Vehicle Vibration Characteristics of an Additional-Flow-Path-Type Magnetorheological Damper Using a Frequency-Tuned Proportional-Integral Controller

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The article “A Study on Vehicle Vibration Performance of an Additional Euro-Type MR Damper Using a Frequency-based PI Controller” examines a semi-active suspension system that uses an additional flow channel type magnetorheological (MR) damper controlled by a proportional-integral (PI) algorithm tuned to the frequency characteristics of road irregularities. The novelty of the work is associated with an integrated methodological approach - the structural improvement of the MR damper is combined with a frequency control scheme, the purpose of which is to reduce the acceleration of the sprung mass. Although MR dampers and PI control are widely studied topics, the proposed design with an additional flow channel and its combination with frequency-based control form the basis of the originality of the study. The article is relevant for the modeling and control optimization of semi-active suspension systems. The methodology used is sufficient for the goals set. A two-degree-of-freedom quarter-car model was created, into which the dynamics of the MR damper and the PI controller are integrated. The modeling was performed in the AMESim environment. Road irregularities are generated according to the ISO 8608 standard using noise filtering and PSD analysis. The modeling process, parameters and control algorithm are described in sufficient detail to allow replication of the study. Empirical data are not used, therefore the results are limited to numerical simulation. The obtained results are presented in tables and graphs. The MR shock absorber system reduced the acceleration of the sprung mass compared to passive suspension, up to a maximum of 59.5% under class B road conditions. The comparison is presented in RMS format, which is consistent with engineering analysis practice. The analysis of the results is logically related to the frequency characteristics of road irregularities and the tuning parameters of the controller. Statistical analysis of the reliability of the results is not indicated. The conclusions are consistent with the obtained results. They summarize the improvement in comfort, the reduction in energy dissipation and the structural properties of the MR shock absorber. The limitations of the study are indicated - the simplicity of the quarter-car model and the lack of experimental tests. The conclusions are proportional to the data provided. The list of references is neatly compiled. Most of the sources are new (2021–2025), a few are classic, used for theoretical justification. The sources correspond to the topic and cover both MR material physics and control algorithms. In summary, the study is methodologically sound and clearly described. The results logically follow from the applied methodology. Experimental validation and statistical analysis of the results are absent; however, the data presented enable us to infer limited insights into the performance of the proposed system under simulated conditions.

The list of detail remarks is provided below:

Line 2–4: The title of the article is too long, covering both the experimental object and the control method. It would be worth shortening it, for example, to more clearly separate the scope and method.

Line 10–26 (Abstract): The abstract contains too many technical details (e.g., “59.542% improvement” and “B-class roads”). It is recommended to present a summarized result in the scientific abstract without excessive numerical precision.

Line 29–37: The introduction lists general facts about MR fluids, but there is no clear definition of the problem or research hypothesis.

Line 90–97: The first mention of the “additional flow-path type MR damper” is not illustrated or explained before the mention – the explanation is provided only later (Line 136–141).

Line 98–107: It is stated that there is a lack of previous work combining PI control and this type of MR shock absorber, but no clear literature analysis has been performed to prove this statement.

Line 114–127: The research objective is described as “minimizing sprung-mass acceleration”, but it is not specified why this criterion was chosen as the only evaluation parameter (others are not included – road contact, wheel load stability, etc.).

Line 132–139 (Figure 1): The research process is presented schematically, but there is no logical connection between the stages – it is not visible how the control tuning is integrated into the simulation cycle.

Line 134–183: The description of the MR shock absorber model is presented formally, but without any experimental parameters (e.g., MR fluid type, real magnetic induction value, viscosity range).

Lines 143–147: Equation (2) is visually interrupted, some symbols are not explained (“ζ”, “forifice”).

Line 171–177: The descriptions of the AMESim submodels (Table 1) are generic; no information on parameter verification or model validation is provided.

Lines 186–187, 295–307: Modeling assumptions are not provided (e.g., time step, integration method).

Line 188–223: The ISO 8608 road simulation is detailed, but no verification of the time step, discretization, or noise filters, which is important for the accuracy of the results, is provided.

Line 199–202: Formula (10) – discrete road roughness generation equation – no justification for the units of measurement of the variables used or the discretization frequency is provided.

Line 220–221: The Python tool used for PSD calculation is mentioned without validation with standard test data (no comparison with the real road).

Line 239–279: The PI control scheme is presented theoretically, but it is not shown how the specific parameters Kp and Ki are determined (no optimization criterion or error function definition).

Line 265–273: “frequency-response analysis” is mentioned, but no actual Bode plots or phase/gain margin results are shown, only a verbal interpretation.

Line 274–278: It is not shown how the linearized model was checked before applying the “Internal Model Control (IMC)” method.

Line 283–292 (Table 3): PID parameter values are presented without units and without an explanation of the principle by which they were selected.

Line 295–307 (Tables 4–6): The data in the tables are rounded only to three digits, but the differences between the frequencies of the results are minimal (e.g., 0.231 vs 0.229), so the statistical significance is questionable.

Lines 299–307: No repeatability assessment –results are presented for only one modeling scenario without repeated trials.

Line 308–315: “Peak damping effectiveness occurred at…” – it is not specified how the peak value was determined; the RMS calculation procedure is not provided.

Line 317–323: The frequency of 0.55 Hz is discussed, but it is not shown how it corresponds to the natural frequency of the car suspension; dynamic parameters are missing.

Lines 333 and 343: Figure numbering is duplicated (“Figure 8” is used twice).

Line 335–340: The RMS force values are given (174.21 N and 50.53 N), but it is not clear under what conditions they were calculated (what road profile, speed, time window).

Line 345–356: Resonance damping is discussed, but neither resonant frequency nor Bode analysis curves are provided.

Lines 345–347: The evaluative terms used in the discussion (“great significance”) do not correspond to the objectivity characteristic of the scientific style.

Line 383–390: The limitation of the quarter car model is mentioned, but how this affects the transfer of the results to real conditions is not discussed.

Line 395–396: It is acknowledged that the electrical energy consumption in the MR coil is underestimated, but it is not explained why this aspect was eliminated from the analysis.

Line 397–445: The conclusions present several aspects (comfort, energy saving, structural reliability), but they are not measured or quantified.

Line 431–435: The statement that “the controller effectively exploits the nonlinear operating range of the MR damper” is not supported by empirical data.

Line 439–445: A proposal to produce a real prototype is presented as future work, but there is no clear plan or guidelines for the experimental method.

Lines 450–451: Too many repetitions in the authorship section (“SW and CJ” are repeated several times).

Line 455–456: The data availability statement is formal (“available upon request”), but it does not specify what data is being stored.

Line 459–502: The literature is largely new, but some cited sources are not directly related to frequency PI control (e.g., ref. [10], [11]).

Line 461–468: Recent work on energy efficiency in semi-active suspensions is lacking (e.g., publications after 2023).

Line 493–496: The source ISO 8608 (2016) is cited, but it is not mentioned whether the version used is updated according to the 2020 amendments.

Author Response

Dear editor and reviewer

(Journal of Energies)

The authors would like to deeply thank the editor and reviewer for reviewing the paper and providing constructive remarks.

We have revised the manuscript based on the reviewer’s and the editor’s comments. It has greatly helped us to improve our work.

Detailed answers to the review comments were provided in this document. The corresponding modifications in the manuscript are described at each answer, and also highlighted with blue color in the revised manuscript. Big modifications including corrections of English are also progressed in the revised manuscript.

So, please check the highlighted parts of the revised manuscript.

Sincerely yours,

Prof. Jin Wook Lee

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This paper presents a MR damper control evaluation using a frequency-based PI. Although this is a relevant topic, the manuscript requires significant revisions before it can be suitable for publication. Please find my suggestions below:

1. The introduction lacks a comparison of recent, related works on vehicle suspension control, and the techniques that can achieve a robust behavior. Authors should cite and discuss recent, related works such as Robust static output feedback control of a semi-active vehicle suspension based on magnetorheological dampers, Avoiding Lyapunov-Krasovskii Functionals: Simple Nonlinear Sampled–Data Control of a Semi-Active Suspension with Magnetorheological Dampers, and other relevant works by these authors.
2. Section 2 is missing. Only subsections have been presented.
3. Most figures have poor visibility and must be improved. Please update Figures 1, 2, 3, 4, 5, 6, 7, 8.
4. There are 2 Figures labeled as "Figure 8".
5. The explanation behind equation (1) must be refined (lines 143-145).
6. Overall, equation formatting must be refined.
7. Please provide a bibliographic source for equations 1-6.
8. Although the MR damper current is the control input, this does not appear on any equation.
9. Is equation (6) experimental or related to a speficic MR damper model? This must be explained.
10. Table 2 must be improved. What do you mean by vehicle tread? What is the source of the damper response time?
11. The proposed PID solution is straightforward. The novelty of this work must be reinforced.
12. The simulation results should include additional figures showing the vertical acceleration of the sprung mass and suspension deflection over time.
13. The controller gains listed in Table 3 appear to be significantly large. Please revise 
14. A comparison against other state of art controllers should be presented.

Comments on the Quality of English Language

The use of english should be revised.

Author Response

Dear editor and reviewer

(Journal of Energies)

The authors would like to deeply thank the editor and reviewer for reviewing the paper and providing constructive remarks.

We have revised the manuscript based on the reviewer’s and the editor’s comments. It has greatly helped us to improve our work.

Detailed answers to the review comments were provided in this document. The corresponding modifications in the manuscript are described at each answer, and also highlighted with blue color in the revised manuscript. Big modifications including corrections of English are also progressed in the revised manuscript.

So, please check the highlighted parts of the revised manuscript.

Sincerely yours,

Prof. Jin Wook Lee

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The authors developed a two-degree-of-freedom quarter-car model featuring an additional flow-path type MR damper governed by a frequency-based PI controller, with the control objective of minimizing sprung-mass acceleration. Road excitations were numerically generated per ISO 8608 (classes A–C) and applied to the AMESim-implemented model; dynamic responses with the MR damper were quantitatively compared to those of a conventional passive damper under identical conditions. Simulations showed that the additional flow-path MR damper consistently lowered sprung-mass acceleration, achieving up to 59.542% improvement under B-class roads, and that performance was maximized when the controller’s tuning frequency aligned with the dominant frequency content of the excitation. I have some comments about the proposed work:
1. This simplified model does not fully capture the complex dynamics of a full vehicle, such as pitch and roll motions, which are crucial for a comprehensive understanding of vehicle behavior.
2. The damper control coil power consumption is not quantified in the study. The control system's energy efficiency is not adequately examined, which is crucial for practical application and system sustainability.
3. Numerical models and simulations underpin the work. These give a solid foundation, but more research is needed to build a hardware-based MR damper system and test its control performance and energy consumption reduction under real-world situations.
4. The paper  https://doi.org/10.29020/nybg.ejpam.v16i4.4930  can be added to the literature.

Author Response

Dear editor and reviewer

(Journal of Energies)

The authors would like to deeply thank the editor and reviewer for reviewing the paper and providing constructive remarks.

We have revised the manuscript based on the reviewer’s and the editor’s comments. It has greatly helped us to improve our work.

Detailed answers to the review comments were provided in this document. The corresponding modifications in the manuscript are described at each answer, and also highlighted with blue color in the revised manuscript. Big modifications including corrections of English are also progressed in the revised manuscript.

So, please check the highlighted parts of the revised manuscript.

Sincerely yours,

Prof. Jin Wook Lee

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Thank you to the authors for the extensive revisions and for significantly improving the clarity, structure, and contextual grounding of the manuscript. The revised version demonstrates meaningful progress: the MR fluid properties are now explicitly described, the introduction is stronger, the modeling assumptions are clearer, and many missing definitions have been added.

However, after a detailed second-round assessment, the manuscript still contains methodologically critical gaps that must be addressed before it can be considered for publication. Below I provide a continuous analytical evaluation, with explicit line-level references indicating where further corrections are required.

Line 347–349 Although the authors claim substantial frequency-response analysis, the manuscript does not include any of the necessary figures or numerical evidence.

The authors state that the linearized plant exhibits a Phase Margin ≈ 51°.

However:

• no Bode magnitude plot is provided,
• no phase plot is provided,
• no diagram indicates at which frequency the PM was measured,
• no linearization output is shown.

Insert full Bode plots (magnitude and phase) for the linearized system with the phase-margin point clearly marked.

Line 350–353 The manuscript claims that the reduced-order model accurately approximates the full model, but:

• no step-response comparison is shown,
• no Bode comparison is provided,
• no quantitative accuracy metric (RMSE, MAE, fitting error) is reported.

Provide at minimum:

1. A step-response overlay: full AMESim model vs. reduced-order model.
2. A Bode magnitude/phase overlay for the same models.

Line 360–363 The claim that the internal loop has a measured Gain Margin ≥ 60 dB lacks any analytical support. In particular:

• a 60 dB GM is unusually high for an MR suspension system and must be justified,
• the manuscript does not show how this GM was computed,
• no open-loop Bode magnitude plot is shown.

Include the open-loop Bode magnitude plot from which the GM is measured and indicate the GM evaluation point.

Line 353–357 The authors state that Ki ≈ 227000 results from the IMC rule:

Ki = 1/(K₀ λ)

However:

• K₀ is never defined numerically,
• τp and L are not shown,
• no parameter identification results are provided,
• no intermediate step of the IMC calculation is shown,
• Kp derivation is also omitted.

Add a clear numerical demonstration of the IMC-based tuning, including:

• extraction of K₀, τp, and L from Gp(s),
• explicit calculation of Kp and Ki,
• verification of these values with closed-loop performance plots.

Lines 391–400; Tables 4–6 The RMS values are given with extremely high precision (9–10 significant digits), e.g.:

• 0.128563025

Such precision is unrealistic and misleading because:

• only a single ISO 8608 profile realization is used per class,
• no variance or distribution is reported,
• differences as small as 0.000002 m/s² fall below meaningful numerical accuracy.

Generate at least three independent realizations of each ISO 8608 class (A, B, C), then report:

• mean RMS value,
• standard deviation,
• confidence bounds.

This minimal Monte-Carlo robustness check is necessary given the stochastic nature of ISO 8608 profiles.

Lines 330–337 Equations (13)–(17) define the upper and lower force limits, but the manuscript does not present:

• any plot of Fpid vs. FMR,
• the percentage of time the damper saturates,
• how saturation differs between road classes or tuning frequencies.

Add:

1. A scatter plot or time-series plot showing Fpid and FMR simultaneously,
2. A quantitative measure of saturation percentage for each ISO class,
3. A brief analysis of how saturation influences energy dissipation.

Lines 554–557 (Conclusions) The authors state that electrical power consumption was excluded, yet multiple conclusions refer to:

• improved energy dissipation,
• reduced mechanical energy demand,
• damping-force efficiency.

These statements rely implicitly on the control current I(t), which the manuscript never shows.

Provide approximate coil current profiles (I(t)) and compute nominal power consumption:
Pcoil = I²R (or I·V if applicable) , or explicitly state that energy consumption is outside the scope and remove all energy-related interpretations.

Lines 469–487 The manuscript asserts that structural linearity and frequency-domain tuning enhance dynamic stability. However:

• no closed-loop frequency response is shown,
• no resonance peak location is reported,
• no pole/zero movement analysis is provided.

Include:

• the closed-loop transfer function magnitude plot,
• the resonance frequency,
• clarification of how PI control shifts the system’s dynamic characteristics.

Lines 220–233 Even though MR fluid properties are now listed, the manuscript still lacks any experimental or literature-based validation, such as:

• force–velocity curves at 0 A, 0.5 A, 1 A,
• comparison with the reference MR damper data in [20],
• quantitative validation error.

Add at least one comparative figure:

• simulated F(v) vs. published F(v) from ref. [20].

This is essential to demonstrate that the AMESim model faithfully represents the physical damper.

Tables 4–7 RMS and damping-force results are reported with 9–12 significant digits (e.g., 13.181113, 57.261417). Such precision:

• exceeds physical meaning,
• exceeds AMESim numerical resolution,
• obscures statistical uncertainty.

Round values to 4–5 significant digits, which is the standard for simulation-based mechanical systems.

Author Response

Dear editor and reviewer

(Journal of Energies)

The authors would like to deeply thank the editor and reviewer for 2nd reviewing the paper and providing constructive remarks.

We have revised the manuscript based on the reviewer’s and the editor’s comments. It has greatly helped us to improve our work.

Detailed answers to the review comments were provided in this document. The corresponding modifications in the manuscript are described at each answer, and also highlighted with RED color in the revised manuscript. Big modifications including 2nd corrections of English are also progressed in the revised manuscript.

So, please check the highlighted parts of the revised manuscript.

Sincerely yours,

Prof. Jin Wook Lee

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript has been improved and can be accepted now

Author Response

Dear editor and reviewer

(Journal of Energies)

The authors would like to deeply thank the editor and reviewer for 2nd reviewing the paper and providing constructive remarks.

We have revised the manuscript based on the reviewer’s and the editor’s comments. It has greatly helped us to improve our work.

Detailed answers to the review comments were provided in this document. The corresponding modifications in the manuscript are described at each answer, and also highlighted with RED color in the revised manuscript. Big modifications including 2nd corrections of English are also progressed in the revised manuscript.

So, please check the highlighted parts of the revised manuscript.

Sincerely yours,

Prof. Jin Wook Lee

Author Response File: Author Response.pdf

Round 3

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have made substantial improvements to the manuscript and have addressed many of the major issues raised in earlier review rounds. The structure, clarity, and methodological transparency have improved considerably.
However, several critical points remain only partially addressed or still unresolved, and require correction before the manuscript can be considered for acceptance.
Detailed line-by-line comments follow.

Lines 348–356 (Figure 8 – Bode and PID Tuning)

The response states that a “full Bode magnitude plot of the loop-transfer function L(s)” has been added.
However, the manuscript does not contain any actual Bode magnitude or phase plot of L(s)=C(s)Gp(s).

Figure 8 shows only:

• the open-loop plant and FOP comparison,
• a step-response comparison,
• the AMESim PID Tuner interface.

The loop-transfer Bode diagram itself is missing.
This was explicitly requested in the previous review round.

Please add a dedicated figure showing the full Bode magnitude AND phase plots of L(s), including the gain-margin evaluation point.

Lines 360–378 (IMC → final PI gains)

The manuscript now includes numerical IMC calculations (k, τp, λ), but the final PI gains reported in Table 3:

Kp ≈ 400–550

Ki ≈ 226,000–229,000

are 2–3 orders of magnitude larger than the IMC-derived values:

Kp_IMC ≈ 109

Ki_IMC ≈ 6,060

The paper states that these differences arise from “closed-loop refinement,” but it does not describe any optimization criterion, objective function, or tuning rule that justifies the much higher final gains.

Please clearly explain the refinement process, including the tuning criterion used to adjust the IMC initial gains to the final values shown in Table 3.

 Lines 189–233 (AMESim model – Solver settings)

Key simulation details are still missing:

solver type (DASSL, BDF, fixed-step, etc.),

integration time step,

error tolerances,

whether variable-step or fixed-step integration was used.

These parameters are essential for reproducibility and assessment of numerical reliability.

 Please include explicit solver settings and integration parameters used in AMESim.

Lines 146–183 (MR damper model validation)

The revised manuscript still lacks a validation figure comparing the simulated MR damper force–velocity curves with the reference results from [20].

Although the response claims the model “inherently satisfies the upper envelope,” there is:

no F–v plot from [20],

no overlay showing simulation vs literature,

no quantitative validation error.

Please include at least one F(v) comparison figure and quantify the model deviation relative to [20].

Lines 330–337 (Force-limit behavior)

The paper reports a saturation ratio of 93–94% but does not include:

a time-domain segment showing when saturation disengages,

any histogram or statistical distribution of Fpid vs FMR,

any explanation of how these saturation intervals affect controller behavior.

Please include at least a time-series excerpt or distribution plot showing Fpid and FMR across saturated and unsaturated intervals.

Lines 540–566 (Frequency-response analysis)

The paper states that resonance reduction is “5.2 dB,” but:

Figure 11 does not show PSD/Fourier magnitudes in dB,

the method for computing the 5.2 dB value is not explained,

windowing, overlap, and normalization used in the FFT are not specified.

Please explicitly describe how the 5.2 dB value was computed, including the exact spectral amplitude values and PSD/FFT settings (window type, overlap, scaling).

Lines ~350–420 (Textual duplication)

Several sentences in the IMC/PID tuning section appear to be duplicated verbatim (likely due to merging the response letter into the manuscript).
This affects the clarity and readability.

Please remove repeated sentences and streamline the IMC tuning section.

Author Response

Dear Reviewer

The authors would like to deeply thank the editor and reviewer for 3rd reviewing the paper and providing constructive remarks.

We have revised the manuscript based on the reviewer’s and the editor’s comments. It has greatly helped us to improve our work.

Detailed answers to the review comments were provided in this document. The corresponding modifications in the manuscript are described at each answer, and also highlighted with BLUE color in the revised manuscript.

So, please check the highlighted parts of the revised manuscript.

Sincerely yours,

Prof. Jin Wook Lee

Author Response File: Author Response.pdf