Altitude Control of Powered Parafoil Using Fractional Sliding-Mode Backstepping Control Combined with Extended State Observer

Round 1

Reviewer 1 Report

Abstract

- it is well formulated; the purpose of the research is clear.

Introduction

- first, refers to the powered parafoil and to the applications which involve these air vehicle;

- then, the authors describe the problem of control, mainly the altitude control of powered parafoils, with advantage and limitations;

- the connection with different studies are well formulated;

- according to the authors, an alternative of control is proposed in the present paper and is based on fractional sliding-mode backstepping control combined with a linear extended state observer.

Dynamics of Powered Parafoil and Problem Formulation

- the structure of the powered parafoil (Figure 1) and the description of the associated coordinate frames are very well presented;

- the matrix representations, including velocity transformations, are clear;

- as a consequence, the input-state-output relationship (11) is well formulated;

Design of Control System

- start, direct, with a diagram (Figure 2);

- although, the control system of the powered parafoil is well presented, I suggest you to start the section with a description (text), then, with the mentioned configuration;

- the mathematical problem of the state observer is correct;

- also, the mathematical formalism related to tracking error, auxiliary error and virtual control variable are understandable;

- the Caputo fractional calculus is known from literature and it is mentioned in the paper;

- then, based on Lyapunov, results the control law.

Stability Analysis

- according to (36), k is a positive adjustable parameter; according to Theorem 1, if the parameter k < 1, the errors are bounded; here, maybe some additional explanations are needed.

Simulaiton Verification

- see the title (Simulaiton = Simulation ?);

- the parameters of the powered parafoil are presented in Table 1;

- the values used to simulate are given (parameters, initial altitude, gust disturbance etc.);

- simulation results (Figures 4,5,6), compared with other two methods, are compelling;

- also, the simulation results for the altitude control (Figures 7,8,9) look good.

Conclusions

- maybe, a synthesis of the performances (in terms of settling time, overshot etc.) presented in a table would be helpful.

The References are suggestive for the topic. Random check for: 2. Zhu, E.; 3. Li, B.; 7. Yang, H.; 14. Hu, K-Y.; 18. Guettal, L.; 23. Das, S.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

The manuscript proposes a method of altitude control of the powered parafoil with uncertainties and disturbances based on sliding-mode backstepping control combined with a linear extended state observer (LESO). Several details should be illustrated as the following:

1.     More details should be provided for “Configuration of the control system of the powered parafoil (Figure 2)”.

2.     Some quantitative description for the performance of LESO should be concluded in Abstract section.

3.     The experiment or simulation could be done to validate the effectiveness of the proposed LESO.

4.     The English requires more attentions throughout the manuscript. The authors should check the English presentation throughout the manuscript.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf