Application of Disturbance Observer-Based Fast Terminal Sliding Mode Control for Asynchronous Motors in Remote Electrical Conductivity Control of Fertigation Systems

Round 1

Reviewer 1 Report

1.In line 69，“Past research in this domain primarily focused on developing various control methods, such as PID control and SMC, to improve the performance of these systems [20].spite significant advancements, these traditional approaches often fall short in dealing  with the specific challenges posed by the non-linear and dynamic nature of the agricultural environment [21].” What exactly does the specific challenges and the non-linear and dynamic nature of the agricultural environment refer to? 

2.The transition between discussing the challenges in asynchronous motors and the importance of pH and EC parameters is somewhat abrupt. Consider adding a transitional sentence to smoothly connect these two aspects and highlight their interdependence.

3.While the challenges in asynchronous motors and the importance of pH and EC are discussed, a clear problem statement could enhance the introduction. Clearly articulate the gap or challenge that the proposed research aims to address.

4.The objectives of the research are mentioned but could be more clearly stated. Specify what the FTSMC-DO control system aims to achieve and how it addresses the identified challenges in asynchronous motors and nutrient management.

Author Response

Response to reviewer 1

Dear Professor:

Thank you for your careful review of our papers and recognition of our research, and we will learn your attitude towards academics. Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have made serious changes to the questions you have raised. Below, we grouped actions taken in response to your comments, organized under the major headings supplied, and numbered them. We attempted to be succinct while fully explaining our actions. We focus on explaining your problem and we take it seriously and solve the comments of the other reviewers.

Given your patience waiting for our first revision, we wanted to make every effort to return this revision as promptly as possible.  We were able to make this revision our top priority. We have devoted most of our working (and nonworking) days to the revision. As a result, we are able to return the paper earlier than we estimated.

Your and the reviewers’ comments have again stimulated changes we feel further improved the paper.

Best regards,

Huan Wang.

Reviewer#1, Concern # 1: In line 69, “Past research in this domain primarily focused on developing various control methods, such as PID control and SMC, to improve the performance of these systems [20].spite significant advancements, these traditional approaches often fall short in dealing  with the specific challenges posed by the non-linear and dynamic nature of the agricultural environment [21].” What exactly does the specific challenges and the non-linear and dynamic nature of the agricultural environment refer to?

Author response and action: We appreciate the clarification on the specific concern raised by the reviewer. The non-linear and dynamic nature of the agricultural environment, as referred to in the manuscript, pertains specifically to the challenges encountered in remote electrical conductivity control. This includes:

Non-linearity. The relationship between input and output in remote electrical conductivity control is not strictly proportional, given the complexities introduced by factors such as varying moisture levels, soil characteristics, and environmental conditions.

Dynamic Nature. Agricultural environments are subject to continuous changes, including fluctuations in moisture levels, variations in soil properties, and dynamic environmental conditions. These dynamic factors contribute to the challenges faced in maintaining stable electrical conductivity control remotely.

In response to this clarification, we have modified the manuscript to explicitly mention the influence of these factors in creating non-linear and dynamic challenges in remote electrical conductivity control. The revised text aims to offer a more precise understanding of the challenges in the context of the agricultural environment. If there are further suggestions or concerns, please do let us know.(lines 77-86)

Reviewer#1, Concern # 2: The transition between discussing the challenges in asynchronous motors and the importance of pH and EC parameters is somewhat abrupt. Consider adding a transitional sentence to smoothly connect these two aspects and highlight their interdependence.

Author response and action: Thank you for providing your expert insights on our manuscript. We have carefully reviewed your suggestions and implemented modifications to address the identified issues.

We recognized the need for a smoother transition between discussing the challenges associated with asynchronous motors and highlighting the importance of pH and EC parameters. To achieve this, we added a transitional sentence in the revised manuscript (lines 47-58). This addition aims to create a more seamless connection, emphasizing the interdependence of these aspects within the context of agricultural machinery, particularly in fertigation equipment.

Reviewer#1, Concern # 3: While the challenges in asynchronous motors and the importance of pH and EC are discussed, a clear problem statement could enhance the introduction. Clearly articulate the gap or challenge that the proposed research aims to address.

Author response and action: We acknowledged the importance of a clear problem statement in the introduction. In response, we have incorporated a more explicit problem statement at the beginning of the introduction (lines 77-86). This addition articulates the specific gap or challenge that our proposed research aims to address, underscoring the limitations of traditional control methods in handling the non-linear and dynamic nature of remote electrical conductivity control.

Reviewer#1, Concern # 4: The objectives of the research are mentioned but could be more clearly stated. Specify what the FTSMC-DO control system aims to achieve and how it addresses the identified challenges in asynchronous motors and nutrient management.

Author response and action: Thank you for the feedback. We appreciate your thorough examination of our manuscript. In response to your suggestion, we have revised the objectives section to provide a more explicit statement on what the FTSMC-DO control system aims to achieve and how it addresses the identified challenges in asynchronous motors and nutrient management.(lines 97-111)

We hope this clarification aligns more closely with your expectations. If you have any further suggestions or if there are additional areas that require attention, please feel free to let us know. Your insights are invaluable, and we are committed to refining our work based on constructive input.

Author Response File: Author Response.pdf

Reviewer 2 Report

The authors proposed a disturbance observer (EFOSMO) based non-singular fast terminal sliding mode control Asynchronous Motors in Remote Electrical Conductivity Control of Fertigation Systems. However, in the following, the paper has some issues that need to be addressed.

1-      The abstract can be improved by adding some quantitative results. Thus, the main findings should be included in the abstract briefly.

2-      Is this (FTSMC-DO) abbreviation of the disturbance? This is not proper, so it is better to fix all abbreviations along the paper.

3-      The abstract is very wordy and long, it should be rewritten concisely and precisely.

4-      Keywords after Abstract should be improved by considering some abbreviations of concepts.   

5-      Hyperbolic function that is mentioned in the Abstract but is not used in the methodology, I am confused about it.

6-      The Fuzzy Sliding Mode Speed Regulator Design is mentioned in the Abstract and Section 2.4, but the Fuzzification concept does not exist in the paper. This confuses readers.

7-      The visualization of some figures such as Figures 2, 3, 4, and 5, and others.

8-      What are the limitations and difficulties of the investigation of this study?

9-      The estimation performance of the proposed DO is not examined by plotting its estimations.

10-   In the block diagram Figure 5, the ESO estimator does not exist in the paper. In addition, the DO element is not available.  The block diagram should be improved.

11-   Where is the DO? I am confused about it.

12-   The second term in the sliding surface (17) may cause singularity problems, how to avoid singularity issues should be stated.

13-   The stability proof is not completed.

14-   The sliding surface(14)  should be supported by some reference, and why did you select this surface? The sliding surface should be plotted and analyzed.  

15-   There should be some assumptions such as of upper bound of disturbance and bound of reference signals.

The paper quality is very poor due to many theoretical issues. 

Extensive editing of English language required.

Author Response

Response to reviewer 2

Dear Professor:

Thank you for your careful review of our papers and recognition of our research, and we will learn your attitude towards academics. Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have made serious changes to the questions you have raised. Below, we grouped actions taken in response to your comments, organized under the major headings supplied, and numbered them. We attempted to be succinct while fully explaining our actions. We focus on explaining your problem and we take it seriously and solve the comments of the other reviewers.

Given your patience waiting for our first revision, we wanted to make every effort to return this revision as promptly as possible.  We were able to make this revision our top priority. We have devoted most of our working (and nonworking) days to the revision. As a result, we are able to return the paper earlier than we estimated.

Your and the reviewers’ comments have again stimulated changes we feel further improved the paper.

Best regards,

Huan Wang.

Reviewer#2, Concern # 1: The abstract can be improved by adding some quantitative results. Thus, the main findings should be included in the abstract briefly.

Author response and action: We appreciate your suggestion regarding Concern #1. As per your recommendation, we have revised the abstract by incorporating quantitative results to enhance its readability and professionalism. Your insights are invaluable, and we look forward to any further guidance you may

Reviewer#2, Concern # 2: Is this (FTSMC-DO) abbreviation of the disturbance? This is not proper, so it is better to fix all abbreviations along the paper.

Author response and action: Thank you for bringing up Concern #2 regarding the abbreviation FTSMC-DO. We have addressed this concern by modifying and standardizing the usage of FTSMC-DO throughout the paper. Additionally, we have provided detailed explanations of DO both in the text and through graphical representations for clarity.

Reviewer#2, Concern # 3: The abstract is very wordy and long, it should be rewritten concisely and precisely.

Author response and action: Thank you for highlighting Concern #3 regarding the length and verbosity of the abstract. In response to your suggestion, we have revised the abstract to make it more concise and precise, aligning with the clarity and brevity standards expected.

Reviewer#2, Concern # 4: Keywords after Abstract should be improved by considering some abbreviations of concepts.

Author response and action: We have revised the keywords by incorporating appropriate abbreviations for relevant concepts, aiming to enhance the clarity and effectiveness of the provided keywords.

Reviewer#2, Concern # 5: Hyperbolic function that is mentioned in the Abstract but is not used in the methodology, I am confused about it.

Author response and action: Thank you for your feedback. As pointed out in concerns 5 and 6, we have revised the second section to provide a clearer description of our research. In the new version, we explain the role of hyperbolic functions, specifically choosing the tanh function for its excellent continuity and convergence properties. We have designed a load disturbance observer based on the hyperbolic tangent function (tanh) and the Fal function to real-time identify and compensate for load disturbances in the velocity controller. In particular, the Fal function varies with|e_ω|, as indicated in equations (15) and (16). When |e_ω|>δ, we employ tanh|e_ω| μ sgn(e_ω) to rapidly approach the actual value, causing e_ω to converge toward δ. Conversely, when |e_ω|≤δ , tanh(e_ω/δ 1-μ ) acts as a low-pass filter. Therefore, the proposed tanhFal(e_ω,μ,δ) function demonstrates fast convergence, facilitating the convergence of observation errors (lines 205-256).

Reviewer#2, Concern # 6: The Fuzzy Sliding Mode Speed Regulator Design is mentioned in the Abstract and Section 2.4, but the Fuzzification concept does not exist in the paper. This confuses readers.

Author response and action: Thank you for your clarification. Similar to the previous issue, we have incorporated a description of the fuzzy sliding mode control principles, including schematic diagrams and a table of fuzzy control inference rules. We have discussed the adjustment of parameter values when the actual motor speed is high and the load estimate is too low. In such cases, increasing the parameter values promotes rapid convergence and enhances stability. Conversely, when the actual speed is low and the load estimate is high, we advocate decreasing the parameter values to improve the system's disturbance rejection capability (lines 205-289).

Reviewer#2, Concern # 7: The visualization of some figures such as Figures 2, 3, 4, and 5, and others.

Author response and action: Thank you for your feedback. We have made adjustments to the pixel and dimension settings of the mentioned images, ensuring that the text within the figures is now clearer and free of ambiguity. If you have any further suggestions or concerns, please feel free to let us know.

Reviewer#2, Concern # 8: What are the limitations and difficulties of the investigation of this study?

Author response and action: The key issues tackled in this study include the refinement of the two-degree-of-freedom internal model controller using fractional-order functions to explicitly separate robustness and tracking capabilities. To mitigate sensitivity to external disturbances during variable speed operations, a load disturbance observer is introduced, employing hyperbolic tangent and Fal functions for real-time monitoring and compensation. This observer is seamlessly integrated into the sliding mode controller. To address low-speed chattering associated with sliding mode controllers, a revised non-singular fast terminal sliding mode surface is introduced. Additionally, guided by fuzzy control principles, real-time selection of sliding mode approaching law parameters is enabled.

We have rephrased the abstract, main body, and conclusion to make the paper clearer and more detailed. Your input has enhanced the comprehensiveness of the paper in addressing key issues related to the remote control of asynchronous motorized irrigation systems.

Reviewer#2, Concern # 9: The estimation performance of the proposed DO is not examined by plotting its estimations.

Author response and action: Thank you for your assistance. We have comprehensively reworked the section on "2.5 Fast Terminal Sliding Mode Control Method Based on Asynchronous Motor Disturbance Observer," incorporating a substantial amount of your feedback. In this revision, we strived to provide a more refined and accurate description of the Disturbance Observer (DO) and offered a detailed explanation of how the designed non-singular fast terminal sliding mode surface ensures stability and rapid convergence at each stage. Your questions have been immensely helpful for our manuscript, contributing to the overall improvement of our paper. If you have any further suggestions or concerns, please feel free to let us know.

Reviewer#2, Concern # 10: In the block diagram Figure 5, the ESO estimator does not exist in the paper. In addition, the DO element is not available.  The block diagram should be improved.

Author response and action: We have made modifications to Figure 6 in the revised manuscript. Additionally, we have extensively rephrased the description of the Disturbance Observer (DO) in the text, as outlined in the author's response to Concern #11. If you have any further questions or suggestions regarding these changes, please feel free to let us know. (lines 277-289).

Reviewer#2, Concern # 11: Where is the DO? I am confused about it.

Author response and action: Thank you for your feedback. We have recognized that the description of the Disturbance Observer (DO) was not clear enough. As a response, we have made modifications both in the abstract and the main body of the text. Specifically, we have rewritten the section titled "2.5.2 Load Disturbance Observer Design," where we detail the design of the disturbance observer (equation 14). (lines 217-230)

Reviewer#2, Concern # 12: The second term in the sliding surface (17) may cause singularity problems, how to avoid singularity issues should be stated.

Author response and action: Thank you for addressing the issues and contributing to the improvement of our paper. We have made substantial revisions to the second section in response to your questions. Specifically, we have added a new section titled "2.5.1 Fuzzy Sliding Mode Speed Controller Design," where we introduce a non-singular fast terminal sliding mode surface (equation 18). This design aims to further mitigate the chattering phenomenon in sliding mode control. In detail, when |x₁| > δ, the terms  and |x₁|^μsgn(x₁) accelerate the convergence of the error towards the sliding mode surface. As the error approaches the equilibrium point along the sliding mode surface, the introduced term x₁/^1-μ determines the convergence speed. We have demonstrated that the designed non-singular fast terminal sliding mode surface ensures stability and rapid convergence at each stage, effectively reducing chattering. (lines 236-253)

Reviewer#2, Concern # 13: The stability proof is not completed.

Author response and action: As mentioned in our previous responses, we have made significant revisions to the paper. In the revised manuscript, to validate the stability of the proposed sliding mode controller, we selected the Lyapunov function V=s² /2 and provided a proof. From equations 22 to 25, we demonstrated that the designed sliding mode controller satisfies the generalized sliding mode conditions, aligning with stability theory. We appreciate your guidance, which has contributed to enhancing the completeness of the paper. If you have any further feedback or suggestions, please do not hesitate to let us know. (lines 251-258)

Reviewer#2, Concern # 14: The sliding surface(14) should be supported by some reference, and why did you select this surface? The sliding surface should be plotted and analyzed.  

Author response and action: Thank you for addressing your concerns and contributing to the refinement of our paper. We have made substantial modifications to the second section. In this revision, we have introduced a new subsection titled "2.5.2 Fuzzy Sliding Mode Speed Controller Design." In this section, we leverage the characteristics of fuzzy control to construct a dynamic sliding mode surface on the foundation of sliding mode control. We also address the selection of control index approaching law parameter k, aiming to maintain more precise dynamic performance of the asynchronous motor under different states. Furthermore, we have designed a non-singular fast terminal sliding mode surface within this subsection. (lines 231-246)

Reviewer#2, Concern # 15: There should be some assumptions such as of upper bound of disturbance and bound of reference signals.

Author response and action: Thank you for your guidance. In the revised "2.5.2" section, we have defined the domains for the actual speed ω, load estimation , and parameter k. If you have any further recommendations or if there are additional areas that need attention, please feel free to inform us. (lines 264-275)

Reviewer#2, Concern # 16: Extensive editing of English language required.

Author response and action: Thank you for bringing this to our attention. We have carefully reviewed your feedback and acknowledge the need for extensive editing of the English language in our manuscript. In response, we will diligently work on improving the overall language quality to ensure clarity and coherence throughout the document. Your input is invaluable, and we appreciate your assistance in enhancing the linguistic aspects of our paper.

Author Response File: Author Response.pdf

Reviewer 3 Report

Review article: Application of Disturbance Observer-Based Fast Terminal Sliding Mode Control for Asynchronous Motors in Remote Electrical Conductivity Control of Fertigation Systems

The main question addressed by the research is how to enhance the dynamic performance and disturbance resistance of asynchronous motors in fertigation machines, particularly under conditions of remote nonlinear and irregular electrical conductivity fluctuations. The research proposes a novel joint control strategy, referred to as Disturbance Observer-Based Fast Terminal Sliding Mode Control (FTSMC-DO), which combines improved internal model control with FTSMC-DO to address challenges in precision agriculture.

The research addresses a relevant and specific gap in the field by proposing an innovative control strategy to improve the performance of asynchronous motors in fertigation systems. While past research has focused on various control methods like PID and SMC, the study argues that these traditional approaches often fall short in addressing the specific challenges posed by the nonlinear and dynamic nature of the agricultural environment. The proposed FTSMC-DO system aims to fill this gap by integrating robustness, precision, and adaptability under variable and unpredictable agricultural conditions.

The research contributes to the subject area by introducing a novel joint control strategy, FTSMC-DO, and conducting experimental evaluations to demonstrate its effectiveness. The study provides a detailed analysis of motor speed and torque control performance, highlighting the advantages of FTSMC-DO over traditional PID and SMC methods. The field tests further validate the system's adeptness in managing electrical conductivity levels in practical fertigation scenarios, showcasing its potential as a valuable tool for modern, sustainable farming practices.

While the methodology is comprehensive, there are a few considerations for improvement:

The paper could benefit from a more detailed explanation of the design choices and parameters used in the FTSMC-DO system.

        The study may explore additional scenarios or challenges that the system might face in real-world agricultural environments to provide a more robust evaluation.

        Further details on the experimental setup, such as specific conditions, variables controlled, and potential sources of variability, could enhance the transparency and reproducibility of the study.

The Figure 1, Figure 6, Figure 7 have be improve. The components of figures must be written below the figure, not inside the figure

Remove lines from within all graphics. Figure 8, Figure 9, Figure 10 and etc.

 Number of Figure 13 Line 331 have to be change, because it is repeated with the figure number from Line 299

The conclusions are largely consistent with the evidence and arguments presented throughout the research.

In the conclusion, include information on how future research will proceed.

Some references are incomplete and the sources are not put on mdpi format.

Author Response

Response to reviewer 3

Dear Professor:

Thank you for your careful review of our papers and recognition of our research, and we will learn your attitude towards academics. Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have made serious changes to the questions you have raised. Below, we grouped actions taken in response to your comments, organized under the major headings supplied, and numbered them. We attempted to be succinct while fully explaining our actions. We focus on explaining your problem and we take it seriously and solve the comments of the other reviewers.

Given your patience waiting for our first revision, we wanted to make every effort to return this revision as promptly as possible.  We were able to make this revision our top priority. We have devoted most of our working (and nonworking) days to the revision. As a result, we are able to return the paper earlier than we estimated.

Your and the reviewers’ comments have again stimulated changes we feel further improved the paper.

Best regards,

Huan Wang.

Reviewer#3, Concern # 1: The paper could benefit from a more detailed explanation of the design choices and parameters used in the FTSMC-DO system.

Author response and action: We have made substantial revisions to the second section in response to your questions. Specifically, we have added a new section titled "2.5.2 Fuzzy Sliding Mode Speed Controller Design", where we introduce a non-singular fast terminal sliding mode surface (equation 18). This design aims to further mitigate the chattering phenomenon in sliding mode control. In detail, when |x₁| > δ, the terms  and |x₁|^μsgn(x₁) accelerate the convergence of the error towards the sliding mode surface. As the error approaches the equilibrium point along the sliding mode surface, the introduced term x₁/^1-μ determines the convergence speed. We have demonstrated that the designed non-singular fast terminal sliding mode surface ensures stability and rapid convergence at each stage, effectively reducing chattering. (lines 231-244)

Reviewer#3, Concern # 2: The study may explore additional scenarios or challenges that the system might face in real-world agricultural environments to provide a more robust evaluation.

Author response and action: Thank you for your insightful suggestion to explore additional scenarios in the study, a valuable perspective that aligns with our commitment to a more comprehensive evaluation of the control system in real-world agricultural environments.

In response to your feedback, we will conduct further investigations to encompass a broader range of scenarios and challenges reflective of real-world agricultural conditions. This expanded analysis aims to enhance the study's applicability and provide a more thorough understanding of the system's performance under diverse circumstances.

Additionally, we have revisited the content in the Introduction section, addressing any concerns or suggestions provided. We believe these modifications contribute to a clearer and more contextually relevant presentation of our research objectives.

We appreciate your valuable feedback and remain dedicated to continually improving the robustness and relevance of our study. If you have any specific scenarios or challenges in mind or further guidance on the Introduction section, please feel free to share, and we will incorporate your input accordingly.

Reviewer#3, Concern # 3: Further details on the experimental setup, such as specific conditions, variables controlled, and potential sources of variability, could enhance the transparency and reproducibility of the study.

Author response and action: Thank you for your guidance. In the revised "2.5.2" section, we have defined the domains for the actual speed ω, load estimation , and parameter k. If you have any further recommendations or if there are additional areas that need attention, please feel free to inform us. In this section, we leverage the characteristics of fuzzy control to construct a dynamic sliding mode surface on the foundation of sliding mode control. We also address the selection of control index approaching law parameter k, aiming to maintain more precise dynamic performance of the asynchronous motor under different states. Furthermore, we have designed a non-singular fast terminal sliding mode surface within this subsection. (lines 231-274)

Reviewer#3, Concern # 4: The Figure 1, Figure 6, Figure 7 have be improve. The components of figures must be written below the figure, not inside the figure

Author response and action: Thank you for your suggestion. We have relocated the components of the figures from within the graphics to the caption area below each figure, aiming to enhance information readability. We trust that this modification aligns with your expectations and improves the overall comprehension of the figures.

Reviewer#3, Concern # 5: Remove lines from within all graphics. Figure 8, Figure 9, Figure 10 and etc.

Author response and action: Thank you for your suggestion. We have removed internal lines from all graphics, including Figure 8, Figure 9, Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15 and Figure 16, as per your request. This modification aims to enhance the clarity of the visuals. We appreciate your attention to detail and welcome any additional feedback you may have.

Reviewer#3, Concern # 6: Number of Figure 13 Line 331 have to be change, because it is repeated with the figure number from Line 299

Author response and action: Thank you for bringing this to our attention. We have addressed the concern by updating the numbering of Figure 13, ensuring it no longer duplicates the numbering used in Line 299. Additionally, we have thoroughly reviewed and adjusted the numbering of all figures and tables to maintain consistency throughout the manuscript. We appreciate your diligence in identifying this issue, and we believe these changes contribute to the overall clarity of the document.

Reviewer#3, Concern # 7: The conclusions are largely consistent with the evidence and arguments presented throughout the research.

Author response and action: We appreciate your acknowledgment that the conclusions align well with the presented evidence and arguments. This underscores our commitment to maintaining coherence and logical flow in the manuscript. If you have any specific suggestions for improvement or if there are areas where further clarification is needed, please feel free to provide guidance.(lines 407-435)

Reviewer#3, Concern # 8: In the conclusion, include information on how future research will proceed.

Author response and action: Thank you for your valuable suggestion. In response, we have enriched the conclusion by incorporating information on how future research will proceed. This addition aims to provide readers with insights into the potential directions for further exploration in the field. We hope this enhancement aligns with your expectations, and we remain open to any additional recommendations you may have. (lines 407-435)

Reviewer#3, Concern # 9: Some references are incomplete and the sources are not put on mdpi format.

Author response and action: Thank you for pointing out the issue with incomplete references and the non-compliance with the MDPI format. We appreciate your attention to detail, and we have taken immediate steps to rectify these concerns. The references have been thoroughly reviewed, and we have ensured that each citation adheres to the MDPI format.

If you have specific examples or details you would like us to revisit or if there are further guidelines regarding the MDPI format that we might have missed, please provide additional information, and we will promptly address any remaining issues.

We apologize for any oversight in this regard and appreciate your assistance in ensuring the accuracy and conformity of our references.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Still, there are some issues (from the previous round) that are well not addressed such as

1.       Reviewer#2, Concern # 8: What are the limitations and difficulties of the investigation of this study?

2.       Reviewer#2, Concern # 9: The estimation performance of the proposed DO is not examined by plotting its estimations.

3.       Reviewer#2, Concern # 13: The stability proof is not completed. Since the proposed control incorporates the DO element, but its stability is not provided. Thus, it is better to give rigorous stability of the overall closed-loop system including control and observer.

4.       The literature review should be enriched by relevant research on SMC schemes. I suggest the following to be added: https://doi.org/10.3390/act12120433, 10.1109/TIE.2019.2931517.

5.       The motivation of the manuscript must be clearly pointed out in the introduction section.

6.       Reviewer#2, Concern # 14: The sliding surface (18) should be supported by some reference, and why did you select this surface? The sliding surface should be plotted and analyzed.

Author Response

Response to reviewer 2

Dear Professor:

We sincerely appreciate your thorough review and constructive feedback on our manuscript. Your insights have been invaluable in guiding us to enhance the overall quality of the paper.

Following your meticulous examination, we have diligently addressed all the concerns and suggestions raised during the initial review. The revised manuscript incorporates comprehensive modifications, all of which have been highlighted in yellow for your convenience.

Enclosed, please find the revised manuscript. We earnestly look forward to your reevaluation. Any additional comments or suggestions you provide will be carefully considered, and necessary adjustments will be made accordingly.

Thank you once again for dedicating your time to review our work amidst your busy schedule.

Best regards,

Jiawei Zhao.

Reviewer#2, Concern # 1: What are the limitations and difficulties of the investigation of this study?

Author response and action: We have addressed the limitations and challenges associated with refining the two-degree-of-freedom internal model controller using fractional-order functions to explicitly distinguish between robustness and tracking capabilities. To enhance resilience to external disturbances during variable speed operations, we have introduced a load disturbance observer, utilizing hyperbolic tangent and Fal functions for real-time monitoring and compensation. This observer has been seamlessly integrated into the sliding mode controller. In order to tackle the low-speed chattering often associated with sliding mode controllers, we have introduced a modified non-singular fast terminal sliding mode surface. Furthermore, leveraging fuzzy control principles, we have enabled the real-time selection of sliding mode approaching law parameters.

We have revised the "Introduction" section to provide a clearer and more detailed overview of the paper. Your feedback has significantly contributed to improving the paper's comprehensiveness in addressing key issues related to the remote control of asynchronous motorized irrigation systems.

Reviewer#2, Concern # 2: The estimation performance of the proposed DO is not examined by plotting its estimations.

Author response and action: Thank you for your insightful comments. We appreciate your observation regarding the need to examine the estimation performance of the proposed disturbance observer (DO) through plotted representations. In response, we want to express that our manuscript primarily focuses on the analytical derivation and proof of the effectiveness of incorporating fuzzy control principles into sliding mode control. Through mathematical formulations, we demonstrated the construction of a dynamic sliding mode surface based on sliding mode control principles. Additionally, we addressed the selection of control index convergence law parameters (k), ensuring improved dynamic performance of asynchronous motors across various operational states. While we understand the importance of visualizing the estimation performance with plots, our emphasis in this work lies in theoretical development and proof of concept. Nonetheless, we acknowledge the significance of practical validation and will consider incorporating visualizations in future research endeavors.

Reviewer#2, Concern # 3: The stability proof is not completed. Since the proposed control incorporates the DO element, but its stability is not provided. Thus, it is better to give rigorous stability of the overall closed-loop system including control and observer.

Author response and action: Thank you for your thoughtful input, particularly regarding the need for a comprehensive stability proof for the proposed control, considering the incorporation of the Disturbance Observer (DO) element.

To address this concern, we conducted a thorough stability analysis of the entire closed-loop system, encompassing both the control and observer components. To validate the stability of our proposed fuzzy sliding mode speed regulator, we employed the Lyapunov function V=s²/2. The stability test, presented from line 248 to line 259 in the manuscript, demonstrates that , providing robust evidence that our designed sliding mode controller satisfies the generalized sliding mode conditions and aligns with stability theory.

This detailed stability analysis further solidifies the theoretical foundation of our proposed control approach. We believe that this clarification enhances the overall quality and reliability of our work.

Reviewer#2, Concern # 4: The literature review should be enriched by relevant research on SMC schemes. I suggest the following to be added: https://doi.org/10.3390/act12120433, 10.1109/TIE.2019.2931517.

Author response and action: We sincerely appreciate your guidance, especially your suggestion to enrich the literature review with additional relevant research on Sliding Mode Control (SMC) schemes. We have carefully reviewed the recommended articles, and we acknowledge their significant contributions to the field. In response to your suggestion, we have incorporated references to the suggested papers in our revised manuscript. The modifications have been made in the "Introduction" section at line 66-67.

Your valuable input has been instrumental in enhancing both our research methodology and the overall presentation of the paper. We are grateful for your insightful recommendations and remain open to any further suggestions or comments you may have.

Reviewer#2, Concern # 5: The motivation of the manuscript must be clearly pointed out in the introduction section.

Author response and action: We appreciate your valuable feedback, particularly concerning the need for a clear articulation of the manuscript's motivation in the introduction section.

In response to your suggestion, we have carefully revised the "Introduction" section to better highlight the motivation behind our work. The motivation in the introduction section is now explicitly stated, linking the challenges in asynchronous motor control to the broader context of agricultural complexities and the limitations of existing control methods. This connection strengthens the rationale for the proposed control strategy. The modifications aim to explicitly address the limitations and challenges associated with the problem at hand, providing a clearer expression of the manuscript's writing rationale.

Your thoughtful question has significantly contributed to the improvement of our paper's quality. We are grateful for your guidance and are open to any further insights or suggestions you may have.

Reviewer#2, Concern # 6: The sliding surface (18) should be supported by some reference, and why did you select this surface? The sliding surface should be plotted and analyzed.

Author response and action: We appreciate your insightful comment regarding the sliding surface and the request for additional support and analysis. In response, we have made the following enhancements to the manuscript:

Reference Support for Sliding Surface: We have added references (lines 220-222) to provide support for the selected sliding surface, offering a basis for its incorporation into our methodology.

Improved Non-Singular Fast Terminal Sliding Mode Surface: To address low-speed chattering associated with sliding mode controllers, we selected this approach to enhance the non-singular fast terminal sliding mode surface. We have elucidated this choice and its advantages in mitigating chattering issues in the revised manuscript (lines 240-245).

Stability and Convergence Analysis: The manuscript now includes a detailed analysis (lines 240-245) demonstrating that the designed non-singular fast terminal sliding mode surface ensures stable and rapid convergence at each stage, effectively overcoming chattering concerns.

Additionally, we want to emphasize that, guided by fuzzy control principles, we have employed fuzzy control to dynamically construct the sliding mode surface, facilitating the selection of control index convergence law parameters (k) and thereby enhancing the dynamic performance of asynchronous motors across different operational states (lines 252-264).

These amendments aim to address your concerns and provide a more comprehensive understanding of the rationale behind our choices.We appreciate your constructive feedback and remain open to further suggestions or clarifications.

Author Response File: Author Response.pdf