Robust Fixed-Time Adaptive Fault-Tolerant Control for Dynamic Positioning of Ships with Thruster Faults
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe introduction must be enhanced, require more references.
When male the desing of the model how an assure that does not exists pemature convergence and the model effectivele converge in short time.
Figures require bigger and extensively explanations.
Conclusions are to short. Require possible approaches in other areas and future research about the theme.
Author Response
Dear reviewer,
On behalf of all the contributing authors, I would like to express our sincere appreciation for your constructive comments concerning our article. Your comments are all valuable and very helpful for improving our paper and providing crucial guiding significance to our research. Based on your suggestions, we have made corresponding corrections to our paper. The detailed point-by-point responses are listed below. Changes to the manuscript are highlighted within the document by using red-colored text.
Point 1: The introduction must be enhanced, require more references.
Response 1:
Thanks for your kind suggestion. Based on your suggestion, we have carefully revised the introduction and added relevant literatures.
Point 2: When male the designing of the model how an assure that does not exist mature convergence and the model effective converge in short time.
Response 2:
The fixed-time stability is a mature theory that has been validated. As stated in Lemma 1, there exists a maximum upper bound on the convergence time of fixed-time theory. Although the exact convergence time of fixed-time control is unknown, the upper bound of the convergence time can be determined. Therefore, fixed-time stability has been proven through rigorous mathematical analysis. This article proves through rigorous mathematical derivation that the dynamic positioning error is practical stable within a fixed time. The simulation experiment proved the correctness of the theory.
Point 3: Figures require bigger and extensively explanations.
Response 3:
Thank you for your kind suggestion. According to your suggestions, we give a clearer simulation result diagram and enlarge the key areas in the figures to show the results more clearly.
Reviewer 2 Report
Comments and Suggestions for AuthorsThe article is written in an understandable manner, and it combines scientific methodology with practical insights. It provides a thorough explanation of the proposed control strategy, including mathematical formulations and experimental validation, which contributes significantly to the understanding of the topic. The topic of the article is very interesting and while the manuscript provides valuable insights, there are some aspects that could be improved for greater clarity and completeness:
1. The contribution of this work must be more clearly articulated to provide a concise and compelling explanation of its significance. It is necessary to explain the advancements introduced by the study more thoroughly. Give a short explanation why did you used the presented control technique.
2. More references should be added to improve the understanding of the problem. Add more references in the introduction section to improve the article.
3. Can you include a comparison with multiple existing control methods to strengthen the validation of the proposed FT-AFTC scheme.
4. What are the limitations of the proposed method? Discuss potential real-world implementation challenges and considerations, including hardware constraints and computational requirements.
5. Could you implement at least one additional and more varied simulation scenarios to thoroughly test the robustness of the control scheme?
6. In my opinion, the article would benefit from additional annotations to highlight key findings from the figures. Furthermore, the explanations of the results presented in the figures should be improved.
Author Response
Dear reviewer,
On behalf of all the contributing authors, I would like to express our sincere appreciation for your constructive comments concerning our article. Your comments are all valuable and very helpful for improving our paper and providing crucial guiding significance to our research. Based on your suggestions, we have made extensive corrections to our paper. The detailed point-by-point responses are listed below. Changes to the manuscript are highlighted within the document by using red-colored text.
Point 1: 1. The contribution of this work must be more clearly articulated to provide a concise and compelling explanation of its significance. It is necessary to explain the advancements introduced by the study more thoroughly. Give a short explanation why did you used the presented control technique.
Response 1:
Thanks for your kind suggestion. Based on your suggestion, we have carefully revised the introduction and the following main contributions are added.
(1) By creating a novel integral sliding mode surface, the fixed-time integral sliding mode controller naturally eliminates the singularity issue, overcoming a significant limitation of traditional fixed-time terminal sliding mode control.
(2) By adopting the parameter adaptive control to estimate the square of the upper bound of the total uncertainty, the designed controller is smooth with no obvious chattering phenomenon and does not require any information on the upper bound of the total uncertainty.
(3) The practical fixed-time stability of the closed-loop system is proved. The dynamic positioning errors under the designed controller can regulate to the minor fields about zero within a fixed time even subject to model uncertainties, external disturbances, and actuator faults.
Point 2: More references should be added to improve the understanding of the problem. Add more references in the introduction section to improve the article.
Response 2:
Thanks for your kind suggestion. Based on your suggestion, we have carefully revised the introduction and added relevant literatures.
Point 3: Can you include a comparison with multiple existing control methods to strengthen the validation of the proposed FT-AFTC scheme.
Response 3:
Thank you for your suggestion. Based on your suggestion, we have added an additional nonlinear fault-tolerant control method as a comparative solution. In addition, to further demonstrate the effectiveness and superiority of the proposed approach, two quantitative indicators, IAE and ITAE, are introduced. As shown in Tables 2-5, the results indicate that the proposed FT-AFTC scheme has higher transient and steady-state tracking accuracy.
Point 4: What are the limitations of the proposed method? Discuss potential real-world implementation challenges and considerations, including hardware constraints and computational requirements.
Response 4:
The fixed time control theory has its inherent shortcomings, as it can only obtain an upper bound on the convergence time and cannot obtain an accurate convergence time. In addition, the convergence time of fixed time control theory cannot be set by the user in advance. Therefore, designing a control scheme that allows users to set the convergence time in advance will be the focus of our future work.
Point 5: Could you implement at least one additional and more varied simulation scenarios to thoroughly test the robustness of the control scheme?
Response 5:
This article demonstrates the robustness of the designed controller by adding an actuator fault model. The simulation results show that even in the presence of actuator faults and external disturbances, the proposed controller can still make the positioning error converge within a fixed time. In addition, to quantitatively evaluate the effectiveness and superiority of the algorithm, two performance indicators, IAE and ITAE, were introduced. The results showed that the proposed control scheme has higher transient and steady-state tracking performance.
Point 6: In my opinion, the article would benefit from additional annotations to highlight key findings from the figures. Furthermore, the explanations of the results presented in the figures should be improved.
Response 6:
Thank you for your suggestion. Based on your suggestion, we have improved the simulation image and enlarged key local areas to demonstrate the effectiveness of the proposed control algorithm.
Reviewer 3 Report
Comments and Suggestions for AuthorsThe complexity and unpredictability of the marine environment, the reliability and timeliness of the ship dynamic positioning system is yet a problem to be dealt with a careful attention. Here this problem is solved by means of the motion model of the three-degree-of-freedom dynamic positioning ship and moreover the thruster fault model are established. Then a second-order fast fixed-time nonsingular sliding mode surface is designed and an adaptive control scheme is proposed for external disturbances and uncertainties, thus the authors achieve fast convergence of the system in a fixed time. The paper is fluent, the attention of the reader does not wander and the style is acceptable. The English is correct, particular criticisms were not pointed out as well. The authors are urged to follow the following:
- give the definition of matrix of the nominal model in formula 6
- justify in some manner the usage of the coordinate transformation in formula 16
- statement of theorem 1 is not satisfying. Please enunciate theorem 1 in mathematical sense with hypothesis and thesis.
Author Response
Dear reviewer,
On behalf of all the contributing authors, I would like to express our sincere appreciation for your constructive comments concerning our article Your comments are all valuable and very helpful for improving our paper and providing crucial guiding significance to our research. Based on your suggestions, we have made extensive corrections to our previous draft. The detailed point-by-point responses are listed below. Changes to the manuscript are highlighted within the document by using red-colored text.
Point 1: Give the definition of matrix of the nominal model in formula 6.
Response 1:
We apologize for the unclear description of nominal matrix in the previous manuscript. And we have corrected the writing errors in the paper and defined the nominal matrix in Eq. (4) and Eq. (5).
Point 2: Justify in some manner the usage of the coordinate transformation in formula 16.
Point 3: Statement of theorem 1 is not satisfying. Please enunciate theorem 1 in mathematical sense with hypothesis and thesis.
Response 3:
Theorem 1 in this article is different from the theorem defined from a mathematical analysis perspective, and is more of a summary of the content of the paper. Similar approaches are common in other papers, such as the following paper:
- Li J, Xiang X, Yang S. Robust adaptive neural network control for dynamic positioning of marine vessels with prescribed performance under model uncertainties and input saturation[J]. Neurocomputing, 2022(May 1):484.
- Liang K, Lin X, Chen Y, et al. Robust adaptive neural networks control for dynamic positioning of ships with unknown saturation and time-delay[J]. Applied Ocean Research, 2021, 110(3):102609.DOI:10.1016/j.apor.2021.102609.
Reviewer 4 Report
Comments and Suggestions for AuthorsThe authors have developed a fixed-time adaptive fault-tolerant control (FT-AFTC) approach for dynamically positioning ships under thruster faults, comparing its performance with an Adaptive Boundary Surface and Model Compensation (ABSMC) approach. The methods are comprehensively described, results are clearly presented, and the introduction provides sufficient background supported by relevant references. However, the comparison with the ABSMC approach in the conclusions appears somewhat limited. To strengthen the analysis, it is recommended to include comparisons with other relevant control approaches.
Additionally, Figures 1 to 8 could benefit from a zoomed-in view within the interval of 0-10 or the use of a logarithmic scale to highlight significant differences between the models.
Comments on the Quality of English LanguageN/A
Author Response
Dear reviewer,
On behalf of all the contributing authors, I would like to express our sincere appreciation for your constructive comments concerning our article. Your comments are all valuable and very helpful for improving our paper and providing crucial guiding significance to our research. Based on your suggestions, we have made extensive corrections to our previous draft. The detailed point-by-point responses are listed below. Changes to the manuscript are highlighted within the document by using red-colored text.
Point 1: To strengthen the analysis, it is recommended to include comparisons with other relevant control approaches.
Response 1:
Thank you for your suggestion. Based on your suggestion, we have added an additional nonlinear fault-tolerant control method as a comparative solution. In addition, to further demonstrate the effectiveness and superiority of the proposed approach, two quantitative indicators, IAE and ITAE, are introduced. As shown in Tables 2-5, the results indicate that the proposed FT-AFTC scheme has higher transient and steady-state tracking accuracy.
Point 2: Additionally, Figures 1 to 8 could benefit from a zoomed-in view within the interval of 0-10 or the use of a logarithmic scale to highlight significant differences between the models.
Response 2:
Thank you for your kind suggestion. According to your suggestions, we give a clearer simulation result diagram and enlarge the key areas in the figures to show the results more clearly.
Round 2
Reviewer 4 Report
Comments and Suggestions for AuthorsThe authors have conducted the requested changes accordingly. Therefore, the manuscript is now worthy of being published in its revised version.
