A Disturbance Force Compensation Framework for a Magnetic Suspension Balance System
Round 1
Reviewer 1 Report
Future scope need attention, a brief description may be incorporated in Section 7.
Author Response
Dear reviewer
We appreciate the insights and comments of you. According to the constructive suggestions, we have revised the paper accordingly and are now resubmitting the revised version for your evaluation. Appended to this letter is our point-by-point response to the comments raised by you. The comments are reproduced and our responses are given directly afterward in a different color (red).
Best regards.
Wentao xia et al.
Response to Reviewer 1 Comments
Reviewer #1:
Point 1: Future scope need attention, a brief description may be incorporated in Section 7.
Response 1: We are grateful to the reviewer for the recognition of the value of our work. According to your suggestion, we have incorporated a brief description in Section 7.
Author Response File: 
Author Response.docx
Reviewer 2 Report
The paper deals with a control procedure applied to a magnetic suspension system to compensate the effect of disturbance forces. The application is quite interesting and the technique presents effective practical outcomes. However, there some issues that need to be better addressed.
1. The principle of operation described from line 88 to 90 is a little confused. It could be revised adding the proper current polarities and the permanent magnet (PM) magnetization direction in Figure 2 to understand the actual force direction.
2. Figure 1 presents some issues. The axes are not oriented according to the text explanation (e.g., coils 2-4-6-8 seem to operate along the y direction rather than the z one). Please check orientation. In addition, C1 and C2 are not defined anywhere.
3. All the model formulation starting from (3) assumes that the interaction between the PM and the coils only occurs along the coil axis. Therefore, the formulation for a generic x-direction should be revisited considering the actual y coordinate. According to this, at line 100 “the physical equation of the MSBS in the x-direction is deduced” should be replaced with “…in the x-direction with the rod aligned with the coil axis…” or something like that..
4. The authors state that the electromagnetic force changes nonlinearly with the position. This is true for the single coil supply. However, the resultant force with the simultaneous coil supply is almost constant and dependent only on the current. Please explain more clearly if nonlinearity is an issue or not.
5. (10) applies if the coils are series connected. If this is not the case, a mutual induced voltage should be considered. A supply scheme can be helpful.
6. The variable y in (12) is a bit confusing with the vertical spatial coordinate in Figure 2. I suggest modifying the symbol.
7. There are some shortcomings about the parameter choice in the control scheme in Figure 6. How is the PID regulator selected for the position control? And what about the PID controller for the current loop?
8. In the same control scheme, a kind of feed-forward technique is used for the external force compensation. Some more references should be provided on such techniques to understand if the authors propose a novel or a well-assessed approach.
9. Moreover, the choice of the coefficient km is not clear. Its value is assessed after some tests. The conclusion is that the value must not be too large otherwise the system becomes unstable. Consequently, it should be selected as low as possible according to Figure 8. However, the choice seems to differ to such evidence. Finally, what are the proper criteria? For instance, if the mass changes, is the selected value still valid?
10. In Figure 7, the transient with DFCF evidences a marked noise in the starting interval. Can the authors explain why? Is this behavior related to km selection? I think that such a noticeable oscillation can give rise to vibration problems.
11. The control operation is checked consideing a 10 g suspended mass. Which is the actual mass that must be tested in the wind tunnel? I wonder about the extension of the technique to a larger mass. The authors should discuss about this possible issue.
12. It is not clear in Figure 11why the suspended mass does not recover the initial position. I am not expert in aerodynamic testing, however I expect that the device under test should keep the same position by adjusting the coil current to compensate the disturbance forces. Can you explain why is accepted an equilibrium point different than the initial one?
13. Finally, no information are provided regarding the coil design. I suggest the authors to include the guidelines they follow to choose coil size, voltage and current ratings.
Author Response
Dear reviewer
We appreciate the insights and comments of you. According to the constructive suggestions, we have revised the paper accordingly and are now resubmitting the revised version for your evaluation. Appended to this letter is our point-by-point response to the comments raised by you. The comments are reproduced and our responses are given directly afterward in a different color (red).
Best regards.
Wentao xia， et al.
Response to Reviewer 2 Comments
Point 1: The principle of operation described from line 88 to 90 is a little confused. It could be revised adding the proper current polarities and the permanent magnet (PM) magnetization direction in Figure 2 to understand the actual force direction.
Response 1: Thanks for the reviewer’s kind suggestion. According to your advice, we amended the relevant part of the manuscript. The proper current polarities and the permanent magnet (PM) magnetization direction is added in Figure 2.
Point 2: Figure 1 presents some issues. The axes are not oriented according to the text explanation (e.g., coils 2-4-6-8 seem to operate along the y direction rather than the z one). Please check orientation. In addition, C1 and C2 are not defined anywhere.
Response 2: We are sorry for these mistakes. Thanks for your criticism and advice. We corrected the direction and added the definitions of C1 and C2 in paper.
Point 3: All the model formulation starting from (3) assumes that the interaction between the PM and the coils only occurs along the coil axis. Therefore, the formulation for a generic x-direction should be revisited considering the actual y coordinate. According to this, at line 100 “the physical equation of the MSBS in the x-direction is deduced” should be replaced with “…in the x-direction with the rod aligned with the coil axis…” or something like that.
Response 3: We are sorry for this confusion. There is a problem with our statement. “The physical equation of the MSBS in the x-direction is deduced” is replaced with “…in the x-direction with the rod aligned with the coil axis…”
Point 4: The authors state that the electromagnetic force changes nonlinearly with the position. This is true for the single coil supply. However, the resultant force with the simultaneous coil supply is almost constant and dependent only on the current. Please explain more clearly if nonlinearity is an issue or not.
Response 4: We do apologize for the unclarity. The electromagnetic force is Formula 9. Its relationship with current is linear, but its relationship with position and coil shape is nonlinear.
Point 5: (10) applies if the coils are series connected. If this is not the case, a mutual induced voltage should be considered. A supply scheme can be helpful.
Response 5: The coils are series connected.
Point 6: The variable y in (12) is a bit confusing with the vertical spatial coordinate in Figure 2. I suggest modifying the symbol.
Response 6: Sorry for this confusion. The variable y in (12) is modified.
Point 7: There are some shortcomings about the parameter choice in the control scheme in Figure 6. How is the PID regulator selected for the position control? And what about the PID controller for the current loop?
Response 7: Thank you for this precious suggestion. In theory, PID controller can be used in current loop. But in practice, the ripple of current signal is large, and the differential control coefficient is difficult to choose. In the future, we will work to reduce the current ripple and make PID controller applied in the current loop.
Point 8: In the same control scheme, a kind of feed-forward technique is used for the external force compensation. Some more references should be provided on such techniques to understand if the authors propose a novel or a well-assessed approach.
Response 8: Thank you for this precious suggestion. We have added references of auto-disturbance rejection technology in paper. See references 21-24 for details
Point 9: Moreover, the choice of the coefficient km is not clear. Its value is assessed after some tests. The conclusion is that the value must not be too large otherwise the system becomes unstable. Consequently, it should be selected as low as possible according to Figure 8. However, the choice seems to differ to such evidence. Finally, what are the proper criteria? For instance, if the mass changes, is the selected value still valid?
Response 9: On the premise that the system does not diverge, the larger the km, the better. If the quality changes little, the selected value is still valid. However, if the quality exceeds a certain range, the selected value may be invalid
Point 10: In Figure 7, the transient with DFCF evidences a marked noise in the starting interval. Can the authors explain why? Is this behavior related to km selection? I think that such a noticeable oscillation can give rise to vibration problems.
Response 10: Because the control system is in the initial state, each state quantity has a certain distance from the equilibrium point, the system will be affected by the interference supplement algorithm and cause vibration during the adjustment process. We will further study the oscillation and explore ways to eliminate vibration in the future. Thank you for this precious suggestion.
Point 11: The control operation is checked consideing a 10 g suspended mass. Which is the actual mass that must be tested in the wind tunnel? I wonder about the extension of the technique to a larger mass. The authors should discuss about this possible issue.
Response 11: Sorry again for this unclarity. The model weight is 78g, and the applied axial interference force is 0.098N. We have modified the text in paper.
Point 12: It is not clear in Figure 11why the suspended mass does not recover the initial position. I am not expert in aerodynamic testing, however I expect that the device under test should keep the same position by adjusting the coil current to compensate the disturbance forces. Can you explain why is accepted an equilibrium point different than the initial one?
Response 12: The suspension gap of the suspension model in MSBS is large, and the electromagnetic force generated by the electromagnet is relatively small. At the moment of interference, it can not immediately return to the balance position, and it needs to reach the balance position slowly by integral control.
Point 13: Finally, no information are provided regarding the coil design. I suggest the authors to include the guidelines they follow to choose coil size, voltage and current ratings.
Response 13: The axial coil diameter is 0.13m, the number of coils is 252, and the distance between coil 0 and coil 9 is 0.312m. The power supply voltage of chopper is 110VDC. According to your opinion, we added this information to the paper.
Author Response File: 
Author Response.pdf
Reviewer 3 Report
The authors proposed a disturbance compensation framework for vehicles in wind tunnel testing. The reviewer's major comments are:
1. The title does not specify the content of the paper. The authors should highlight "wind tunnel experiments" in the title.
2. The paper uses a lot of inaccurate or unclear terminologies.
a. The proposed system applies to aircraft, missiles, and UAVs. However, it is typically referred to as a “vehicle” rather than aircraft in this type of research.
b. The so-called "interference force" is better described as "disturbance" or "disturbance force/moment."
3. The proposed control/estimation framework lacks stability analysis, even without any disturbance.
4. When the gust disturbs the vehicle in suspension, the aerodynamic forces depend on the aircraft's orientation, wind speed, and angular velocity. This is not considered in the proposed framework. These additional dynamics may cause instability of the control and estimation system. The authors need to specify the conditions in that the system remains stable.
5. The proposed setup is innovative. However, there is a fundamental issue in the experiment design. The purpose of the wind tunnel experiments is to get the aerodynamic forces and moments. If there is a certain level of electromagnetic actuation model inaccuracy, the experiment results may not be able to differentiate the aerodynamic forces and electromagnetic forces. This may defeat the purpose of wind tunnel testing.
6. The floating vehicle's 6 DOFs need to be controlled. However, the current framework only considered the control of one DOF. The aerodynamic disturbance is highly coupled. The authors need to explain how the forces and moments in other DOFs can be addressed in simulations and experiments.
7. There is a lack of experiment details. The authors need to specify the type of CCD camera for positioning feedback, its sampling frequency, the control bandwidth and Bode diagram, the way external disturbances are generated (gust speed, duration, etc.). The MSBS setup lacks details and dimensional information.
8. It is observed that the disturbance estimation/rejection scheme yields a steady-state error in its experimental results. This may be addressed by adding integrators in the observation or compensation framework. This could significantly enhance the disturbance compensation results. The authors need to implement this or explain why this is not feasible in their setup.
9. The authors need to quantify their electromagnetic actuation model accuracy from experiments. Without knowing the modeling error's characteristics, the disturbance compensation algorithms can easily lead to the instability of the system.
10. The proposed method is claimed to be a fast disturbance estimation method. However, from the simulation results shown in Figure 5, the high-frequency transient has a significant estimation error. Therefore, the effectiveness of the fast disturbance estimation is questionable.
11. There are too many typos and formality issues. For example, there should be spacings between the word and contents in "()" and "[]". Also, the authors should avoid using fh to represent a single nonlinear function.
Author Response
Dear reviewer
We appreciate the insights and comments of you. According to the constructive suggestions, we have revised the paper accordingly and are now resubmitting the revised version for your evaluation. Appended to this letter is our point-by-point response to the comments raised by you. The comments are reproduced and our responses are given directly afterward in a different color (red).
Best regards.
Wentao xia et al.
Response to Reviewer 3 Comments
Point 1: The title does not specify the content of the paper. The authors should highlight "wind tunnel experiments" in the title.
Response 1: Thanks for the suggestion. This paper mainly studies the anti-interference control method and electromagnetic field modeling. According to your suggestion, we add wind tunnel experiments to the keyword.
Point 2: The paper uses a lot of inaccurate or unclear terminologies.
- The proposed system applies to aircraft, missiles, and UAVs. However, it is typically referred to as a “vehicle” rather than aircraft in this type of research.
- The so-called "interference force" is better described as "disturbance" or "disturbance force/moment."
Response 2: Thank you for pointing out the problem. We have standardized the terms in the text according to your suggestion.
Point 3: The proposed control/estimation framework lacks stability analysis, even without any disturbance.
Response 3: Thank you very much for this valuable suggestion. We have added the stability proof of the estimation framework. The control framework is based on the improvement of the PID controller framework. It is stable in the simulation and experiment by adjusting the parameters, and some other references of stability proof are cited. In the future, we will further prove the stability region of parameters.
Point 4: When the gust disturbs the vehicle in suspension, the aerodynamic forces depend on the aircraft's orientation, wind speed, and angular velocity. This is not considered in the proposed framework. These additional dynamics may cause instability of the control and estimation system. The authors need to specify the conditions in that the system remains stable.
Response 4: Thank you very much for this valuable suggestion. The aircraft's orientation and angular velocity of the model will have an impact on the dynamic performance of the system, but the impact is small. Because the coils in other directions will control the levitation model and keep the pitch angle being zero. The influence of wind speed change is reflected in the interference applied on the model, and the step interference reflects the sudden change of wind speed. The algorithm is verified by simulation and experiment in this paper. In the future, the impact of dynamic coupling of various impacts on the system will be further studied.
Point 5: The proposed setup is innovative. However, there is a fundamental issue in the experiment design. The purpose of the wind tunnel experiments is to get the aerodynamic forces and moments. If there is a certain level of electromagnetic actuation model inaccuracy, the experiment results may not be able to differentiate the aerodynamic forces and electromagnetic forces. This may defeat the purpose of wind tunnel testing.
Response 5: We usually calibrate the error through calibration experiments. This paper mainly studies the modeling and control methods of MSBS, so there is no detailed description of the calibration experiment.
Point 6: The floating vehicle's 6 DOFs need to be controlled. However, the current framework only considered the control of one DOF. The aerodynamic disturbance is highly coupled. The authors need to explain how the forces and moments in other DOFs can be addressed in simulations and experiments.
Response 6: This paper mainly studies the influence of the airflow in the x-direction on the model, and proposes a control algorithm to reduce the influence of the interference. X is basically not affected by other degrees of freedom and can be designed independently. The characteristics of degrees of freedom in other directions are different from those in the x direction, and other directions will be coupled with each other. It is necessary to design another controller for multi-degree of freedom decoupling control.
Point 7: There is a lack of experiment details. The authors need to specify the type of CCD camera for positioning feedback, its sampling frequency, the control bandwidth and Bode diagram, the way external disturbances are generated (gust speed, duration, etc.). The MSBS setup lacks details and dimensional information.
Response 7: Thanks for the suggestion. According to your suggestion, we introduce the position output frequency, control frequency, details and size information of the MSBS of the CCD sensor. The CCD sensor is designed and manufactured by ourselves.
Point 8: It is observed that the disturbance estimation/rejection scheme yields a steady-state error in its experimental results. This may be addressed by adding integrators in the observation or compensation framework. This could significantly enhance the disturbance compensation results. The authors need to implement this or explain why this is not feasible in their setup.
Response 8: Although the integral part of PID can eliminate the steady-state error, the integral part needs to slow down its function. The problem error cannot be eliminated at the moment of step response. It takes a long time to eliminate the steady-state error, and the air flow will change with time.
Point 9: The authors need to quantify their electromagnetic actuation model accuracy from experiments. Without knowing the modeling error's characteristics, the disturbance compensation algorithms can easily lead to the instability of the system.
Response 9: The model has been verified and modified in the experiment to make its error smaller. Because PID control is included in the interference compensation algorithm, it has a certain ability to adjust the error. Based on your opinion, we will further study the impact of uncertainty and model error on the system.
Point 10: The proposed method is claimed to be a fast disturbance estimation method. However, from the simulation results shown in Figure 5, the high-frequency transient has a significant estimation error. Therefore, the effectiveness of the fast disturbance estimation is questionable.
Response 10: Thank you for your criticism and correction. We will further improve the algorithm later.
Point 11: There are too many typos and formality issues. For example, there should be spacings between the word and contents in "()" and "[]". Also, the authors should avoid using fh to represent a single nonlinear function.
Response 11: Thank you for your detailed correction. We have revised the paper.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
The authors have answered to the comments and concerns raised in the review report. The paper has been satisfactorily modified.
