Combined Robust Control for Quadrotor UAV Using Model Predictive Control and Super-Twisting Algorithm

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

please see the attachment.

Comments for author File: Comments.pdf

Comments on the Quality of English Language

No comments

Author Response

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Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

The article proposes combining the Adaptive Super Twisting Sliding Mode Control with the Super Twisting Sliding Mode Disturbance Observer and the model predictive control to design a robust control strategy for trajectory tracking of a quadrotor subject to disturbances. The authors conducted various simulations, presenting a comparison with the model predictive control. There are many issues that authors should address to improve the quality of the article.

 

1. The main criticism is that this article is an extension of reference [25], which is a work by the same authors. They argue that the only difference is the implementation of STSMDO. The authors should emphasize the paper's contributions and novel insights into the existing literature.
2. Proper references to the quadrotor model, model predictive control, and sliding-modes approach should be added.
3. Please ensure that the variables given in the paragraphs are in math mode.
4. The authors state that a time delay is introduced in the numerical simulations. Nevertheless, the article lacks a mathematical proof that demonstrates that the designed control law can handle these time delays. Indeed, there is no mathematical proof. How can the authors conclude that the designed control strategy is capable of handling the perturbations? How do you ensure that the trajectory will be followed correctly by the quadrotor?
5. Explain in more detail how the linear systems (15)-(16) are obtained. It is unclear how the nonlinear system is converted into a linear system. What happens with parameters such as mass and gravity?
6. Justify why the continuous system is transformed into a discrete one. Which method did the authors use?
7. How is equation (20) obtained? How can this input be related to the system (17) or (18)? Why is \psi_c equal to zero? Does equation (20) have singularities?
8. In line 167, m can be confused with the mass. Review all the variables.
9. It is encouraged that a native English speaker revise the document before submitting it. There are many typos.
10. In equation (33), how is \Delta \hat{U}_{mpc} obtained?
11. Figures 2 and 3 are not explained.
12. Why is the Adaptive Super Twisting Sliding Mode Control obtained without considering the perturbation?
13. In lines 218-220, give the references that support such a statement.
14. In the numerical simulations, the authors have considered an increment of the mass, but this is not reflected in the equations.
15. Tables 2 and 3 are not explained. How were the gains of the controllers adjusted?
16. It is clear that the authors' proposal achieves better quadrotor performance. However, note that the comparison with the MPC is not entirely fair, as they argue, because it is not capable of handling disturbances on its own. Therefore, I encourage the authors to conduct a comparison with a robust method, such as active disturbance rejection control, H-infinity, or backstepping with sliding modes. Here are some references:

doi: 10.1109/TLA.2016.7459596

https://doi.org/10.3390/pr9111951

https://doi.org/10.3390/act13090340

https://doi.org/10.3390/drones6090258

Author Response

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Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

This paper proposes combining Model Predictive Control (MPC) with Adaptive Super Twisting Sliding Mode Control (ASTSMC) and Super Twisting Sliding Mode Disturbance Observer (STSMDO) for quadrotor trajectory tracking. The paper essentially combines existing techniques without significant innovation and misses important recent developments in UAV control, particularly fixed-time control methods and advanced observer designs. Revisions are needed to strengthen the theoretical foundation and experimental validation.

1. The STSMDO design is basic compared to modern neural observer techniques. Guo et al. (2025) showed that neural observers achieve better estimation accuracy and faster convergence for multi-agent systems. The authors should justify why simpler observers are sufficient or adopt advanced designs.

2. UAV control involves competing objectives (tracking vs energy vs robustness), but the paper lacks systematic multi-objective optimization. Game-theoretic approaches like those in Tan et al. (2025) for quadcopter finite-time safe control could better handle these trade-offs. Some comparisons are required.

3. Comparisons with only basic methods (PID, LQR) are insufficient. Recent advanced UAV control techniques should be included.

4. No systematic parameter selection methodology is provided for the numerous tuning parameters.

5. The combination of MPC (which requires solving optimization problems at each time step) with sliding mode control creates significant computational burden. The paper should analyze the computational complexity, and the sampling time and prediction horizon choices should be justified based on computational constraints.

6. The wind disturbance validation uses only the Dryden model with a 2kg mass increase. Real UAV operations face more diverse disturbances including wind gusts, aerodynamic effects, ground effects, and sensor noise. I suggest the authors should test their method against a broader range of disturbance scenarios and compare robustness with other methods under varying uncertainty levels.

7. A step-by-step algorithm summarizing the complete control procedure would improve understanding.

Author Response

Please see the attached file.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

No comments

Reviewer 2 Report

Comments and Suggestions for Authors

I do not have any more questions. The authors addressed all my doubts.

Reviewer 3 Report

Comments and Suggestions for Authors All my comments have been addressed.