Fractional Order Adaptive Fast Super-Twisting Sliding Mode Control for Steer-by-Wire Vehicles with Time-Delay Estimation
Round 1
Reviewer 1 Report
1. Please read again the paper for English. Some of the sentences should be corrected (e.g in line 17, in line 21, in line 56, in line 159...)
2. Maybe a block diagram emphasizes better the control scheme and the functional signals.
3. In line 155 and relation 11 the variable Je should be multiplied with the double derivative of the rotational angle (see also relation 8).
4. How does relation 19 from line 204 result? At least some references should be added.
5. More attention to explaining the differences between relationships 22 and 23. Which relationship is obtained and which is modified? Maybe the explanations should be made before relationship 23 and not after that.
6. I recommend specifying who are the variables ?1 (?), ?2 (?) (gain parameters), and for what are they used from the first occurrence (relation 19 in line 204) even if they are calculated/adjusted in detail later.
7. Please define correctly in line 200 the new variable introduced.
8. How the authors chose relation 25 from line 242. Eventually some references.
9. Please reformulate the matrix C=[1 0] in line 272.
10. The quality of figure 1 should be improved.
11. Please see the definition of the state vector x in line 329.
12. Relations 5 and 7 contain variables Je and Be, while model 34 in line 329 contains Jeq and Beq. Also, the rotation angle of the front wheel Theta_fw is the same as the rotation angle of the steering motor shaft? See relations (7), (5), (34).
13. Please also check the variable d defined in line 329.
14. Please explain/define all the variables from the control model 37 in line 341. Also some references for the control law?
15. How were the values for the parameters specified in section 4.1.4 deduced/chosen?
16. How were relations 41 and 42 obtained? If the references are used then at least explain the notations or specify more clearly where the values for the constants in these relations from lines 380-385 and Table 2 are taken. How do the three scenarios from line 387 result?
Author Response
Please see the attachment.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The paper is difficult to read. A criticial point is the notion of delay which is not clearly presented, which is major shortcoming, considering the topic under consideration. The authors seems to confuse input, output delays with dynamics lags. This is detrimental to the tutoriality of the presentation.
The style of writing is unbalanced. Some proofs are elegantly presented with appropriate equations, some other facts are just loosely treated. For example, I do not understand what the authors mean by: "The estimation of system lumped dynamics can be realized by means of tuning Δ?. And it does not lead to a lag in the time phase of the system." This is totally unclear.
More generally, and importantly, the literature review is totally subpar. The subject treated here is covered, in a more general setup in
Adaptive control scheme for uncertain time-delay systems D Bresch-Pietri, J Chauvin, N Petit, Automatica 48 (8), 1536-1552, 2012
and also
Delay-adaptive control for nonlinear systems, D Bresch-Pietri, M Krstic
IEEE Transactions on Automatic Control 59 (5), 1203-1218, 2014and
Adaptive backstepping controller for uncertain systems with unknown input time-delay. application to SI engines D Bresch-Pietri, J Chauvin, N Petit
49th IEEE Conference on Decision and Control (CDC), 3680-3687This is important to relate the presented work to the vast literature of adaptive control of delay systems.
Finally, I am not satisfied with the presentation of the estimation of the delay itself which is a worked problem (and a difficult one). I could not clearly understand what the authors are proposing here.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
The authors have tried to address my concern, but I am not satisfied by their answers. They always write "The problems have been modified", but beside beeing very polite, they do not do what is needed. In particular, lietrature review does not include any of the reference I suggested, which, again, treat the same subject is a more general setup.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 3
Reviewer 2 Report
no further remarks
