Model-Independent Adaptive Fault-Tolerant Tracking Control for High-Speed Trains with Actuator Saturation
Round 1
Reviewer 1 Report
A final check of the English grammar and spelling can be done before publication.
For example, to the abstract. "for the effects from the lumped uncertainty" needs to be written as "for the effects of the lumped uncertainty"...
Author Response
Point: A final check of the English grammar and spelling can be done before publication. For example, to the abstract. "for the effects from the lumped uncertainty" needs to be written as "for the effects of the lumped uncertainty"
Response: A final check of English grammar and spelling has been done and the main modifications are listed as follows:
To the abstract. "for the effects from the lumped uncertainty"( Line 21) has been written as "for the effects of the lumped uncertainty". Line 36,"entirely or partly" has been corrected as "entire or partial". Line 65, "radical basis function" has been corrected as "radial basis function". Line 79, "satisfied" has been corrected as "satisfactory". Line 85, "on" has been corrected as "upon". Line 143, " float type of fault " has been corrected as "float type fault". Line 149, 224 and 229, "follows" has been corrected as "follow". Line 152-153, " indicates the actuator is totally failed; indicates the actuator is healthy " has been revised as " indicates the actuator totally failed; indicates the actuator healthy". Line 177, "to track" has been revised as "tracking". Line 201-203, "The objective is to design a model-independent passive fault-tolerant tracking control scheme based on adaptive technology and variable-gain PID-type sliding mode surface for HSTs mentioned above" was revised as" The objective of this paper is to design a model-independent passive fault-tolerant tracking control scheme ,which based on adaptive technology and variable-gain PID-type sliding mode surface for HSTs mentioned above". Line 208-209, "in order to deal with" was changed into" for HSTs subject to". Line 356, "ensure" was revised as "to ensure". Line 388, "testify" was revised as "verify".Author Response File: 
Author Response.docx
Reviewer 2 Report
The article concerns interesting and contemporary issues of tracking control. It provides an overview of the current state of knowledge in the subject of the article. The Authors solved the problem of control using an adaptive method, carried out proof of stability and presented the results of the simulation. The problem was solved using modern methods of nonlinear controlling systems.
I am asking Authors to pay attention to two comments:
1. In the line 65 should be "radial" instead of "radical".
2. Train model presented in chapter 2.1. contains elementary error. The model described by equation (2) refers to the situation when the train is moving horizontally. However, when the tracks are inclined as in Fig. 1 (ramp angle different from zero), then the force of gravity gives a projection on the direction parallel to the track. Gravity can help or hinder movement depending on whether the angle is positive or negative. The authors must take this into account in both the model and the simulation results. In the current situation, the model applies only to horizontal movement.
Author Response
Point 1: In the line 65 should be "radial" instead of "radical".
Response 1: Sorry for our negligence, and "radical" in the line 65 has been corrected as "radial".
Point 2: Train model presented in chapter 2.1. contains elementary error. The model described by equation (2) refers to the situation when the train is moving horizontally. However, when the tracks are inclined as in Fig. 1 (ramp angle different from zero), then the force of gravity gives a projection on the direction parallel to the track. Gravity can help or hinder movement depending on whether the angle is positive or negative. The authors must take this into account in both the model and the simulation results. In the current situation, the model applies only to horizontal movement.
Response 2: As what you have pointed out, when the tracks are inclined as in Fig. 1 (ramp angle different from zero), the force of gravity can help or hinder train movement depending on whether the angle is positive or negative. It was our negligence that we did not make this point clear. In our algorithm, the projection of gravity on the direction parallel to the track, as an unknown disturbance term, has been included in the lumped uncertainty, so no matter the force of gravity hinders or helps train movement, it would be compensated by the compensation term F1 of the proposed algorithm. Therefore, no matter the gravity hinders or helps train movement, our model and algorithm are applicable. In order to make the expression clearer, we added a statement stated in Remark 5.
Author Response File: Author Response.docx
This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.
Round 1
Reviewer 1 Report
This paper investigates the fault-tolerant tracking control problem for high-speed trains HSTs) subject to unknown model parameters with unavailable uncertainties, unmeasured additional disturbance and unpredictable actuator faults constrained by actuator saturation.
Although the paper is quite well-written there are several issues that should be improved before it can be accepted:
If Assumption 3 follows from Assumption 1 and 2, it is not required as an assumption. But, instead the reasoning included in Remark 2 can be included in the proofs presented later in the paper. The problem statement in Section 2.2 is very poor. It should be stated in a more formal way. Moreover, there is a typo: "2.2 problem statement" -> "2.2 Problem Statement. The fault-tolerant scheme is not described. It looks more an adaptive scheme that is sold as fault-tolerant. Which are the type of faults you are considering? It is not clear at all. They should be presented in the model of the system in the problem statement in order to see the effect. Regarding saturations, it not very clear how they are handled. The design of the controller only guarantees stability. What about performance guarantees? The simulation section is very poor. It is not clear the physical meaning of the faults. They look more a change of parameter.
Reviewer 2 Report
Some improvements should be made before any consideration for publication:
1) The authors should perform further proofreading to correct some small English mistakes (starting from the abstract).
2) For the reader's sake, the authors should add some references in the first paragraph of subsection 2.1; those references will be pointing out to some works were the single-point-mass model was as well used for tracking control of HSTs.
3) Whether in the control design process or in the stability analysis, it is not clear how the proposed controller and its dynamic parameters compensate the lumped disturbance. This should be clarified.
4) In the simulation part, it seems like the initial values for solving Eqs. 19a and 19c are missing; they should be added and line 311 should be revised.
5) For simulation purpose, the lower and upper bounds of the control input are missing.
Reviewer 3 Report
This paper is well organized and the controller design is reasonable.
So this paper is enoug to be published with the following minor concerns.
Minor Concern:
1) Actuator output saturation and Actuator fault is very important, so to overcome the actuator fault. the author should deal with the case of actuator fault of above 90%, i.e. kc=0.1. In that case there happens a big position and velocity errors but the author should show the robustness of the proposed controller.
