Fractional Order PID Design for a Proton Exchange Membrane Fuel Cell System Using an Extended Grey Wolf Optimizer

Round 1

Reviewer 1 Report

This manuscript presents a novel algorism or simulation approach to optimize the design of fuel cell electrical circuit. It is a very interesting study which could guide the future design of fuel cell system to promote its commercialization. This topic could attract a wide readership from researchers in the area of fuel cells. Therefore, I recommend its publication after addressing the following issues.

1. The insets in Fig. 9-12 are too small, especially the numbers in them.
2. It seems that this algorithm can apply to other electrical circuit system in addition to that with fuel cell stacks. More description about the great power of the algorism should be added.
3. Can the authors describe how the development of this algorism can guide the design of fuel cell systems?
4. There are some grammatical errors in the text. For example, “which affected” in line 38 should be “which are affected”; “are occurred” in line 126 should be “occur”; “finally forming” in line 141 should be “finally form”.
5. Relevant recent literatures about fuel cells should be cited such as Electrochim. Acta 2016, 190, 817–828; ACS Appl. Energy Mater. 2018, 1, 411−420; J. Colloid Interface Sci. 2022, 613, 515–523.

Author Response

Response to the reviewer comments

First of all, the author would express their sincere gratitude to the Editors and the Reviewers who gave us many constructive comments and valuable suggestions in order to improve this paper. The authors have revised the paper according to the reviewers’ comments and the changes made in the paper have been written in blue color. While the mistakes have been depicted in red color. The responses to the reviewer comments can be found below their respective comments.

Reviewer 1

This manuscript presents a novel algorism or simulation approach to optimize the design of fuel cell electrical circuit. It is a very interesting study which could guide the future design of fuel cell system to promote its commercialization. This topic could attract a wide readership from researchers in the area of fuel cells. Therefore, I recommend its publication after addressing the following issues.

1. The insets in Fig. 9-12 are too small, especially the numbers in them.

Response: The authors have taken into consideration the reviewer comment about the insets and the numbers size. Hence, the Figures. 9-12 are improved.

2. It seems that this algorithm can apply to other electrical circuit system in addition to that with fuel cell stacks. More description about the great power of the algorism should be added.

Response: The authors have added more description about the great power of the algorithm in line 272 to 281 and line 306 to 311 for the new version of manuscript.  These paragraphs are reproduced below:

272 “Figure 9 shows the PEMFC stack output current signal under EGWO-FOPID, GWO-FOPID, EGWO-PID and GWO-PID. It’s clearly seen that the EGWO-FOPID has faster and  high  performance  in  tracking  the  reference  current  than  the  other  approaches, while the EGWO-FOPID has shown at the beginning an overshoot of 0.091A and high current accuracy equal to 9.741A with an error 0.001A between the output current and the desired in comparison with the GWO-FOPID, which gives an overshoot equal to 0.095 A and current accuracy equal to 9.722 A with an error equal to 0.018 A, which is an acceptable result to having the second grade of performance.  As seen in Figure 9, at t=4s the EGWO-PID shows an undershoot of 0.058A in comparison with 0.131A for the original GWO-PID.”

306 “As a result, the advantage of a modern optimization approach is seen as a complementary solution to improve the performance of the conventionally designed FOPID and PID controllers, which has a great impact on the output quality. However, there are many techniques that can be used as optimization tools, and the EGWO is one of the recent and effective optimization tools that has a fast convergence to the optimal value within 40 iterations while the GWO reached this point within 200 iterations.”

3. Can the authors describe how the development of this algorism can guide the design of fuel cell systems?

Response:  The main objective of our research is to stabilize and optimize the PEMFC output power quality which is the important part of the fuel cell system design. To improve output power quality performance, we developed the FOPID tuning using the EGWO for DC/DC boost converter that gives high current accuracy equal to 9.741 with an error 0.001A between the output current and the desired. In addition to this, the developed algorithm gives a minimal overshoot which is equal to 0.091A compared to the other algorithms as shown in the obtained results.

4. There are some grammatical errors in the text. For example, “which affected” in line 38 should be “which are affected”; “are occurred” in line 126 should be “occur”; “finally forming” in line 141 should be “finally form”.

Response: The authors have revised the paper and some grammatical errors have been corrected according to the reviewer comments.

5. Relevant recent literatures about fuel cells should be cited such as Electrochim. Acta 2016, 190, 817–828; ACS Appl. Energy Mater. 2018, 1, 411−420; J. Colloid Interface Sci. 2022, 613, 515–523.

Response: The authors have updated these references in the new version of the manuscript according to the reviewer comments.

Reviewer 2 Report

Some comments are given as follows:

1. The contribution from  the  paper  is  modest,  so  significant  improvement  of  the

quality is necessary.
2. The author should check and revise the English expressions of this paper carefully. There are many sentences that are obscured.

3. The number of decisions variables should be discussed.
   4. The references part need to be carefully checked and revised.

The review of the Research Article titled " Fractional Order PID Design for a Proton Exchange Membrane Fuel Cell
System Using an Extended Grey Wolf Optimizer" submitted to Processes, has been completed, and I am pleased to inform you that your manuscript should be accepted for publication in the journal after minor changes.

Author Response

Response to the reviewer comments

First of all, the author would express their sincere gratitude to the Editors and the Reviewers who gave us many constructive comments and valuable suggestions in order to improve this paper. The authors have revised the paper according to the reviewers’ comments and the changes made in the paper have been written in blue color. While the mistakes have been depicted in red color. The responses to the reviewer comments can be found below their respective comments.

Reviewer 2

Some comments are given as follows:

1. The contribution from the paper is modest, so significant improvement of the quality is necessary.

Response: The contribution of the paper has been clearly presented in the introduction of the revised manuscript (please see lines 86-98 revised manuscript). We think that the paper has an important contribution since it proposed a novel algorithm aiming to improve the performance of the fuel cell system. A comparison study of four optimized algorithms (GWO-PID, GWO-FOPID, EGWO-PID, EGWO-FOPID) has been performed to validate the pros of the proposed algorithm. Moreover, it should be noted that this theoretical study has been done based on the technical data of a commercial Heliocenris fuel cell system since a practical validation of the proposed algorithms will be done later. On the other hand, we think that the quality of the revised manuscript is significantly improved since we have carefully revised the manuscript based on the reviewer’s suggestions.

2. The author should check and revise the English expressions of this paper carefully. There are many sentences that are obscured.

Response: The paper has been revised by a fluent speaker and many mistakes along the paper have been corrected. All changes are highlighted with blue-color in Revised Manuscript-Marked. For example:

• In line 14 of the introduction, the statement “the research in energy” is revised in the same line of the revised manuscript as follows: “energy research”.

• In line 14 of the introduction, the statement “mainly cover” is revised in the same line of the revised manuscript as follows: “mainly covers”.

• In line 16 of the introduction, the statement “are indeed with” is revised in the same line of the revised manuscript as follows: “are with”.

• In line 17 of the introduction, the statement “and for fissile fuels” is revised in the same line of the revised manuscript as follows: “and fissile fuels”.

• In line 24 of the introduction, the statement “through the use of renewable energies” is revised in the same line of the revised manuscript as follows: “through renewable energies”.

• In line 33 of the introduction, the statement “considered to be the best appropriate” is revised in the same line of the revised manuscript as follows: “considered the best appropriate”.

• In line 38 of the introduction, the statement “nonlinear systems which affected” is revised in the same line of the revised manuscript as follows: “nonlinear systems which are affected”.

• In line 38 of the introduction, the statement “gases pressures besides fluctuations” is revised in the line 39 of the revised manuscript as follows: “nonlinear systems gases pressures and fluctuations”.

• In line 44 of the introduction, the statement “transistor (MOSFET) which can be controlled by a command law” is revised in the same line of the revised manuscript as follows: “transistor (MOSFET) controlled by a command law”.

• In line 44 of the introduction, the statement “This candidate connection, which is one of the most” is revised in the line 45 of the revised manuscript as follows: “This candidate connection is one of the most”.

• In line 50 of the introduction, the statement “in the literature for the control of DC-DC converters” is revised in the line 51 of the revised manuscript as follows: “in the literature to control DC-DC converters”.

• In line 89 of the introduction, the statement “The proposed controller is capable of stabilizing the PEMFC” is revised in the line 94 of the revised manuscript as follows: “The proposed controller can stabilize the PEMFC”.

• In line 90 of the introduction, the statement “the entire operating range in the presence of significant variations in the load power and supply voltage” is revised in the line 95 of the revised manuscript as follows: “the entire operating conditions and the presence of significant load variations.

• In line 91 of the introduction, the statement “It maintains the robustness of the system and provides” is revised in the line 97 of the revised manuscript as follows: “It maintains the system's robustness and provides.

• In section 2.2, in line 1, the statement “The activation losses are occurred ” are revised in the same line of the revised manuscript as follows: “ The activation losses occur " ”.

• In section 2.3, in line 1, the statement “The ohmic losses are occurred ” are revised in the same line of the revised manuscript as follows: “ The ohmic losses occur " ”.

• In section 2.5, in line 2, the statement “which finally forming a "stack" ” are revised in the same line of the revised manuscript as follows: “which finally form a "stack" ”.

• In section 4, in line 2, the statement “is correspond” are revised in the same line of the revised manuscript as follows: “corresponds”.

3. The number of decisions variables should be discussed.

Response: The authors have included information about the decisions variables in the revised manuscript version. Please see Section 3.3 line 248 of the revised manuscript.

4. The references part need to be carefully checked and revised.

Response: The reference style has been revised and corrected according to the reviewer comment.