Discerning Discretization for Unmanned Underwater Vehicles DC Motor Control

Round 1

Reviewer 1 Report

This work performed the analysis of different types of discretization methods applied to a DC motor drive in unmanned underwater vehicles controlled by deterministic artificial intelligence techiniques. Simulation results were presented.

Although the work can be of use for researchers and engineers in the field, the presentation shall improve a lot prior to any publication. Below my comments:

1. Avoid using acronyms in the paper title.

2. The abstract is confused and does not clear appoint to the work performed and results.

3. In the introduction, traditional PI control is not even mentioned. Is it not an alternative for the application? Why? 

4. Figure 1 is not cited in the text and Figure 2 is cited only in the legend of Figure 1. This should be fixed.

5. Line 164: The technical data of the system under consideration (DC motor drive) should be presented here. The authors cannot expect that the reader will read another reference prior reading their paper.

6. Line 169: I think this is the stability condition for continuous-time systems, not for discrete-time ones.

7. Line 181: Is equation (3) for discrete-time systems? If so, consider using "k" instead of "t".

8. Lines 260-261: please verify if the sentences are in accordance to the authors intention.

9. The results need to be better explained. What is the meaning of RLS, ARMA, ELS and DAI? I suspect these are the control methods acronyms, but they are not explained in the text. It is also important to compare de control methods.

10. Figure 6: The results for tracking the input (trajectory?) seems awful to me. There are huge delay and amplitude errors. Please comment about it.

11. Table 2: It seems odd to me that smaller sample times conduct to worse results, since it is expected a better approximation of the continuous-time system. Please comment about it.

Finally, I had a hard time to identify that several control techniques were being analysed for several discretization methods. This should be clear since the begining of the text (i.e. abstract and introduction). 

Author Response

REVIEWER 1

Although the work can be of use for researchers and engineers in the field, the presentation shall improve a lot prior to any publication. Below my comments:

1. Avoid using acronyms in the paper title. → The authors appreciate the given recommendation which has been ceded and accommodated in the revision.
2. The abstract is confused and does not clear appoint to the work performed and results. → Thank you for the comment. The review has been ceded in the abstract of the revised paper.
3. In the introduction, traditional PI control is not even mentioned. Is it not an alternative for the application? Why? → The authors thank the reviewer for the valuable comment. Classical control is now elaborated in the introduction of the revision and specified why PD control is emphasized over PI control.
4. Figure 1 is not cited in the text and Figure 2 is cited only in the legend of Figure 1. This should be fixed. → Thank you for the recommendation. The paper has been revised to accommodate the given recommendation in line no. 27.
5. Line 164: The technical data of the system under consideration (DC motor drive) should be presented here. The authors cannot expect that the reader will read another reference prior reading their paper. → The authors appreciate the recommendation provided by the reviewer. The recommendation is ceded & accommodated in the revised paper with several structural changes & improved organization.
6. Line 169: I think this is the stability condition for continuous-time systems, not for discrete-time ones. → The authors appreciate the review provided which has been ceded & accommodated in the revised paper.
7. Line 181: Is equation (3) for discrete-time systems? If so, consider using "k" instead of "t". → The authors appreciate the review provided which has been ceded & accommodated in the revised paper.
8. Lines 260-261: Please verify if the sentences are in accordance with the authors intention. → The authors appreciate the review provided. The statement is not made by the authors based on the current work. It is a standard characteristic of the least squares discretization method over the Tustin and the zero-pole approach. The statement has been deleted to avoid further confusion.
9. The results need to be better explained. What is the meaning of RLS, ARMA, ELS and DAI? I suspect these are the control methods acronyms, but they are not explained in the text. It is also important to compare these control methods. → The authors thank the reviewer for the valuable feedback. The full form of the techniques has been provided which have been explained in detail under section 1.2.
10. Figure 6: The results for tracking the input (trajectory?) seems awful to me. There are huge delay and amplitude errors. Please comment about it. → Thank you very much for the comment. The point is ceded with new figure & verbiage added to clarify the impact. The trajectory tracking becomes more awful as sample time is reduced (which is surprising). The plots presented are in accordance with the results obtained in the latest literature that demonstrate the efficacy with discretized implementations for deterministic artificial intelligence.
11. Table 2: It seems odd to me that smaller sample times conduct to worse results, since it is expected a better approximation of the continuous-time system. Please comment about it. → The authors thank the reviewer for the comment. This does seem counterintuitive about the performance of deterministic artificial intelligence with discretized implementations. This has been stipulated for future research in the discussion.
12. Finally, I had a hard time to identify that several control techniques were being analyzed for several discretization methods. This should be clear since the beginning of the text (i.e. abstract and introduction). → The authors appreciate the review. The recommendation has been ceded and accommodated for at the end of the introduction section for more clarity.

Reviewer 2 Report

The authors carried out an extensive analysis of existing methods for discretization of a continuous system. The simulation results are obtained and the statistical characteristics of the error are calculated.

It follows from the text of the paper that the deterministic artificial intelligence method was used to synthesize the parameters of the PD controller, but it is not entirely clear where this controller is present in the block diagram in Figure 5.

It also does not describe the details of obtaining the coefficients, how exactly the method was applied and what limitations of the method exist.

In the text (line 169), the authors state that for the stability of the system, the poles should not be located in the right half-plane, but for discrete systems, the condition |z(i)|<1 must be satisfied.

It is not clear from Figure 6 what the abbreviations RLS, ARMA, ELS, DAI mean.

In their results, the authors give the optimal value of the sampling step of the model T = 0.1. It is stated that a decrease in the step will lead to worse results, however, this value of the sampling step may not be sufficient for high-speed real-time systems. The choice of the reduced value of T is also not obvious.

Author Response

REVIEWER 2

1. The authors carried out an extensive analysis of existing methods for discretization of a continuous system. The simulation results are obtained, and the statistical characteristics of the error are calculated. → Yes, that is exactly what we have presented in this work.
2. It follows from the text of the paper that the deterministic artificial intelligence method was used to synthesize the parameters of the PD controller, but it is not entirely clear where this controller is present in the block diagram in Figure 5. → Thank you very much for the comment. However, unlike the ubiquitous stochastic artificial intelligence approaches, deterministic artificial intelligence is not used to determine the gains of the PD controller. This has been stated in the revised abstract for clarity. Instead, deterministic artificial intelligence achieves an autonomously determined trajectory using a PD feedback adaption to follow the target path.
3. It also does not describe the details of obtaining the coefficients, how exactly the method was applied and what limitations of the method exist. → Thank you very much for the comment. The deterministic AI approach is not used to obtain any coefficients. Instead, it involves the assertion of self-awareness statements and uses optimal learning to compensate for the deleterious effects of error sources.
4. In the text (line 169), the authors state that for the stability of the system, the poles should not be located in the right half-plane, but for discrete systems, the condition |z(i)|< 1 must be satisfied. → The authors appreciate the review provided which has been ceded & accommodated in the revised paper.
5. It is not clear from Figure 6 what the abbreviations RLS, ARMA, ELS, DAI mean. → The authors thank the reviewer for the valuable feedback. The full form of the techniques has been provided which have been explained in detail under section 1.2.
6. In their results, the authors give the optimal value of the sampling step of the model T = 0.1. It is stated that a decrease in the step will lead to worse results, however, this value of the sampling step may not be sufficient for high-speed real-time systems. The choice of the reduced value of T is also not obvious. → Thank you very much for the comment. To clarify, the sampling time of T_s = 0.1 s is found to be a lower threshold of sample time for most discretization methods because a sample time lower than this will result in high errors and delays in the trajectory tracking. This does seem counterintuitive with regards to conventional strategies and will be covered in future research to get a better explanation for the performance of deterministic AI with discretized implementations. We have stated this in the augmented discussion and future work.

Round 2

Reviewer 1 Report

First of all, I would like to thank the authors for the revised manuscript and for the answers. Almost every comment was satisfactorily attended.

I would like just to emphasize that I was expecting the motor drive data that resulted in the transfer function presented in (2) instead of a list of several dc motors (provided now in Appendix B). Will all this motors result in the same transfer function? (I do not think so.) This is important to allow other researchers to replicate the results.

Author Response

Thanks for the great recommendation. The authors cede to the reviewer's recommendation, since the authors agree: Repeatability by the readership is paramount, and accordingly section 2.1 is modified to maximize overtness of motor modeling in the revision.

Reviewer 2 Report

I thank the authors for clear and detailed answers.

All comments have been taken into account. The article is interesting and understandable.

I recommend the paper for publication.

Author Response

Thanks for your diligence and recommendations for manuscript improvements.  The authors are grateful to the reviewer.