A Novel Anti-Saturation Model-Free Adaptive Control Algorithm and Its Application in the Electric Vehicle Braking Energy Recovery System

Round 1

Reviewer 1 Report

The paper tries to address a topical problem in nowadays field of EVs, namely focuses on the control strategy for improving the energy recovery in case of vehicle braking.

I would see useful an improvement of the title. See the "Anti-Actuator Saturation" part. Also I would recommend revising the "anti-actuator" term (as it is used starting from line 90, "anti-saturation", seems more apropriate);
lines 112-115: is good to have balanced statements/phrases length (one very long vs. very short);
Fig. 1 not mentioned in the text, nor its source;
In Fig.2 some labels have missing letters (Batter, Machiner). Please check also the used terms ("Electric Machinery"?);
In Fig. 3 there is not clear which is W1; 
lines 151,161, W1 and W2 are defined the same (reaction force of the ground facing the front wheel). In line 161, check the capitalization for the measurement unit;
In fig. 3 is used v and in equations u, are they the same or different?
In eq. 3 term g is not defined;
In eq. 4 unknown term φ can be found;

F_μ1 and F_μ2 are the same with F_u1 and F_u2 from Fig. 3?

In eq. 7 h_g term is not defined;

Line 196 check the definition of f function (defined with values in?); idem. line 240;

Line 247: there is "equation (1) "?

Eq. 12 should be revised as in this form is confusing. Also some term are not explained (eg. see e*);

line 291: "MFAC system control" is about "MFAC control system"?

line 302: "Substituting equation (11) into equation (14) " but eq. 14 is not yet defined it just follows;

line 305: considering this statement the eq. 15 just results from nowhere;

line 335: check the proposed acronym typing "aas-mfac algorithm";

lines 503, 505, 508: there seems to be overlapped characters in equations;

line 504: "Φck f from";

 

 

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Overall: The authors present a control method based on anti-actuator saturation model-free adaptive control (AAS-MFAC). In general, the idea of the paper is clear, but it needs many improvements. The article presents simulation results using a Simulink software to validate this strategy.

There are some points that in my opinion should be further discussed and improved:

1. The paper's contribution should be made more evident in the introduction and conclusion in the face of the available literature. It is unclear whether the contribution is on the control method or its application to the braking system.
2. When you mention "free-model", it means for me that the proposed strategy is not based on any dynamic and/or kinematic model. Is it not? Why do you mention the free model? 
3. Some figures are not referenced in the whole text, e.g., Fig. 1 is not mentioned in any paragraph of the paper, so in this case, you can remove it. 
4. Describe more the set-up of your experiments? which sensors and measurements are employed in the framework of the proposed methodology?
5. How did you choose the friction and slippage parameters? 
6. For that, I recommend you to extend state of the art by including extra works addressing real-time slippage/sliding variables estimation approaches (linear and nonlinear), references related to this topic.   

   •  Titre: Nonlinear Tire Cornering Stiffness Observer for a Double Steering Off-Road Mobile Robot.  

   • Title: Lateral vehicle velocity estimation using fuzzy sliding mode obsever.
7. Finally, the authors could include more references on Dynamic Path Tracking Control on slippery environments (e.g., guaranteed NMPC to account for the system's uncertainties, constrained controllers NMPC, etc.). Please find below some recent potential references: 
   • Title: Constrained model predictive control for dynamic path tracking of a bi-steerable rover on slippery grounds.
   • Title: Model predictive visual servoing of fully-actuated underwater vehicles with a sliding mode disturbance observer.
   • Title: Experimental validation of a guaranteed nonlinear model predictive control.

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Dear Authors, thank you for the provided reply. I really appreciate your effort for revising! However in the process  of editing or due to previous unclear requirements there are left or were introduced few issues recommended to be checked:

line 16/105/106/224: hyphenation not needed: simi-larity, decelera-tion, re-turn, de-sign, posi-tions and maybe in other parts too;

In the statement that follows line 143: before mentioning F, its meaning introduction would enhance the readability (even if it defined later in the text);

line 190: check if there is expected meaning ("where b>0 is a constant" ?)

Related to  the previous comment market as "Point 18", thank you for the effort of explaining he result, however the ambiguity came from the statement (and still persist): "Taking the derivative of u(k) and letting it equal 0 obtains:" (one would understand that  u(k) is derived but instead sees that functional J() is derived and then that is equaled with 0). What about if there is mentioned that is implied the necessary condition for extremum of the mentioned index function?

line 240: typing issue "233vehicle".

Author Response

Thank you very much for your comments. The modified paper is still attached to the response. Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Thanks for the clarifications. The paper can be accepted in the present form.

- Write the reference [20] correctly  : M. Fnadi, and J. Alexandre dit Sandretto. Experimental Validation of a Guaranteed Nonlinear Model Predictive Control. Algorithms, 14(8), 248, 2021.

Author Response

Thank you very much for your comment. We have completed the modification. You can view attachments.

Author Response File: Author Response.pdf