Robust Backstepping Control Combined with Fractional-Order Tracking Differentiator and Fractional-Order Nonlinear Disturbance Observer for Unknown Quadrotor UAV Systems

Round 1

Reviewer 1 Report

This paper is about a fractional-order robust backstepping control combined with a fractional-order tracking differentiator and a fractional-order nonlinear disturbance observer for a quadrotor unmanned aerial vehicle (UAV) system. Although both the topic and the presented results appear meaningful, there are some technical issues the authors have to address

1. Since the number of studies about UAV in Introduction seem to be less, this paper should supplement some researches on quadrotor UAV in the past five years.

2. The contribution and novelty seem to be slightly limited. Please reemphasize the contributions of this paper.

3. Moreover, the contributions of this paper should be reemphasized.

4. Figures and tables in this study should be clear, such as Figs 3 and 4, Tables 4 and 6, such that the reader can understand the effectiveness of the proposed method.

5. why does the proposed method have the small error for one-dimensional motion control and large error for three-dimensional motion control. Please supplement the relevant reasons.

Author Response

This paper is about a fractional-order robust backstepping control combined with a fractional-order tracking differentiator and a fractional-order nonlinear disturbance observer for a quadrotor unmanned aerial vehicle (UAV) system. Although both the topic and the presented results appear meaningful, there are some technical issues the authors have to address

Authors thank for the reviewer 1’s helpful comments and suggestions. We have carefully revised the manuscript according to reviewer’s comments and suggestions. The modified parts in the revised submission were colored by yellow color. The detail replies to the reviewers’ comments are as follows:

1. Since the number of studies about UAV in Introduction seem to be less, this paper should supplement some researches on quadrotor UAV in the past five years.

Ans: We changed the old references with the new literature according to your comments. Six literatures are changed within the past 5 years

2. The contribution and novelty seem to be slightly limited. Please reemphasize the contributions of this paper.

Ans: The contribution of our study is the design of fraction-order based controller and disturbance observer with fractional-order tracking differentiator. We inserted the statements for the motivation and contribution of the presented control method in Introduction.

3. Moreover, the contributions of this paper should be reemphasized.

Ans: To emphasize the contribution of this paper, many literatures are added and background of the research and contribution of the presented methods are written in the revised submission.

4. Figures and tables in this study should be clear, such as Figs 3 and 4, Tables 4 and 6, such that the reader can understand the effectiveness of the proposed method.

Ans: Figs 3 and 4 (Figs 4 and 5 in the revised version) were redrawn by the new data obtained from the changed simulations due to modification of controller. Tables were rewritten with new data. The contents of the table were modified to enhance the readability.

5. Why does the proposed method have the small error for one-dimensional motion control and large error for three-dimensional motion control. Please supplement the relevant reasons.

Ans: In the previous submission, some figures were drawn erroneously. In the revised submission, new simulations were conducted by the modified control system and resulting figures were redrawn to clearly match the results.

Reviewer 2 Report

I don’t think this article present a necessary or important work in this area. The reasons are that:

1) The motivate of constructing Fractional-Order nonlinear controller is unclear. In reviewer’s opinion, there are so many other methods can achieve the control objective of the considered problem of this paper, other methods has more simple construction than Fractional-Order controller. Which suggests that the research is trivial by complicated design with little contribution.

2) I don’t believe the considered problem can only be solved by so complicated control design, to facilitate the application of method and to benefit readers, more control design should be considered with explicit problems that no other works solved.    

Author Response

Authors thank for the reviewer 2’s valuable comments and suggestions. We have carefully revised the manuscript according to reviewer’s comments and suggestions. The modified parts in the revised submission were colored by yellow color. The detail replies to the reviewers’ comments are as follows:

1) The motivate of constructing Fractional-Order nonlinear controller is unclear. In reviewer’s opinion, there are so many other methods can achieve the control objective of the considered problem of this paper, other methods have more simple construction than Fractional-Order controller. Which suggests that the research is trivial by complicated design with little contribution

Ans: In the previous submission, the sufficient explanations for the advantages of the fractional-order control were not provided. Many works of the fractional-order based control were restated and studies for fractional-order sliding mode control were added. Backstepping control examples for quadrotor UAV designed fractional-order calculus were also added. The contributions of this paper are given as follows:

1. There is little fractional-order backstepping control for quadrotor UAV. This paper presents the efficient backstepping control design method for quadrotor UAV by introducing fractional-order tracking differentiator to avoid the repeated differentiation of the conventional backstepping control scheme.

2. The fractional-order based tracking differentiator for the backstepping control of UAV system was little considered in the traditional backstepping control. The fractional-order tracking differentiator has enhanced performance than the previous ones.

3. The fraction-order disturbance observer the backstepping control of UAV system was little studied in the traditional backstepping control. The considered fraction-order disturbance observer is proved to have efficient performance than the previous ones.

4. The fraction-order filtered error surface is utilized to guarantee proper control performance and simpler controller structure.

2) I don’t believe the considered problem can only be solved by so complicated control design, to facilitate the application of method and to benefit readers, more control design should be considered with explicit problems that no other works solved.  

Ans: The main reason of complexity of the design control system is owing to the fractional-order filtered error surface which is used in the controller design procedures. Hence, we replace this by other surface, which guarantees the appropriate controller performance and provides simpler controller structure. The proposed controller was redesigned and new simulations were conducted. The obtained control performances are a little low than the previous submission but the complexity of the whole controller is significantly improved. Hence, the implementation issue of the proposed control system is much improved.  The comparative property of the revised filtered error surface is provided in Section 3.4 comparing with the resulting figure to other surfaces.

Round 2

Reviewer 2 Report

I think the revision is almost satisfactory, however, the background on backstepping control in the introductions is incomplete that, some recent researches on simple backstepping control design with high performance should be included such as ‘Distributed control of nonlinear systems with unknown time-varying control coefficients: A novel Nussbaum function approach, IEEE Transactions on Automatic Control, doi: 10.1109/TAC.2022.3206135’ and ‘Adaptive neural control for a class of pure-feedback nonlinear systems via dynamic surface technique. IEEE Transactions on Neural Networks and Learning Systems’.

Author Response

We appreciate the reviewer 2's work on our submission.

We inserted the complementary reference on backstepping control according to the reviwer 2' comment. However, the recommended second paper is the study  on dynamic surface control, in which the tracking differentiator is not used. Thus, this paper is not included due to different research scope for our study.

Authors thank for the reviewer 2 again.