Neural Network Sliding Model Control of Radial Translation for Magnetically Suspended Rotor (MSR) in Control Moment Gyro
Round 1
Reviewer 1 Report
The paper proposes a sliding mode controller augmented by a neural network, in order to control magnetic bearings in a magnetically suspended control moment gyro. The neural network is used to approximate the nonlinear, and hard to model parameters of the plant. The paper presents interesting results, however much work can be done to improve its clarity and readability.
Remarks, in order of appearance in the text:
1) Equation (1): it is not entirely clear, why the force of gravity is omitted from these equations?
2) Below equation (1) and again in a number of places in the work: “where m is ….” is a continuation of the previous thought, and therefore should not be indented.
3) Below Fig 4. “Scheme 30. m as case 1 and that”, obviously some typo is present here.
4) Page 11: the proposed method has a number of parameters to choose, the authors should explain how they have selected them, not only show their values.
5) A general remark with respect to the results section: Some of the results are obtained in simulations, and some on the experimental stand. The authors should more clearly show which are which.
6) At the beginning of section 4.2 two angular speed values are given, one in radians and one in degrees per second, however these values do not correspond to each other?
7) Figure 7, and in several other places: the figure description should be on the same page as the figure itself.
Some improvements to the level of english can be made. For example in the abstract:
"one of the main factors that make the control accuracy of radial translation for magnetically suspended rotor (MSR) be poor."
"that make the" should not be used with "be poor", the sentence should end witth just "suspended rotor (MSR) poor".
The authors should check the whole manuscript for similar problems.
Author Response
I wish to thank the reviewers for their useful comments. In the manuscript the comments for reviewer 1 are all highlighted in green, those for reviewer 2 are highlighted in yellow. Here are our one-by-one responses to the reviewers’ comments/questions.
Reviewer #1:
Comment 1:
Equation (1): it is not entirely clear, why the force of gravity is omitted from these equations?
Response:
Sincerely thank you for your valuable constructive feedback on us, and we will provide you with detailed answers.
Firstly, equation (1) needs to be clarified: it includes three translational equations and two rotational equations. Then explain why gravity is omitted: The dynamic analysis and control method design of magnetically suspended control moment gyroscope (MSCMG) are based on the mathematical model of the magnetic bearing-rotor system, the established mathematical model must reflect the mechanical characteristics of the system. The modeling of magnetic bearing rotor systems mainly considers gyroscopic effects, rigid rotors, nonlinear magnetic bearing forces, etc. Gravity has no effect on the mechanical properties of the system, and it is only a bias constant for the system, so it is not considered.
Thank you!
Comment 2:
Below equation (1) and again in a number of places in the work: “where m is ….” is a continuation of the previous thought, and therefore should not be indented.
Response:
Thank you very much for this constructive recommendation, and we completely accept your suggestions and comments.
Your opinion is very correct. We have made corresponding modifications according to your opinion. All these changes are highlighted in green in the manuscript.
Thank you!
Comment 3:
Below Fig 4. “Scheme 30. m as case 1 and that”, obviously some typo is present here.
Response:
Thank you very much for this constructive recommendation, and we completely accept your suggestions and comments.
Your opinion is very correct. We have made corresponding modifications according to your opinion. It should be “Set the displacement of MSR drifting from its equilibrium position is within 30μm as case 1 and that…” All these changes are highlighted in green in the manuscript.
Thank you!
Comment 4:
Page 11: the proposed method has a number of parameters to choose, the authors should explain how they have selected them, not only show their values.
Response:
Sincerely thank you for your valuable constructive feedback on us, and we will provide you with detailed answers.
According to the design rules of Gaussian function, the width b of Gaussian function is generally assigned a moderate value, and the center vector of each neuron's Gaussian function. The closer it is to the input value, the more sensitive the function is to the change of the input, the value of should cover the change range of the input. and (in line 358-359 at p11) are these obtained values through several optimization.
As explained in line 359-361, p11 in manuscript, The parameters ，and(in Table 3) for general PID control are optimized and tunned by nonlinear least squares functionand least square indicator in MATLAB software. The variables and in line 363 at p11 are processing variables in simulation, they are cancelled in the revised manuscript.
Thank you!
Comment 5:
A general remark with respect to the results section: Some of the results are obtained in simulations, and some on the experimental stand. The authors should more clearly show which are which.
Response:
Thank you very much for this constructive recommendation, and we completely accept your suggestions and comments.
For 4.1. Radial translation control of MSR without gimbal moving, these results from Figure 9-12 are simulation results. As explained in in line 461-464, p14, the results of Figure 13 are tested ones.
Similarly, for 4.2. Radial translation control of MSR with gimbal moving, these results from Figure 14-17 are simulation results, as explained in in line 588-592, p18, that of Figure 18 are tested ones.
All these changes are highlighted in green in the manuscript.
Thank you!
Comment 6:
At the beginning of section 4.2 two angular speed values are given, one in radians and one in degrees per second, however these values do not correspond to each other?
Response:
Thank you very much and we explain here.
At the beginning of section 4.2, there is a sentence “the gimbal of MSCMG must be rotated. Generally, the maximum rotary speed of gimbal for MSCMG is ± 15 °/s, namely the maximum angular velocity of gimbal is ±1.6328rad/s.” That is ± 15 °/s equals ±1.6328rad/s because the maximum rotary speed of gimbal is expressed by two different unit system, respectively. ± 15 °/s is expressed by degree-s unit system because we are accustomed to it, and 1.6328rad/s is by rad-s unit system because when we calculate the control moment generated by rotating the gimbal of MSCMG, the unit of rotary speed of gimbal must be rad/s.
Comment 7:
Figure 7, and in several other places: the figure description should be on the same page as the figure itself.
Response:
Thank you very much for this constructive recommendation, and we completely accept your suggestions and comments.
Your opinion is very reasonable. We have adjusted the position of the images and annotations according to your suggestion.
Thank you!
Comments on the Quality of English Language
Some improvements to the level of english can be made. For example in the abstract:
"one of the main factors that make the control accuracy of radial translation for magnetically suspended rotor (MSR) be poor."
"that make the" should not be used with "be poor", the sentence should end with just "suspended rotor (MSR) poor".
The authors should check the whole manuscript for similar problems.
Response:
Thank you very much for this constructive recommendation, and we completely accept your suggestions and comments. Your opinion is very reasonable.
"one of the main factors that make the control accuracy of radial translation for magnetically suspended rotor (MSR) be poor." has been modified to " one of the main reasons for the poor accuracy of radial translation control of magnetically suspended rotor (MSR). " Other similar problems have also been addressed as much as possible. These changes are highlighted in green in the manuscript
Thank you!
Author Response File: 
Author Response.pdf
Reviewer 2 Report
This is an interesting idea and has excellent application prospects. At the same time, I think this is an adequate, well-scientific, high-quality study. However, I still have two comments that I hope the author will revise or provide an explanation. Firstly, a permanent magnet biased radial magnetic bearing is applied experimentally, but the mathematical model is established based on a differentially controlled electromagnetic bearing. There are significant differences between the two types of magnetic bearings, which will affect the reliability of the simulation results. Second, the accuracy and control effect of the simulation if not verified in the experiment. For example, the signal noise of the sensor in the experimental results is larger than 10 µm, which cannot verify the 0.0001mm steady-state error written in the conclusion. Therefore, I suggest to revise the conclusion and the corresponding part of the text and to describe the simulation results and the experimental results separately to avoid misunderstanding.
It is recommended to check the grammar and make minor edits.
Author Response
I wish to thank the reviewers for their useful comments. In the manuscript the comments for reviewer 1 are all highlighted in green, those for reviewer 2 are highlighted in yellow. Here are our one-by-one responses to the reviewers’ comments/questions.
Reviewer #2:
Comment 1:
A permanent magnet biased radial magnetic bearing is applied experimentally, but the mathematical model is established based on a differentially controlled electromagnetic bearing. There are significant differences between the two types of magnetic bearings, which will affect the reliability of the simulation results.
Response:
Thank you very much for this constructive recommendation, maybe we do not explain clearly in this manuscript and we explain here.
All these magnetic bearings used in MSCMG all are permanent magnet biased hybrid magnetic bearings, they can be classified into radial permanent magnet biased hybrid magnetic bearings and axial ones. There are two radial permanent magnet biased hybrid magnetic bearings in MSCMG to control rotor’s radial translation and tilting around radial axes, and there are also two axial permanent magnet biased hybrid magnetic bearings to control rotor’s axial translation. In this paper, to simplify the expression of these magnetic bearings, we named radial permanent magnet biased hybrid magnetic bearings as radial magnetic bearings, axial permanent magnet biased hybrid magnetic bearings as axial magnetic bearings, respectively. We have added this expression of magnetic bearing in section 1in the revised manuscript. These changes are highlighted in yellow
Thank you!
Comment 2:
The accuracy and control effect of the simulation is not verified in the experiment. For example, the signal noise of the sensor in the experimental results is larger than 10 µm, which cannot verify the 0.0001mm steady-state error written in the conclusion.
Response:
Thank you very much for this constructive recommendation, and we completely accept your suggestions and comments.
Your opinion is very correct. Perhaps the explanation of the results of simulation analysis and experimental verification in this article is not clear enough, and a clear explain will be made between the results obtained from simulation and experiment.
To verify the radial translation control of MSR without gimbal moving as expressed in 4.1, the conclusion that “the neural network SMC converges rapidly when t=0.3s, and the steady-state error is only 0.0001mm”( line382-383,p12, highlighted in blue) is the simulation results, and that “But for the neural network SMC, the average rotor translation displacement as shown in Figure 13c, is up to 5μm,” ( line475-476,p12, highlighted in blue) is the tested results, the related sentence in section of Conclusion “the steady-state error of rotor’s radial translation controlled by neural network SMC is 0.0001mm, which is less than 5% of that controlled by general PID” is modified as “The tested average rotor translation displacement controlled by neural network SMC is up to 5μm, the position accuracy is improved by 50% compared to that of general PID.”(highlighted in yellow).
Similarly, to verify the radial translation control of MSR with gimbal moving as expressed in 4.2, the conclusion that “It can be seen that the position error of MSR controlled by neural network SMC is only7×10-5mm, which is only 1% of the that controlled by PID plus cross-feedback method, it is clear that this presented neural network SMC has a better control effect on improving the position accuracy of MSR when the gimbal is rotated and other uncertain disturbances acting on it.” (line550-554, p17, highlighted in blue) is the simulation results, and that “It can be seen that the average displacement of MSR controlled by general PID is 20μm, that controlled by adaptive SMC is 16μm, which is improved by 20% of that controlled by general PID. Furthermore, the average displacement of MSR controlled by neural network SMR is only 10 μ m, which is improved by 50% compared to that controlled by general PID” (line601-604,p18-19, highlighted in blue) is the tested results, the related sentence in section of Conclusion “the steady-state error controlled by neural network SMC is 0.0002mm, which is only 0.125% of that controlled by PID plus cross-feedback method” is modified as “the tested average displacement of MSR controlled by neural network SMR is only 10 μ m, which is improved by 50% compared to that controlled by controlled by PID plus cross-feedback method” (highlighted in yellow)
After this modification, the conclusion of paper is more correct and more accurate.
Thank you!
Comments on the Quality of English Language
It is recommended to check the grammar and make minor edits.
Response:
Thank you very much for this constructive recommendation, we checked the grammar of this paper carefully try our best, the corresponding editing errors have also been corrected.
Thank you!
Author Response File: Author Response.pdf
