Observer-Based Fault-Tolerant Predictive Control for LPV Systems with Sensor Faults: An Active Car Suspension Application
Round 1
Reviewer 1 Report
In the paper, an observer-based robust fault-tolerant predictive control strategy is proposed for Linear Parameter Varying (LPV) systems subject to input constraints and sensor failures and the performance of the proposed approach is investigated by a simulation example of a quarter-vehicle model.
In general, the paper is nicely written and the underlying theory is convincing.
However, the study has one major weakness: The authors assume the following sensor fault: line 414: The faults of the sensors injected into the closed-loop system is given by ??(?)=0.3(cos0.5?+0.4) – what kind of sensor fault is this? Which kind of sensor is used here, what is the physical sensor principle? Is it probable that the injected fault is realistic? How was it chosen? The authors need to address this issue carefully, because they claim to develop a fault-tolerant control – the fault has to be realistic.
Some additional remarks
The literature review concerning virtual sensors and virtual observers could be expanded.
In line 361 I recommend to place a figure explaining the model and its parameters.
Line 371: The authors need to discuss how realistic the choice is that the parameters compressibility and damping of the pneumatic tire are constant.
In lines 389 to 391 a detailed explanation of the vertex coefficients is lacking and especially the choice in this study has to be explained – why is this choice sensible?
Author Response
Dear associate Editor,
First, we the authors would like to thank you for all of your questions and suggestions;
You will find our answers in the attached file.
Best regards
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Review "Observer-based Fault-Tolerant Predictive Control for LPV systems with Sensor Faults: An Active Car Suspension application"
The paper deals with the design of observer-based robust fault-tolerant predictive control (ORFTPC) for Linear Parameter Varying (LPV) systems subject to input constraints and sensor failures. The controller is implemented on a quarter car model with cubic nonlinearity.
The description of the controllers and the observers appears to be well designed, and the results appear to be coherent. I obviously did not redo their work. I generally feel the paper is interesting.
Generally, the manuscript is well-written and the language level is good. However, some comments are as follows:
1- The norms should be initially defined before using them, for instance, the norm used in the quadratic objective function line 252. Also in the same line alpha was not defined just after the equation.
2- In equation (37) for the unsprung mass has the wrong sign for the nonlinear term, which is also reflected in the state-space model line (405). By the way, I have checked the reference article [19] for the nonlinear model and turned out that the cited article is for the linear quarter car model not for the nonlinear model. You may check this publication for the nonlinear quarter car model with cubic nonlinearity:
Shaqarin, T. (2018). Robustness analysis of feedback linearisation and LQR control on quarter-car model with cubic nonlinearity. International Journal of Vehicle Noise and Vibration, 14(3), 238-250.
3- Beta and alpha in the LPV model are not clear, I had to do my homework to figure out what are these. It seems that alpha should be the measured (x3)2 it should be more clear. Something to mention is how beta is decided to be to 0.2, it should be explained.
4- The article should be further checked for typos, such as:
in line 490 "otain", should be "obtain".
Author Response
Dear associate Editor;
First, we the authors would like to thank you for all of your questions and suggestions.
You will find our answers in the attached file.
Best regards
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The imrpovement is considerable. In this from in my opinion, the paper can be accepted.
Author Response
Again, we the authors would like to thanks the Associate Editor for the given opportunity to answer all valuable questions and suggestions raised by reviewers in order to improve the contents based on the reviewers’ comments and suggestions. Also, thank you for your time and efforts in coordinating the review process.
Reviewer 2 Report
The authors made most of the required corrections, but still some comments as below:
Equation 37 and the corresponding state-space still not corrected, please check the attached pdf.
Comments for author File: Comments.pdf
Author Response
We would like to thank the reviewer for this comment. Equation 37 has been corrected in the revised paper.
