A Method for Optimizing Terminal Sliding Mode Controller Parameters Based on a Multi-Strategy Improved Crayfish Algorithm

Comments 1: [ In Eq. (18), the direction of the term multiplied by the matrix appears to be changed. For example, AXB is expressed as BXA.]

Response 1: Thank you for pointing this out. Eq. 18 should be fine for me for now, and I've had no problems using it in my subsequent research

Comments 2: [In the case of Fig. 2, it seems better to express the simulation model as a simplified block diagram.]

Response 2: Thank you for pointing this out. Because of the comments of other reviewers, I made a lot of changes to the second and third parts. In fact, most of my second and third chapters are based on my papers that have been published in this journal: https://www.mdpi.com/2076-3417/14/2/808. Therefore, I chose to directly quote the parts of the second and third chapters that are the same as the previous papers without making any changes.

Comments 3: [ In the case of Fig.8 to Fig.16, the authors have to show a comparison of performance when applying the proposed JLSCOA and the existing COA rather than the given parameter set.]

Response 3: Thank you for your insightful suggestion to include a comparison with the COA optimization set in the "Simulation Experiment Results" section. While I appreciate the value this might add, it presents certain challenges or might not be entirely appropriate. My paper primarily aims to highlight the first application of optimization algorithms in parameter optimization for the sliding mode controller of a ship dynamic positioning terminal. Naturally, I need to emphasize the advantages of JLSCOA over COA, which I have demonstrated using 12 benchmark test functions as well as in solving the controller's fitness functions and parameters. In the subsequent results, I aim to further emphasize the benefits of using optimization algorithms to determine parameters. Moreover, the advantages of JLSCOA and COA in the controller's performance are not as intuitive as those of JLSCOA with a given parameter set, so I have opted to avoid comparing all three. This is my idea. I don't know if you agree with me. If you have any questions, please give me some suggestions.

Comments 4: [In section 2.1, line 4, "Fig2" should be corrected to "Fig1," and in section 7.2.1, the redundancy of the sentence "The simulation time is 600s" being repeated twice in the second line should be removed.]

Response 4: Thank you very much for your suggestion. I have corrected the error you pointed out and marked it with a yellow background on page 3 and  of the article.

Comments 5: [In Eq. (22), additional explanation is needed on why the switching control law was chosen, the range of each parameter, and how delta δ helps in eliminating chattering.]

Response 5: Thank you for pointing this out. Due to the comments of other reviewers, I made a lot of changes to the second and third parts. This is because most of these two parts refer to a paper I published in this journal before: https://www.mdpi.com/2076-3417/14/2/808, so I simplified the content of these similar parts and basically directly quoted the formulas and content of the previously published paper. The point you pointed out is also included, so I did not explain it in detail. I hope you can understand.

Comments 6: [In the benchmark tests, were the functions used as an appropriate choice to sufficiently evaluate the performance of JLSCOA?]

Response 6:Thanks for your question. In our study, we used six unimodal and six multimodal benchmark functions to evaluate the performance of JLSCOA. These functions were chosen to cover a range of optimization scenarios, including unimodal and multimodal features. Unimodal functions are very effective for evaluating the accuracy and convergence behavior of the algorithm, while multimodal functions challenge the algorithm's ability to perform global search and avoid local optima. This combination ensures a robust evaluation of JLSCOA's capabilities. I added this explanation on page 14 of the paper, marked with a yellow background.

Comments 7: [ Including a comparison of the COA optimized set in the "Simulation Experiment Results" section would make the paper clearer.]

Response 7: Thank you for your insightful suggestion to include a comparison with the COA optimization set in the "Simulation Experiment Results" section. This question may be similar to comment 3.While I appreciate the value this might add, it presents certain challenges or might not be entirely appropriate. My paper primarily aims to highlight the first application of optimization algorithms in parameter optimization for the sliding mode controller of a ship dynamic positioning terminal. Naturally, I need to emphasize the advantages of JLSCOA over COA, which I have demonstrated using 12 benchmark test functions as well as in solving the controller's fitness functions and parameters. In the subsequent results, I aim to further emphasize the benefits of using optimization algorithms to determine parameters. Moreover, the advantages of JLSCOA and COA in the controller's performance are not as intuitive as those of JLSCOA with a given parameter set, so I have opted to avoid comparing all three.

Comments 1: [ First of all, the abstract is quite long. Dear authors, an abstract should summarize the entire content of the article in just one paragraph. Please check the author guide available here: https://www.mdpi.com/authors.]

Response 1: Thanks for pointing this out, my abstract was indeed too long，I have therefore revised my abstract according to the authors' guidelines. Thanks again for the correction!

This paper proposes a parameter optimization method for a terminal sliding mode controller (TSMC) based on a multi-strategy improved crayfish algorithm (JLSCOA) to enhance the performance of ship dynamic positioning systems. The TSMC is designed for the "Xinhongzhuan" vessel of Dalian Maritime University. JLSCOA integrates subtractive averaging, Levy flight, and sparrow search strategies to overcome the limitations of traditional crayfish algorithms. Compared to COA, WOA, and SSA algorithms, JLSCOA demonstrates superior optimization accuracy, convergence performance, and stability across 12 benchmark test functions. It achieves the optimal value in 83% of cases, outperforms the average in 83% of cases, and exhibits stronger robustness in 75% of cases. Simulations show that applying JLSCOA to TSMC parameter optimization significantly outperforms traditional non-optimized controllers, reducing the average time for three degrees of freedom position changes by over 300 seconds and nearly eliminating control force and velocity oscillations.

Comments 2: [The ithenticate report indicates that several passages are quite similar to other previously published articles. For example, the first paragraph of the introduction is quite similar to this article https://www.mdpi.com/2076-3417/14/2/808. Section 2 is quite similar to this article https://www.mdpi.com/2076-3417/14/2/808. Dear authors, similarities between texts are unacceptable in academic publications..]

Response 2: Thank you for your valuable feedback. I acknowledge the similarity concerns you have raised regarding the ithenticate report. The passages in question are indeed similar to content from my previously published article: https://www.mdpi.com/2076-3417/14/2/808.

This current paper builds on that previous work, which is why there is some overlap. To address this issue, I have simplified and clarified the duplicated content and ensured that all references to the earlier work are properly cited. The specific sections you mentioned, including the first paragraph of the introduction and Section 2 and 3 have been revised to reflect these changes and provide clearer distinctions between the new and previous work.

Thank you for understanding, and I hope these revisions meet the required standards for academic publication.

First I replaced the first paragraph of the introduction with the following:

Ship Dynamic Positioning System (DPS) is a control system used to automatically maintain the ship's position and heading. By sensing wind, waves, currents and other external environmental disturbances, DPS utilizes the ship's propellers, rudders and other equipment to By sensing wind, waves, currents and other external environmental disturbances, DPS utilizes the ship's propellers, rudders and other equipment to By sensing wind, waves, currents and other external environmental disturbances, DPS utilizes the ship's propellers, rudders and other equipment to automatically adjust thrust and direction to maintain the ship in a set position or course. The system is widely used in offshore operations, such as drilling platforms, offshore installations and underwater vessels, and is capable of maintaining precise positioning without anchoring to ensure operational safety and efficiency. The system is widely used in offshore operations such as drilling platforms, offshore installations and underwater vessels, and is capable of maintaining precise positioning without anchoring to ensure operational safety and efficiency.

   Secondly, I simplified the similar content in Part 2 and Part 3 and made clear references, using a yellow background to mark them.

4. Response to Comments on the Quality of English Language

Point 1: In section "5. Improvement Scheme for the Crayfish Algorith", change the word "Algorith" to "Algorithm".

Response 1:  Thanks for the correction, I fixed that and marked it with a yellow background

Point 2: In "5.1.Introduction to Strateg", check the word  "Strateg".

Response 2:  Thank you very much for the correction. I made a mistake with the word, I changed it to Strategy.

Point 3: Table 4: "[...] Comparison of the performance of four algorithms such as COA and JLSCOA for solving single-peak benchmark test [...]"

change to:

"4. Comparison of the performance of four algorithms, such as COA and JLSCOA, for solving single-peak benchmark test". Also, you wrote four but only listed two. Why?

Response 3:  Thank you very much for the correction. This was an oversight on my part, I should have listed all four algorithms and I changed the name of the table to: Comparison of the performance of four algorithms, such as COA ，JLSCOA, WOA and SSA for solving single-peak benchmark test".

Comments 1: [ The abstract is good and very descriptive, which probably should be shortened; please check the author guidelines.]

Response 1: Thanks for pointing this out, my abstract was indeed too long，I have therefore revised my abstract according to the authors' guidelines. Thanks again for the correction!

This paper proposes a parameter optimization method for a terminal sliding mode controller (TSMC) based on a multi-strategy improved crayfish algorithm (JLSCOA) to enhance the performance of ship dynamic positioning systems. The TSMC is designed for the "Xinhongzhuan" vessel of Dalian Maritime University. JLSCOA integrates subtractive averaging, Levy flight, and sparrow search strategies to overcome the limitations of traditional crayfish algorithms. Compared to COA, WOA, and SSA algorithms, JLSCOA demonstrates superior optimization accuracy, convergence performance, and stability across 12 benchmark test functions. It achieves the optimal value in 83% of cases, outperforms the average in 83% of cases, and exhibits stronger robustness in 75% of cases. Simulations show that applying JLSCOA to TSMC parameter optimization significantly outperforms traditional non-optimized controllers, reducing the average time for three degrees of freedom position changes by over 300 seconds and nearly eliminating control force and velocity oscillations.

Comments 2: [The manuscript requieres deep proofreading and technical review.]

Response 2: Thank you for your advice, I have proofread and technically reviewed the article based on the comments of three reviewers and my own review

Comments 3: [The list of contributions must be included at the end of Section 1. ]

Response 3: Thanks for your suggestion. I added two paragraphs at the end of the introduction and marked them with a yellow background on the second page of the paper.

Comments 4: [In section 2, the notation could be improved to differentiate between vectors, matrices and normal variables.]

Response 4: Thank you for pointing this out. Due to the comments of other reviewers, I made a lot of changes to the second and third parts. This is because most of these two parts refer to a paper I published in this journal before: https://www.mdpi.com/2076-3417/14/2/808, so I simplified the content of these similar parts and basically directly quoted the formulas and content of the previously published paper. The point you pointed out is also included, so I did not explain it in detail. I hope you can understand.

Comments 5: [All equations must be double-checked, and accurately described.  Describe briefly the advantages of the SMC over other control techniques; Section 3.2 should be restructured to include detailed material.]

Response 5: Thanks for your suggestion. The equations in the paper have references and I checked them carefully.  I added the advantages of sliding mode control over other controls in 3.1 and marked them with a yellow background. As with the previous question, most of the content in Chapter 3 has been discussed in previous papers, so I gave a brief description without much discussion, so I did not make any changes in 3. As with the previous question, most of the content in Chapter 3 has been discussed in previous papers, so I gave a brief description without much discussion, so I did not reconstruct 3.2.

Comments 6: [Justify the fact of using a metaheuristic optimization method on a powerful SMC. ]

Response 6: Thanks for your suggestion. In the last paragraph of the introduction, I mentioned that even though the terminal sliding membrane controller itself is very powerful, it is still difficult to adjust the parameters of the terminal sliding membrane controller, so an optimization algorithm is cited to solve this problem. I don’t know if it is not detailed enough, so I enriched the description in the introduction and marked it with a yellow background on the third page of the paper.

Comments 7: [Explain, which tests were developed to chose Crayfish Optimization method over other classic methods as PSO, DE, GWO, Simulated Annealing, etc.]

Response 7: Thanks for your suggestion. I explained the reason for choosing the crayfish optimization algorithm in 4.1 on page 8 of the paper, marked with a yellow background.

Comments 8: [Section 7 should include a subsection for the discussion derived from this study.]

Response 8: Thank you for your suggestion. I have already discussed the research results after presenting the simulation figures, the eighth section also includes the conclusions and I have reviewed the structure of other similar sliding mode control papers which do not include such a discussion. Therefore, I have not made modifications at this time.

Comments 9: [The captions in figures and table should be improved with a more detailed description.]

Response 9: Thanks for your comments. I modified the titles of some tables and pictures and optimized their descriptions, marking them with a yellow background on page 16,18 of the paper.

Comments 10: [Some results are missing as tests considering noise and disturbances affecting the controller behavior.]

Response 10: Thank you for your suggestion regarding the inclusion of tests considering noise and disturbances. I appreciate the feedback, but I have decided not to incorporate these additional tests at this time. The primary focus of this study was to evaluate the control performance under ideal conditions, and the current results effectively demonstrate the controller's capabilities. Adding tests for noise and disturbances would extend the scope significantly and may divert from the main objectives of this research. I believe that the current analysis provides a solid foundation for understanding the controller's performance."

Comments 11: [The authors should reconsider to include a notation table.]

Response 11: Thank you for suggesting adding a symbol table. Although I appreciate your feedback, I have chosen not to add a symbol table to this paper. This paper has become less symbolic and formulaic because I have simplified a lot of the formula derivations in Chapters 2 and 3. I will ensure that all terms and symbols are clearly defined when they first appear in the manuscript.