Tuning a PI/PID Controller with Direct Synthesis to Obtain a Non-Oscillatory Response of Time-Delayed Systems
Round 1
Reviewer 1 Report
Comments and Suggestions for Authors
The paper deals with the tuning of PI/PID controllers for 1st and 2nd order systems with time delay.
The paper is well written and quite clear.
Despite this fact, the proposed method relies on the well know tuning techniques of direct synthesis and pole-zero matching without adding no new insight about the widely studied PID tuning matter. The imposing of a pair of coincident closed loop poles using root locus rules is just an academic exercise that is not worth a journal paper.
Minor issues are:
1 – When an acronym is defined, the related “in full” words should have the initial in capital, so to put in evidence the acronym definition. For example Internal-Model Controller (IMC), page 1 and Direct Synthesis (DS).
2 – When a symbol is used in an equation it must be defined, even if its meaning is obviuos: for example G_r and G_p in equation (1) and theta in equation (12).
3 – In section 2, starting from section 2.1 the specific form of the used PI/PID has to be explicitly given, in order to simplify the checking of equations. They are given further ahead in the paper, but not here.
4 – Section 3.3: “The transfer” is the beginning of the 2nd sentence.
5 – Section 4.2: “Example 3” should be “Example 2”; figure 3 is not referred in the text. Same for figure 4 in Section 4.3.
6 – Section 4.4 is missed.
7 – To which transfer functions are the 2 responses in figure 5 referred?
8 – In Section 5, the numerical references must be added, the surnames only can be misleading.
9 – In Section 5.1 what kind of controllers was used? PI for CHR method and PID (being G3 a 2nd order t.f.) by the author? Then, of course, the PID gives better results.
10 – Section 5.2: are the 3 cited methods “equivalent” (same for Section 5.3)? And why in the 1st sentence another method (Pannil) is cited? Value “6.17” on line 423 should be “8.17”. Figure 8: “answer” instead of “answere” (same for figure 9) and it must be referenced by its number, not by “below”.
11 – Section 5.4: “Chien’s method”, which one? Two references are given in the Bibliography. Line 446: reference to equations (33,35) seems wrong. Line 448: reference to figure 12 seems wrong, 10 perhaps. Line 457: “Laplace’a” should be “Laplace’s” or better simply “Laplace”.
12 – Section 5.5: cost function (62) is incomprehensible, why the error is weighted twice? Moreover, in the cited paper [28] there is no trace of the cost function (62) or of the Example 2 t.f. Is this reference [28] correct? Figure 11 is not referenced in the text.
Comments on the Quality of English Language
Avoid colloquial language (Many times: "Let's consider …" and similar).
Author Response
RESPONSE TO THE REVIEWERS applsci-3021051
I would like to thank the Reviewers of our manuscript for their efforts in preparing the comments that enabled me to improve the quality of this manuscript. In reading through their comments, I have tried to make use of them wherever I am able. I will respond to each of them below.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsThe paper presents a "Tuning a PI/PID controller by Direct Synthesis to obtain non-oscillatory response of time-delayed systems". Overall, the contribution of this paper is relatively limited. Moreover, there are certain issues that the authors should be clarified and improved upon:
1. There are many grammatical mistakes throughout the manuscript.
2. Add the Nomenclatures and Abbreviations in order to improve the quality and readability of the manuscript. Moreover, the symbols/variables used in the equations, Please make table for this.
3. The abstract should effectively provide a clear picture for the whole contribution of the manuscript and it should be revised.
4. Please check your section. I think you have too many mistakes in section numbering. Especially sections 3 and 5.
5. In order to better represent the superior performance of the proposed strategy to the existing strategy, the authors are advised to give the following four performance indices:
6. (a). ISE (Integral of Squared Error) (b). ITSE (Integral of Time-Squared Error) (c). IAE (Integral of Absolute Error), and (d). ITAE (Integral of Time-Absolute Error).
7. Please review the following references for inclusion in the manuscript. Additionally, it would enhance the quality of the research if the authors incorporate recently published papers in the same research domain and conduct a thorough review of the manuscript. A more comprehensive literature review presented in the form of a table (matrix) would provide readers with increased confidence in the research contribution and this is a good example of the closed-loop system.
R1. https://doi.org/10.1080/15325008.2023.2196663
8. Please, could you add the difference between the first inertial order, FOPD, and SOPDT?
9. Present the proof of sensitivity and robustness formulations of the proposed work and validation.
10. It is necessary that the authors should illustrate/present the modeling/design and data of the studied system, system constraints/data/parameters, etc. Moreover, state the system constraints, in other words, the upper and the lower boundaries of the optimization algorithm/system variables, etc.
11. Please clarify the differences between the calculated solutions obtained by the proposed method and other existing methods.
Comments on the Quality of English Language1. There are many grammatical mistakes throughout the manuscript.
Author Response
RESPONSE TO THE REVIEWERS applsci-3021051
I would like to thank the Reviewers of our manuscript for their efforts in preparing the comments that enabled me to improve the quality of this manuscript. In reading through their comments, I have tried to make use of them wherever I am able. I will respond to each of them below.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for Authors
Despite the improved minor issues listed in the previous review, the paper still lack totally of originality and no improvements about this matter were given in this new paper version.
Direct synthesis and pole-zero matching (about this last design technique, at least some consideration on unstable plant should be given) are well known techniques and their application to PID design is not a novelty. Maybe, the only original contribution is the analytical solution given in section 3.1 by applying one of the well know root locus rules, but this is not enough to justify a journal paper.
Comments on the Quality of English Language
Abstract: “method’s” must be “method” (misuse of Saxon genitive).
Section 3.2: rewrite "Let's consider …" (colloquial language).
Figure 10: “answere” must be “answer”.
Author Response
Round 2
Answer to the reviewer 1
As for the merits of the matter, this method of controller tuning is for me the missing link in research on the development of an autotuning system for the PID controller. The development of algorithms for creating more accurate process models has opened up the possibility of effective use of the controller tuning rule, which would allow the better model quality to be transferred to better control performance. And we managed to do it - although the biggest obstacle to achieving the control objective will remain the random impact of the environment, nevertheless, from a theoretical perspective, such a tool offers really great opportunities.
In my opinion, the proposed method is a real phenomenon, which ensures accurate achievement of the defined control goal (desired closed-loop transfer function, which is to ensure response without overshoot, zero control error, minimum settling time) and at the same time "smooth" control flow.
It should also be emphasized that Applied Sciences creates the opportunity to publish longer articles. This allows the reader to be presented with the derivation of the presented arguments and is not limited to, for example, only providing ready-made relationships for Kp, Ti, Td. Yes, it is sometimes trivial, as Reviewer 1 perceives it, but I am sure that such articles are much better received, especially by younger scientists.
Anticipating this perception of our work, I conveyed our point of view in a cover letter sent to the editor. So such opinions are no surprise to me. Nevertheless, I wouldn't like to lose the main message of this article: it can be simple, it can be better than it was.
Author Response File: Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsI have no comments on this manuscript. The author did an excellent job.
Author Response
Round 2
Answer to the reviewer 2
Thank you once again for all your valuable advice to improve my manuscript.
