conditions.

Additionally, in future work, it could be good to include a simulation with more than two wind turbines as a potential goal. It would be interesting to see how the balance between energy savings and blade loads changes when the number of turbines is scaled, potentially strengthening the results of this research. In general, the Future Work section of this report is very sparse, and it could be worth elaborating a sentence for each segment of future work provided. For example, “realistic LiDAR integration” is presented, but how that would impact these results and why that is necessary is not explained clearly. There is no mention of the impact of the LiDAR modeling on the results of the study, so the potential impact of this area of future work is not clear.

Small Suggestions (line number(s) given in parentheses)

• (43) citation issue
• (89) WFFC used but not defined earlier, first appeared on (21)
• (79) consider this capitalization: “(Light Detection And Ranging)
• (79) consider replacing “remote method” with “remote sensing method”
• (~105) it could be beneficial to have a figure here illustrating how a MBC transform goes from a nonrotating to fixed frame, if such a figure exists (it is difficult to conceptualize this when only looking at the equation for the linear transformation)
• (115) equation three has V_∞, but the following line references U_∞
• (183) double check axes labels for Figure 3
• (~225) figure 5 should be placed much higher in the paper. Also, it should be referenced in the text or removed entirely
• (~276) this is a possible run on sentence, and should be reworded
• (297) broken reference
• (325) Equation 16 has a scalar 0.4, but where this scalar comes from is not clearly established
• (356) should be OL₃
• (375) should say "section" instead of "chapter"
• (386) the results of Figure 12 seem to demonstrate worse oscillations compared to open loop operation. Consider adding an explanation for why this is the case
• (~400) Figure 13: the bottom row has vertical grid lines, unlike the top two rows