A Band-Stop Filter-Based LQR Control Method for Semi-Active Seat Suspension to Mitigate Motion Sickness

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This study develops an innovative semi-active seat suspension system that synergistically integrates band-stop filtration mechanisms with LQR collaborative control. The paper is well-written in general, some suggestions could be considered.

1. It is suggested to add "frequency domain weighting" to the keywords to enhance the relevance of literature retrieval.
2. For frequently used specialized terms (e.g., MOBOA, MR, MSI), it is recommended to consistently adopt their abbreviated forms in the text, ensuring that the full term is provided upon first occurrence.
3. To improve the readability of the paper, it is advised to include a "List of Abbreviations" in the appendix. This section should systematically catalog all specialized terms used in the paper along with their corresponding abbreviations for readers' reference.
4. How about the comparison of the equation (2) and the real-scene road surface input (Fig. 2). Some research about road modelling could be helpful, e.g., 10.1007/s10409-023-23367-x.
5. For fractional-order theory and semi-active suspension, some existing research is advised to be discussed, 10.1016/j.ymssp.2025.112880.
6. Some equations should be checked, e.g., the symbol in line 258 is not show appropriate.

Author Response

We sincerely appreciate the time and effort you have dedicated to reviewing our manuscript. Your insightful comments and constructive suggestions have significantly improved the quality of this work. We have carefully addressed all your concerns in the revised manuscript, with all modifications highlighted for your convenience.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript presents a LQR for semi-active suspension. The problem is not well-described; it seems an active suspension instead of a semi-active suspension. Simulation results only include random road profiles, which limit the practical application. Find some comments below:
1. The semi-active suspension model is not adequate, as it does not capture the MR damper dynamics. It is assumed that the MR damper provides a force F(t), but how that force varies is not analyzed. It is necessary to further describe this. Please do not overlook this issue. It is recommended to cite relevant works such as https://doi.org/10.3390/app142210336
2.  There are several typo errors, such as "vecter"; in line 258.
3. Please improve the equation format.
4. Given that you aim to use a coupled suspension system that takes into account the seat, the state-space (6) is not correct.
5. LQR requires full state knowledge. Is that feasible for vehicle suspensions? What sensors can you use? Are these included in user vehicles? It is recommended to explore output-feedback techniques, and cite relevant works
6.  Given that simulation results only present random road profiles, it is required to conduct further tests using a road bump. This will analyze how the proposed suspension system reacts against a high energy disturbance.
7. Please provide a figure that depicts the control input; this will increase the reader's trust in this work.
8. The power spectral density of the vertical acceleration is required to analyze comfort during driving.
9. Please provide some numerical indicators at the conclusion in order to demonstrate the validity of your work.

Author Response

We sincerely appreciate the time and effort you have dedicated to reviewing our manuscript. Your insightful comments and constructive suggestions have significantly improved the quality of this work. We have carefully addressed all your concerns in the revised manuscript, with all modifications highlighted for your convenience.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript proposes a semi-active seat suspension control strategy aimed at mitigating passenger motion sickness. To attenuate vibrations in the motion sickness-inducing frequency range (0.1–0.5 Hz), the authors design a frequency-domain fractional-order band-stop filter and integrate it into a linear quadratic regulator (LQR) control framework. Furthermore, a multi-objective butterfly optimization algorithm (MOBOA) is employed to tune the weighting matrices of the LQR controller. The proposed method is validated through simulations using both ISO-classified road profiles and real-world pavement data, demonstrating improved performance in terms of acceleration and ride comfort compared to conventional approaches.

This paper addresses a practical and relevant problem and proposes a technically interesting solution. The integration of a frequency-targeted filter into an LQR framework represents a moderate contribution to semi-active control strategies. However, several issues need to be addressed to improve the scientific rigor and clarity of the manuscript:

 

(1) The assumption that 0.1–0.5 Hz vibrations cause motion sickness is used throughout the manuscript, but no physiological models, empirical studies, or objective indicators are provided to support this claim. The authors should either explicitly state that the study focuses on mechanical vibration attenuation as a proxy for motion sickness mitigation or strengthen the justification through relevant literature.

(2) The design rationale and numerical implementation of the fractional-order filter (e.g., Oustaloup approximation) are not clearly explained. A more detailed explanation of the filter design process, its stability assurance, and the role of its parameters is needed. Including a sensitivity analysis would further strengthen this part.

(3) The use of MOBOA introduces significant complexity. The necessity and effectiveness of this method should be validated through comparison with conventional LQR tuning techniques or simpler optimization methods.

(4) The study is entirely simulation-based, with no discussion of experimental validation or implementation feasibility. The authors should explicitly acknowledge this limitation and outline future plans for real-world testing or hardware-in-the-loop experiments.

(5) The feasibility of the proposed control inputs is not discussed. Analysis of the control effort (e.g., RMS or peak values), actuator limits, or bandwidth constraints should be provided to confirm whether the proposed method can be realistically implemented in semi-active seat suspension systems.

Author Response

We sincerely appreciate the time and effort you have dedicated to reviewing our manuscript. Your insightful comments and constructive suggestions have significantly improved the quality of this work. We have carefully addressed all your concerns in the revised manuscript, with all modifications highlighted for your convenience.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

Authors addressed my concerns. The manuscript can be accepted now

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have sincerely addressed all of the reviewer’s comments and revised the manuscript accordingly. I believe the manuscript is now suitable for publication.