Control of Electromagnetic Formation Flight of Two Satellites in Low Earth Orbits
Round 1
Reviewer 1 Report
The paper “Control of Electromagnetic Formation Flight of Two Satellites in LEO” is devoted to control algorithm development. The topic of the paper is interesting and the proposed control strategies and algorithms are promising. The paper is well-written, though some sections of the text should be improved before the publication. There are several comments and suggestions.
All the abbreviations should be explained at the first appearance in the text. Also, the abbreviations should be avoided in the abstract (see line 23 – ADRC). EMFF is not “satellite formation flying” (line 30).
The meaning of the first sentence of introduction is not correct, it should be reformulated.
In eq. (1) and (14) designation “R” is not explained in the text.
It seems that the relative position vector expressed in the orbital reference frame and in the electromagnetic frame are mixed up (lines 154 and 155).
The electromagnetic reference frame has three axis. It is not clear why the force vector (eq. (2) and (4)), magnetic dipoles (eq. (3)) have only two components, thought torques have two components in eq. (4).
It is not clear what does “included angles” mean (line 169)?
The authors included the term “-Ωxh” in the control torque, though usually it is considered as a part of the gyroscopic torque, that has to be compensated. The authors should provide more comments with explanation concerning this term.
The statement in lines 212-213 is not quite correct since the inter-satellite electromagnetic force could be less than the disturbance force at large inter-satellite distances.
In Fig. 2 the dimensions of the all the components of the geomagnetic field vector should be presented (now it is only for the B_E_x). The axis limits should be changes to show the two curves at i=0. The statement at lines 244-245 should be corrected, since the z-component of magnetic field is not a constant at orbits with nonzero inclinations and it is changing with Earth rotation period.
The sections 3.1 and 3.2. should be significantly revised, because now it is not clear. It seems that it contains some results from author’s previously published work [22], though without more details the reading of these sections is difficult. The authors should explain what is the “energy optimization strategy”, “magnetic dipole solution differentiable strategy”, what is shown in Fig. 4, how this strategies should be applied?
What is the gain parameters of the electromagnetic force between satellites (line 337), what is their meaning? Why is there no such parameters in the model in eq. (4)?
What does it mean the “the satellite model equation (13) is fully measurable” (line 364)? Does it mean that the phase state is fully observable?
What is the relative rotation period of satellites (line 401)? The authors should provide the vector of the initial relative angular velocity vector.
The considered spherical inertia tensor J=[20;20;20] kg*m^2 is not representative, since with such a J the gyroscopic terms in equations are zero.
The authors should avoid the qualitative statements about the algorithm results (such as “good performance”), better the quantitate characteristics should be provided. What does it mean “little significant convergence error”? Is it little or significant?
Since the authors consider different control strategies, some summary table with resulting accuracy will be useful.
The authors provided the results of polarity reversal strategy with switching every 100s. It will be interesting to show the results with different switching time for this strategy.
Why does the authors showed the plots with performance of tracking errors for relative position and velocity only for the case of frequency division strategy, but omit it for the other strategies?
Author Response
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Author Response File: 
Author Response.pdf
Reviewer 2 Report
The research discusses the use of electromagnetic force for electromagnetic formation flight of two satellites.
Simplifications of the models may be presented in a clearer manner.
Constructed models are presented in the literature and references to them are needed to give the proof that they are used in the literature.
The model given does not have time domain, yet the control is in time domain which also directly effects the energy use and optimization. A discussion on this dimension will add the research an important place in the literature.
A brief introduction about the simulation environment/developed code/library etc is needed.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 3 Report
In the Introduction:
· The acronym “EMFF” seems not to stand for the term “satellite formation flight.”
· For the paper to convey better to readers, before introducing the formation flight of satellites, the importance and popularity of satellites should be mentioned. Some recently published papers should be referred to: Energy-efficient disturbance observer-based attitude tracking control with fixed-time convergence for spacecraft; Constrained Nonsingular Terminal Sliding Mode Attitude Control for Spacecraft: A Funnel Control Approach.
· The text in lines 94 to 108 should be revised. Not only the satellite formation flight but also every single satellite in the formation faces external disturbances that degrade the control performance. The related information can be found in the paper Tan-Type BLF-Based Attitude Tracking Control Design for Rigid Spacecraft with Arbitrary Disturbances.
Lemma 1 is never cited in the manuscript.
Equation (21) seems to be problematic. Further, the variable satu is defined but never used in the paper.
The proposed work should be compared to some existing ones to highlight its advantages.
Generally, the paper is not written very well and should be reconstructed. Also, there are some typos.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The authors carefully addressed all the questions and sugesstions, the paper quality is improved. It can be accepted for the publication
Reviewer 3 Report
I have no more comments. The paper has been extensively reconstructed, and its quality has been significantly improved. However, the English language should be minor checked.
