Receding Galerkin Optimal Control with High-Order Sliding Mode Disturbance Observer for a Boiler-Turbine Unit
Round 1
Reviewer 1 Report
This paper proposes a receding Galerkin optimal controller with a high-order sliding mode disturbance observer in a composite scheme, the high-order sliding mode disturbance observer is employed to estimate the lumped disturbances based on a deviation form of the mathematical model of the boiler-turbine unit, a receding Galerkin optimal controller is designed to compensate the lumped disturbances by embedding their stimates into the mathematical based predictive model at each sampling time instant, I have the following suggestions to present to the authors for further revision:
1) In the introduction part, the author only summarizes nonlinear control, gain scheduling control , adaptive control, for the Boiler-Turbine Unit, it is recommended that the author add an overview of advanced robust control techniques, because the main design content of the paper is to design the interference estimator and compensate it in Boiler–Turbine Unit,;
2) Line 107 should not only be followed by the y3 equation, the equation (1) is too long, it is recommended to separate it; for Table I Model Parameters of Boiler–Turbine Unit, the reason and source of these parameter selections should be explained;
3). For Main Results: Method, High-Order Sliding Mode Disturbance Observer Design, it is necessary which ones are the author's contribution, which ones are derived from lemmas or references; at the same time, remarks should be added for the advanced nature of the design controller;
4). For Case 1: Wide-range load tracking without lumped disturbances, lines 266 to 272 should be merged to increase readability;
5). I encourage the author to present the experimental results, which is very helpful for improving the quality of the paper and improving the reference of subsequent researchers;
This paper only has a small number of expression errors that need to be corrected.
Author Response
The reviewer provided many constructive and relevant comments, and we made revision and provided responses in the text, as shown in attached word file.
Reviewer 2 Report
In this paper, a receding Galerkin optimal controller with high-order sliding mode disturbance observer is proposed to improve the control performance of a boiler-turbine unit. There are several issues suggested for revision.
1. In terms of innovation, further explanation is needed to describe how the designed composite controller improves upon existing methods.
2. All simulation cases require comparative experiments to demonstrate the advantages of the proposed method. The method for comparison should include the Galerkin Optimal Control.
3. There are some contents that can be simplified in this paper, such as the problem statement in Part 2 and the description of working conditions in Part 4.2.
4. The format of the formula in the manuscript needs to be uniform.
5. It is suggested to add some quantitative error analysis to the simulation results.
Author Response
Thanks for many constructive comments provided by reviewer, and we made revision in the paper and provided responses in the text, as shown in attached word file.
Author Response File: 
Author Response.docx
Reviewer 3 Report
The article has great contribution, in which they propose an optimal Galerkin controller with backtracking with a high-order sliding mode disturbance observer in a composite scheme. They also designed a second Galerkin backward optimal controller to compensate for the grouped disturbances by incorporating their estimates into the mathematically based predictive model at each sampling time instant. Simulations were carried out on a boiler turbine unit mathematical model to demonstrate disturbance rejection. However, the work has some observations, which must be addressed.
1.- It is necessary to add more references, I leave some works for your consideration related to the control of complex processes, this with the aim of enriching his work:
“Morales, J. Y. R., López, G. L., Martínez, V. M. A., Vázquez, F. D. J. S., Mendoza, J. A. B., & García, M. M. (2020). Parametric study and control of a pressure swing adsorption process to separate the water-ethanol mixture under disturbances. Separation and Purification Technology, 236, 116214.”
“Morales, J. Y. R., Mendoza, J. A. B., Torres, G. O., Vázquez, F. D. J. S., Rojas, A. C., & Vidal, A. F. P. (2022). Fault-tolerant control implemented to Hammerstein–Wiener model: Application to bio-ethanol dehydration. Fuel, 308, 121836.”
“Martínez García, M., Rumbo Morales, J. Y., Torres, G. O., Rodríguez Paredes, S. A., Vázquez Reyes, S., Sorcia Vázquez, F. D. J., ... & Renteria Vargas, E. M. (2022). Simulation and state feedback control of a pressure swing adsorption process to produce hydrogen. Mathematics, 10(10), 1762.”
“Ortiz Torres, G., Rumbo Morales, J. Y., Ramos Martinez, M., Valdez-Martínez, J. S., Calixto-Rodriguez, M., Sarmiento-Bustos, E., ... & Buenabad-Arias, H. M. (2023). Active Fault-Tolerant Control Applied to a Pressure Swing Adsorption Process for the Production of Bio-Hydrogen. Mathematics, 11(5), 1129.”
2.-It is necessary to add a naming table of the variables used. This table must be added in an annexes section.
3.-It is necessary to put the name of the controllers in the figures where they are compared, since it is not understood that it is being compared. Put the names of the controllers.
4.- What does it add to the subject area compared with other published material?
5.-Are the conclusions consistent with the evidence and arguments presented and do they address the main question posed?
Author Response
The reviewer provided many constructive and relevant comments, and we made revision and provided responses in the text, as shown in attached word file.
Author Response File: Author Response.docx
Reviewer 4 Report
The manuscript should be improved before it is acceptable for publication. Especially the authors should clearly point out what relevance the present work has to address about sustainability topics.
#Abstract should have one sentence per each: context and background, motivation, hypothesis, methods, results, conclusions. What problem did you study and why is it important? What methods did you use? What were your main results? And what conclusions can you draw from your results? Please make your abstract with more specific and quantitative results.
# Introduction: The authors described a lot of control theory and pros and cons, but no statements about the problems regarding the sustainability issues, which is the scope of the journal. In addition, the novelty and level of detail are not satisfactory.
# The originality of the paper needs to be further clarified. The knowledge gap needs to be clearly addressed
#Relevant references should be provided to support your results.
# A completed nomenclature should be provided
Moderate editing of English language required
Author Response
Thanks for many constructive comments provided by reviewer, and we made revision in the paper and provided responses in the text, as shown in attached word file.
Author Response File: Author Response.docx
Round 2
Reviewer 2 Report
The quality of manuscripts has been improved.
Reviewer 4 Report
The manuscript has addressed all the issues.
Minor editing of English language required
