Tracking Control and Backlash Compensation in an Inverted Pendulum with Switched-Mode PID Controllers

Response to Reviewer 1 Comments

1. Summary

Thank you very much for taking the time to review this manuscript “Tracking Control and Backlash Compensation in an Inverted Pendulum with Switched Mode PID Controllers”. Please find the detailed responses below and the corresponding revisions/corrections  in the re-submitted files

2. Questions for General Evaluation

Reviewer’s Evaluation

Response and Revisions

Does the introduction provide sufficient background and include all relevant references?

Yes

Are all the cited references relevant to the research?

Yes

Is the research design appropriate?

Yes

Are the methods adequately described?

Yes

Are the results clearly presented?

Can be improved

Are the conclusions supported by the results?

Can be improved

3. Point-by-point response to Comments and Suggestions for Authors

Comments 1: The equation for determining the RMSE should be provided and so also its range.

Response 1: Thank you for pointing this out. We agree with this comment. Therefore, we have incorporated this revision in line 265-266. The RMSE is empirically calculated by utilization of the formula mentioned in the result section

  Comments 2: The discussion should explain the mechanism involved in the results so obtained, for example what happens when “surges occur when the system transitions into backlash mode which….”

Response 2: Agree. We have meticulously revised the Result section and included performance metrics (settling time, rise time, peak time and overshoots ) for the performance comparison between Target Tracking of Inverted Pendulum with Switched mode Drive-Anti Drive and with single drives. This comprehensive approach ensures a thorough evaluation of the systems' capabilities, highlighting their respective strengths.

Comments 3: The conclusion should be independent of the discussion ad should be in accordance with the objectives of the paper.

Response 3: Agree. We have, included one more section that contains discussions in the following lines (276-291).

Comments 4: The model result should be validated using an existing model.

Response 4: Agreed. The validation of Tracking Control of  the Inverted Pendulum model with the Drive-Anti Drive configuration has undergone successful validation, demonstrating its effectiveness in maintaining system stability. To further assess the robustness and versatility of the model, it was also tested with single drive configurations. New Performance evaluation metrics [risetime,settling time, overshoots and peak time] were also used to compare the efficacy and robustness of the approaches. Details can be seen in Results section

Comments 5: What is the practical application of the model? This should be stated in the recommendation.

Response 5: Agree. ABB and KUKA, leading robotics manufacturers, employ advanced control algorithms to compensate for backlash. These algorithms include drive anti-drive mechanisms, where the system alternates driving and counter-driving forces to minimize the impact of backlash. These details are included in the recommendation section of the paper as well (276-291).

4. Response to Comments on the Quality of English Language

Point 1:

   The English language is moderately good. Minor modification of English language is required.

Response: We have  checked and improved the document for grammar and accuracy.

Thank you very much for taking the time to review this manuscript” “Tracking Control and Backlash Compensation in an Inverted Pendulum with Switched Mode PID Controllers”.”. Please find the detailed responses below and the corresponding revisions/corrections highlighted/in track changes in the re-submitted files

3. Point-by-point response to Comments and Suggestions for Authors

Comments 1: The dynamics of controlled plant has been mentioned as nonlinear systems similar with the switching case f_0-2. Beside of that the contributions along this problem formulation should be clarified especially with the switching algorithm comparing with the previous works studied before. 

Response 1: Thank you for pointing this out. Therefore, we have included  switching algorithm and performance metrics. The performance comparison between Switched mode Drive-Anti Drive and Drive only in terms of robustness,efficiency and accuracy has been carried out for the analysis. These details are included in Results and Conclusion.

Comments 2: Considering the nonlinear dynamic of controlled plant has some fixed points and each fixed points have its own suitable PID's gains. In this sense, this analysis should be conducted first in order to validate the existence of all three control modes. 

Response 2: We thank the reviewer for this suggestion. We have modified the manuscript to elaborate on the fixed points of the nonlinear system. We have included the equilibrium points of the system and the linearized model of the system around one of these equilibrium points to design the PID controllers for all modes. The results demonstrate that the PID controllers, designed using the linearized model for all three models, achieve good tracking performances for the non-linear switched system.  Details can be found in following lines (164-176)

Comments 3: Numerical system has been employed. In order to evaluate the controller, the plots of control efforts are required. Unfortunately, only the plots of tracking performance are given.  

Response 3: We thank the reviewer for the suggestion. We have modified the manuscript to incorporate the plots of control efforts. In addition, to this, new performance evaluation metrics, i.e., rise-time, settling time, overshoot and peak time, were also added to demonstrate the efficacy and robustness of the approaches compared to the conventional control system without Anti-Drive system.

Comments 4: It has (most likely) saturation in Fig. 8. Is the simulation system has sufficient constrain regrading to the physical limit of plant? Is the closed-loop system still stabilized? 

Response 4: The apparent clipping of the plot in Figure 8 of the manuscript is not due to saturation, but due to the limits on the Y-axis in the plot. We have zoomed out the plot to show the entire response in Figure 8. As is clear from the plot, the closed-loop system is stabilized.

4. Response to Comments on the Quality of English Language

Point 1: Moderate modification of English language is required.

We thank the reviewer for the comment on Quality of English. We have checked the manuscript for such errors and made several modifications to improve the quality of language/presentation.

1. Summary

Thank you very much for taking the time to review this manuscript “Tracking Control and Backlash Compensation in an Inverted Pendulum with Switched Mode PID Controllers”. Please find the detailed responses below and the corresponding revisions/corrections highlighted/in track changes in the re-submitted files

2. Questions for General Evaluation

Reviewer’s Evaluation

Response and Revisions

Does the introduction provide sufficient background and include all relevant references?

Can be improved

All the sections were improved as per the recommended suggestions

Are all the cited references relevant to the research?

Must be improved

Is the research design appropriate?

Must be improved

Are the methods adequately described?

Must be improved

Are the results clearly presented?

Must be improved

Are the conclusions supported by the results?

Must be improved

3. Point-by-point response to Comments and Suggestions for Authors

Comments 1: 1. The article states that backlash is the most common problem of electromechanical systems. This is not true. Such a statement can only apply to positional electromechanical systems, which are a partial case of a broad class of electromechanical systems.

Response 1: Thank you for pointing this out. We agree with this comment. Therefore, we have incorporated this revision in line section Introduction

Comments 2:  The ratio of the power of the two motors is not clear from the article.

Response 2: Agree. The ratio of power of two motor is turned out to be 3.4.

Comments 3: . In line 84, there is no reference to the literature.

Response 3: Agree. We have, accordingly, revised and incorporated the literature in the prescribed lines. This missing reference is included.

Comments 4: In chapter 3, references to the literature are not consistent.

Response 4: Agree. We have, accordingly, revised and made it consistent by revising the text in Results (section-3) section.

Comments 5:  The model in fig. 4, it is necessary to somewhat describe and clarify the accepted assumptions.

Response 5: Agree. We have, included the assumptions that we took for the model shown in Figure 4.

Comments 6:  Transition processes for each DC motor must be added to the research results.

Response 5: Agree. Therefore, in order to explain transition process of each motor, we have included the results of control efforts done by Drive and Antidrive in Switched mode configuration.