A Hybrid Nonlinear Active Control Strategy Combining Dry Friction Control and Nonlinear Velocity Compensation Control

Round 1

Reviewer 1 Report

The article analyzes the hybrid control of the friction damping process, taking into account both the friction force in the active control law and the non-linear force of velocity compensation. The proposed method takes into account the combination of pure friction force control law with the active control method, which is very beneficial in the higher frequency ranges. The reviewed paper requires considerable modifications to be considered for publication in the Applied Sciences journal. After studying the article, it is difficult to find any information regarding the practical implementation of this method. My next comment concerns the lack of analyzes for frequencies significantly exceeding 30Hz (> 50Hz). What is the effect of the hybrid method? Here, in my opinion, the scope of analyzes should be extended to include higher frequencies. In addition, the bibliographic review seems to be quite poor for this type of issue and needs to be encouraged.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

The paper is devoted to a vibration suppression strategy which is presented by an example of a system of three coupled oscillators. The novel approach combines dry friction control and nonlinear velocity compensation control.

The text is quite well written, and its structure is appropriate. However, the paper includes a few shortcomings which should be eliminated to improve its quality:

1) In Sect. 3.2.2, the results are presented for two cases: a low and a higher excitation frequency (13 Hz and 25 Hz). For a reader who wants to assess the proximity to resonance, it would be desirable to give the values of the natural frequencies of the linear system (without friction etc.). Obviously, I can see from Fig. 2 that the eigenfrequencies are about 14 Hz and 25 Hz, but it is not a precise insight into the mechanical system.

2) In Figs. 6 and 8, time histories of the control forces are shown. What about the friction force and its time history? Since the paper combines to types of vibration control, it would be a good idea to present what are the values of the friction force compared to the control forces.

3) Lines 112-114: in my opinion, the use of subscripts i and j is confusing. As one can conclude from Eq. (5) and vector Y explained below, i = 1 and j = 2. So, the expressions y_i = x_i - x_j and y_j = x_i + x_j should be replaced with y_1 = x_1 - x_2 and y_2 = x_1 + x_2. Indeed, once could think that i = 1, 2 and j = 1, 2, which is not the case.

4) There are some grammar and logic errors:
- Line 110: "Since the friction force is a function of relative velocity and relative displacement." (it is a continuation of the previous sentence? 
or this sentence should be continued?) 
- Line 174: "the control effect of ... are provided" ("are" should be replaced with "is")
 
5) There are some typographical errors:
- scalars like m_1, m_2, miu (friction factor) should not be written in bold (Lines 89, 95, 99)
- subscripts of the symbols for vectors/matrices should not be written in bold (Eq. (3), Eq. (6), Eq. (8), Lines 98, 118-124, and so on)
- in the text, mathematical symbols (like x and a) should be written in italics (Lines 101-102) 
- in the text, mathematical symbols for vectors (like X and Y) should be written in bold (Line 130) 

6) Section 4 is very short (one paragraph). Maybe it would be better to inlcude this paragraph in Sect. 3. It should be noticed that a broad discussion of the results is present in Sect. 3. So, the paragraph that forms Sect. 4 could constitute the final remarks related to the presented results.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Thank you for submitting your paper. The work done here draws attention to a significant subject in hybrid nonlinear active control strategies for material analysis. I have found the paper to be interesting. However, several issues need to be addressed properly before the paper is being considered for publication. My comments including major and minor concerns are given below:

1. Please consider reviewing the abstract and highlight the novelty, major findings, and conclusions. I suggest reorganizing the abstract, highlighting the novelties introduced. The abstract should contain answers to the following questions:
2. What problem was studied and why is it important?
3. What methods were used?
4. What conclusions can be drawn from the results? (Please provide specific results and not generic ones). Please use numbers or % terms to clearly shows us the results in your experimental work. Please expand the abstract.
5. Introduction is too short and must be expanded, it does not critically discuss past literature and problem in hand.
6. Please consider reporting on studies related to your work from mdpi journals.
7. Please add a list of nomenclatures and abbreviations at the end of the manuscript for all the Greek symbols and letters used in this study.
8. The authors are strongly encouraged to move some of the formulas in the manuscript in an appendix instead of presenting it in the 2. Theoretical aspects section and instead just refer to it from the appendix.
9. Theoretical aspects what are the limitations of your proposed hybrid model? Please compare it against past models and highlight its advantages.
10. Table 1 where did the authors get this data from, please reference it.
11. Lines 185-187 “This observation is reasonable since dry friction has a better damping effect in the high-frequency band than low-frequency resonance” please support this claim with references.
12. Line 187 “The results are also reasonable according to [22].” This sentence is vague, it does not confirm whether results are showing similar trends or not, reasonable here is not clear. Please provide robust findings and discuss further.
13. Line 222 “increases slightly” by how much, please specify this using numbers or % terms.
14. Line 226-227 “reducing the external energy input to a certain extent.” By how much? Again use % terms or numbers.
15. Remove discussion section and merge with previous one, the current one is too short and small to be considered as a section.
16. Some of the results are merely described and is limited to comparing the experimental observation and describing results. The authors are encouraged to include a more detailed results and discussion section and critically discuss the observations from this investigation with existing literature.
17. Conclusion can be expanded or perhaps consider using bullet points (1-2 bullet points) from each of the subsections.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

The introduction can be further expanded as comment 5 was not answered properly. please check and resubimit.

Author Response

The introduction can be further expanded as comment 5 was not answered properly. please check and resubimit.

Comment 5: Introduction is too short and must be expanded, it does not critically discuss past literature and problem in hand.

Reply: Thank you very much for your comments on the introduction. The introduction has been expanded in the revised manuscript.