A Hybrid Linear Quadratic Regulator Controller for Unmanned Free-Swimming Submersible

Round 1

Reviewer 1 Report

Control systems of linear and nonlinear phenomena described by hybrid dynamics are an important part of modern control theory and applications. In fact, several studies have appeared in the literature concerning the extension or the adaptation of classic results on fundamental control problems to a vast class of systems, in particular, those involving hybrid control systems. Thus, the paper under review is relevant to the field and of particular scientific importance. The paper discusses the possibility of implementing a hybrid Linear Quadratic Regulator (HLQR) controller for Unmanned Free-Swimming Submersible (UFSS).

The paper is well-written and easy to follow. However, I have several questions and suggestions for the Authors. Please, find my remarks below.

1. First, clarify the scientific contribution of this study. Many hybrid control system are known from the literature, and all authors claim their efficiency as a result. Is the proposed approach, which uses "two linear quadratic regulators /controllers and a mathematical structure of the Riccati equation " really novel ? (by the way, what kind of novelty? Maybe it is of reason to clarify it directly in the Abstract?). I disagree with the authors when they state that, necessarily, other controllers don’t consider enough environmental effects in simulation results. Please provide further clarification about the contribution of the current paper.
2. How the efficiency of handling parametric uncertainties was evaluated in this work?
3. What is the computational complexity of the proposed controller? Can it be implemented as embedded software? What about real-time control?
4. Additional proofreading is needed to fix some typos (ex: Riccati rather than "Raccati" (Line 181 and in Fig. 4 (page 7)).
5. A Preliminary section containing the main Definitions, Concepts and Theorems used could be helpful to improve the understanding of this work.
6. The authors state that simulations were performed using MATLAB. Nonetheless, more detailed information should be provided, e.g., which numerical methods were used in the experimental simulations? Please, clarify the properties (packages and/or toolboxes) and the precision of these methods.
7. The Conclusion section could be expanded with a more detailed description of the achieved results.

Author Response

Please find the attachment for the response of reviewer 1.

Author Response File: Author Response.docx

Reviewer 2 Report

Major remerks:

1. Section 2 needs a significant improvement. The authors refer to the book given in the bibliography as [16] and immediately write down some equations that do not know what they come from and what is their relationship with the controlled object. What do the coefficients in the equations depend on? - it is not known. Not even a drawing / diagram / photo of the object was presented. Such a drawing should be included. It should contain control inputs and coordinates related to the state of the system.
2. The relationship of equations (3) - (5) is unclear. Where is K1 in equations (4) and (5)? It is similar with equations (8) - (10).
3. The stability issue in section 3 was dealt with marginally. Basically no analysis was carried out.
4. The relationship of sections 3 and 4 is completely unclear.
5. The work concerns control with the help of LQR. I have doubts whether the regulator can be called hybrid, since only LQR's is used and not a combination of two different types of regulators. 

Minor remarks: 

1. The language and terminology used need to be improved (perhaps this is due to an unfortunate translation).
2. The sentence (lines 59-61) is incomprehensible to me: "However, these intelligent controller create crucial problems when they consume considerable power with the change in the input and disturbance." What is it about consume considerable power when using intelligent controllers? Is it computing power or something else?
3. In subsection 1.2, the authors mention several drawbacks of the current solutions and claim that their design is to eliminate them. They wrote:  "We believe that the aforesaid concerns can be reduced by employing a hybrid approach to design the UFSS system controller. " It is not known what actions were taken to achieve the goal.

Author Response

Please find the attachment for the response of reviewer 2.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

After re-reading the revised version of the paper, I recognize the authors' effort to provide the changes required.

In my opinion, the paper has improved and it can be accept. Nonetheless, the list of references has not a standard formatting. I recommend that authors visit the MDPI Reference List and Citations Style Guide ( https://www.mdpi.com/authors/references)
in order to provide citations in accordance to the Journal.

Author Response

The file is attached. 

Author Response File: Author Response.docx

Reviewer 2 Report

Thanks for the answers, clarifications and corrections. I accept all amendments except one. I renew my first remark"

"Section 2 needs a significant improvement. The authors refer to the book given in the bibliography as [16] and immediately write down some equations that do not know what they come from and what is their relationship with the controlled object. What do the coefficients in the equations depend on? - it is not known. Not even a drawing / diagram / photo of the object was presented. Such a drawing should be included. It should contain control inputs and coordinates related to the state of the system."

In response, the authors included block diagrams, but it still does not explain what the dynamics of the system are due to. What are the equations of motion? Because it is from them that the transfer functions arise. The system drawing is also missing (it is not about block diagrams but a drawing showing the control object).

Author Response

The file is attached. 

Author Response File: Author Response.docx