Automatic Decentralized Vibration Control System Based on Collaborative Stand-Alone Smart Dampers

Round 1

Reviewer 1 Report

1. Do the Position of actuators and sensors on the test rig have effect on the results? other scenarios should be tested or at least discussed 

2. Do the proposed method perform well if one sensor doesn't sense properly? 

Author Response

• Do the Position of actuators and sensors on the test rig have effect on the results? other scenarios should be tested or at least discussed 

The research presented in this article is based on the use of devices embedding sensors, actuators and control algorithm. In this condition, the control to suppress vibration is co-located. It is known that the performance of such systems depends on the ability of the sensors to recognize the vibratory state of the structure (observability) and of the actuators to exercise authority over the modes of vibration involved (controllability). A clarification in this regard was included in the article (Section 5.1). Since these aspects are known in the literature and considering the extension of the article in its current form, it is not believed that the presentation of further results obtained with different positions of the devices provides elements of novelty.

• Do the proposed method perform well if one sensor doesn't sense properly?

At present no "fault-tolerant" algorithms have been developed. For this reason, if the sensor were to have a fault (e.g. introduction of noise), the performance of the system could significantly decrease. This aspect has been clarified by introducing a note in Section 6.

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper considers a vibration control system based on smart dampers. The topic is of prime importance, especially with the view to a recent earthquake in Turkey, or multiple others, as El Centro. In the introductory part of the paper, the overview of control approaches is given, with characterization of the selected references. 

In section II the authors mention adaptive control (line 75), and form a bizzare statement that it is the control action which is tuned. Well, we tune gains, modify conrtol policies, but never tune control. Line 78 - as the system is inherently multivatiable and has cross-couplings, what is the methodology to detect particular natural frequencies without exciting the other cross-coupled dynamics? 

Section III - should not a Lyapunov-method based or MIT-rule based method be selected to identify gains in an automatic fashion? 

I cannot agree with the statements of Section IV where the authors state the gain is stable or unstable. The closed-loop system can be stable or unstable, not the gain. This should be modified and proper control engineering terminology should be used. 

Figure 2 - can a control law have its Nyquist plot? Shouldn't it be an open-loop Nyquist plot instead? 

Section 4.2 - as per stroke saturation, why is not the describing function approach considered actually? If not, there is no discussion concerning the limits on the gain in the stroke loop and the shape of the hitherto discussed Nyquist plots. 

Some important papers are missing, like the ones of prof. Roman Lewandowski of Poznan University of Technology whose work is focused on this field. 

Author Response

REVIEWER 2

The paper considers a vibration control system based on smart dampers. The topic is of prime importance, especially with the view to a recent earthquake in Turkey, or multiple others, as El Centro. In the introductory part of the paper, the overview of control approaches is given, with characterization of the selected references. 

• In section II the authors mention adaptive control (line 75), and form a bizzare statement that it is the control action which is tuned. Well, we tune gains, modify conrtol policies, but never tune control.

Correct. The sentence was not appropriate. We modified it according to the suggestion of the reviewer.

• Line 78 - as the system is inherently multivatiable and has cross-couplings, what is the methodology to detect particular natural frequencies without exciting the other cross-coupled dynamics? 

We thank the reviewer for this observation. Concerning the superimposition of coupled modes of vibration, this is known to be a problem with regards to modal identification, although this usually happens at high frequencies. At present, the control system has been verified only if the modes of vibration are sufficiently distant to be clearly identified. This clarification has been added in the paper (Section 2).

• Section III - should not a Lyapunov-method based or MIT-rule based method be selected to identify gains in an automatic fashion? 

We agree with the reviewer about different methods in the literature to perform the modal identification of a structure. However, the technological constraints linked to the inevitable simplicity that each device must possess (especially as regards the electronics and the corresponding algorithms) forced us to use a custom method which, however, proves to be effective in its implementation.

• I cannot agree with the statements of Section IV where the authors state the gain is stable or unstable. The closed-loop system can be stable or unstable, not the gain. This should be modified and proper control engineering terminology should be used. 

Correct. The sentence was not appropriate. We modified it according to the suggestion of the reviewer.

• Figure 2 - can a control law have its Nyquist plot? Shouldn't it be an open-loop Nyquist plot instead? 

Also in this case the description of the figure is probably not correct. The graph represents the Nyquist diagram of the closed loop system. The text has been changed to be clearer.

• Section 4.2 - as per stroke saturation, why is not the describing function approach considered actually? If not, there is no discussion concerning the limits on the gain in the stroke loop and the shape of the hitherto discussed Nyquist plots. 

The synthesis of the gain useful for avoiding saturation of the actuator stroke represents a more restrictive condition than that identified by the ideal system represented in the diagram in Fig.2. Since this condition does not affect the stability of the system, but at most reinforces it, it is not considered necessary to add further considerations on this issue.

• Some important papers are missing, like the ones of prof. Roman Lewandowski of Poznan University of Technology whose work is focused on this field. 

We went through papers published by prof. Lewandowski and we found out a specific work related to this field, which is “Dynamic analysis of structures with multiple tuned mass dampers”. Then we added this work in our reference list.

Author Response File: Author Response.pdf

Reviewer 3 Report

Some suggestions are listed as follows.

1. It is suggested to further describe the modeling process of the actuator.

2. The frequency points of simulation and experiment are not completely consistent, so further explanation is suggested.

3. It is suggested to further indicate the meaning of the two curves in Figure 5 and Figure 7.

4. It is suggested to further explain the reason for the large fluctuation of the experimental curve in Figure 7.

Author Response

REVIEWER 3

• It is suggested to further describe the modeling process of the actuator.

We thank the reviewer for the suggestion. A footnote in Section 5.1 has been added, with the reference to the paper where the extensive description of the device is reported.

• The frequency points of simulation and experiment are not completely consistent, so further explanation is suggested.

We agree with the reviewer about this issue. Unfortunately, due to similar names between the picture files, we reported on the previous version of the manuscript the wrong results in terms of numerical simulations pictures (they were related to an older version of the model). Now, the plots in Fig. 5 are related to the correct version of the numerical model, which are consistent with the results described in Tab. 3. Moreover, Tab. 2 has been added to the manuscript to shown the evaluation of the natural frequencies both for numerical simulations and experimental tests.

• It is suggested to further indicate the meaning of the two curves in Figure 5 and Figure 7.

We agree the figures lack of labels and legenda. A clearer description has been done.

• It is suggested to further explain the reason for the large fluctuation of the experimental curve in Figure 7.

Fluctuations can be traced back to noise affecting the measurements. This is obviously completely missing in numerical analysis. A description of this has been added in the paper (Section 5.3.2).

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Thank you for amending your paper. However, please take a look at G(s)H(s) transfer function. Should you consider the transfer function between D(s) and Y(s), than it actually is an open-loop transfer function, definitely not the closed-loop one! (Considers Fig. 2 and the other figures). 

Author Response

We thank the reviewer for his/her remark. We in fact did a mistake in the caption of Figure 2, but G(s)H(s) is obviously the open loop transfer function. Changes have been done accordingly.
A final revision of language and typos has been done.

Author Response File: Author Response.pdf