An Improved Extraction Scheme for High-Frequency Injection in the Realization of Effective Sensorless PMSM Control

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This manuscript proposes a method for extracting rotor position error information in a tracking loop system for rotor position estimation in the HFI technique using EMA.

1. A clear summary of the contributions should be presented in the Introduction.
2. The authors are encouraged to elaborate on the controller’s stability, particularly its response to sudden dynamic load changes.
3. A comparative analysis should be provided to highlight the advantages and performance improvements of the proposed method over regular methods.
4. The technical content requires further elaboration. This includes clearly stating relevant assumptions, providing details on parameter tuning, and explaining the rationale behind rule design choices.
5. The literature review needs further enhancement. Please include more recent and seminal works to strengthen the background, such as 10.1016/j.etran.2024.100353.
6. The figures in the manuscript are unclear, and some font sizes are too small. Please improve the resolution and readability of the figures to ensure clarity for readers.

Author Response

Response to Reviewer 1

Respected Reviewer 1,

On behalf of both the authors, I would like to convey my sincere thanks for your time and efforts to provide the prompt review of this paper with key comments and suggestions to improve the manuscript. Truly, your comments have helped to improve the readability and significance of this paper. The modified and improved version of the manuscript is prepared by addressing all the comments and suggestions. YELLOW COLOUR represents the modifications in response to the all Reviewers throughout the manuscript. Further, the pdf file of the revised manuscript is attached. Please see below, in blue, for a point-by-point response to the reviewer’s comments and concerns. All page and line numbers, used in the author’s responses, refer to the revised manuscript file with tracked changes.

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

The paper is devoted to the development of an improved rotor position error extraction scheme in sensorless control systems of permanent magnet synchronous motors (PMSM) based on high-frequency injection. The relevance of the study is determined by the growing need to abandon mechanical sensors in electric drives in order to increase reliability, reduce costs and reduce system complexity. Accurate rotor position estimation is especially important at low speeds and with abrupt changes in dynamic conditions. Existing methods based on bandpass and low-pass filters have problems with delays and computational costs, which reduces accuracy and performance. In this paper, we propose the use of exponential moving average (EMA) for position error extraction, which allows achieving high accuracy, noise immunity and reduced computational load. The experimental results confirm a significant improvement in accuracy and dynamic characteristics compared to traditional approaches, which makes the proposed solution a significant contribution to the development of sensorless PMSM control systems. The paper is devoted to a relevant topic, but at the same time, the paper needs to be improved:
1. The Introduction section covers the problem of rejecting position sensors well, but the literature review is limited to a few approaches. It would be desirable to more fully characterize the existing methods, especially those based on alternative HF signal processing strategies such as adaptive filters or neural network observers.
2. Lines 87–90. The BPF/LPF elimination method via the Notch Filter is discussed, but its weaknesses are briefly mentioned without sufficient analysis. It would be worthwhile to explain in more detail why it turned out to be insufficiently effective for the problem under consideration.
3. Model (3) is based on the assumption that the motor is equivalent to an ideal inductive element. This assumption greatly simplifies the real dynamics, especially when taking into account the heating of the windings. The limitations of the applicability of such a model should be at least briefly discussed.
4. Formulas (9) and (10) express quadratic dependences on the position error, but there is no discussion of how the sensitivity of these expressions changes for small values ​​of ∆θ. This is important, since too small amplitudes can reduce the accuracy of the estimates.
5. Formulas (16–18) describe EMA, but there is no indication of how exactly the time windows Tw are selected in different situations (e.g., for different injection frequencies).
6. The rationale for using EMA claims a reduction in the computational load, but no estimate of the computational time or clock delays is provided. Data should be provided, such as a comparison of the execution times for EMA and LPF.
7. The simulation results demonstrate a reduction in the transient time, but no statistical analysis is provided (e.g., the mean and standard deviation of the error over several tests). This weakens the argument.
8. Using LPF after numerical differentiation may introduce delays. The magnitude of this delay and its impact on the control loop should be indicated. 9. Under sudden load, EMA showed a smaller error, but there is no analysis of how exactly stability is achieved: filtering, PI controller parameters, or system inertia.
10. The conclusion states a reduction in the average error by 26.64%, but it does not indicate how this value was calculated: by what metric and for what set of scenarios. The original numerical data should be provided.
11. The article does not discuss temperature effects that could affect the motor parameters and the accuracy of position estimation. This may be significant in real industrial conditions.
12. The article does not consider the effect of discretization and ADC and PWM delays on the accuracy of rotor position estimation at high injection frequencies.

Author Response

Response to Reviewer 2

Respected Reviewer 2,

On behalf of both the authors, I would like to convey my sincere thanks for your time and efforts to provide the prompt review of this paper with key comments and suggestions to improve the manuscript. Truly, your comments have helped to improve the readability and significance of this paper. The modified and improved version of the manuscript is prepared by addressing all the comments and suggestions. YELLOW COLOUR represents the modifications in response to the all Reviewers throughout the manuscript. Further, the pdf file of the revised manuscript is attached. Please see below, in blue, for a point-by-point response to the reviewer’s comments and concerns. All page and line numbers, used in the author’s responses, refer to the revised manuscript file with tracked changes.

Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

This paper proposes an exponential moving average (EMA)-based rotor position error extraction method for sensorless control of permanent magnet synchronous motors (PMSMs). Compared with conventional band-pass/low-pass filter solutions, the proposed method demonstrates faster dynamic response and lower computational burden, with its effectiveness being experimentally validated.This work could be accepted after minor revisions. Other questions were shown below.

1. The article's explanation of the basic theory of EMA is overly simplistic, merely illustrating its principle through formulas, and it lacks theoretical justification for the selection of the EMA smoothing factor α. It is recommended to supplement the relevant content.
2. The speed validation section of the article only tests low-speed conditions and does not cover medium- or high-speed experimental testing, resulting in lower robustness of the findings. It is recommended to supplement the study with medium- and high-speed experiments.
3. In practice, high-frequency injection signals may introduce nonlinear distortion, causing the EMA-extracted error signal to contain harmonic components. However, the article overlooks the impact of nonlinearity, and it is recommended to supplement relevant analysis.
4. The method proposed in this paper is only compared with the traditional BFP+LPF solution, without benchmarking against other advanced approaches, making it difficult to demonstrate the comprehensive advantages of EMA. It is recommended to supplement relevant comparative studies.
5. The article does not mention the advantages and disadvantages of EMA in practical applications, nor does it discuss how to optimize it in future development. It is recommended to supplement this relevant content.

Author Response

Response to Reviewer 3

Respected Reviewer 3,

On behalf of both the authors, I would like to convey my sincere thanks for your time and efforts to provide the prompt review of this paper with key comments and suggestions to improve the manuscript. Truly, your comments have helped to improve the readability and significance of this paper. The modified and improved version of the manuscript is prepared by addressing all the comments and suggestions. YELLOW COLOUR represents the modifications in response to the all Reviewers throughout the manuscript. Further, the pdf file of the revised manuscript is attached. Please see below, in blue, for a point-by-point response to the reviewer’s comments and concerns. All page and line numbers, used in the author’s responses, refer to the revised manuscript file with tracked changes.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

All comments have been revised.

Reviewer 2 Report

Comments and Suggestions for Authors

The authors generally did a good job of revising the manuscript based on my comments, especially in terms of expanding the theoretical foundations and structuring the explanations.

Reviewer 3 Report

Comments and Suggestions for Authors

All comments have been addressed.