Novel Strategy of Adaptive Predictive Control Based on a MIMO-ARX Model

Round 1

Reviewer 1 Report

The presented paper about predictive control has good quality and contains everything a paper should have: the research is based on previous works in the field, the math behind the controller is described in detail and seems to be sound, the results are mostly clearly presented, and the authors have plans to make their findings applicable in practice.

But there are also some major and minor shortcomings:

• The introduction is insufficient. There is only one reference less than three years old. And that is true for the entire paper, not only the introduction. The rest of the references are at least 6 years old. The authors must prove using recent references that their research is still relevant and truly novel.
• The English language must be improved. There are many typos through the text.
• Figures 3, 4 and 5 have wrong caption on x-axis. Figures 7 and 8 have a correct x-axis caption.
• The abstract is little ambiguous how the controller was tested. From the abstract it seems there was an experimental work done, but in the text are only simulations and the confirmation that no experiment was done is in the Conclusions.
• How were the simulations carried out? What tools were used?
• Nomenclature should contain all variables and abbreviations.
• Try to place Table 1 nearer to the relevant text.

Otherwise, this is interesting research and if the authors can correct the mentioned issues and prove the relevance of their research, it will be suitable for publication.

Author Response

The presented paper about predictive control has good quality and contains everything a paper should have: the research is based on previous works in the field, the math behind the controller is described in detail and seems to be sound, the results are mostly clearly presented, and the authors have plans to make their findings applicable in practice.

But there are also some major and minor shortcomings:

1. The introduction is insufficient. There is only one reference less than three years old. And that is true for the entire paper, not only the introduction. The rest of the references are at least 6 years old. The authors must prove using recent references that their research is still relevant and truly novel.
2. The English language must be improved. There are many typos through the text.

R: Thank your for your suggestion.Introduction has been extended, the relevance of the Adaptive predictive control. The application of this SISO strategy in different applications including the implementation of the algorithm  in Embedded systems, the use of Recursive least square as part of the adaptive block and identification strategy.

Typo Errors were also corrected.

1. Figures 3, 4 and 5 have wrong caption on x-axis. Figures 7 and 8 have a correct x-axis caption.

R: Thanks. Typo error in seg instead of sec. This was corrected in the 3 figures.

1. The abstract is little ambiguous how the controller was tested. From the abstract it seems there was an experimental work done, but in the text are only simulations and the confirmation that no experiment was done is in the Conclusions.

R: Thanks for your comments on this regard. The target of the paper is to show the ARX MIMO approach, in order to validate the performance we took to examples from the literature in which a MPC controller was used. We simulate the plant and the controller in matlab/Simulink.

1. How were the simulations carried out? What tools were used?

R: For validate the proposed controller we used Matlab R2015 and Simulink. Based on your question, we mentioned in the abstract what software was used during the simulation.

1. Nomenclature should contain all variables and abbreviations.

R: Thanks this has been updated.

1. Try to place Table 1 nearer to the relevant text.

R: Tanks for this recommendation. Table has been moved closer to text.

Reviewer 2 Report

The Introduction section presents the general information about the predictive control strategy with connection to the references.
There are no information about the MIMO systems/processes and the classical control strategies for them.

2. Adaptive Predictive Control (APC)
- presents the general scheme for the Adaptive Predictive Control strategy with some explanations.
- this part is too short for a separate section/chapter in the paper; maybe, these information could be covered in the Introduction section.

3. Predictive Control for MIMO-ARX Process
- first, I suggest to complete the section with a block diagram of the MIMO system which highlights the direct and cross section input-output influences/variables, the position of the MIMO controller etc.;
- the mathematical approaches used for the prediction model and the value of the control signals are well written and logical.

4. Results and Discussion
- I think that a scheme of the UAV included into a closed-loop block diagram would be helpful, in order to understand the MIMO control strategy (i.e.: eq. 39...47);
- the simulation results are interesting and suggestive for the control purpose;
- here is mentioned the Figure ?? (you need to check this!);
- in Figures 3 and 5, the control effort seems to be high; maybe some additional explanations are needed;
- the input-state-output model of the quadruple tank is taken form the reference 16; however, there are no information about the D matrix (D=0?);

Finally, the resulted from Figure 3,4,5, 7 and 8 confirm the proposed MIMO strategy.

The References are suggestive for the topic. Random check for: 1. R.Haber; 2. C.Hong; 4. J.M.Martín-Sánchez; 6. A.Nevado; 11. I.De la Cruz-Malagón; 14. A.Hernandez; 16. K.H.Johansson; 19. R.Scattolini.
However:
- I suggest to check the data about reference 1: author/authors, pages etc.;
- the recent studies are: only one title from 2021 and only one title from 2019;
- I suggest to extend the references list with recent studies.

Author Response

The Introduction section presents the general information about the predictive control strategy with connection to the references.
There are no information about the MIMO systems/processes and the classical control strategies for them.

R: Some references regarding to control strategies in MIMO systems had been included in line 74. Those control strategies inlude Fuzzy, neural network, adaptive predictive and MPC applications.

2. Adaptive Predictive Control (APC)
- presents the general scheme for the Adaptive Predictive Control strategy with some explanations.
- this part is too short for a separate section/chapter in the paper; maybe, these information could be covered in the Introduction section.

R: Thank you for your comments. I agree with this suggestion, this short part of the chapter 2 has been defined as subsection.

3. Predictive Control for MIMO-ARX Process
- first, I suggest to complete the section with a block diagram of the MIMO system which highlights the direct and cross section input-output influences/variables, the position of the MIMO controller etc.;

R: Thank you for this suggestions. We tried to use the general scheme Figure 1 to show the inside part of the controller. The APC control we proposed as explained in line 81 is made of 3 blocks, the Driver Block, the predictive Model and adaptation mechanism.

• 
  - the mathematical approaches used for the prediction model and the value of the control signals are well written and logical.

R: Thank you for your Feedback.

4. Results and Discussion
- I think that a scheme of the UAV included into a closed-loop block diagram would be helpful, in order to understand the MIMO control strategy (i.e.: eq. 39...47);

R: Thank you for this suggestion, in order to understand in a better way the simulation between drone-Controller a paragraph in line 212 has been included.

R: I don
- the simulation results are interesting and suggestive for the control purpose;- here is mentioned the Figure ?? (you need to check this!);

R: Thanks for this comment. Typo error in the latex file so figure was not called correctly.

in Figures 3 and 5, the control effort seems to be high; maybe some additional explanations are needed;

R: Thanks, this is a really good observation. The saturation of the control action in this examples is due to we do not considered actuators or plant constraints for this controller. As shown in Future work we are working on include the actuators constraints in the driver block model.

• 
  - the input-state-output model of the quadruple tank is taken form the reference 16; however, there are no information about the D matrix (D=0?);

R: D=0, This was added to the article.

Finally, the resulted from Figure 3,4,5, 7 and 8 confirm the proposed MIMO strategy.

The References are suggestive for the topic. Random check for: 1. R.Haber; 2. C.Hong; 4. J.M.Martín-Sánchez; 6. A.Nevado; 11. I.De la Cruz-Malagón; 14. A.Hernandez; 16. K.H.Johansson; 19. R.Scattolini.
However:
- I suggest to check the data about reference 1: author/authors, pages etc.;

R: I Apologize for this Error, i found the error and is already corrected in the paper. Thanks for your very detailed feedback.
- the recent studies are: only one title from 2021 and only one title from 2019;
- I suggest to extend the references list with recent studies.

Reviewer 3 Report

The paper addresses the design of a MIMO-APC (MIMO adaptive predictive controller) validated by using a quadrotor drone and a quadruple tank process.

All in all, even if the theoretical contributions are not outstanding, this is an interesting paper, with technical soundness and written in a comprehensive manner.

Comments and remarks:

1. The introduction and the literature survey are good but can be improved. Some additional titles and discussions about the MPC and adaptive control should be addressed.
2. The importance of the results from practical point of view and their application should be highlighted in a more pronounced manner.
3. The simulation for the quadrotor drone should be improved by taking into consideration some realistic conditions, such as measurement noise and/or disturbances that act on the process.
4. The same remarks for the quadruple tank system. Simulations should be more realistic. However, in order to be interesting for the readers, some real experiments should be performed (for example, by using some laboratory prototypes).
5. Minor typos should be corrected.

Author Response

1. The introduction and the literature survey are good but can be improved. Some additional titles and discussions about the MPC and adaptive control should be addressed.

R: Thanks for your Comments. Introduction was improved, we add information regarding the importance of the propose APC strategy in MIMO systems. Evaluation of this strategy in embedded systems and the importance of this controller to tackle industrial challenges.

1. The importance of the results from practical point of view and their application should be highlighted in a more pronounced manner.

R: Thanks for your feedback

1. The simulation for the quadrotor drone should be improved by taking into consideration some realistic conditions, such as measurement noise and/or disturbances that act on the process.

R: Than you for the suggestion. In terms of the Drone we simulate this system based on the information reported in the literature. We were not able to test the controller with the physical drone (this will be part of the next steps), so we took the same original conditions in order to validate our proposal.  As next steps we want to embedded the MIMO controller and validate the results with a real lab prototype.

1. The same remarks for the quadruple tank system. Simulations should be more realistic. However, in order to be interesting for the readers, some real experiments should be performed (for example, by using some laboratory prototypes).

R: We agreed with your comments. As part of the next steps we plan to validate our control strategy with lab prototypes. In these cases we simulated the plant based on original parameters and assuming the same conditions reported in literature.

1. Minor typos should be corrected.

R: Thank you for your feedback regarding to our research. We reviewed the article check spelling and typos errors.

Round 2

Reviewer 1 Report

The authors answered the questions and reservations and improved their manuscript, which is now suitable for publication.