Enhanced Model Predictive Speed Control of PMSMs Based on Duty Ratio Optimization with Integrated Load Torque Disturbance Compensation
, Abdelsalam A. Ahmed 2, M. M. Ahmed 3, Amr El Zawawi 3, Z. M. S. Elbarbary 4, M. S. Arafath 4 and Mosaad M. Ali 1
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsAn enhanced model predictive direct speed control method with load torque estimation and compensation is proposed for PMSMs. Here are my commects:
1) The stability and convergence of the duty ratio model predictive direct speed control and torque estimation methods are not addressed, making it difficult to determine whether the proposed approach can guarantee global convergence of both speed tracking and torque estimation error.
2) In addition to unknown load torque, PMSMs are subject to a wider range of disturbances, such as current measurement errors, dead-time effects, and unmodeled dynamics in the dq-axis current loops, as well as cogging torque, flux harmonics, and nonlinear friction in the speed loop. All these multi-source disturbances should be taken into account.
3）The proposed method should be categorized within the FCS-MPC framework and results presented in this work have already been extensively documented in existing literature. Relevant previous publications are listed as follows, please provide the differences from these papers.
1 Wang Junxiao, Liu Yibin, Yang Jun, Wang Fengxiang, and Rodriguez, Jose. Adaptive Integral Extended State Observer-Based Improved Multistep FCS-MPCC for PMSM[J]. IEEE Transactions on Power Electronics, 2023, 38(9): 11260-11276.
2. He Long, Wang Fengxiang, Wang Junxiao, and Rodriguez, Jose. Zynq Implemented Luenberger Disturbance Observer Based Predictive Control Scheme for PMSM Drives[J]. IEEE Transactions on Power Electronics, 2020 35(2): 1770-1778.
Author Response
Response to Reviewer 1
We sincerely thank the reviewer for the constructive and detailed comments, which have helped us improve the clarity and rigor of the manuscript. Our detailed responses to each point are provided below.
Comment 1: The stability and convergence of the duty ratio model predictive direct speed control and torque estimation methods are not addressed, making it difficult to determine whether the proposed approach can guarantee global convergence of both speed tracking and torque estimation error.
Response 1: We appreciate this valuable remark. A new subsection entitled “Stability and Convergence Discussion” has been added (end of Section 3.5). It explains that the closed-loop stability is ensured by the convex cost function minimization at each sampling instant and the integral-based torque observer that drives prediction error to zero. Although a formal global proof is beyond the scope of this paper, both simulation and experimental results confirm robust convergence.
Comment 2: In addition to unknown load torque, PMSMs are subject to a wider range of disturbances, such as current measurement errors, dead-time effects, and unmodeled dynamics in the dq-axis current loops, as well as cogging torque, flux harmonics, and nonlinear friction in the speed loop. All these multi-source disturbances should be taken into account.
Response 2: We agree with this observation. A new paragraph has been added to Section 6 (Conclusions) noting that PMSMs are affected by multi-source disturbances beyond load torque, such as current measurement errors, dead-time, cogging torque, flux harmonics, and nonlinear friction. While this paper focuses on load torque compensation, we clarified that extending the proposed framework to handle such disturbances will be an important direction for future work.
Comment 3: The proposed method should be categorized within the FCS-MPC framework and results presented in this work have already been extensively documented in existing literature. Relevant previous publications are listed as follows, please provide the differences from these papers.
1 Wang Junxiao, Liu Yibin, Yang Jun, Wang Fengxiang, and Rodriguez, Jose. Adaptive Integral Extended State Observer-Based Improved Multistep FCS-MPCC for PMSM[J]. IEEE Transactions on Power Electronics, 2023, 38(9): 11260-11276.
2. He Long, Wang Fengxiang, Wang Junxiao, and Rodriguez, Jose. Zynq Implemented Luenberger Disturbance Observer Based Predictive Control Scheme for PMSM Drives[J]. IEEE Transactions on Power Electronics, 2020 35(2): 1770-1778.
Response 3: We thank the reviewer for this valuable observation. We agree that the proposed method belongs to the FCS-MPC framework. However, its main contributions clearly distinguish it from the cited works. Specifically, unlike [Wang et al., 2023], which relies on a multi-step predictive controller with an adaptive extended state observer, and [He Long et al., 2020], which employs a Luenberger disturbance observer implemented on a Zynq platform, our method introduces: (i) a dual-stage cost function that separates speed tracking from ripple minimization, thus eliminating the need for manual weighting factors; (ii) a simplified integral-based load torque observer that reduces computational burden while preserving robustness; and (iii) real-time validation on a dSPACE DS1202 platform using both simulations and hardware experiments. These aspects ensure reduced torque ripple, lower THD, and practical feasibility, which have not been simultaneously addressed in the referenced studies.
We appreciate the reviewer’s insightful comments, which have significantly contributed to strengthening the manuscript. We believe that the revisions and clarifications provided fully address the concerns raised and improve both the technical depth and clarity of the paper.
Reviewer 2 Report
Comments and Suggestions for AuthorsSome comments and suggestions are given here:
- Compare the results obtained by your methods with others recently published (DTC, SMC, Bacstepping, etc.).
- Define the constants of the cost function.
- Abbreviations must be defined only once.
- Interpret the overshoot that exists in the torque.
- Other results need to be analyzed as THD of the current.
- Discuss the complexity of the proposed method.
Author Response
Response to Reviewer 2
We sincerely thank the reviewer for the constructive and detailed comments, which have helped us improve the clarity and rigor of the manuscript. Our detailed responses to each point are provided below.
Comment 1: Compare the results obtained by your methods with others recently published (DTC, SMC, Backstepping, etc.).
Response 1: We agree with this important suggestion. A new comparative discussion has been added in Section 4, where we highlight that Direct Torque Control (DTC) generally suffers from higher steady-state torque ripples, Sliding Mode Control (SMC) is sensitive to parameter uncertainties and may induce chattering, and Backstepping often introduces greater computational and implementation complexity. In contrast, the proposed DR-MPDSC achieves superior dynamic accuracy with reduced torque ripple and THD, while maintaining moderate computational burden, as verified through both simulation and experimental results.
Comment 2: Define the constants of the cost function.
Response 2: We have clarified the constants in Section 3.5. The weights were fixed as Ks = 1 for speed tracking and. Owing to the dual-stage cost function design, manual tuning of weights is avoided, thereby simplifying implementation in real-time systems.
Comment 3: Abbreviations must be defined only once.
Response 3: We have carefully revised the manuscript to ensure that each abbreviation is defined only at its first occurrence and not repeated unnecessarily throughout the text.
Comment 4: Interpret the overshoot that exists in the torque.
Response 4: We have added an explanation in Section 4.2, noting that the small torque overshoot arises from the interaction between the predictive model and the integral torque observer during abrupt transients. Importantly, this overshoot is significantly smaller compared with conventional FOC and MPDSC, confirming the improved damping properties of the proposed controller.
Comment 5: Other results need to be analyzed as THD of the current.
Response 5: The current THD analysis has been expanded in Section 5.1. We explicitly state that the proposed DR-MPDSC achieves approximately 5.5% THD under steady-state operation, which represents a substantial improvement compared with conventional controllers. This demonstrates the method’s effectiveness in enhancing current quality and reducing harmonic stress on the motor windings.
Comment 6: Discuss the complexity of the proposed method.
Response 6: A new paragraph has been added in Section 6 (Conclusions), where we analyze the computational requirements of the proposed method. The DR-MPDSC evaluates only three candidate vectors in the first stage, followed by a closed-form duty ratio calculation in the second stage. This significantly reduces the number of operations compared with traditional multi-weight MPC schemes and ensures feasibility for real-time implementation on embedded platforms such as dSPACE DS1202.
We appreciate the reviewer’s insightful comments, which have significantly contributed to strengthening the manuscript. We believe that the revisions and clarifications provided fully address the concerns raised and improve both the technical depth and clarity of the paper.
Reviewer 3 Report
Comments and Suggestions for AuthorsThe authors present an extensive article on the subject, including simulation and experimental results.
In contrast to usual practice, the equations use a small l instead of a large L, which can be more easily substituted for current.
Why was the simulation performed on a different motor than the actual testing?
The issue of K1 tuning is not addressed.
It is interesting to compare it with other methods, whose settings are not specified anywhere, to assess whether it is sufficiently accurate. I suspect that this would greatly increase the scope of the article.
The article mentions PWM improvement. This is not entirely clear from the text, and it would be interesting to compare the three voltage curves for the tested methods to see exactly what the improvement consists of and why there was such a significant decrease in THD.
In Figure 2 for conventional FOC, a deviation in steady-state time can be seen, which could indicate an incorrect algorithm setting.
Figure 3 shows a greater current ripple. Is this caused by the modulation used or the control settings?
In experimental testing, there is a gradual decrease in torque compared to its increase. What is the cause of this, and could the dynamics of the decrease be accelerated?
It is good that the authors do not shy away from negative findings in their conclusion and mention potential avenues for future research.
Notes to the text:
In Figure 1, correct the idq entry.
Why are lines 170 and 171 and 179 and 179 separated?
In Table 1, correct the units for voltage and flux and add the units for moment of inertia. Do the same for Table 3 for the real motor.
Author Response
Response to Reviewer 3
We sincerely thank the reviewer for the thorough evaluation and constructive remarks, which have helped us to further improve the clarity and quality of the manuscript. Our point-by-point responses are given below.
Comment 1: In contrast to usual practice, the equations use a small l instead of a capital L, which can be more easily substituted for current.
Response 1: We agree with this observation. All inductance symbols have been corrected from lowercase (ld, lq) to uppercase (Ld, Lq) throughout the equations, tables, and figures to avoid any confusion with current notation.
Comment 2: Why was the simulation performed on a different motor than the actual testing?
Response 2: A smaller-rated motor was used in simulations to accelerate numerical evaluation and controller prototyping, while a larger laboratory PMSM was adopted for experimental testing to ensure realistic validation under practical operating conditions. This dual-motor approach is widely used in predictive control research to balance computational efficiency with practical accuracy.
Comment 3: The issue of K1 tuning is not addressed.
Response: We appreciate this remark. Section 3.4 has been updated to explain that the coefficient K1 was empirically tuned to balance convergence speed and noise sensitivity. A value of K1 = 0.8 provided fast disturbance compensation without introducing oscillations and was consistently applied in both simulation and experimental tests.
Comment 4: It is interesting to compare it with other methods, whose settings are not specified anywhere.
Response 4: We have clarified in Section 4 that the benchmark FOC and MPDSC controllers were implemented using standard parameter settings commonly reported in the literature. This ensures fairness and reproducibility in the comparative evaluation.
Comment 5: The article mentions PWM improvement. This is not entirely clear, and it would be interesting to compare the three voltage curves for the tested methods to see the improvement and THD decrease.
Response 5:
We sincerely appreciate the reviewer’s insightful comment. To avoid ambiguity, the direct reference to “PWM improvement” has been removed from the manuscript. In order to keep the paper concise and focused on its main objectives—namely duty-ratio-based predictive control, torque ripple reduction, and load torque disturbance compensation—a detailed discussion of PWM voltage waveforms was not included in the text. Instead, the effect of the proposed modulation strategy is quantitatively demonstrated through the harmonic performance of the stator currents, where the reported THD values (Table 2) provide a direct and widely accepted indicator of waveform quality.
For clarification in this response, Figure below compares the line-to-line voltage (Vab) for FOC (blue), MPDSC (yellow), and the proposed DR-MPDSC (red). Under FOC, the PWM-based waveform appears highly modulated with continuous switching, which introduces noticeable harmonic components. The conventional MPDSC produces discrete voltage steps with frequent commutations between active vectors, leading to higher ripple and increased switching stress. By contrast, the proposed DR-MPDSC exhibits more regular and smoother transitions due to the duty-ratio application of active and zero states, resulting in a waveform closer to the reference, reduced switching activity, and improved harmonic quality. These observations are consistent with the lower torque ripple and THD reported in the quantitative results.
Since detailed PWM analysis is not the primary focus of this work, these clarifications and the additional figure are provided here in the review response only, while the main manuscript remains concentrated on the proposed control objectives.
Comment 6: In Figure 2 for FOC, a deviation in steady-state time can be seen. Figure 3 shows greater current ripple. Please clarify.
Response 6: The deviation in Figure 2 is due to the slower response of the PI regulators in FOC, while the higher ripple in Figure 3 results from the single-vector modulation scheme of conventional MPDSC. Both issues are mitigated by the proposed DR-MPDSC, as shown in Figure 4.
Comment 7: In experimental testing, there is a gradual decrease in torque compared to its increase. Could the dynamics of the decrease be accelerated?
Response 7: We thank the reviewer for this insightful remark. Section 5.2 has been updated to clarify that the slower torque decay is mainly due to the mechanical inertia of the coupled DC load emulator, which resists rapid torque reduction. Future work will investigate alternative load emulation methods to accelerate torque decrease dynamics.
Comment 8: Notes to the text (Figure 1 entry, line separation, table units).
Response 8: We thank the reviewer for pointing out these issues. The idq entry in Figure 1 has been clarified to denote the measured stator currents after Clarke–Park transformation, which are subsequently used in the prediction equations and in the load torque compensation scheme. In addition, line separation errors have been corrected, and the units of voltage, flux, and inertia in Tables 1 and 3 have been revised to V, Wb, and kg·m², respectively.
We sincerely appreciate the reviewer’s detailed and constructive comments, which have allowed us to improve the technical accuracy, clarity, and presentation of the manuscript. We believe that the revisions made fully address the concerns raised
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsThis paper can be accepted. No more comments.
Reviewer 2 Report
Comments and Suggestions for AuthorsThe authors have revised the work according to the requested recommendations. The article can be accepted for publication.
