Optimization Design and Flight Validation of Pull-Up Control for Air-Deployed UAVs Based on Improved NSGA-II

Round 1

Reviewer 1 Report (Previous Reviewer 1)

Comments and Suggestions for Authors

The revised manuscript shows substantial improvement. The authors have expanded the abstract, clarified the novelty of the controller, added more recent references, corrected terminology, explicitly defined variables, introduced modeling assumptions and limitations, and included detailed simulation and robustness results. Overall, most of your original concerns appear to have been properly addressed, and the technical contribution is now clearer. However, some issues remain.

The justification of parameter values could be better supported by references or sensitivity analysis rather than only “multiple attempts.”

Differences between simulation and test environments are acknowledged, but the consistency of conditions is not fully established.

While robustness tests were expanded, the manuscript should better clarify to what extent flight test results quantitatively match simulation predictions. At present, the results are more qualitative.

Please improve figure annotations and polish the language. 

The majority of the references are conference proceedings and technical reports from Chinese research groups. While these are valid, the paper would benefit from a broader inclusion of international journal articles to give a more global perspective.

I recommend a careful proofreading to address several issues of style, grammar, and typographical errors.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report (Previous Reviewer 4)

Comments and Suggestions for Authors

- For table1, in comments DOC, please also include classical text book as Anderson or Stengel or Cook etc....
- Line 49, in paper, chinese characters have to be fixed, what is this?
- For all classical EOMs, please provide a text book reference, like Anderson, or Cook, or Stengel, some very classical book, and verify that EOMs are correct.
- In Fig3, there are different stages to flight, and this almost always introduces switches between different modes, which also introduces jumps, and discontinuities, in many cases. Justify and show evidence as to how this stage transition and mode switching is not introducing any jumps, and everything is continuous?
- The figures need to be bigger, Fig4 for instance, is very small, make sure the width of the figure, when needed covers the page width as well, as needed in Fig.4
- In line 230 you claim PID but contoller is PI (acting on error, ,ref-output), while the D term is acting only on the q-rate, and that's pure proportional control. Fix this please. The actual structure is you have a PI and P control on two different loops.
- Fig 5 is hard to read, it needs to be landscape, whole page.
- Bigger Fig.9, please, it is hard to read and judge the results.
- Table 5 shows the computational cost, and it is clear that genetic strategy is mostly for offline compute. Can you please comment, based on this compute cost, what is the approximate frequency you can run those in real time or not? I think it is quite clear this is offline, but what I am getting at is, are there any segments, or sub-routines, sub-sections that you can do on-line in real-time, while you do some calculations offline? With those msec time values, can you run this in realtime say at 0.1Hz, or 1Hz, etc... Please comment.
- For table6, how come mean, and minimum are the same calues? This does not make sense. Please rediscuss this again, how is it possible for a distribution to have a mean and min, to be the same? imagine +/-3sigma distribution, how come mean and min, could b the same? This needs to be discussed.
- Give table8 without cutting in 2 pages, provide it as a whole, in 1page.
- The results I received in the comments Doc, is different than what I see in the paper, In the comments DOC I received, Fig2, c, d,f figures are very uncertain and the robustness is very weak, meaning some worst case scenarios are all over the place, and it is not tidy, and you can see the system is not robust, and the results are usually not within a bandwidth, but instead in the paper, Fig.5 does not reflect the same things, and there are some discrepancies. This has to be justified.
- Comment especially for Fig2, in comments documents for a, b,d and f, and there are very unstable behaviours, and you can see the settling is different, steady state is different, the amplifications is different, and way excessive (showing true lack of robustness, and in some cases amplification is almost 50%+, and this is incredibly bad. Please justify this, and comment more. As it stands this needs more work. 
- For Fig.3 in comments DOC, you show the response of the actuator, but please show the TF and the actual dynamics, pole, zero location, time constant etc...
- Response5 is good, thank you.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report (Previous Reviewer 3)

Comments and Suggestions for Authors

The author has addressed the reviewer's concerns and feedbacks.

Author Response

Thank you very much for your recognition!

Reviewer 4 Report (New Reviewer)

Comments and Suggestions for Authors

1. Error on line 49?
2. Lines 43-44 mention near-vertical orientation—specify the deviation range or cite references. What constraints affect the three degrees of freedom?
3. Line 95: Are alternative methods available, or is this the optimal approach?
4. Lines 151-152: If the assumption is accurate, is the study still valid if it proves inaccurate?
5. 155-156 lines: Maximum speed is 7500 r/min, but two instances of 7500 are listed.
6. The drone used in the final experiment differs from the one in the earlier simulations. Does this affect the results?
7. Figure 13.b has unclear annotations.
8. Figure 3 specifies stage 3 conditions as VI > 25 m/s and θ > 5°, but the text description only mentions θ > 5°.
9. In Figure 5, for all three disturbance simulations of parameter conditions, is the number of individuals successfully lifted greater than 20 or equal to zero? The word “successfully” appears to have a space between ‘succes’ and “fully”.
10. Table 2 lists four factors determining pull-up success criteria, which do not correspond with Figure 8.
11. Should the x and y axes be added to Figure 8?
12. Some small figures in Figure 16 lack explanations. Are they unnecessary, or are the figures unused?
13. In the self-pull flight test at line 498, the UAV was released from 350m above ground level. The reason for choosing this height is not stated.
14. The simulation used a release height of 620m, while the flight test used 350m. Does this height discrepancy affect the results?

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report (Previous Reviewer 4)

Comments and Suggestions for Authors

• Adjust Fig 7a and b to be under one another, not side by side, it gives better detail and visibility
• Fig 8 should be page width figure, adjust others as needed too, for better visibility
• Fig 10 too, it looks way too crowded as is, more visible details is better for all viewers
• Fig 12 too
• Fig, 14, why is K saturated beyond certain speed? Please explain this more and justify
• Fig15, g throttle, you need to show the accumulated and clustering in the upper bound, as of now the figure seems that it is getting out of picture, then comes back in. This is saturating and capping at some point, you need to show this. If you need to adjust fig Y-lim to something more than 0.8 like 1.0 or 1.2, this may work too, but clearly show the upper bound and accumulation
• Fig16 c, especially between times 1.8s-4sec, the behaviour on pitch rate-q is extremely oscillatory and almost unacceptable, this is extreme swings, and if you check magnitude is literally from 80, to -30, then to 60, 0, 35, 20 deg etc.... These are extreme pitching swings and in reality this cannot be implemented. It is almost like you are pointing to sky and then pure down, and then up and then pure down. This defeats the whle purpose of steady state error elimination of controller. This has to be improved drastically and still remains an issue. This has to be tuned better, and controller robustness has to be beter.
• Same issue with Fig.16.f, around 5 sec, the jump in a_z is extreme and has to be justified. This is very bizzarre.

Author Response

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Reviewer 4 Report (New Reviewer)

Comments and Suggestions for Authors

1.Provided a comprehensive correction and response to the question I raised earlier.
2.Careful proofreading of grammar is required.
3.Chart optimization is required.

Author Response

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Author Response File: Author Response.docx

Round 3

Reviewer 2 Report (Previous Reviewer 4)

Comments and Suggestions for Authors

Thank you for the comments, and please make sure all thos explanations are also included in the text to make it solid, and easy to read. 

Author Response

Comments 1: [Thank you for the comments, and please make sure all thos explanations are also included in the text to make it solid, and easy to read.]

Response 1: [According to your suggestion, we have added explanations for comments 5 and 8 from the previous round of review comments to the latest manuscript on lines 500 to 502 and 567 to 571, respectively.]

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This manuscript addresses an important problem by proposing a variable-parameter PID controller optimized with an improved NSGA-II algorithm for UAV pull-up after airdrop. However, I feel the paper needs improvement before it can be accepted. The manuscript lacks clear novelty, sufficient model details, justification for algorithm parameters, and quantitative validation to ensure reproducibility and demonstrate improvement over standard NSGA-II.

I recommend major revisions. 

1. Abstract: Dear authors,

I consider that the abstract is technically sound but overly compact.

I suggest clearly articulating the novelty of the proposed controller as well as the specific contributions beyond standard PID tuning or NSGA-II adaptations.

1. Introduction: Dear authors,

L.39–42: The mention of prior control strategies (PID) lacks detail on their limitations.

Please include a more explicit statement of the specific research gap this work addresses. I suggest discussing the limitations of these existing methods in more detail, especially regarding their practical performance in real flight tests.

Suggest distinguishing more clearly between methods designed for takeoff transitions and those applied specifically to airdrop recovery to contextualize the novelty.

While multiple NSGA-II improvements are cited, I consider that the introduction lacks a concise comparative synthesis.

The proposed controller is introduced clearly. However, explain more precisely what “quadratic function variation” refers to.

I recommend expanding the citation list to include more recent and diverse studies

2. System Model and Problem Description: Dear authors,

I consider that it is necessary to present the ground frame to the body frame in Figure 1.

Please explicitly define all variables and symbols used in the equations upon first introduction. I suggest Including a discussion on the assumptions and limitations of the UAV model, especially regarding wind and disturbance effects during airdrop.

Why was a quadratic function chosen for the variation of the PID parameter K?

I was looking for more information on how the initial conditions quantitatively influence controller design. Could this be elaborated or supported with data?

Provide more quantitative details or examples about initial conditions and their impact on controller performance during the pull-up phase.

3. Target Priority and Fuzzy Sorting Based Adaptive NSGA-II: Dear authors,

The integration of fuzzy sorting and target priority appears central to the proposed algorithm, but the explanation lacks clarity on how it specifically supplements or overrides the standard NSGA-II selection mechanism

The section introduces several algorithmic parameters without explaining how these values were chosen. It is not clear how the improved algorithm handles constraints related to UAV dynamics.

4. Simulation Results and Flight Tests: Dear authors,

I consider that the section lacks critical information about the simulation environment and setup.

Although the authors state that their improved algorithm outperforms the standard NSGA-II, no quantitative metrics are presented to support this claim.

The section does not clearly explain whether the parameters and conditions used in the simulations are consistent with those of the flight tests.

While Section 4 presents flight and simulation results, I am certain that the simulations shown in the figures do not clearly demonstrate that the controller effectively ensures UAV stability and safety during the pull-up after airdrop, which is a key focus of the article.

5. Conclusion and Prospect: Dear authors,

I find the conclusions concise and well-structured; however, I recommend a more explicit discussion on the broader implications of the proposed control strategy for UAV deployment across diverse operational environments.

I recommend including a reflection on the current limitations and challenges of the approach.

 

Author Response

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Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

This paper focuses on the optimal design and verification of automatic pull-up control for small low-cost UAVs after airdrop, and the research topic has certain engineering application value. However, after careful review, significant flaws are found in the scientific logic of the research methods, which are insufficient to support the validity of the research conclusions. Therefore, it is considered that this paper is not suitable for publication for the time being. The specific comments are as follows:

 

1. Mismatch between the method for handling nonlinear problems and research objectives

   The paper explicitly identifies the nonlinear problems in the pull-up process of UAVs after airdrop as one of the core research points, but adopts a completely linear model in the aerodynamic modeling. During the pull-up phase after airdrop, the flight state of the UAV (such as altitude, airspeed, angle of attack, etc.) will change drastically, and the longitudinal channel parameters show significant nonlinear characteristics (as mentioned in the paper's reference to the research conclusions of Cheng et al.). However, the linear model cannot accurately capture such complex nonlinear dynamic characteristics. The contradiction between this modeling method and the research objectives leads to the lack of a reliable model foundation for the subsequent controller design and optimization, making it difficult to truly solve the nonlinear control problem.

 

2. Doubts about the scientificity and effectiveness of the optimization method

   The paper uses the NSGA-II algorithm to optimize the control gains to achieve goals such as avoiding stall, controlling maneuvering overload, reducing altitude loss, and not exceeding the maximum speed limit. However, although adjusting the control gains may improve the above indicators to a certain extent, this process does not fully consider key performance parameters of the control system such as stability and overshoot. The optimization results may be coincidental, more like trial and error rather than a systematic scientific design. 

   In fact, the hierarchical design method of "first determining the gains of each feedback loop through PID parameter tuning, then adjusting the outer loop control parameters" can not only ensure the stability of the control system but also optimize various performance indicators in a targeted manner. It is a more scientific and mature control strategy, which can completely achieve the control objectives described in this paper. In contrast, the advantages of the method proposed in the paper are not obvious, and there is no comparative analysis of the performance differences between the two methods, making it difficult to prove its scientificity and superiority.

Author Response

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Reviewer 3 Report

Comments and Suggestions for Authors

The paper proposes a parameter-adaptive PID controller based on indicated airspeed to address the control problem of the automatic pull-up process after airdrop for small low-cost UAVs.

The methodology indicates fundamental fixed-wing UAV flight dynamics, PID control and optimization algorithms.

Could the author clearly explain the optimization strategy and variable parameters?

How does the system ensure dynamic gains for the PID controller?

The pull-up process and stages is assumed to be longitudinally controlled. Has the author considered the atmospheric disturbances during the drop?

Are there any metrics to support the optimization model as applied to the problem solved? 

Some sections, e.g. (43-59) are AI written. 

Grammatical error in line 85

Figure 5 has no axis label. 

Figure 6,8 and 9 are not clearly displayed, explained and analysed.

Figure 13 has not been clearly labelled.

 

Author Response

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Reviewer 4 Report

Comments and Suggestions for Authors

- Can you please provide any classical text book for referencing the EOMs of A/C?
- If you have variable parameter K, what's the purpose of pure gain? Why not make it 1-one passthrough (in Kp) and just use K as tuning param? Have you tried it? Can you comment about the results and outcomes? Because it becomes weighting of a weighting, and it is double penalizing.
- Where is actuator dynamics in your fig.3? Block diagram? How about sensor dynamics? Noise dynamics, those are important missing pieces and need to be included in the analysis as well.
- Do you have any constraints? Actuator constraints? CMD constraints etc... Real-life works under constraints and you will need to consider constrained optimization problem. Please comment on this, it is lacking analysis on this section as well. (I do see Table-1 is provided, but my comment was mostly on actuation, and actuators, and sensor dynamics. This needs to be discussed as well.)
- WRT all sorting algorithms, this is going to be computationally very very expensive, and real-time implementation needs to be discussed. How fast can you run this search? Can you run this at 50Hz? Like classical control, or 100Hz?? If you cannot run how fast? There is no analysis for such discussion.
- One of the most important part of robustness and uncertainty analysis is missing. Everything is uncertain and coupled in real-life, and there is no discussion for any kind of robustness analysis and uncertainty analysis. In presence of uncertainties what happens? Can you guarantee robustness? Can you guarantee stability? This has to be discussed extensively.

Author Response

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