Direct Torque Control of PMSM with Modified Finite Set Model Predictive Control
Round 1
Reviewer 1 Report
The aim of the Energies — Journal of Energy Research, Engineering and Policy is to present and discuss on the scientific research, technology development, engineering, and the studies in policy and management of the energy area in the last period of time. The proposed techniques and applications should be innovative and significant enough for the community interested of this area of knowledge. The considered, here - because of me a second time, paper can be classified as an article belonging to the group of works, in which new methods and ways are being sought that prediction and control of the torque values of synchronous magnetoelectric motors (PMSM). In the reviewed paper, the Authors have been proposed the direct torque control (DTC) with a modified finite set model predictive strategy. Here, the eight voltage space vectors of two-level inverters (i.e. the inserters for the 3 phase machines) are taken as the finite control set and applied to the model predictive DTC method of a permanent magnet synchronous motor (PMSM). The duty cycle of each voltage vector in the finite set can be estimated by a cost function, which is designed based on factors including the torque error, maximum torque per ampere (MTPA), and stator current constraints. In the proposed approach Authors have used the Lyapunov control theory in the determination of the weight coefficients of the cost function to guarantee stability in order to obtain for the optimal module value of the voltage reference vector in the inverter. The Authors have shown that compared with the traditional DTC method, the torque ripple can be reduced and the robustness of the system can be improved.
The method proposed by Authors makes it possible to improve - decrease of the range of torque pulsation of the magnetoelectric machine powered from the inverter. However, this improvement applies to the power electronics side. In my opinion the causes of torque pulsations in "real" machines with permanent magnets should be sought elsewhere, i.e. in four areas resulting from: (a) non-sinusoidal magnetic field distribution in the air gap of the machine generated by magnets; (b) non-sinusoidal distribution of magnetomotive force generated by winding; (c) cogging torque; and/or (d) reluctance torque. Currently, in research on the development of electric drives, there are trends in which algorithms and methods are being sought that allow reducing the pulsation of machine torque in the four areas I have mentioned. Unfortunately, none of these areas is taken in account by authors. In addition, the they have limited only to discuss the simplest case. I think that a good verification of the proposed method would be to include a reluctance moment in the model, i.e., take into consideration that Ld <> Lq. The inclusion of this condition would confirm the usefulness of this method in the application.
Unfortunately, the authors have not referred to the above-mentioned my comments in the new version of paper.
Further - although the authors revised and removed some shortcomings, the article requires further changes. Not all of my previous comments have been taken into account. Below I give to the selected elements which should be still revised:
"The PMSM has the characteristics of multivariable, strong coupling, and nonlinearity…" Unfortunately, the authors do not specify what means for them the multivariable and strong coupling in relation to the considered model of PMSM.
Phrase: "electrical rotor velocity" - and as before I must also admit that with this phrase I also meet in people dealing with the power electronics. I want to note (again), that according to the theory of electric machines, this phrase is not correct. In the classical theory of electrical machines in the relation to rotor the phrase of "the mechanical angular speed" of rotor is used whereas "electrical angular speed" refers to description of the variability of waveforms of voltages and currents in the machine's windings.
Statement that “Flux F is the flux linkage of the PMSM”, in my opinion is not correct. From electrical machines theory PSI represents a flux associated with the given phase winding and is generated by permanent magnets.
The equation (2) is unclear. It is difficult for me to find such a situation in a PMSM machine, when the voltage waveforms on the inductances of Ld and Lq are consistent in terms of values and phases?
Authors should also verify used in symbols, and give their meaning in first used. The article still has these weaknesses. For example: in the formula (3) there is used the symbol ‘p’, which the meaning is given a few pages further (in the Table III), etc.
And – the phrase "It is assumed that the magnet motive force of each phase of the rotor is sinusoidal in space" is not understandable. The sentence “magnet motive force” is incorrect. Please see to the books from electrical machines theory. Moreover, the authors do not inform anywhere that there are windings on the machine's rotor?
Such examples of phrases in the paper can be found more. Still I think that Authors should ask for the professional help in this matter.
Author Response
Please see the attachment
Author Response File: 
Author Response.docx
Reviewer 2 Report
Dear Authors,
you have presented the FCS-MPC for three-phase motor drives, which uses Lyapunov control theory in the determination of the weight coefficients of the cost function and that was verified both with simulations and experiments.
My comments are as follows:
1) Mainly I am concerned about the novelty of the paper. You have not stressed the comparison with the state-of-the-art methods, also ceased to cite really similar work considering basically the same approach [1]. I think it is crucial that you show what is the real contribution of your work, and to compare your method to one developed in [1], rather than to compare your approach with traditional DTC.
2) All the formulas within the text are floating above the text.
3) Various lemmas and proofs better to introduce in the APPENDIX than in the text.
4) ''Fig. 6 is the simulation results'' Fig. 6 shows the simulation results? English language should be checked better.
5) Figs 8 and 9 please define caption for a) and b).
6) Fig. 10, the names inside the picture are blank.
[1] K. S. Alam, M. P. Akter, D. Xiao, D. Zhang and M. F. Rahman, "Asymptotically Stable Predictive Control of Grid-Connected Converter Based on Discrete Space Vector Modulation," in IEEE Transactions on Industrial Informatics, vol. 15, no. 5, pp. 2775-2785, May 2019.
doi: 10.1109/TII.2018.2876274
Author Response
Please see the attachment
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
Dear Autors,
I am glad that you have responded positively to my comments and corrected the manuscript text in accordance with them. At the moment the paper requires only minor corrections. Please improve the quality and readability of the used Figures and please fill in the missing descriptions on some of them.
Author Response
I would like to thank you again for your valuable suggestions on my manuscript.According to your opinion, I have made corresponding modifications.
Reviewer 2 Report
Dear Authors,
1) I have clearly asked you to consider the reference [x] and to show the contribution of your analysis. You have not included [x] in the biography, nor commented in the introduction part. I think it is crucial in order to understand the novelty.
[x] K. S. Alam, M. P. Akter, D. Xiao, D. Zhang and M. F. Rahman, "Asymptotically Stable Predictive Control of Grid-Connected Converter Based on Discrete Space Vector Modulation," in IEEE Transactions on Industrial Informatics, vol. 15, no. 5, pp. 2775-2785, May 2019.
2) Fig. 10 the letters are not visible, as well as newly added figs. 11 and 13.
3) English language should be improved, like ''When the load torque changes abruptly, proposed FCS-MPC can also track the change of torque
quickly, and the corresponding speed is faster.'' (should be rephrased, speed is faster compared to what?), ''the proposed method has small torque ripple'' (has smaller torque ripple?), and so on.
4) How much is the reduction in the torque ripple??
Author Response
Please see the attachment
Author Response File: Author Response.docx
This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.
Round 1
Reviewer 1 Report
The aim of the Energies — Journal of Energy Research, Engineering and Policy is to present and discuss on the scientific research, technology development, engineering, and the studies in policy and management of the energy area in the last period of time. The proposed techniques and applications should be innovative and significant enough for the community interested of this area of knowledge. The considered, here, paper can be classified as an article belonging to the group of works, in which new methods and ways are being sought that prediction and control of the torque values of synchronous magnetoelectric motors (PMSM). In the reviewed paper, the Authors have been proposed the direct torque control (DTC) with a modified finite set model predictive strategy. Here, the eight voltage space vectors of two-level inverters (i.e. the inserters for the 3 phase machines) are taken as the finite control set and applied to the model predictive DTC method of a permanent magnet synchronous motor (PMSM). The duty cycle of each voltage vector in the finite set can be estimated by a cost function, which is designed based on factors including the torque error, maximum torque per ampere (MTPA), and stator current constraints. In the proposed approach Authors have used the Lyapunov control theory in the determination of the weight coefficients of the cost function to guarantee stability in order to obtain for the optimal module value of the voltage reference vector in the inverter. The Authors have shown that compared with the traditional DTC method, the torque ripple can be reduced and the robustness of the system can be improved.
The method proposed by Authors makes it possible to improve - decrease of the range of torque pulsation of the magnetoelectric machine powered from the inverter. However, this improvement applies to the power electronics side. In my opinion the causes of torque pulsations in "real" machines with permanent magnets should be sought elsewhere, i.e. in four areas resulting from: (a) non-sinusoidal magnetic field distribution in the air gap of the machine generated by magnets; (b) non-sinusoidal distribution of magnetomotive force generated by winding; (c) cogging torque; and/or (d) reluctance torque. Currently, in research on the development of electric drives, there are trends in which algorithms and methods are being sought that allow reducing the pulsation of machine torque in the four areas I have mentioned. Unfortunately, none of these areas is taken in account in the reviewed paper. In addition, the authors have limited only to discuss the simplest case. I think that a good verification of the proposed method would be to include a reluctance moment in the model, i.e., take into consideration that Ld <> Lq. The inclusion of this condition would confirm the usefulness of this method in the application.
The authors should also make every effort to improve the syntax and quality of the article. Below I referred to a few selected elements that need to be changed or should be revised:
Below sentences are not clear and should be explained by the authors in a more precise (correct) way:
"The PMSM has the characteristics of multivariable, strong coupling, and nonlinearity…" Unfortunately, the authors do not specify what means for them the multivariable and strong coupling in relation to the considered model of PMSM.
Phrase: "electrical rotor angular speed" - I must admit that I quite often meet with this phrase in people dealing with the power electronics. I would like to note, however, that according to the theory of electric machines, this phrase is not correct. In the classical theory of electrical machines in the relation to rotor the phrase of "the mechanical angular speed" of rotor is used whereas "electrical angular speed" refers to description of the variability of waveforms of voltages and currents in the machine's windings.
“Aiming at the multi-objective dynamic optimization assignment problem of the weight coefficients of dq-axis current and switching times in the cost function, Lyapunov control theory is introduced in the duty circle calculation, so the stability information from a Lyapunov function is evaluated at each input to select the switching configuration of the inverter to guarantee stability rather than using continuous reference inputs and state-space averaging assumptions as in traditional pulse width modulation (PWM) generation” – the sentence repeatedly folded which makes it difficult to understand the authors' thoughts…
Statement that “Flux F is the flux linkage of the PMSM” is not correct. From electrical machines theory PSI represents a flux associated with the given phase winding and is generated by permanent magnets.
Phrase "It is assumed that the magnetomotive force of each phase of the rotor is sinusoidal in space" is not understandable. Moreover, the authors do not inform anywhere that there are windings on the machine's rotor?
In Figure 5 please check the spelling of the word of “minimization”, etc...
Such examples of phrases in the paper can be found more. I think that Authors should rewrite again the article avoiding such phrases.
The authors should also check the key switching sequence in Table II. In my opinion, I do not agree with the sequence of vectors Vn.
Authors should also verify used in symbols. For example: in the formulas and the text different symbols are used, (see, e.g. in the formula (4) it is used the symbol ‘p’ (number of pole - although in table III the authors define ‘p’ as pole-pairs) whereas in the text the Greek symbol ‘r’ was used.
Moreover, the text contains symbols whose meaning has not been explained, e.g. see formula (8) - symbol S or formula (10) and symbol b, etc.
Finally, the level of English should be revision both in terms of grammar and stylistic. I think that Authors need professional help in this matter.
Reviewer 2 Report
The article deals with interesting problem related do development new algorithms of PMSM control. Unfortunately, the article is quite difficult to read as relations between individual sections of the article are not sufficiently explained. The article is mixing DTC (which is not a predictive technique itself) and SVM based DTV, with traditional FCS-MPC and newly proposed modification of FCS-MPC. The proposed approach is not significantly novel but can provide some improvement. There are several unclear points that shall be explained:
What is the prediction horizon length used in you experiment? DTC can be partially compared with MPC with one step prediction. Current constraint is introduced just by penalization in cost function. This is generally possible and well-known as barrier function, but usually this barrier function needs to be significantly “steep”. This is not case with the quadratic function selected by you. So with which precision is the current constraint maintained? Voltage limitation is discussed at Figure 4, but I cannot see any approach to handle this constrain. So are you able to achieve automatic field weakening to lower back emf and achieve higher speed? FCS-MPC can do this with for longer prediction horizons, but it looks like your approach is dealing with current/torque control only and speed control is solved by additional controller as in traditional FOC or DTC scheme. Can you explain results at Figure 13. In article, you are saying that the proposed algorithm has better dynamics comparing to traditional FCS-MPC. And as FCS-MPC should be better comparing with pure DTC (or at least the same), it is strange that at Figure 13 DTC is significantly faster than the proposed algorithm. Your experiments show that your algorithm is more robust to parameters change than DTC algorithm. This is strange, as robustness is main advantage of DTC and is caused by low reliance on machine model. On the other hand, any MPC scheme relies heavily on machine model and this leads generally to lower algorithm robustness. Can you explain/prove, that your algorithm is really more robust than DTC? In conclusion, it is mentioned that computational time for your algorithm is doubled comparing to MPC-DTC . Do you mean DTC or FCS-MPC?