Analytical Synthesis of Non-Linear Control Algorithms of a Chemical Reactor Thermal Mode

Round 1

Reviewer 1 Report

Please see my report in the attached file

Comments for author File: Comments.pdf

Author Response

   Dear Reviewer,

Thank You for the review of our submitted manuscript. Individual reviewers had various comments on some parts of the article (even contradictory). We have tried to make changes and improvements in the article based on the compromise and your comments.

 

Comments and Suggestions for Authors

The authors consider the non-linear control process in a liquid-phase reactor, where the target is stabilizing the internal temperature with respect to perturbations on several parameters. The authors face the problem by exploiting the movement of the system’s depicting point through a hierarchy of manifolds such that, step after step, the dimensionality of the problem is reduced. The target is achieved in a twofold way: by using the standard Analytical Design of Aggregated Regulators (ADAR) approach, and by using such an approach in a two-step way in which the system is divided in two subsystems interconnected. A computational exemplification is given.

I think that the paper is interesting and well structured. It also treats a topic of general interest since the method could be applied also to the control of similar dynamical systems.

I can recommend the publication in Processes once the following minor points are taken into account.

 

Response to Broad comments

1. A bibliographic reference to the slow manifold phenomenology in dynamical systems is perhaps due, especially for those readers not confident with the matter. For instance, the topic is treated at the general level in the following book:
2. N. Gorban and D. Roose (Editors), Coping with complexity: Model reduction and Data Analysis Lecture Notes in Computational Science and Engineering (Springer-Verlag, 2011)

This book (or a similar one, or some review paper) could be cited at the beginning of section 2.1.

 

Response:

The listed link has been added to the article.

 

2. In section 2.1, it could be appropriate to state from beginning that two tuning parameters (the time constants T1 and T2) will be introduced. Otherwise, it is seems difficult to understand Eq. (3), where T1 is not commented.

 

Response:

A description of parameters T₁ and T₂ was added after equation (3) on page 4.

 

3. In section 2.3, the authors make a simulation to illustrate the two approaches (classical ADAR and the two-subsystem approach). They refer to quite specific parameters but it is not said which is the reaction under consideration. Still in this section, the authors should complete the comments to Figures 4 and 5. It is said that the two approaches give comparable results. Which are the pros and cons of the two-subsystem approach? Why should one adopt the two-subsystem approach? Some indication here, or in the conclusions, would improve the paper.

 

Response:

We consider the first stage of the butyl alcohol oxyethylation reaction which has a significant practical importance. From Figures 4 and 5 it also follows that the use of the two-subsystem approach gives a lower value of control time, which is very important for the control system. The main advantage of the cascade control is its efficiency under the action of disturbances fed with the control action. In our case such disturbance is the inlet temperature of the coolant (t_cⁱⁿ). In the case of such disturbance, i.e. there are fluctuations of the coolant temperature at the jacket inlet, the use of a cascade system will be appropriate. This is caused by the reason that the state variable t_c (jacket coolant temperature) responds faster to a given disturbance than the main controlled variable t (reaction mixture temperature). In other words, the “t_cⁱⁿ → t_c” channel is less inertial than the “t_c → t” one.

 

4. Minor points: The are some typos to be corrected and some specific parts to be checked (with responses):
   • Should be in place of k₁₀ at page 3, line 77.

The value k₁₀ was incorrect; it was replaced by the value of k₁⁰.

• At page 3, line 95, better write s = 1, , m (or say by words, s from 1 to m).

The text in line 95 has been modified.

• At page 3, line 98: perhaps “approximates” should be replaced by “approaches”.

The expression in line 98 has been replaced.

• At the bottom of page 3. Please better comment what “the state variables are interconnected in statics” means.

This means that the state variables are influenced by each other. For instance, the temperature of the process is influenced by the temperature of the coolant in the jacket as well as the concentrations of the components in the reaction mixture. Therefore, a change in these state variables will also cause the temperature in the apparatus to change. This feature of the object can be used when synthesizing the control system and selecting appropriate invariant manifolds.

The "in statics" part has been removed and the expression will only be "the state variables are interconnected".

• At page 4 after Eq. (2): unknown function “from t” should be perhaps “of t”.

The expression at page 4 after equation (2) has been replaced.

• At page 6, line 172. Please check the subscript of : ().

We apologize, this is a typo. The correct version would be .

• At page 7, line 213. “the applying” Þ “applying”.

The expression at page 7 in line 213 has been replaced.

• Important: please be sure that all curves in Figures 4 and 5 are visible in print. In my PDF file the profiles 2 are not visible in print, and are visible on the screen depending on the zoom level. Please check these figures.

Figures 4 and 5 have been completely redrawn and replaced by new versions.

Author Response File: Author Response.docx

Reviewer 2 Report

The manuscript describes two approaches for non-linear control of the thermal regime of liquid-phase chemical reactions. The control algorithms is carried out by the method of analytical design of aggregated regulators (ADAR), which is a very innovative approach. The first variant assumes the temperature control by classic ADAR method on the basis of a sequential set of invariant manifolds. The second one is based on the cascade control system structure. Computer simulation is then used to study and compare the synthesized control systems.

The work has some clear merits, and would fit to the scope and readership of Processes. However, there are some aspects that require further improvement prior to publication:

-Please improve the English - there are several mistakes and typos in the text.

-Is it possible to use some experimental data from the literature to see the fitting between the model and the experimental results?

-In the introduction, when discussing continuous-flow systems, the authors say "To date, the reactors thermal regime has been controlled in 40 most cases by means of single-circuit or cascade automatic control systems based on 41 linear PID algorithms". It would make sense to add a citation to the recent excellent papers that also discuss this topic. Please refer to: A Sivo, R de Souza Galaverna, GR Gomes, JC Pastre, G Vilé, React. Chem. Eng. 2021, doi: 10.1039/D0RE00411A; S Tortoioli et al., Green Chem. 2020, 22, 3748-3758.

-Is it possible to use the same model for continuous-flow reactions in a PFR reactor?

Based on these remarks, I recommend a revision at this point and I would be happy to review again the modified version for publication approval.

Author Response

   Dear Reviewer,

Thank You for the review of our submitted manuscript. Individual reviewers had various comments on some parts of the article (even contradictory). We have tried to make changes and improvements in the article based on the compromise and your comments.

 

Comments and Suggestions for Authors

The manuscript describes two approaches for non-linear control of the thermal regime of liquid-phase chemical reactions. The control algorithms is carried out by the method of analytical design of aggregated regulators (ADAR), which is a very innovative approach. The first variant assumes the temperature control by classic ADAR method on the basis of a sequential set of invariant manifolds. The second one is based on the cascade control system structure. Computer simulation is then used to study and compare the synthesized control systems.

 

Response to comments and suggestions

The work has some clear merits, and would fit to the scope and readership of Processes. However, there are some aspects that require further improvement prior to publication:

1. Please improve the English - there are several mistakes and typos in the text.

 

Response:

English in the article has been modified and improved.

 

2. Is it possible to use some experimental data from the literature to see the fitting between the model and the experimental results?

 

Response:

The mathematical model of the reactor was developed by the example of the first stage of the butyl alcohol oxyethylation reaction. Relevant data on reaction kinetics were taken from literature. However, it is not possible to compare experimental data and the mathematical model at the stage of chemical reactor design because there is no real object. It was the main purpose of this study to show the methodology of analytical synthesis of the chemical reactor control system, which can be used for reactions of a similar type.

 

3. In the introduction, when discussing continuous-flow systems, the authors say "To date, the reactors thermal regime has been controlled in 40 most cases by means of single-circuit or cascade automatic control systems based on 41 linear PID algorithms". It would make sense to add a citation to the recent excellent papers that also discuss this topic. Please refer to: A Sivo, R de Souza Galaverna, GR Gomes, JC Pastre, G Vilé, React. Chem. Eng. 2021, doi: 10.1039/D0RE00411A; S Tortoioli et al., Green Chem. 2020, 22, 3748-3758.

 

Response:

Listed references have been added to the article.

 

4. Is it possible to use the same model for continuous-flow reactions in a PFR reactor?

 

Response:

PFR reactor is described by the plug flow model, which is a system of partial differential equations. Therefore, the same model cannot be applied directly to the plug flow reactors.

Author Response File: Author Response.docx