Torque Ripple Reduction in Switched Reluctance Machines Considering Phase Torque-Generation Capability

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In this manuscript, an improved online compensated torque distribution function (OCTSF) control method based on the phase torque generation capability is proposed for the torque fluctuation problem of switched reluctance motors (SRMs) during phase change. Specifically, the authors propose three key improvements based on the traditional OCTSF: (1) separating the phase conduction angle from the TSF start angle, which allows the phase to build up the current in advance, thus providing a stronger torque response capability when entering the phase change region; (2) utilizing the torque per unit of current (TPA) characteristic to divide the phase change region, which realizes a low-cost but effective compensation of the torque error; (3) introducing a PWM regulation mechanism on top of the DITC control (3) introducing a PWM regulation mechanism based on DITC control to adapt to the problem of high torque rate of change under restricted control frequency. The combination of these strategies effectively improves the torque tracking accuracy during phase change and significantly suppresses the torque fluctuation.

The selected topic has high engineering practical value, especially in the field of electric vehicles and aeromotors, where SRM systems have attracted attention due to their simple structure, high temperature resistance, and adaptation to a wide speed domain. However, their applications are often limited by large torque pulsations, especially in high-performance applications. In this study, starting from the control level, a larger torque fluctuation improvement can be realized without changing the hardware structure, which is innovative and has the potential to be popularized. Compared with the common methods of structure optimization and MPC in the existing literature, the method proposed in this paper is more advantageous in terms of computational complexity, real-time and hardware deployability.

In terms of specific technical contributions, firstly, the decoupling of TSF and conduction angle allows the current to be built up in advance before the TSF allocation, which helps to improve the torque response in the initial magnetization stage; secondly, the division of the phase change region through the TPA intersection is an approximation, but it avoids the on-line calculations and table checking, which makes the method concise and effective; and thirdly, the introduction of the PWM regulating logic, which dynamically adjusts the duty ratio under the constrained control period, helps to limit the actual torque overshoot. Again, the introduction of PWM regulation logic, which dynamically adjusts the duty cycle under the restricted control period, helps to limit the real torque overshoot and improve the error caused by the insufficient control bandwidth. The above improvements are empirically supported by experimental verification.

Regarding the methodology, the authors' explanation is clear, but the following additions and improvements can be made: (1) the selection of the TPA cutoff point of 4.9° mainly relies on graphical observation, and it is suggested that sensitivity analysis or fitting expression be added to enhance the persuasive power; (2) it is suggested to explain the basis for the selection of the adjustment strategy of ±5% of the PWM duty cycle, and to clarify whether it is tuned through experiments or whether it is equipped with the convergence mechanism; (3) the input and output power acquisition methods are not described in the efficiency measurement, and it is suggested to add the test method; and (4) the efficiency measurement is not explained in the study. output power acquisition method, it is suggested to add the details of the test platform, including whether the torque sensor is used for mechanical power calculation and other information; (4) the method is validated based on 12/8 structure SRM, it is suggested that the authors briefly discuss its applicability in other typical topologies (e.g., 6/4, 8/6), especially whether the separation angle selection is scalable or not.

From the results, several sets of simulation and experimental data under speed and load conditions are provided in the paper, all of which show that the improved method can reduce the torque fluctuation by more than 30% without affecting the efficiency. The results are of significant utility. It should be noted that the high-speed region (>1500 rpm) is not discussed in depth, and the authors have pointed out in Section 5 that this region needs to be studied separately, and it is suggested that the current application boundary of the method should also be appropriately hinted at in the conclusion.

The references are well cited, covering a variety of directions such as structural design, control algorithms, model predictive control, and so on. If space permits, it is suggested that the authors may consider supplementing citations on emerging methods such as data-driven torque prediction and hybrid DTC-MPC strategy in recent years to further broaden the perspective of comparison.

Regarding the graphs and charts, the overall design is reasonable and the information is clearly expressed, especially Figures 6-8 and Figures 12-14 support the theoretical content well. Figure 13 can be further labeled with the effective zone of PWM regulation in the range of 4° to 7° to enhance the correspondence of the graphs, and the TPA characteristic graph is suggested to add a legend to distinguish the current level. The key performance data are already available in Table 1, and the addition of a column for “fluctuation suppression rate” would help to quantify the effect more intuitively.

In summary, this manuscript has good performance in method design, experimental validation and engineering applicability, with clear innovation points, clear contributions and solid technical details. It is recommended that the authors accept it after adding some method details and reinforcing the data description. My recommendation: acceptance after minor revision.

Author Response

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Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript addresses an important challenge in switched reluctance machines (SRM), torque ripple reduction, using an improved online compensated torque sharing function (OCTSF). The authors clearly identify the limitations of existing approaches and present a promising methodology supported by experimental validation. Nevertheless, several critical points require clarification, and the manuscript could be significantly improved by addressing these concerns.

1. The authors briefly mention the experimental setup but do not provide comprehensive technical details of the SRM prototype used in the tests. This information is crucial for reproducibility and comparison.
2. Although efficiency data are provided, the authors do not adequately discuss why the improved method sometimes yields slightly better efficiency. The theoretical underpinnings or practical reasons for efficiency improvement need further explanation.
3. The authors approximate the optimal separation point as a fixed value, which may not be ideal across various operational conditions. A deeper justification or a sensitivity analysis could strengthen this assumption.
4. The method described for PWM duty ratio adjustment appears arbitrary (increment/decrement by 5%). There should be a theoretical or empirical justification for this choice, or a more systematic approach should be introduced.
5. Can authors develop more on how sensitive is the proposed method to variations in load conditions beyond those tested?
6. What is the impact of temperature variation on torque ripple and overall performance?
7. Could the use of adaptive or predictive methods improve the accuracy of the separation point?
8. Have the authors considered other optimization techniques, such as genetic algorithms or neural networks, to refine the torque sharing function further?
9. I recommend to include detailed technical specifications of the SRM, such as dimensions, rated power, voltage, current, and materials used, to enable reproducibility.
10. Authors should elaborate on the reasons behind the efficiency gains in the improved method. It is recommended to discuss energy losses, including iron, copper, and switching losses, to provide a complete efficiency breakdown.
11. They should also conduct a sensitivity analysis on the separation point approximation to ensure robustness and validate the chosen fixed value.
12. Provide experimental or theoretical justification for the chosen PWM duty ratio adjustment increments. If possible, explore more systematic methods, such as feedback control or real-time adaptive duty cycle optimization.
13. It is important to perform tests at higher rotational speeds to confirm the proposed method's effectiveness under broader operational conditions and to explore the impact of higher back electromotive force.
14. Authors should include experimental results demonstrating the performance of the method at different operational temperatures, as temperature variations could affect the magnetic characteristics and torque ripple.
15. It would be beneficial to provide comparative data or benchmarks against other recent torque ripple reduction methods cited in the literature to highlight the superiority or unique benefits of the proposed approach clearly.

I recommend major revision.

Author Response

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Reviewer 3 Report

Comments and Suggestions for Authors

1. What are the improvements of the optimization method proposed in this article compared to existing methods. Compare your work with the most advanced technological solutions.

 

2. Is it necessary to clearly indicate the specific innovative points of the proposed technical method in the abstract?

 

3. In the introduction, provide specific application cases of Switched Reluctance Motors (SRN) in high-precision scenarios such as servo systems to illustrate the necessity of this research.

 

4. Add the relationship between inductance slope and rotor position after formula (1) to clearly explain its nonlinear characteristics?

 

5. The article only explains the shortcomings of TSF and lacks practical examples to support it. Can you provide specific examples of how “exponential TSF” is affected by angle parameters in practical applications?

 

6. In the derivation of formulas (4) to (13), what is the actual physical meaning and specific range of values for the compensation coefficient?

 

7. Only the trend is shown in Figure 8, lacking mathematical statistical analysis. Is it necessary to supplement quantitative analysis of the impact of different values on negative torque?

 

8. Add pseudocode for the actual PWM duty cycle adjustment algorithm after formula (20), and explain how to dynamically balance the current change rate and switching frequency?

 

9. Add key setting parameters such as sampling frequency and PWM resolution of the controller used in the experimental section?

 

10. Provide concise quantitative and qualitative comparative analysis of experimental results?

 

11. Conduct statistical analysis - confidence interval/hypothesis testing to determine the effectiveness of the proposed controller?

 

12. What challenges do we need to face when applying the technical methods proposed in this article to practice?

Author Response

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Reviewer 4 Report

Comments and Suggestions for Authors

Review Comments:

The paper demonstrates innovative torque-ripple reduction strategies for switched reluctance machines (SRMs) supported by substantial experimental validation, though would benefit from enhanced graphic presentation standards, contemporary reference support, and comprehensive comparative evaluation. Recommended revisions include: 

1. Revise figure labeling and clarity issues. For example: The axis labels of some figures (e.g., Figures 1 and 3) are incomplete, with the vertical axis lacking explicit units (e.g., current in "A," torque in "Nm"). It is recommended to uniformly supplement axis labels for all figures and provide detailed descriptions of key regions in the captions. The flowchart in Figure 5, particularly subfigures (a) and (b), lacks clarity in arrow directions and compensation logic descriptions. It is advised to use more intuitive symbols (e.g., "+"/"–" to indicate error directions) or add textual explanations for the compensation paths. The discriminability of the four curves in Figure 10 is insufficient; adjust the vertical axis display range from 3.5°–6.5° to 4°–5.5°, and include insets if necessary. Figures 16–19 require higher resolution to avoid blurred details, and the axis labels (both horizontal and vertical) are too small to discern. Redraw these curves with improved resolution and adjust the font sizes of the axes appropriately for better readability.
2. Address formula standardization issues. Symbols are incompletely defined upon their first appearance. For instance, L_k​(i_k​,θ) should be explicitly stated as "the inductance of the k -th phase as a function of current and rotor position." The derivation process for the differential equations in Equations (16)–(20) omits critical steps (e.g., the derivation of the initial condition C₀). Supplement intermediate derivations or cite relevant mathematical methods from references to enhance readability.
3. Improve the timeliness of references. The citation of recent advancements in SRM torque ripple suppression is insufficient: current references end in 2023, with only two post-2023 citations. Incorporate the latest research from 2023–2025 and prioritize references from the past five years to reflect the authors’ awareness of cutting-edge developments.
4. Refine linguistic precision. The opening sentence of the abstract, "In this paper, an improved torque sharing function (TSF) is proposed...," is overly vague. Specify the exact mechanism of the TSF improvement (e.g., "a dynamic compensation mechanism based on phase torque generation capability").
5. Strengthen the articulation of innovation. The description of contributions and novelty is overly generalized. Quantify the improvement effects (e.g., "the phase turn-on angle separation reduces torque tracking error by XX%") and explicitly contrast the limitations of existing OCTSF methods (e.g., [31]) to highlight the uniqueness of the proposed approach.
6. Address experimental design limitations. The experiments only compare the traditional OCTSF with the proposed method, lacking horizontal comparisons with mainstream approaches such as model predictive control (MPC [27–29]) or fixed-frequency PWM [25–26]. Supplement comparative data on torque ripple and efficiency to demonstrate the comprehensive advantages of the proposed method.

Author Response

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Reviewer 5 Report

Comments and Suggestions for Authors

The paper entitled Torque Ripple Reduction in Switched Reluctance Machine Considering Phase Torque Generation Capability presents a thorough study on reducing the torque ripple of switched reluctance machine and several control methods are presented and evaluated.

The introduction of some bibliographic indications regarding the mathematical apparatus describing the behaviour of OCTSF in part II are welcome.

Figure 6, 7, 15, 16 can be enlarged for better understanding.

At the begging of section 5. Experimental Verification the paragraph This section is not mandatory but can be added to the manuscript if the discussion is unusually long or complex. should be removed.

At row 374 should be 4Nm instead of 4 N.

In part 4, more discussions are welcome regarding the efficiency of the method compared to the conventional/known one.

If it is possible to evaluate the proposed method on other motor variants available to researchers in order to extend the field of use of the proposed method.

Some mentions/ recommendations are necessary regarding the application domain of the method on load range, speed, torque.

Conclusions must be extended with some results from part 3 and 4.

Author Response

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Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have improved the manuscript and revised it. I recommend its publication in the present form.