The Design of a Tracking Controller for Flexible Ball Screw Feed System Based on Integral Sliding Mode Control with a Generalized Extended State Observer

Round 1

Reviewer 1 Report

It is very good that the authors do introduce the uncertainty of parameters in the FRF in Figure 3. However, this uncertainty should be also quantified using statistical techniques (statistical distributions, statistical processes) in the governing equations. 

The introduction of the controller is interesting. Especially appealing is the vibration compensation design of the controller mechanism. However, the authors do completely ignore the formal stability analysis of the controller. As mentioned previously, some some system parameters are assumed to be more or less random (the actual randomness should be quantified).  Then, a formal rigorous proof of the robustness of the controller to perturbations is a must. 

The same holds true for external perturbations induced by vibrations. The stability regions of the controller should be formally introduced, explained, and discussed. 

It is surprising to observe that computations simulations do not directly incorporate the randomness of system parameters. 

Experimental tests are interesting and promising. However, the manuscript needs to be improved from the formal point of view. 

Minor editing of the presentation style is recommended. 

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Dear Authors

The Authors' intention was to develop a servo control strategy to compensate for any disturbances that could disturb the operation of the flexible ball screw feed system. As the Authors wrote in the abstract, the tracking controller was to be based on integral sliding mode control with a GENERALIZED, EXTENDED state observer. This means that the subject of the manuscript is consistent with the Aims&Scope of the Actuators Journal. After briefly reading the manuscript, it seemed to the reviewer that the Authors had achieved their intended goal, with a few exceptions.

Namely, the most important model describing the dynamics of the controlled object (flexible ball screw feed system) is too simple, because it is presented in the form of two blocks and only two degrees of freedom (DoF). In the literature (attached), models with 9 DoF are used as standard. Moreover, only the final form of the two dynamics equations is given with a very sparse description and without reference to the literature. Moreover, at least an outline of the derivation of the equations is missing, i.e. formulas for potential and kinetic energy and the Euler-Lagrange equation. Hence the conclusion that the model was intended for the reader. knowing (or being able to imagine), e.g. the problem of ball contact with a threaded groove. An advanced reader also had the opportunity to familiarize himself with a more complicated model, for example taking into account clearances in the system or non-linearity of contact between balls and rytern tube or end caps or deflector depending on the type of ball screw used. However, for a beginner reader who wants to become familiar with the problem, the block model (as a black box) is useless. It is necessary to at least refer to the literature (attached) showing the contact of balls in the thread grooves of the screw and nut. Additionally, nothing was mentioned about the method of identifying model parameters, such as stiffness, damping and friction coefficients. The method of generating disturbances in these governing equations is also not provided. The reviewer had to find the source [1] (attached below) on his own, which describes this model in a little more detail. Although also without the necessary derivation of equations (because these are not classical dynamics equations, despite only having 2 DoF) and without identifying the parameters of the systems, because these are not standard equations.

In summary, one should consider whether the state observer that the Authors used together with the sliding mode control in the construction of the tracking controller can be called GENERAL and EXTENDED?

The reason for asking this question is:

a) using a very simple dynamics model of flexible ball screw and only with a single nut, instead of two nuts, to check the tracking controller,

b) in the literature (including in the appendix [1, 2, 9-15]) we can learn about the more advanced methods of controlling the sliding mode with various state observers in which disturbance techniques, fuzzy sets, artificial intelligence, robust iterative learning, various types of compensation, etc. wear used.

The Authors should answer the questions after reading the cited literature.

A minor note: the same literature item is repeated twice [7] and [10].

Best regards, Reviewer.

1)       Chong-Li Huang, Tao Wang, Meng Li and Yang Yu. Sliding Mode Control of Servo Feed System Based on Fuzzy Reaching Law. Appl. Sci. 2023, 13, 6086. https://doi.org/10.3390/app13106086

2)        Fuhua Li, Yao Jiang , Tiemin Li, Kornel F. Ehmann. Compensation of dynamic mechanical tracking errors in ball screw drives Mechatronics 55 (2018) 27–37  

3)        Lei Zhang, Taiyong Wang, Guofeng Wang and Songling Tian. Hybrid dynamic modeling and analysis of a ball-screw-drive spindle system† Journal of Mechanical Science and Technology 31 (10) (2017) 4611~4618  

4)        Lin Li, Qiangwei Zhang, Tie Zhang, Yanbiao Zou. Vibration suppression of ball-screw drive system based on flexible dynamics model Engineering Applications of Artificial Intelligence 117 (2023) 105506  

5)        Chang Liu, Chunyu Zhao, Zhendong Liu and Shuai Wang Dynamic Analysis of Ball Screw Feed System with the Effects of Excitation Amplitude and Design Parameters. Appl. Sci. 2021, 11, 7070. https://doi.org/10.3390/app11157070

6)        ISO 3408-4: 2006, Ball screws – Part 4: Static axial rigidity

7)        Jerzy Z. Sobolewski. Vibration of the ball screw drive. Engineering Failure Analysis 24 (2012) 1–

8)        M. A. Vargas-Trevino,  J. Lopez-Gomez,· S. Vergara-Limon,  A. Palomino-Merino,  R. Torres-Reyes,  P. Garcia-Ramirez. A mechatronic approach for ball screw drive system: modeling, control, and validation on an FPGA-based architecture. The International Journal of Advanced Manufacturing Technology (2019) 104: –2346

9)        Jamaludin Z., Van Brussel H., Van Brussel H.; Swevers J. Quadrant glitch compensation using friction model-based feedforward and an inverse-model-based disturbance observer. International Workshop on Advanced Motion Control, AMCVolume 1, Pages 212 – 217. 2008. Article number 451606810th International Workshop on Advanced Motion Control, AMC'0826 March 2008through 28 March 2008Code 79810

10)    Liu, Junming, Zhang, Weigui, Tao, Guibao, Huang, Tao. Data-driven Friction Compensation Depending on Modified Disturbance Observer for Ball screw Feed-drive System. ACM International Conference Proceeding SeriesPages 25 - 2921 July 2023 2023 International Conference on Robotics, Control and Vision Engineering, RCVE 2023Tokyo21 July 2023through 23 July 2023Code 191433.

11)    Kenneth Renny Simba, Ba Dinh Bui, Mathew Renny Msukwa, Naoki Uchiyama. Robust iterative learning contouring controller with disturbance observer for machine tool feed drives. / ISA Transactions 75 (2018) 207–215.

12)    Duc Giap Nguyen, Duc Thien Tran and Kyoung Kwan Ahn. Disturbance Observer-Based Chattering-Attenuated Terminal Sliding Mode Control for Nonlinear Systems Subject to Matched and Mismatched Disturbances. Appl. Sci. 2021, 11, 8158. https://doi.org/10.3390/app11178158.

13)    Tushar Vikas Bhaskarwar, Huzein Fahmi Hawari, Nursyarizal B. M. Nor. Sliding Mode Controller with Generalized Extended State Observer for Single Link Flexible Manipulator. Applied Sciences 12(6):3079  2022 10.3390/app12063079.

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The authors did perform a good revision according to the comments from the reviewers. The manuscript can be recommended for publication in the present form. 

Author Response

Dear Reviewer,

We are so grateful for your positive evaluation and recommendation for publication of our manuscript in its current form. We value your input and believe that your comments have significantly improved the quality and impact of our research.

We look forward to future opportunities for collaboration and would be happy to work with you again if the opportunity arises. We remain committed to quality research and to maintaining a high standard of academic excellence in our field.

Thank you again for your time and effort in reviewing our manuscript.

Best regards,

Muzhi Zhu

Reviewer 2 Report

Dear Authors,

Congratulations. After the reviewers' comments, the manuscript is read with much greater interest. And it is easier to understand more difficult issues. This means that it will be useful for younger scientists interested in screw drives. It is a pity that the authors did not refer to the paper in which the derivation of equations (1) was discussed in detail (or maybe I forgot to write about it in the previous review). The problem is not as simple as it would be if it resulted from a model of two bodies with masses m1 and m2 connected by a spring and a damper.

Best regards, Reviewer

Author Response

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Author Response File: Author Response.pdf