Trajectory Tracking Control Method Based on Adaptive Higher Order Sliding Mode
Round 1
Reviewer 1 Report
The paper present a tracking control method based on adaptive higher order sliding mode. The model has been clearly presented and comprehensively described. Conclusions must be more supported by data, introducing more stress cases.
Author Response
Comments:
The paper presents a tracking control method based on adaptive higher order sliding mode. The model has been clearly presented and comprehensively described. Conclusions must be more supported by data, introducing more stress cases.
Reply
To further verify the performance of proposed adaptive high-order sliding mode trajectory tracking controller (AHSTC) method, linear quadratic regulator (LQR) method is introduced as a comparison example. The simulation results show that the proposed AHSTC method shows faster convergence and improved tracking effect. Therefore, the proposed AHSTC method has a good results and engineering application value.
Reviewer 2 Report
Please find the review attached.
Comments for author File: 
Comments.pdf
Author Response
Comments:
Specific Comment 1
In the introduction, the authors note that chattering is an issue and that methods have been proposed
to overcome it, if not completely solve it. The proposed approach in this paper focuses on a method to overcome such chattering. The authors reference the works of Liu et al. and Li et al. on lines 59 and 61. As these two works attempt to solve the problem of chattering, I would suggest the authors compare the proposed approach to these methods to clearly demonstrate the benefits of the proposed approach.
Specific Comment 2
The use of sliding mode for such a problem is not new. Below is a (incomplete) list of publications that are similar. The authors are requested to:
- provide a more detailed literature review of the state-of-the-art,
- Discuss the drawbacks of the approaches in the literature
- Clearly outline the contribution of the present work.
Specific Comment 3
Following comments 1 and 2, the authors are requested to comment on why ADRC is chosen as the test case to compare to the proposed approach. Comparison to other methods that specifically deal with chattering would be more meaningful.
Specific Comment 4
The authors are requested to provide the initial and terminal conditions to allow the reader to
reproduce Figures 1 and 2.
Specific Comment 5
Section 3.1 shows graphs of the proposed approach and Section 3.2 shows graphs of ADRC. Having two separate sections does not seem necessary. The authors are requested to combine the sections and show the comparison on the same graph, using different colors, line styles to denote the different
approaches.
Specific Comment 6
Some terms in Section 2 have been used without defining them. The authors are requested to define
and explain them.
As the authors themselves note, some of the models produce are quite poor. Could the authors add a sub-section after 4.2 to elaborate on ways to improve accuracy?
Specific Comment 7
The manuscript can benefit from a typo, spelling, and grammar check. An inexhaustive list is below:
- The sentence starting on line 68 is long and hard-to-follow. The authors are requested to rewrite.
â‘¡To be consistent with the notation of using subscript n to denote the nominal, n_{yn} should be
n_{y_n}
â‘¢When referencing a paper at the start of the sentence, please use Author et al.
Reply
(1) In Liu and Li methods, the design of tracking controller is used for Single Input Single Output (SISO) system, rather underactuated system. Therefore, the above two methods cannot be used as a comparison method. For underactuated systems, LQR method is introduced as a comparison method to demonstrate the superiority of the proposed method.
(2) The introduction about sliding mode has been revised in details.
(3) The ADRC method is selected because it can observe interference (state deviation) and has stronger robustness and anti-interference than the traditional PID trajectory tracking method.
LQR method is introduced as a comparison method at the same time.
(4) The initial and terminal conditions have been provided to reproduce Figures 1 and 2.
(5) The comparison of three methods has been integrated on the same graph.
(6) Some terms in Section 2 have been defined in details. And we add a sub-section to introduce some ways to improve accuracy of ADRC and LQR method.
(7)
- : The sentence has been rewritten carefully.
- : The problem has been revised in Eq. (7).
- : The problem has been revised.
Author Response File: 
Author Response.docx
Reviewer 3 Report
This paper establishes the nominal trajectory that takes into account the flight time and the rate of change in the control quantity by using the Gaussian pseudo spectral method and nonlinear programming. Based on the sliding mode control disturbance rejection, the high-order sliding mode control introduced in this work further reduces the chattering problem of the control variables. The authors investigate that how adaptive control method makes the controller design maintains a good control effect in the presence of interference. Furthermore, the simulation results show that the proposed adaptive high-order sliding mode trajectory tracking control method shows faster convergence and improved tracking effect.
In conclusion: Some results obtained in this work are novel. Moreover, they are incremental improvements of earlier results. The level of mathematical and physical difficulty and originality of these results makes them suitable for publication. The experts in this field of Trajectory Tracking Control will appreciate some technical progress exposed in this work. However, there are some minors comments:
· The abstract must be rewritten to show clearly the new results.
· The introduction can be improved
· The legends and labels of figures are not clear
· The authors have to investigate the similarities and differences among their work and the literatures of this proposed work
In general, the authors have to describe in more detail the purpose of their study and its original contents. A clear explanation, what is the new result in their work, and how it is build up upon previous work in the field.
If the authors submit a modified version according to my suggestions where they also give more details/explanations about the abovementioned criticisms, I could recommend the paper for publication.
Author Response
Comments:
However, there are some minors comments:
(1) The abstract must be rewritten to show clearly the new results.
(2) The introduction can be improved.
(3) The legends and labels of figures are not clear.
(4) The authors have to investigate the similarities and differences among their work and the literatures of this proposed work
Reply
(1) The abstract has been written to introduce the proposed method.
(2) The abstract has been revised in details.
(3) The legends have been revised in particular.
(4) Literature research has been introduced in the revised introduction.
Round 2
Reviewer 1 Report
the paper has been deeply revised and now it can be published
Author Response
(1) The results in LQR method have larger height error than AHSTC, so the proposed AHSTC has better control performance.
The talk above the problem has been revised in Section 3.1.
(2) Table 2, 3, 4 have been referenced in text. Tracking error is being measured by all-state sensors.
(3) The figure has been made easier for readers. Sub-figure has been used in figure.
(4) The few grammar and stylistic issues have been revised.
Reviewer 2 Report
Please find the review attached.
Comments for author File: Comments.pdf
Author Response
(1) The results in LQR method have larger height error than AHSTC, so the proposed AHSTC has better control performance.
The talk above the problem has been revised in Section 3.1.
(2) Table 2, 3, 4 have been referenced in text. Tracking error is being measured by all-state sensors.
(3) The figure has been made easier for readers. Sub-figure has been used in figure.
(4) The few grammar and stylistic issues have been revised.
