PONE-D-24-49019Vibration control of a class of flexible mechanical systems with output constraints based on partial differential equationsPLOS ONE

Dear Dr. Tang,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

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We look forward to receiving your revised manuscript.

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Omer Saleem, Ph.D.

Academic Editor

PLOS ONE

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Additional Editor Comments:

The author have presented a control strategy for vibration suppression in flexible mechanical systems (FMSs), which are critical in applications like aerospace, robotics, and precision manufacturing. Specifically, the study focuses on a system modeled as an Euler-Bernoulli beam with a centrally attached rigid body, which represents a flexible structure subject to vibrations and rotations. The scheme's effectiveness is validated through simulations that show its ability to handle displacements and rotations caused by unexpected disturbances while respecting the system's output constraints. Overall, the paper is interesting and contributes to advancing robust control mechanisms for flexible mechanical systems, ensuring their reliability and performance under challenging operating conditions.

The paper was reviewed by two (02) reviewers. According to reviewer's comments, the paper cannot be accepted in the present form. They have raised some valuable concerns regarding the theoretical justifications, clarity in terminology, and expansion of simulation details. The paper should also include statitical data analysis tests to substantiate the robustness of the proposed control scheme. Detailed reviewer's comments are included below.

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Partly

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2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: No

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3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

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4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

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5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: The manuscript presents a promising approach to vibration suppression in flexible mechanical systems using a robust control scheme based on partial differential equations and Barrier Lyapunov Functions. This study contributes meaningfully to the field by addressing critical stability and control issues for applications in aerospace, robotics, and precision manufacturing. With some revisions to enhance theoretical context, simulation applicability, and overall clarity, this paper has strong potential for impactful publication.

1. Theoretical Justification and Limitations: The paper introduces a control scheme for flexible mechanical systems that is robust and based on Barrier Lyapunov Functions (BLF) and Partial Differential Equations (PDEs). Nevertheless, the theoretical foundation does not provide a comprehensive rationale for the selected control approach in comparison to other Lyapunov-based methods or Model Predictive Control (MPC). The control strategy's foundation would be fortified by elaborating on the specific rationale behind BLF in this context. Furthermore, the clarification of the model's constraints, particularly in environments with severe external disturbances, would facilitate the development of future applications.

2. The Relationship Between Simulation and Real-World Application: Although the paper contains simulation-based validations, it would be advantageous to explore the extent to which these findings are applicable to real-world scenarios. The study's impact would be enhanced by providing information on the practical challenges of tangible implementation and assessment. Additionally, if simulation assumptions, such as simplified disturbance models or ideal conditions, are inconsistent with real-world complexities, recognizing these would facilitate a more comprehensive comprehension of potential application barriers.

3. Clarity in Terminology and Definitions: Certain terms, including "disturbance compensation" and "robust control," are employed without a comprehensive initial definition. The paper would be more accessible to readers who are less familiar with these concepts if concise explanations were included when these terms first appear.

4. Mathematical Notation Consistency: The manuscript occasionally contains inconsistent mathematical notation, which may cause readers to become perplexed. For instance, variables should be standardized throughout the equations with respect to their subscripts and superscripts. The legibility of time-dependent and state variables would be enhanced by the use of consistent notation.

5. Expansion of Simulation Details: The simulation section contains certain parameter values, but the rationale behind their selection is absent. The results would be more credible if additional context were provided regarding the rationale behind the selection of specific values for variables such as control gains and disturbance levels.

6. Visual Presentation of Results: The figures that compare the displacement responses of controlled and uncontrolled objects are informative; however, they could be enhanced by the inclusion of more descriptive captions. The intelligibility of the text would be improved for readers who may not have the time to read the entire text in detail by providing concise interpretations of the results directly in the figure captions.

7. Abstract Summary Improvement: The abstract effectively summarizes the control scheme; however, it would be enhanced by a more explicit mention of the primary findings, such as quantifying the degree of vibration reduction observed. This addition would offer a more concise overview of the paper's contributions.

Addressing these revisions will help clarify the research contribution and its broader implications, making the paper more accessible and impactful for readers in fields like control engineering and applied mechanics.

Reviewer #2: The paper aims to present the challenge of vibration suppression in Flexible Mechanical Systems (FMSs), which are systems with deformable components that can experience unwanted vibrations during operation.

The challenge has been addressed by proposing a robust control scheme using Partial Differential Equations (PDEs) and Barrier Lyapunov Function (BLF), implemented through backstepping technology.

Although the development of the proposed scheme has been rigorously presented, the paper lacks clear and extensive results section. The proposed methodology was only tested on a simulated model without any experimentation on any kind of hardware setup. Experimentation on a hardware setup would have revealed the robustness of the proposed scheme in response to unmodeled dynamics. This brings me to state that even if simulated systems are used for evaluation of the proposed scheme, then the results, in current form, are not sufficiently representative of capability of the proposed scheme. Moreover, comparison between system response with the control scheme implemented and system response without control scheme implemented doesn’t prove the novelty or significant contribution of the proposed scheme.

The author must present detailed experimentation results where the response of the proposed scheme is rigorously evaluated in response to several parameter changes, unmodeled dynamics, uncertain disturbances etc.

Some of the specific comments are:

Line # 273 and 274: A simple sinusoidal function is used to represent disturbance. The author should explain why such a simple function has been used as disturbance and in real-life situations which FMSs encounter this kind of disturbance?

Line # 281: Fig 1 and Fig 2 are presenting the same plot but with different colors! Both figures are displaying exactly the same thing. However, the text claims that the response has become stable and within bounds, whereas the figure differs. The response, as shown in Fig 1 and 2, is same with control or without control. This might be some kind of mistake where the author mistakenly inserted the wrong figure in the manuscript.

Line # 301: Fig 4 compares the control input under the proposed scheme with ‘no control implemented’. It would have been much more beneficial and supportive of the proposed scheme if a comparison between the control input of the proposed scheme had been compared with some other published scheme aimed at vibration reductions in FMSs.

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Reviewer #1: Yes: Ahmad Hamza

Reviewer #2: No

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PONE-D-24-49019R1Vibration control of a class of flexible mechanical systems with output constraints based on partial differential equationsPLOS ONE

Dear Dr. Tang,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

Please submit your revised manuscript by Mar 12 2025 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

• A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.
• A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.
• An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: https://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols.

We look forward to receiving your revised manuscript.

Kind regards,

Omer Saleem, Ph.D.

Academic Editor

PLOS ONE

Journal Requirements:

Please review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript. If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice.

Additional Editor Comments:

The second round of reviews are complete. The paper's quality is substantially improved. However, Reviewer # 1 has suggested minor revisions. Therefore, the authors are requested to address the reviewer's minor comments and resubmit the article.

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: All comments have been addressed

Reviewer #2: All comments have been addressed

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2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

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3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: N/A

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4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

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5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: While the paper addresses a significant challenge in vibration control for flexible mechanical systems (FMSs), particularly those modeled using partial differential equations (PDEs). However, the paper could benefit from a few enhancements to improve its overall clarity and impact.

1. Conduct experiments to validate the control strategy on physical systems, showcasing its robustness and reliability under real-world conditions.

2. Simplify or summarize the mathematical framework to make the paper more accessible to a wider audience, including engineers and system designers.

3. Include a detailed comparative analysis with existing control methodologies to highlight the unique advantages of the proposed approach.

4. Address the computational demands of the control system to ensure feasibility in real-time applications.

5. Expand the discussion on potential generalizations of the method to other types of FMS or broader industrial applications.

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7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: Yes: Ahmad Hamza Nayyar

Reviewer #2: No

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[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

Vibration control of a class of flexible mechanical systems with output constraints based on partial differential equations

PONE-D-24-49019R2

Dear Dr. Yuzhi Tang,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

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If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org.

Kind regards,

Omer Saleem, Ph.D.

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

The paper is well revised. The comments of Reviewer # 1 have been duly addressed.