Development of a Force Feedback Controller with a Speed Feedforward Compensator for a Cable-Driven Actuator

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper deals with a 2-DoF control method (feedback and feedforward) for cable actuation units. The authors seem interested in the relevant application sector of rehabilitation robotics, where cable actuation is still extremely widespread, but they are encouraged to explore other potential sources of innovation. For example, the field of cable-driven parallel robots and continuum robots employ cable actuation units and provide insightful state-of-the-art results. See for example:

Santos, J. C., & Gouttefarde, M. (2021, June). A simple and efficient non-model-based cable tension control. In International Conference on Cable-Driven Parallel Robots (pp. 297-308). Cham: Springer International Publishing.

Idà, E., & Mattioni, V. (2022, October). Cable-driven parallel robot actuators: state of the art and novel servo-winch concept. In Actuators (Vol. 11, No. 10, p. 290). MDPI.

Troncoso, D. A., Robles-Linares, J. A., Russo, M., Elbanna, M. A., Wild, S., Dong, X., ... & Axinte, D. (2022). A continuum robot for remote applications: From industrial to medical surgery with slender continuum robots. IEEE Robotics & Automation Magazine, 30(3), 94-105.

That being said, the manuscript proposed some novel concepts, in the reviewer's opinion but should undergo substantial review before publication.

• the authors do not justify their modeling choice, and simply put equations. Reasoning and explaining why some transfer functions are used would help understand why some strategies were chosen and eventually implement and improve the authors' work. This way, the paper is written as an internal lab report.
• It is a very bad practice in model identification experiments to include human factors if they can be removed. The authors clearly state that a test person was the one "holding the cable still" while the motor was exerting torque for model identification and parameter setting purposes. This is a very bad scientific practice, as experiments and results cannot be reproduced even the slightest. in static tests, the cable could just be fixed on a frame, and in dynamic tests, it could be hooked to another position servo-controlled motor replicating the human movement. Expecting a human to reproduce a sinusoid with its arm and a metronome is not a scientific experiment; it is a preliminary internal result justifying buying a motor for experiments. The authors are candid about the test subject not being able to stay still during experiments.
• In the introduction, the authors mention that one of the worst limitations of existing controllers is that to compensate for friction, lengthy experiments are to be done. They then propose a different controller and perform experiments to tune its parameters. The reviewer does not understand the added value of the authors' methodology, as it is neither qualitatively nor quantitatively compared to the literature.

Smaller comments

• there is no paper structure in the introduction, and the reader does not know what to expect from the paper: this should be rectified
• there is no mention of which force sensor is employed, and its accuracy data. It is impossible to know if 5N is a good tracking performance without knowing which sensor is used to measure it.
• there is no rationale for understanding why 5 N is a good overall force error
• Figures should be put where relevant with respect to text

Author Response

We thank the reviewer’ precious comments (black font below). A detailed point-by-point response to the comments is provided below (red font). Corresponding changes have also been highlighted in red font in the updated manuscript itself.

Substantial changes have been made in the updated manuscript. Thanks to the reviewer feedback, the resubmitted manuscript is much better than the last version.

Review comments and author reply:

The paper deals with a 2-DoF control method (feedback and feedforward) for cable actuation units. The authors seem interested in the relevant application sector of rehabilitation robotics, where cable actuation is still extremely widespread, but they are encouraged to explore other potential sources of innovation.

We agree completely with the reviewer.

In the updated manuscript, a more comprehensive overview of CDA application is provided in Lines 46-52. Different applications are presented, not only in rehabilitation, but also in astronomy, aerospace and construction. Furthermore, different research areas such as adaptive position control, tension distribution optimisation, model parameter identification for tension prediction and sagging prevention are also introduced in Lines 63-71.

1. For example, the field of cable-driven parallel robots and continuum robots employ cable actuation units and provide insightful state-of-the-art results. See for example:

Santos, J. C., & Gouttefarde, M. (2021, June). A simple and efficient non-model-based cable tension control. In International Conference on Cable-Driven Parallel Robots (pp. 297-308). Cham: Springer International Publishing.

We agree completely with the reviewer. We thank the reviewer for the recommended paper.

This recommended paper is very relevant to our study. It is cited as Reference 40 in the updated manuscript.

This recommended paper controlled the force using the indirect force control methods, which means that the force was regulated through control of cable velocity. Our study investigated the direct force control, where the motor ran in the torque mode.

Based on the information presented in this paper, different control approaches are presented in Lines 75-81 in the updated manuscript. This paper was discussed in Lines 79-80, and Line 110.

Idà, E., & Mattioni, V. (2022, October). Cable-driven parallel robot actuators: state of the art and novel servo-winch concept. In Actuators (Vol. 11, No. 10, p. 290).

We agree completely with the reviewer.

This recommended paper analysed the existing architectures of servo-winches, which is relevant to our study. This paper is cited as Reference 20 in the updated manuscript, and was discussed in Lines 63-64.

Troncoso, D. A., Robles-Linares, J. A., Russo, M., Elbanna, M. A., Wild, S., Dong, X., ... & Axinte, D. (2022). A continuum robot for remote applications: From industrial to medical surgery with slender continuum robots. IEEE Robotics & Automation Magazine, 30(3), 94-105.

We agree completely with the reviewer.

The paper describes various applications of CDA in scenarios for aerospace assets, nuclear installations, and robot-assisted surgery, which is very relevant to our paper. This paper is cited in Line 49 as Reference 7 in the updated manuscript.

2. That being said, the manuscript proposed some novel concepts, in the reviewer's opinion but should undergo substantial review before publication.

We agree completely with the reviewer.

In the updated manuscript, substantial changes were made in the Introduction section. Apart from introduction of a more comprehensive overview of CDA, such as different applications and different research areas, two common methods of force control (direct and indirect) are also introduced. Different algorithms of direct force control are reviewed. Some new studies [45-47] are discussed in the review.

3. The authors do not justify their modeling choice, and simply put equations. Reasoning and explaining why some transfer functions are used would help understand why some strategies were chosen and eventually implement and improve the authors' work. This way, the paper is written as an internal lab report.

We agree completely with the reviewer. Therefore, we addressed this issue in Lines 181-187 of the updated manuscript as follows:

“According to Newton’s second law, the cable force in a steady static state should ex-hibit a proportional relationship to the motor torque, governed by a gain kCDA. After considering a certain time required for the force to achieve the final value in the phys-ical system, a first-order transfer function was used to approximate the dynamics of the CDA. A first-order transfer was also used in a study of a similar force control setup [50].”

4. It is a very bad practice in model identification experiments to include human factors if they can be removed. The authors clearly state that a test person was the one "holding the cable still" while the motor was exerting torque for model identification and parameter setting purposes. This is a very bad scientific practice, as experiments and results cannot be reproduced even the slightest. in static tests, the cable could just be fixed on a frame, and in dynamic tests, it could be hooked to another position servo-controlled motor replicating the human movement. Expecting a human to reproduce a sinusoid with its arm and a metronome is not a scientific experiment; it is a preliminary internal result justifying buying a motor for experiments. The authors are candid about the test subject not being able to stay still during experiments.

We agree with the reviewer completely that a unified test setup without any human-involved subjective factors should be designed to perform the identification tests to remove the human-involved factors. However, this study performed the test on a test person because of potential vibration issue and practical application of the CDA in the current study.

This study involved two types of tests: static and dynamic tests. For the static test, the coauthors did perform a preliminary test by mechanically fixing the cable through a stiff mechanism. However, vibration was sometimes observed when different torque pulses were sent to the actuator. Vibration occurred because of the spring-damper property of the cable (low stiffness and low damping). In a very stiff environment, a spring-mass system can easily oscillate (see the cited reference 23). However, no oscillation was observed when the cable was pulled by hand. The reason might be an increased damping during pulling by hand.

During the practical usage of the system, we seldom use the CDA in such a stiff environment. Instead, the CDA was developed for neuromuscular rehabilitation, where people are always involved. Therefore, the identification tests were performed by a person.

Due to the potential vibration observed in a stiff-fixation of the cable, and given the application of the CDA as a neuromuscular rehabilitation device, the tests were performed with a test person in the current study. Nevertheless, a strategy for vibration suppression, such as the strategies described in the cited papers [23, 54] need to be investigated in future work to stabilise the physical interaction of CDA.

After the vibration is suppressed in a stiff fixation, then during the dynamic test, the cable could be hooked to another position servo-controlled motor. Such a loading system is still under development in our lab. But it is often employed in the literature to perform such a dynamic force control test by a person, as seen in the cited work 50.

Based on the comments, we addressed the limitations raised by the reviewer in Lines 442-455 of the updated manuscript.

5. In the introduction, the authors mention that one of the worst limitations of existing controllers is that to compensate for friction, lengthy experiments are to be done. They then propose a different controller and perform experiments to tune its parameters. The reviewer does not understand the added value of the authors' methodology, as it is neither qualitatively nor quantitatively compared to the literature.

We agree with the reviewer mostly that the contribution of the study should be highlighted clearly through comparison of our approach with the literature.

Therefore, the force control accuracy from the literature was listed in the updated manuscript. However, the force control accuracy is highly dependent on actual dynamic cable speed. Given the variations in speeds across different studies, direct comparisons with literature should be made with caution to ensure appropriate interpretation.

This paper proposed a new strategy for accurate force control of CDA. As described in Introduction section, in the literature, force control strategies often integrate friction compensation through repetitive tests (see the cited studies [12, 14, 18, 33]). Meanwhile, force control strategies are often derived through sophisticated theoretical analysis after considering the spring-damper property into the system dynamics (see the cited studies [2, 3, 16, 43].). However, the current study developed the strategy through a series of open-loop and closed-loop tests. The approach was practical and straightforward to implement and still produced comparable force control accuracy that is reported in the literature. This is the added value for the innovative methodology proposed in the current study.

Based on the reviewer’s comment, we summarised the force control accuracy from the literature in Lines 422-435.

The innovation of this study is summarised in Discussion section (Lines 435-437) and Conclusions section (Lines 475-480).

6. Smaller comments

• There is no paper structure in the introduction, and the reader does not know what to expect from the paper: this should be rectified.

We agree completely with the reviewer. We provided the paper structure and the expected results in Lines 136-144.

• There is no mention of which force sensor is employed, and its accuracy data. It is impossible to know if 5N is a good tracking performance without knowing which sensor is used to measure it

We agree completely with the reviewer. The information of the force measurement is addressed in Lines 159-166.

• There is no rationale for understanding why 5 N is a good overall force error.

We agree completely with the reviewer. We added the rationale for the criterion in the updated manuscript.

The criterion of 5 N was determined based on subjective testing feedback and insights from relevant literature.

During the dynamic test with a reference force of 100 N, when a force error was smaller than 5 N, and the test person couldn’t observe the difference, and felt it as a constant force training during dynamic movement. Therefore, a force error smaller than 5 N was considered as a very good control strategy. Furthermore, in the literature, most of studies presented a force control error larger than 5%. Therefore, an error smaller than 5 N for a target force of 100 N, i.e., error smaller than 5%, is considered as a very good control strategy.

Based on the reviewer’s comment, the rationale of the force control accuracy criteria is addressed in Lines 276-280 in the updated manuscript.

• Figures should be put where relevant with respect to text.

We agree completely with the reviewer. We put the figures close to the relevant texts in the updated manuscript.

Reviewer 2 Report

Comments and Suggestions for Authors

This paper presents a force feedback controller integrated with a speed feedforward compensator for cable-driven actuator (CDA) in rehabilitation robotics. Dynamic tests with the PI force controller highlighted the impact of speed disturbances on force output, leading to the improvement of the feedforward compensator.  The control strategy successfully tracked the force at different speeds in dynamic tests. The combination of feedback and feedforward controllers shows potential for accurate force control in cable-driven systems, which is crucial for precise movement in cable-driven rehabilitation robots. However, there are areas for improvement, and the authors are encouraged to consider these suggestions to enhance the paper's clarity and quality.

1. The author's writing of the abstract is evidently comprehensive; however, a more concise and structured abstract is necessary, as it would help readers quickly grasp the research background, methods, results, and other key elements of the manuscript.
2. The author should further elaborate on the comparison between the proposed control method and existing control methods in the "Introduction". This would help highlight the advantages of the proposed controller in the manuscript. For instance, the mere mention of "PID controller or lead controller" for force control is insufficient; a more comprehensive overview of force control methods should be included. Relevant literature can be referenced:

(1)   Force control for active chassis balancing (https://doi.org/ 10.1109/TMECH.2016.2612722)

(2)   Horizon-stability control for wheel-legged robot driving over unknow, rough terrain (https://doi.org/10.1016/j.mechmachtheory.2024.105887)

3. At the end of the "Introduction", the author should include an outline of the manuscript's structure to help readers quickly understand the overall organization and content framework of the manuscript.
4. In lines 105-110, the author lists the research methods employed in this study. However, the specific implementation process and details of using the "System Identification Toolbox" to determine the dynamic model of the CDA are not provided. These details should be included in the subsequent sections under "Methods". The author is requested to provide this additional information.
5. In lines 105-110, the author lists the research methods employed in the manuscript. Although Figure 2 illustrates the control strategy, the subsequent sections under "Methods" do not provide an introduction to the MATLAB/Simulink simulation model. Additionally, there are no details regarding the simulation modules, process, or parameters. Given the control strategy presented in "Figure 2", it is necessary to include these additional details regarding the MATLAB/Simulink implementation.
6. For "2.1. Mechanical Description", a detailed introduction to the experimental setup should be provided, including but not limited to: the key parameters of the motor (EC60), the force sensor, and the servo controller, as well as the experimental procedure and operational steps of the setup.
7. The core design in the manuscript is the feedforward compensator. The authors are requested to further elaborate on the derivation process of Equation (5) and provide relevant explanations for the formulas.
8. The research method proposed in the manuscript is applied to the field of rehabilitation. The authors are requested to supplement information regarding the test person, including but not limited to: the number of participants, selection criteria, whether they are healthy individuals or patients, etc., in order to mitigate the risk of generalizing the conclusions.
9. It is evident that the authors have provided a thorough description of the experimental results. However, the authors are asked whether they have considered the potential human errors introduced by "manually pulling the cable" during dynamic testing.
10. The authors have indicated that "the fitting degree of system identification is 57%", which is evidently low. The authors are asked whether this 57% fitting degree affects the accuracy of the experimental results in the manuscript, and to identify the potential causes (such as the neglect of cable stiffness nonlinearity).
11. In Figures 4(a), 5(a), 6(a), 9(a), and 10(a)(d), the solid and dashed black lines could be represented using different colors. This can make the comparison of experimental data more intuitive and clearer. Additionally, the authors are requested to check the format and layout of all the figures to ensure consistency in font sizes. Furthermore, the authors should ensure that the axis labels are properly aligned between the different figures.
12. Regarding the dynamic testing, in the simulation for the combined PI force feedback controller and the speed compensator, the is 18.8%. Compared to the static test, the torque error in the dynamic test is significantly higher. The authors are requested to provide an explanation for this. Additionally, the of 18.8% seems to contradict the later statement of "satisfactory simulation". What is the objective standard for achieving a "satisfactory simulation"?
13. The "Conclusions" section of the paper should be more comprehensive, providing a thorough summary of the study, including the research background, research methods, and research findings.
14. The author should summarize the main contributions of the research in concise language, either at the end of the "Introduction" or in the "Conclusions", highlighting the core aspects of the study.
15. The authors should cite more references to support the superiority of the methods presented in the manuscript. Currently, the manuscript's literature support is clearly insufficient. Additionally, it would be beneficial to further verify the timeliness of the references to ensure that the cited literature includes the latest research findings.
16. The language of the paper is generally clear, but some sentences are quite lengthy. It is recommended to simplify some sentence structures to improve readability.
17. The authors are requested to standardize the format of all references in strict accordance with the publication requirements of MDPI.

Comments on the Quality of English Language

The language of the paper is generally clear, but some sentences are quite lengthy. It is recommended to simplify some sentence structures to improve readability.

Author Response

We thank the reviewer’ precious comments (black font below). A detailed point-by-point response to the comments is provided below (red font). Corresponding changes have also been highlighted in red font in the updated manuscript itself. We removed the grammar mistakes and improved the overall manuscript. 

Substantial changes have been made in the updated manuscript. Thanks to the reviewer feedback, the resubmitted manuscript is much better than the last version.

Review comments and author reply:

This paper presents a force feedback controller integrated with a speed feedforward compensator for cable-driven actuator (CDA) in rehabilitation robotics. Dynamic tests with the PI force controller highlighted the impact of speed disturbances on force output, leading to the improvement of the feedforward compensator.  The control strategy successfully tracked the force at different speeds in dynamic tests. The combination of feedback and feedforward controllers shows potential for accurate force control in cable-driven systems, which is crucial for precise movement in cable-driven rehabilitation robots. However, there are areas for improvement, and the authors are encouraged to consider these suggestions to enhance the paper's clarity and quality.

1. The author's writing of the abstract is evidently comprehensive; however, a more concise and structured abstract is necessary, as it would help readers quickly grasp the research background, methods, results, and other key elements of the manuscript.

We agree completely with the reviewer. To address this comment, we restructured the abstract in Lines 13-38 of the updated manuscript, with the parts for background, objective, methods, results, and conclusions specifically clarified.

2. The author should further elaborate on the comparison between the proposed control method and existing control methods in the "Introduction". This would help highlight the advantages of the proposed controller in the manuscript. For instance, the mere mention of "PID controller or lead controller" for force control is insufficient; a more comprehensive overview of force control methods should be included. Relevant literature can be referenced:

We agree mostly with the reviewer regarding the comments. In the “Introduction” section of the updated manuscript, a more comprehensive overview of CDA is provided, including two common methods of force control (direct and indirect), and different algorithms of direct force control. Lines 84-89 explain more information of "PID controller or lead controller" for force control.

In order to compare the proposed control method and existing control methods clearly, the control accuracy should be presented. Therefore, this can only be presented after the Results section. Therefore, detailed comparison between the proposed control method and existing control methods is presented in Lines 422-435 in “Discussion” section, instead of in “Introduction” section recommended by the reviewer. However, in “Introduction” section (Lines 142-144), we summarised the advantages of the force control proposed in the current study, as recommended by the reviewer.

(1) Force control for active chassis balancing (https://doi.org/ 10.1109/TMECH.2016.2612722)

(2) Horizon-stability control for wheel-legged robot driving over unknow, rough terrain (https://doi.org/10.1016/j.mechmachtheory.2024.105887)

We agree completely with the reviewer. The two papers described the force control to solve the balance issue and position regulation. They have been cited as Reference s31 and 32 in Lines 72-73 in Introduction section, and Lines 439-441 in Discussion section.

3. At the end of the "Introduction", the author should include an outline of the manuscript's structure to help readers quickly understand the overall organization and content framework of the manuscript.

We agree completely with the reviewer. Based on this comment, we updated the manuscript with the paper structure in Lines 136-142.

4. In lines 105-110, the author lists the research methods employed in this study. However, the specific implementation process and details of using the "System Identification Toolbox" to determine the dynamic model of the CDA are not provided. These details should be included in the subsequent sections under "Methods". The author is requested to provide this additional information.

We agree completely with the reviewer. Based on this comment, we reorganised the updated manuscript with an additional section of “System identification” (Section 2.1.1) in Lines 178-225 of the updated manuscript.

5. In lines 105-110, the author lists the research methods employed in the manuscript. Although Figure 2 illustrates the control strategy, the subsequent sections under "Methods" do not provide an introduction to the MATLAB/Simulink simulation model. Additionally, there are no details regarding the simulation modules, process, or parameters. Given the control strategy presented in "Figure 2", it is necessary to include these additional details regarding the MATLAB/Simulink implementation.

We agree completely with the reviewer. Based on this comment, we introduced MATLAB/Simulink simulation model in Lines 148-149, 150-152 of the updated manuscript. Then, an additional section “Simulation of Force Control Strategy” is presented in Section 2.3 (Lines 252-282 of the updated manuscript), where details regarding the simulation model, process, and parameters are provided in Lines 253-261. Lastly, an additional Figure 3 is provided to describe the Simulink model.

6. For "2.1. Mechanical Description", a detailed introduction to the experimental setup should be provided, including but not limited to: the key parameters of the motor (EC60), the force sensor, and the servo controller, as well as the experimental procedure and operational steps of the setup.

We agree completely with the reviewer. Based on this comment, we made following changes:

The key parameters of the motor (EC60), the force sensor, and the servo controller are described in Lines 158-163 of the updated manuscript. The experimental setup is shown through the updated Fig. 1. The experimental procedure and operational steps are provided in Lines 179-180, 192-195, and Lines 206-214 in Section 2.2.1.

7. The core design in the manuscript is the feedforward compensator. The authors are requested to further elaborate on the derivation process of Equation (5) and provide relevant explanations for the formulas.

We agree completely with the reviewer. Based on this comment, we further elaborated on the derivation process of the feedforward compensator in Lines 245-247 with explanations for Eqs (8-9).

8. The research method proposed in the manuscript is applied to the field of rehabilitation. The authors are requested to supplement information regarding the test person, including but not limited to: the number of participants, selection criteria, whether they are healthy individuals or patients, etc., in order to mitigate the risk of generalizing the conclusions.

We agree completely with the reviewer. Based on this comment, we provided more information regarding the test person in Lines 152-156 of the updated manuscript. The tests were performed on a healthy person (age of 28 yrs, height of 1.74 m, body mass of 85 kg). The selection criterion of the test person was that she/he was able to perform neuromuscular training of the arm with a load higher than 150 N. This is a single-case study, and the data are not generalisable.

9. It is evident that the authors have provided a thorough description of the experimental results. However, the authors are asked whether they have considered the potential human errors introduced by "manually pulling the cable" during dynamic testing.

We agree completely with the reviewer. We considered the potential human errors introduced by "manually pulling the cable" during dynamic testing. Due to the potential vibration observed in a stiff-fixation of the cable, and given the application of the CDA as a neuromuscular rehabilitation device, the tests were performed with a test person in the current study. Nevertheless, getting a testing person to perform the dynamic testing is often used in the literature, as seen in the cited paper [50]. Therefore, human errors introduced by "manually pulling the cable" during dynamic testing were considered as a limitation in the study.

Based on this comment, we addressed the limitations induced by "manually pulling the cable" during dynamic testing in Lines 442-455 of the updated manuscript.

10. The authors have indicated that "the fitting degree of system identification is 57%", which is evidently low. The authors are asked whether this 57% fitting degree affects the accuracy of the experimental results in the manuscript, and to identify the potential causes (such as the neglect of cable stiffness nonlinearity).

We agree with the reviewer mostly that the goodness of fit as 57% is not perfect, but the plant model simulated the force output and the target torque which are similar to the experimental value in the static test (mean F_{exp_sim} of 4 N, mean RMSE_T_{exp_sim} of 6%). This supported that the first-order transfer function is considered to provide VERY GOOD simulation in the static test. This is addressed in Lines 296-301 of the updated manuscript.

The potential causes of the fitting of 57% include overlooking the spring-damper characteristics of the cable and the nonlinear behaviour of its stiffness.

In order to find out whether approximation of the system with a first-order system affected the force control accuracy, a new study should be performed, where a new model, probably a second-order or a third-order model is estimated, and then the similar static and dynamic tests are performed. This investigation will be performed in the future.

Based on the comments, the potential improvement in the model identification and the future work have been addressed in Lines 393-396 in the updated manuscript.

11. In Figures 4(a), 5(a), 6(a), 9(a), and 10(a)(d), the solid and dashed black lines could be represented using different colors. This can make the comparison of experimental data more intuitive and clearer. Additionally, the authors are requested to check the format and layout of all the figures to ensure consistency in font sizes. Furthermore, the authors should ensure that the axis labels are properly aligned between the different figures.

We agree completely with the reviewer that using different colours can make the comparison of experimental data more intuitive and clearer. In the manuscript, these figures, which are Figures 5(a), 6(a), 7(a), 10(a), and 11(a)(d) in the updated manuscript, are replotted where the reference force is presented in a green line. We also checked and improved the format and layout of all figures.

12. Regarding the dynamic testing, in the simulation for the combined PI force feedback controller and the speed compensator, the is 18.8%. Compared to the static test, the torque error in the dynamic test is significantly higher. The authors are requested to provide an explanation for this. Additionally, the of 18.8% seems to contradict the later statement of "satisfactory simulation". What is the objective standard for achieving a "satisfactory simulation"?

We understand the reviewer’s point here. We apologise that we didn’t put this clearly in the first manuscript.

The "satisfactory simulation" was based on the force control accuracy, while the torque was the resultant signal from the control strategy. We can’t control the torque signal to achieve a satisfactory simulation.

To make this statement clear, we addressed in the updated manuscript that the "satisfactory simulation" referred to the force output comparison between the experiment and simulation. The force error smaller than the threshold of 7.5 N was considered as "satisfactory simulation". This information is provided in Lines 273-282 of the updated manuscript.

Since the difference between the experimental and simulated force RMSE_F_{exp_sim} was only 5.4 N, therefore, we considered the Simulink model provided "satisfactory simulation". This information is provided in Lines 347-351 of the updated manuscript.

The difference between the simulated and experimental torque probably came from factors such as the force measurement noise, system friction, and spring-damper property of the cable, which jointly produced a more dynamic experimental torque T_exp than the simulated torque T_sim. Nevertheless, the simulated torque and the experimental torque shared a similar curve shape.

Based on this comment, the explanations for the difference between the calculated torque are provided in Lines 351-356 of the updated manuscript.

13. The "Conclusions" section of the paper should be more comprehensive, providing a thorough summary of the study, including the research background, research methods, and research findings.

We agree completely with the reviewer upon the "Conclusions" section. Based on this comment, we updated the "Conclusions" section in Lines 468-480 of the updated manuscript with a thorough summary of research background, methods, findings as well as the contribution to the control of general cable-driven rehabilitation robotic systems.

14. The author should summarize the main contributions of the research in concise language, either at the end of the "Introduction" or in the "Conclusions", highlighting the core aspects of the study.

We agree completely with the reviewer upon the summary of the contributions of the research. Based on this comment, we summarise dthe main contributions in the Introduction section (Lines 142-144) and highlighted the core aspects of the study in Conclusions section (Lines 475-480) in the updated manuscript.

15. The authors should cite more references to support the superiority of the methods presented in the manuscript. Currently, the manuscript's literature support is clearly insufficient. Additionally, it would be beneficial to further verify the timeliness of the references to ensure that the cited literature includes the latest research findings.

We agree completely with the reviewer upon the references. We performed an extensive literature review through study on more papers. There are 55 references in the updated manuscript. 18 out of them were published in the past 5 years.

16. The language of the paper is generally clear, but some sentences are quite lengthy. It is recommended to simplify some sentence structures to improve readability.

We agree completely with the reviewer upon the language. We simplified some sentences. The language has been checked in the updated manuscript.

17. The authors are requested to standardize the format of all references in strict accordance with the publication requirements of MDPI.

We agree completely with the reviewer upon the reference format. The format of all references has been updated in the updated manuscript.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I still do not agree that subjective testing with a person holding the cable end is a sound scientific instrument. Any kind of sensor can be installed on a proper fixture to quantitatively measure what is subjectively perceived buly the experimenter, who introduces a strong bias in the experiment. Yet, the paper is finely written and sound in the rest, and I won't oppose to publishing on this journal