Modeling, Simulation, and Temperature Control of a Thermal Zone with Sliding Modes Strategy

Round 1

Reviewer 1 Report

This paper presents a mathematical model and its experimental verification for  heat transfer and control in a closed box. It aims to capture the relevant thermodynamics of a closed room, which is a first step towards the optimization of heat comsumption in a realistic model of a building. For the mathematical model, the paper relies on the analogy with electrical systems. This allows the authors to write a set of differential equations. They also do an experimental realization of the system at a smaller scale, that is, with a small box reproducing the system under scrutiny. To tune the parameters from the theoretical model, the authors use an optimization algorithm, which minimizes the error between the experimental results and the simulated ones. Once the model is settled, they use it to evaluate control strategies. The topic is timely an interesting; the methods are  appropriate and the results are relevant. Therefore I recommend publication. The following is a list of concerns that may help improve the manuscript:

1. The simplified model [section 2.1, Eqs. (7)-(8)] is not properly justified, in my opinion. Why this is a good description of the system at hand? How the simplifications made are justified in comparison to the mode complete model in setion 2.1?

2. In lines 150-153, the comment on figure 5 is very succinct. Is this the only test they made (apart from figure 4)? A more detailed explanation of the experimental set up, figure and results is necessary, I believe. 

3. Why control is made with simplfied model? why it works? Is it only that is more difficult doing it with the complete model? 

This is a list of minor comments: 

1. All captions has to be extended. They have to be self-explicative, that is, explain what we see in the figure, what system, which parameters, what are the results. 

2. I'm not sure what the authors mean with a one dimensional vector (line 111).  

3. The English has to be improved. Some examples: line 5: an proposed-> a proposed; line 9 the needs the mathematical model-> the needs. The mathetmatical model; line 40: another need-> others need or another needs; line 73: shows an energy-> shows energy savings; line 76: aN easy task; line 91: accuracy Subsequently->accuracy. Subsequently; line 95: Section 3 describeS; Line 131: In Figure 3 shows-> Figure 3 shows or In Fugure 3 we show, it is shown; Line 138: needS or needED;    

4. All equations have to be punctuated as sentences (commas, full stops, etc.)

5. Eqs. (11)-(14) and (15)-(18) can be put in a single line, e.g. x_1=\,\,x_2=\,\,...\mbox(and)\,\,\dot)x)_2=.

5. Equations, when referred in text, I think it is better to use parenthesis. 

Author Response

Please see our responses in attached.

Author Response File: Author Response.pdf

Reviewer 2 Report

In their manuscript mathematics-483197, the Authors adapt the so-called sliding control technique
to the problem of temperature control in buildings with different thermal zones. For that purpose
they adopt a "lumped parameter method" to map the highly complex control problem onto an effective
one characterized by a few parameters. In addition to the mathematical modeling, the Authors
developed a reduced-scale model for the comparison of with their own experimental results.
The Authors conclude that their approach to regulate the temperature in a thermal zone is both
simple and reliable so that extension to larger zones may be envisaged.

The article could be publishable if the Authors can seriously address the following points:

1. Despite the chosen norm of a measured accuracy of ~2%, the difference between absolute values
of temperature reaches ~2 deg. which is huge (figure 5). Authors should explain the discrepancy
or improve their model/calculatioj.

2. In the experiment an air leakage and a humidity changes are not taken into account. The

simplification should be justified.

3. In the experiment the ratio between radiative and convective heat transfer is much higher than
in a standard room. How would a change of the ratio influence the obtained results?

4. Authors should prove the added value and advantages of their approach over other
well-established "naïve" control techniques such as proportional or an On/Off controllers.


Important remarks: the quality of writing must be improved; a native speaker of English should
proofread the manuscript to increase its readability: as one reads the manuscript it is not always
clear what the authors wish to state. Further, by all means, *avoid* vague sentences that convey
no useful information. For instance, the first half of the abstract should be revised to be
suitable for a readership with scientific background; the Introduction also should be revised
and sharpened. To illustrate this criticism: "The UN and other researchers" ??? "Some factors
and phenomenon are easily handled etc" ??? "the responsibility rest on the researcher etc." ???
"in the majority of research it is acceptable to use etc." ??? "some researchers" ??? the list
is long... Anything vague and unsubstantiated renders the article uninteresting.

Recommendation: Major revisions.

Author Response

Please see attached our responses.

Author Response File: Author Response.pdf

Reviewer 3 Report

I checked modeling process and formulas of this manuscript. 

Then I verified its results. 

It seems that they are right.

Author Response

Thank you for your appreciation.

Round 2

Reviewer 2 Report

The Authors of the manuscript have satisfactorily enough answered the points raised.

I can recommend publication of the manuscript in Mathematics.