A New Fuzzy Robust Control for Linear Parameter-Varying Systems
, Ardashir Mohammadzadeh 4 and Ebrahim Ghaderpour 5,*Round 1
Reviewer 1 Report
The article is interesting and well written. I did not find any flaws in its theoretical part. However, I have the following remarks on its content.
The English language needs improvement (e.g. ‘angel’ -> ‘angle’).
Is the inverted pendulum a good example? The article is about linear objects with varying parameters, and the pendulum is a nonlinear object with fixed parameters.
Please describe in more detail the construction, operation and parameters of the fuzzy module.
Author Response
Original Manuscript ID: mathematics-1888838
Original Article Title: A New Fuzzy Robust Control for Linear Parameter Varying Systems
Dear Reviewer,
We sincerely thank you for the time spent and effort in the reviewing process. Following the insightful comments and valuable suggestions, we have further revised the paper. All changes have been highlighted in yellow color.
Please kindly see the attached word file for our point-by-point responses to your comments. We hope that the changes that we made are satisfactory. Please kindly let us know if you have any further comments.
Thank you!
Best regards,
The authors
Author Response File: 
Author Response.docx
Reviewer 2 Report
1. Definitions in the preliminary should be clearer. It is suggested to remove them to where they first appear in the article.
2. A brief review of existing methods for finding the gain $K$, especially the fuzzy-based approaches, is suggested below (11) to justify the motivation of the paper.
3. Equation (29) should be modified as $b(t)\geq a_i(t) \geq 0$, and the next equation followed up should be erased.
4. Since fuzzy control is adopted, a brief introduction of fuzzy control methodology is suggested as a subsection in this article.
5. The simulated system (60) is actually a nonlinear system. Since $f_1$ and $f_2$ there depend on the state vector, whether pure linear state feedback could stabilize the system is plausible. The authors are suggested to clarify this point therein.
6. Grammar errors are easily found in the article which should be carefully found and then corrected.
Author Response
Original Manuscript ID: mathematics-1888838
Original Article Title: A New Fuzzy Robust Control for Linear Parameter Varying Systems
Dear Reviewer,
We sincerely thank you for the time spent and effort in the reviewing process. Following the insightful comments and valuable suggestions, we have further revised the paper. All changes have been highlighted in yellow color.
Please kindly see the attached word file for our point-by-point responses to your comments. We hope that the changes that we made are satisfactory. Please kindly let us know if you have any further comments.
Thank you!
Best regards,
The authors
Author Response File: Author Response.docx
Reviewer 3 Report
Comments and Suggestions for Authors
This paper focuses on research and development of a method for robust, i.e. reliable control of Linear Parameter Varying (LPV) systems based on a fuzzy system to ensure control stability. The proposed method of reliable control makes it possible to strengthen feedback on the state of the control object using a fuzzy system and bring the state of the object to equilibrium points, which is the goal of the control system.
In this study, the fuzzy control system is used to create a signal regulator combined with the main signal controller to speed up the stabilization operation, and the Lyapunov theory is used to ensure the stability of the control system. Thus, the main result of this study, which is novel, is that a new robust control of the planned amplification is proposed for LPV systems with stability assurance based on the Lyapunov theory.
The relevance of the work can be determined by the importance and necessity of providing stable and reliable control systems for many objects in various industries based on a fuzzy system that considers the experience, knowledge and intuition of subject matter experts. The results obtained can be used in the development of robust, stable control systems for complex systems that require high reliability.
Two sets of new planning parameters are used, which are created on the basis of minimizing and maximizing the uncertain planning parameters at any time over the entire interval, parametric uncertainties during the process of solving the problems of parametric uncertainties. A theorem on the asymptotic stability of the investigated closed system under certain conditions is formulated and its proofs are given. Unlike many similar works, in which the feedback gain Ki is determined by trial and error, the authors estimate this parameter using a fuzzy system.
An inverted pendulum was studied as an example to evaluate the effectiveness of the proposed control system. Based on the results of the study of the inverted pendulum, the efficiency and performance of the proposed fuzzy robust control (FRC) method is shown compared to traditional robust control (TRC).Overall, the work in theoretical and practical terms is useful and important, since the results of the study can be used to create a more reliable, sustainable control system. Paper can be evaluated positively, and it can be recommended for publication after minor revisions.
The following can be noted as minor comments and recommendations for improving the structure and content of the work:
1. In Section 1-Introduction the authors should mention the control methods of technological objects in a fuzzy environment based on mathematical models, referring, for example, to the works
https://doi.org/10.3390/math8030448 and DOI 10.1109/WCICA.2016.7578783
2. In Figure 2, it would be desirable to expand the "Fuzzy" block, its structure and content, for example, what rule base is used, what fuzzy conclusions are applied.
3. The structure would be more coherent if authors transfer the discussion of the obtained results in a separate section named “Discussion".
4. As a recommendation, it would be better if the authors in future studies tested the proposed FRC for production control facilities.
Authors are encouraged to address the above minor issues and consider the recommendations before the editor makes a final decision.
Author Response
Original Manuscript ID: mathematics-1888838
Original Article Title: A New Fuzzy Robust Control for Linear Parameter Varying Systems
Dear Reviewer,
We sincerely thank you for the time spent and effort in the reviewing process. Following the insightful comments and valuable suggestions, we have further revised the paper. All changes have been highlighted in yellow color.
Please kindly see the attached word file for our point-by-point responses to your comments. We hope that the changes that we made are satisfactory. Please kindly let us know if you have any further comments.
Thank you!
Best regards,
The authors
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
The authors have revised the paper in accordance with the reviewers' suggestions. In my opinion, in its current state, the paper is suitable for publication.
Reviewer 2 Report
The revised version improves significantly. However, the simulated system seems not fully consistent with the general system (5). An explanation therein is suggested.
