Design of Active Boundary Control to Suppress Vibrations in String

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper focuses on designing active boundary control for string vibration suppression using displacement actuators and sensors. The content is comprehensive and the conclusions are credible. Here are some comments.

1. This paper mainly considered the string's linear vibration when designing the PIPO controller. But in practice, nonlinear factors (like geometric or material nonlinearity) can affect strings. How applicable and robust is this controller for nonlinear vibrations? Do you plan to improve it for nonlinear cases in the future?
2. The paper doesn't detail compare the proposed method with existing passive or semi - active devices. How can the superiority of the proposed method be highlighted?

Author Response

See the attached paper.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

1. This paper extends the PIPO scheme previously reported, but to a uniform string, without clearly explaining what forms its core novelty compared to the existing research on boundary control and modal-space designs. The novelty needs to be emphasized and a comparison made with the most relevant existing work.
2. The experimental gain (0.15) was chosen “through trial and error”. Provide a systematic tuning rationale (root‑locus‑based criterion, optimization, or robustness margin) and include sensitivity analyses.
3. Plots show attenuation qualitatively, yet no numerical indicators are reported (e.g., peak FRF reduction in dB, settling time, modal damping ratios before/after control). Add such metrics for both simulation and test‑bed results and discuss uncertainties.
4. Only one string length, tension and damping setting were examined. Demonstrate robustness to parameter variations (tension drift, added payload, temperature) or justify why the presented case is representative.
5. High‑frequency spill‑over is said to be negligible, but no residual mode amplitude or stability margin is reported beyond the third mode. Include higher‑order measurements or provide a theoretical bound.
6. Specify sampling frequency, real‑time latency, sensor noise level, encoder resolution, and how dead‑band in the linear motor was mitigated (it currently causes residual vibrations).
7. Figure 6 caption duplicates that of Figure 
8. Due to the occurrence of several typographical errors, close proofreading is required.
9. Consider the potential significance of the boundary-actuated mechanism for real-world uses across the fields of musical stringing, long civil engineering cables, or the automotive industry, and compare these prospects with the piezoelectric or semi-active alternatives investigated in HALs hal-04662767 and hal-02394177 in terms of cost-effectiveness, energy efficiency, and installation convenience. It should be noted that acceptance of this work is not based on the proposed literature enhancements.

Author Response

See the attached paper.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have addressed several earlier concerns: (i) novelty is explained in the reply letter, (ii) experimental set-up details and sampling parameters are now documented, (iii) numerical and experimental damping gains are reported, and (iv) most typographical issues are fixed. However, gain-selection methodology, robustness analyses, quantitative performance indices, and high-order spill-over evidence are still weak.

1. The reply letter clarifies the distinction from previous single-input analyses; however, the paper does not integrate these claims into a concise comparative state-of-the-art section in the Introduction. It is crucial to directly integrate the new points elaborated in the letter into the paper and cite the closest competing boundary-control demonstrations relevant to strings.
2. Although a root-locus justification has been described, the experimental 0.15 gain choice is made using trial-and-error; no stability margin analyses or sensitivity factors are given. A limited parametric study (for instance, a ±20% gain variation with respect to damping ratio and settling time) would increase confidence level in the system robustness.
3. Modal damping improvements are now reported, but peak FRF attenuation in dB, rise/settling times, and residual RMS amplitudes are still missing.
4. The paper asserts that modes >3 are unaffected because Figure 5 changes little, yet no residual amplitude ratios or closed-loop pole plots beyond 10 Hz are supplied. Either include a table of uncontrolled/controlled modal magnitudes up to, say, the 7^th mode, or present an analytical spill-over bound.
5. Robustness to tension variation, added tip mass, or temperature remains untested. Even a brief simulation showing controller stability for ±10 % tension would partially address this concern.

Author Response

See the attached paper.

Author Response File: Author Response.pdf