Review Reports - Precise Control of MIMO Motion Under the Torque Disturbances of the Gap Flow Field

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper deals with a "Precise Control of MIMO Motion Under the Torque Disturb
ances of the Gap Flow Field". I would like to point out follpwing as:

The description of precious work is weak. Thus, I hope authors add it by using Table including their advantage and shortfalls although authors mentioned it in the Table 2.
The description of object of this paper also ambigious.
Please add the figures or table for experimental results including control input vesus control output to easily understand by reader instutively.
What is control input?
In section 3. Experiments and Results , please add the real dynamic system for Figure 17. Experimental apparatus.
Figure 17. Experimental apparatus also need a more detail expression and explanation for each part because many readers do not understand the appartus.

Author Response

Comments 1: The description of precious work is weak. Thus, I hope authors add it by using Table including their advantage and shortfalls although authors mentioned it in the Table 2.

Response 1: Thank you for pointing this out. We have strengthened the description of precious work about disturbance rejection control and decoupling control, provided more references, and compared the advantages and disadvantages of four disturbance rejection control methods in Table 1. We have revised the description of the entire Introduction chapter, in page1~page3.

Comments 2: The description of object of this paper also ambigious.

Response 2: Thank you for pointing this out. We have strengthened the description of object, and added Figure 1 for explanation, in page1~page2.

Comments 3: Please add the figures or table for experimental results including control input vesus control output to easily understand by reader instutively.

Response 3: Thank you for pointing this out. We added Table 3 in Page 17, Table 4 in Page 18, Table 5 in Page 19.

Comments 4: What is control input?

Response 4: Position tracking error of each axis.

Comments 5: In section 3. Experiments and Results , please add the real dynamic system for Figure 17. Experimental apparatus.

Response 5: We have added an image in Figure 17 to illustrate the dynamic system.

Comments 6: Figure 17. Experimental apparatus also need a more detail expression and explanation for each part because many readers do not understand the apparatus.

Response 6: We have added a new Figure 1 and related descriptions in Page 1, and added an image in Figure 17 to explain the apparatus.

4. Response to Comments on the Quality of English Language

We used MDPI's English editing service and revised the paper

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Overall Recommendation: Major Revision

1. In the system identification section, what are the input and output data used respectively? In addition, this part uses existing methods. Can the error of system identification be characterized? Furthermore, can the identified system be described using state-space equations? It is recommended to present the final system form.

2. After the system is decoupled, to facilitate the controller design, it is recommended to provide the state-space equations for each decoupled system and present the controller design scheme instead of using block diagrams. This control system design approach can refer to the system characterization and controller description in the paper [Gradient-Free Cooperative Source-Seeking of Quadrotor Under Disturbances and Communication Constraints, IEEE TIE].

3. In the High-Order Reference Trajectory Planning section, what is the specific design method?

4. The so-called innovation of this paper lies in the construction of a control system with high open-loop gain, sufficient phase margin, and stable closed-loop by using various existing technologies and control theories, which lacks theoretical innovation.

5. The introduction section could use high-quality references to replace the existing ones, such as research on sliding mode control [Sliding mode control design principles and applications to electric drives, TIE; Input-to-State Stability of the Nonlinear Fuzzy Systems via Small-Gain Theorem and Decentralized Sliding-Mode Control, TFS], and Observer design [Disturbance-Observer-Based Control and Related Methods—An Overview, TIE; A Leader-Following Consensus Problem Via a Distributed Observer and Fuzzy Input-to-Output Small-Gain Theorem].

Author Response

Comments 1: In the system identification section, what are the input and output data used respectively? In addition, this part uses existing methods. Can the error of system identification be characterized? Furthermore, can the identified system be described using state-space equations? It is recommended to present the final system form.

Response 1: Thank you for pointing this out. We used the identification method described in Section 2.2. The 6 SISO axes were controlled in closed-loop under the flow field, with a control period of 10kHz. We sequentially inputted 0-2000Hz 10s sweep data for each axis, and obtained the position data of the 6 axes corresponding to each axis input. Then, frequency response data of 36 plants were obtained through calculation. The transfers of 16 plants were used for subsequent controller design. We have supplemented the fitting process and results of their transfers, as shown in Table 2 and Figure 10, in Page11~Page12. The fitted MSE, order, and some parameters are provided.

Comments 2: After the system is decoupled, to facilitate the controller design, it is recommended to provide the state-space equations for each decoupled system and present the controller design scheme instead of using block diagrams. This control system design approach can refer to the system characterization and controller description in the paper [Gradient-Free Cooperative Source-Seeking of Quadrotor Under Disturbances and Communication Constraints, IEEE TIE].

Response 2: Thank you for pointing this out. We added Equation 10-13 to explain the controller design in section 2.3.1, and Equation 14-17 to explain the controller design in section 2.3.2.

Comments 3: In the High-Order Reference Trajectory Planning section, what is the specific design method?

Thank you for pointing this out. We used the S-curve 4th order trajectory planning algorithm. We added Equation 25 to explain the High-Order Reference Trajectory Planning.

Comments 4: The so-called innovation of this paper lies in the construction of a control system with high open-loop gain, sufficient phase margin, and stable closed-loop by using various existing technologies and control theories, which lacks theoretical innovation.

Response 4: This article has two innovative points. Firstly, In this study, due to complex flow field disturbances and complex inter axis couplings, single disturbance rejection and single decoupling methods cannot solve the problem. This study proposes a composite hierarchical disturbance rejection and decoupling control method. In terms of decoupling control, the following methods were used for the design. Secondly, in response to the unmodeled Z/Rx/Ry axis coupling disturbances introduced by the flow field, improved MIMO disturbance observers were designed to achieve decoupling. We have revised the description of the article in Page 3-4.

Comments 5: The introduction section could use high-quality references to replace the existing ones, such as research on sliding mode control [Sliding mode control design principles and applications to electric drives, TIE; Input-to-State Stability of the Nonlinear Fuzzy Systems via Small-Gain Theorem and Decentralized Sliding-Mode Control, TFS], and Observer design [Disturbance-Observer-Based Control and Related Methods—An Overview, TIE; A Leader-Following Consensus Problem Via a Distributed Observer and Fuzzy Input-to-Output Small-Gain Theorem]

Response 5: Thank you for pointing this out. We have replaced references 5 to 33, including the 4 references you mentioned.

4. Response to Comments on the Quality of English Language

We used MDPI's English editing service and revised the paper

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

In this paper a MIMO system identification method based on closed-loop control was used to obtain the frequency response of the plants. The impact of torque disturbance and MIMO inter-axis coupling effects on control accuracy was evaluated. Then, a control method incorporating acceleration feedforward, position feedback, and matrix decoupling based on a dynamic model is employed. The limitations of this study were fairly identified in the Conclusions section.

Some remarks:

Concerning Fig. 2: on the vertical axis is mentioned “Disturbance Force (m)”. The meaning of (m) is unclear.
Concerning Fig.3: the unit of measurement for the Amplitude must be specified.
For better clarity, The sentence before Eq.(11) must be moved after this equation
In the conclusion part, some limitations of this study are mentioned, but future directions and improvement ways in this field should be clearly highlighted.

Author Response

Comments 1: Concerning Fig. 2: on the vertical axis is mentioned “Disturbance Force (m)”. The meaning of (m) is unclear.

Response 1: Thank you for pointing this out. The unit of “Disturbance Force” should be N. We have modified Figure 2, witch new is Figure 3.

Comments 2: Concerning Fig.3: the unit of measurement for the Amplitude must be specified.

Response 2: Thank you for pointing this out. The unit is N. We have modified Figure 3 and now it is Figure 4.

Comments 3: For better clarity, The sentence before Eq.(11) must be moved after this equation

Response 3: Thank you for pointing this out. We have modified the description before Eq.(11) and now it is Eq.(19)

Comments 4: In the conclusion part, some limitations of this study are mentioned, but future directions and improvement ways in this field should be clearly highlighted.

Response 4: Thank you for pointing this out. Regarding the issue of further decoupling control needed for the system, observer-based feedback compensation correction may be a good solution. Regarding the issue of parameter optimization, offline simulation and intelligent parameter optimization may be good solutions. We have modified the description in the conclusion.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

The manuscript entitled “Precise Control of MIMO Motion Under the Torque Disturbances of the Gap Flow Field” addresses the problem of high-precision motion control of a six-degree-of-freedom system operating under disturbances generated by a mesoscale gap flow field. The authors propose a control strategy combining MIMO system identification, decoupling matrices, and disturbance observer–based control with an H∞-designed filter. The topic is relevant for precision mechatronic systems and semiconductor equipment, where disturbance rejection and inter-axis decoupling are critical. The manuscript presents experimental validation and shows promising improvements in positioning accuracy. However, several aspects of the methodology and presentation require clarification and improvement before the manuscript can be considered for publication.

I have the following comments for the authors to improve their manuscript:

1. The manuscript states that the disturbance observer Q-filter is designed using the H∞ method, but the actual design procedure, optimization problem, and tuning criteria are not described. The authors should clarify how the H∞ design was implemented and provide sufficient detail to ensure reproducibility.

2. The identification procedure is described in Section 2.2, but the final mathematical model of the system (transfer functions or state-space representation) is not provided. Presenting the identified models or at least their order and fitting accuracy would improve transparency and reproducibility.

3. The proposed controller integrates several well-known techniques (PID control, disturbance observers, decoupling matrix, feedforward, filters). The manuscript should more clearly explain the main novelty compared with existing disturbance-rejection or MIMO control strategies.

4. The experimental validation mainly compares the proposed method with a basic SISO control approach. To better demonstrate the method's advantages, the authors should compare it with other advanced approaches (e.g., ADRC, MPC, or robust control strategies).

5. The proposed controller includes many parameters (PID gains, filters, disturbance observer parameters, coupling gains), but the paper does not explain how these parameters were selected or tuned. The authors should describe the tuning procedure or provide guidelines for parameter selection.

6. The consistency of the results presented in Table 1 should be carefully verified. The axis Rx appears twice in the table, which may indicate a typographical or labeling error. In addition, the reported values for some axes seem inconsistent with the discussion of the experimental results in the text. The authors are encouraged to revise the table and ensure that all axes and corresponding error values are correctly reported.

7. The discussion mainly summarizes the obtained results but does not sufficiently analyze the limitations of the proposed method, possible robustness issues, or its applicability to other motion control systems.

8. The manuscript contains several grammatical issues and stylistic inconsistencies that reduce readability. A thorough revision of the English language would improve the clarity of the manuscript. Authors should use Grammarly to improve their English.

9. The reference list should be carefully revised. Many cited journal articles lack DOI identifiers, although these are available for most references (e.g., MDPI and Elsevier publications). Including DOIs would improve the traceability and accessibility of the cited literature.

In conclusion, the manuscript addresses an interesting and relevant problem in precision motion control and presents promising experimental results. The paper is generally well structured, but several aspects of the methodology description and presentation should be clarified and improved. Therefore, I recommend the manuscript for publication after minor revision addressing the comments above. I wish the authors success in improving and finalizing their work.

Comments on the Quality of English Language

The overall quality of English is acceptable, but minor grammatical and stylistic improvements would enhance the clarity and readability of the manuscript.

Author Response

Comments 1: The manuscript states that the disturbance observer Q-filter is designed using the H∞ method, but the actual design procedure, optimization problem, and tuning criteria are not described. The authors should clarify how the H∞ design was implemented and provide sufficient detail to ensure reproducibility.

Response 1: Thank you for pointing this out. We have added Equations 14 to 17 to describe the design results of H∞ DOBC. Please refer to our previous paper for a detailed design process. [Luo, J.; Ruan, X.D.; Wang, J.; Su, R.; Hu, L. Precise Control of Following Motion Under Perturbed Gap Flow Field. Actuators, 2025, 14, 364. DOI:10.3390/act14080364.]

Comments 2: The identification procedure is described in Section 2.2, but the final mathematical model of the system (transfer functions or state-space representation) is not provided. Presenting the identified models or at least their order and fitting accuracy would improve transparency and reproducibility.

Response 2: Thank you for pointing this out. We used the identification method described in Section 2.2. The 6 SISO axes were controlled in closed-loop under the flow field, with a control period of 10kHz. We sequentially inputted 0-2000Hz 10s sweep data for each axis, and obtained the position data of the 6 axes corresponding to each axis input. Then, frequency response data of 36 plants were obtained through calculation. The transfers of 16 plants were used for subsequent controller design. We have supplemented the fitting process and results of their transfers, as shown in Table 2 and Figure 10, in Page11~Page12. The fitted MSE, order, and some parameters are provided.

Comments 3: The proposed controller integrates several well-known techniques (PID control, disturbance observers, decoupling matrix, feedforward, filters). The manuscript should more clearly explain the main novelty compared with existing disturbance-rejection or MIMO control strategies.

Response 3: Thank you for pointing this out. We have added a description of this in Page 3.

“In this study, due to complex flow field disturbances and complex inter axis couplings, single disturbance rejection and single decoupling methods cannot solve the problem. This study proposes a composite hierarchical disturbance rejection and decoupling control method. In terms of decoupling control, the following methods were used for the design. Firstly, the system was decoupled into six SISO systems using the nominal decoupling matrix to reduce motion coupling caused by non-coincidence of control points and centroid. Then, the SISO controllers were designed using a feedback and feedforward structure. Among them, acceleration feedforward correction was used to reduce inertial couplings, and position feedback control was used to suppress residual couplings. Then, in response to the unmodeled Z/Rx/Ry axis coupling disturbances introduced by the flow field, improved MIMO disturbance observers were designed to achieve decoupling. In terms of disturbance rejection control, a method of combining outer loop of PID and inner loop of H∞DOBC was used to achieve hierarchical disturbance rejection. In inner loop, DOBC was used to estimation disturbance and feedforward for wideband time-varying disturbance force and disturbance torque, unmodeled dynamics and parameter uncertainty. And the Q filter was designed using the H-infinity method. In outer loop, flexible dynamic disturbances were reduced through notch filters, measurement noise was reduced by a low-pass filter, peak disturbances caused by the flow field was reduced by anti-interference filters, and residual disturbances were suppressed through feedback control.”

Comments 4: The experimental validation mainly compares the proposed method with a basic SISO control approach. To better demonstrate the method's advantages, the authors should compare it with other advanced approaches (e.g., ADRC, MPC, or robust control strategies).

Response 4: Thank you for pointing this out. Due to the lack of research on other advanced approaches, we are unable to compare experimental data. But we have demonstrated the effectiveness of our work through experimental results of three continuously optimized controllers.

Comments 5: The proposed controller includes many parameters (PID gains, filters, disturbance observer parameters, coupling gains), but the paper does not explain how these parameters were selected or tuned. The authors should describe the tuning procedure or provide guidelines for parameter selection.

Response 5: Thank you for pointing this out. We have changed the original equation 10-17 to new equation 18-25 and added a new equation 10-17. In the explanation of these equations, it is described how the parameters are designed. Offline simulation and intelligent parameter optimization are our future research directions.

Comments 6: The consistency of the results presented in Table 1 should be carefully verified. The axis Rx appears twice in the table, which may indicate a typographical or labeling error. In addition, the reported values for some axes seem inconsistent with the discussion of the experimental results in the text. The authors are encouraged to revise the table and ensure that all axes and corresponding error values are correctly reported.

Response 6: Thank you for pointing this out. We have revised the table of experimental results, which now includes Tables 3, 4, and 5.

Comments 7: The discussion mainly summarizes the obtained results but does not sufficiently analyze the limitations of the proposed method, possible robustness issues, or its applicability to other motion control systems.

Response 7: Thank you for pointing this out. In our previous paper, we discussed the robustness of the SISO controller for H_∞ BODC. [Luo, J.; Ruan, X.D.; Wang, J.; Su, R.; Hu, L. Precise Control of Following Motion Under Perturbed Gap Flow Field. Actuators, 2025, 14, 364. DOI:10.3390/act14080364.] In MIMO systems, through decoupling design, the robustness of the system can be guaranteed. The detailed analysis and argumentation process may be the focus of our future research. In addition, this research method can be applied to disturbance rejection control for wideband time-varying disturbances, kinematic decoupling control, and decoupling control that cannot model coupling.

Comments 8: The manuscript contains several grammatical issues and stylistic inconsistencies that reduce readability. A thorough revision of the English language would improve the clarity of the manuscript. Authors should use Grammarly to improve their English.

Response 8: Thank you for pointing this out. We used MDPI's English editing service and revised the paper.

Comments 9: The reference list should be carefully revised. Many cited journal articles lack DOI identifiers, although these are available for most references (e.g., MDPI and Elsevier publications). Including DOIs would improve the traceability and accessibility of the cited literature.

Response 9: Thank you for pointing this out. We have added DIO for all references.