System of Energy-Saving Optimal Control of Metal Heating Process in Heat Treatment Furnaces of Rolling Mills

Round 1

Reviewer 1 Report

This manuscript studies a very interesting topic. The presentation is very clear and the organization is in a clear logic. The developed technique is sound. I never saw similar development of this technique in literature. The writing is clear and I can follow the authors well. 
My minor concern is that the motivation is not well described in the Introduction.
1. I suggest to find more materials in 2019 to support your statement, for example "Sensors 2018, 18, 3024; IEEE Sensors Journal, 18(9): 3806-3812; Ocean Engineering, 2019, 183C：372-383".
2. Please clear point out your contributions in the last paragraph in the Introduction.
3. What is your future plan?

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

The paper describes a mathematical model for the optimization of metal heating in a rolling mill furnace . The topic is of interest in the field and the need for optimization is well explained in the paper. Before acceptance, the manuscript should be revised in many aspects. The main revisions are for the following topics. (1) The author should clearly highlight what the novelty of the paper is. The introductory section includes some literature references, but it is not clearly described what novelty and addition are coming from the current manuscript. (2) Regarding the mathematical model description, the author should describe better what the U(tau) (firstly introduced in Equation 1, line 102)), which is the main objective function of the model, is. It is not clear what this term is, what the unit of measure is and how Equation 2 is derived. What is, again, U(tau)? And how is it related to the temperature function in Equation 2? What is the control law? I am assuming the PI (line 138) is the proportional integral?? In Figure 2, it is not clear how the U*(tau) function is updated every iteration. Or, maybe, what is the law?? (3) Regarding the results section, this part of the manuscript should be revised widely. This section is not comprehensive and it is not clear if there is any real comparison with any actual plant and any measured quantity. To this regard, from Figure 6 it is clear the fuel consumption reduction, but there is no mention of what the constraints values (measured??) are (i.e. DTmax, maximum heating medium temperature Tmax, etc.). This is critical to verify that the projected fuel consumption actually gave the same outcomes in terms of temperatures and, in general, performance. What is, also, the maximum fuel consumption constrain (in terms of mass of fuel)? Was this calculated from Figure 6 and compared? (4) the paper is well written but there are some sentences that need to be checked and modified (e.g. as only one example, in the abstract section, lines 15-19, the sentence is too long and very difficult to follow)

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The paper has been improved. I would suggest checking the English for a few minor things but the paper has been improved a lot.