Design of Vehicle Stability Controller Based on Fuzzy Radial Basis Neural Network Sliding Mode Theory with Sideslip Angle Estimation

Round 1

Reviewer 1 Report

An adaptive fuzzy radial basis function neural network sliding mode control algorithm for vehicle stability control is presented. The algorithm is based on an adaptive double-layer unscented Kalman filter for sideslip angle estimation. After that, given the uncertain vehicle disturbance caused by parameter perturbation or the external environment, a nonlinear vehicle dynamic model involving system uncertainty disturbance and additional yaw moment is established. A vehicle stability controller based on the sliding mode control theory is designed.

Originality/Novelty: I have verified the originality of the presented work, and it seems that it is original and has not been previously published. 

Significance: The algorithm design procedure and testing methods presented in this paper are appropriately written, but it can still be improved.

Quality of Presentation: All aspects of work, paper organization, and results presentations are substantial. The used terminology is OK. 

Interest to the Readers: This article is devoted to topics and questions that are interesting to the academic community. Overall, it is a highly targeted application article.

The paper represents an exciting approach to control a nonlinear dynamic system such as vehicle stabilization.

• In the abstract, the authors use the term radical (?) basis function neural network. This is repeated several times in the text of the article. Authors probably think radial basis function neural network. If not, then please explain it accordingly.
• You can also colect all labels and tags of variables and parameters used in the paper on the list.
• In line 177, explain the importance and label index i of the wheel tire. Is not missing an index written in the measuring status vector?
• How was the simulation performed? To understand what exactly was simulated and how the proposed controller impacts a process, it is necessary to describe the used simulation model precisely. For example, what is the sample time in the simulation?
• It would help if you unified fonts in all illustrations. All figures can be improved.

 

Author Response

Response to Reviewers

Thanks for the insightful comments from the reviewer concerning our manuscript (applsci-1057313) entitled “Design of vehicle stability controller based on fuzzy radial basis neural network sliding mode theory with sideslip angle estimation”. These valuable comments have helped to make this manuscript more rational in term of scientific rigor and clarity. We have addressed all the comments and revised the manuscript as best as we could accordingly.

 

Comments # 1:

In the abstract, the authors use the term radical (?) basis function neural network. This is repeated several times in the text of the article. Authors probably think radial basis function neural network. If not, then please explain it accordingly.

Author response:

Thanks to the reviewer for pointing out this error due to our carelessness. As your comment, we use “radial basis function neural network” and not the “radical basis function neural network”. And we correct the above mistakes in the manuscript.

 

Comments # 2:

You can also collect all labels and tags of variables and parameters used in the paper on the list.

Author response:

Thanks for your advice. We list all the parameters in the appendix at the end of the manuscript. In this way, it's convenient to find the parameters.

 

Comments # 3:

In line 177, explain the importance and label index i of the wheel tire. Is not missing an index written in the measuring status vector?

Author response:

Thanks to the reviewer for pointing out this error due to our carelessness. We added the missing vector to the manuscript.

 

Comments # 4:

How was the simulation performed? To understand what exactly was simulated and how the proposed controller impacts a process, it is necessary to describe the used simulation model precisely. For example, what is the sample time in the simulation?

Author response:

Thank you very much for your meaningful suggestion. We state the running process and sampling time of the model, and add it to line 411-415. The details are as follows:

During the simulation, MSC CarSim inputs the real-time state parameters of the vehicle into the controller built by Simulink, and calculates the output control rate through the controller to the MSC CarSim vehicle model to realize the closed-loop control of the system.During the simulation, the simulation step taken as 0.001 seconds.

 

Comments # 5:

It would help if you unified fonts in all illustrations. All figures can be improved.

Author response:

Thanks for your advice. We unified fonts in all illustrations of the manuscript.

Reviewer 2 Report

This paper presents a design method of vehicle stability controller based on fuzzy radial basis neural network sliding mode theory with sideslip angle estimation.
ADUKF is used to compute the sideslip angle and adaptive fuzzy sliding mode control approach is applied to design the controller.

1. The dynamic stability of the estimator error using ADUKF is not analyzed.
Only the stability of the adaptive fuzzy sliding mode control scheme is analyzed in (54)--(56).
When ADUKF (10)--(24) is used, the stability of the estimator error should be analyzed.

2. Basically, the ADUKF and the adaptive fuzzy sliding mode controller used in this paper are well known in the control field.
This paper only applied these well known methods to the system that can be expressed by (8).
There are no any inherent design problems or constraints that is caused from the 7-DOF nonlinear vehicle dynamic model.

In conclusion, the presented result has a minor contribution and is a straightforward application using the existing techniques.

Author Response

Response to Reviewers

We are grateful for such targeted, concise and constructive feedback on our work, which we feel has improved the quality and clarity of the piece. we have endeavoured to address all concerns raised, in cases where we have not made changes to the work we have provided an explanation as to why, and have clarified in the text the concepts at issue. We have made attempts to address all the concerns by the reviewers in faith. If we have misunderstood a question or answered in a way that does not provide the intended revision this was unintentional, please clarify the request and we will attempt to answer correctly.

 

Comments # 1:

The dynamic stability of the estimator error using ADUKF is not analyzed. Only the stability of the adaptive fuzzy sliding mode control scheme is analyzed in (54)--(56).When ADUKF (10)--(24) is used, the stability of the estimator error should be analyzed.

Author response:

Thank you very much for your meaningful suggestion. The ADUKF used in this manuscript is based on UKF, and UKF has been widely used in the field of parameter estimation, and references 13-15 has proved the stability and convergence of UKF in parameter estimation. The ADUKF used in this manuscript has been proved to be effective in parameter estimation in reference 18. In this manuscript, based on the estimation algorithm which has been proved in the control field, the ADUKF is applied to the estimation of vehicle sideslip angle, and the effectiveness of the algorithm is verified. In this case, we don't think the stability of the estimator error analysis of ADUKF is necessary.

 

13. Strano, S.; Terzo, M., Constrained nonlinear filter for vehicle sideslip angle estimation with no a priori knowledge of tyre characteristics. Control Eng Pract. 2017, 71 (feb.), 10-17. https://doi.org/10.1016/j.conengprac.2017.10.004
14. Boada, B. L.; Boada, M. J. L.; Diaz, V., Vehicle sideslip angle measurement based on sensor data fusion using an integrated ANFIS and an Unscented Kalman Filter algorithm. Mech Syst Signal Process. 2016, 72, 832-845. https://doi.org/10.1016/j.ymssp.2015.11.003
15. Chen, J.; Song, J.;  Li, L.;  Jia, G.;  Ran, X.; Yang, C., UKF-based adaptive variable structure observer for vehicle sideslip with dynamic correction. IET Control Theory Appl. 2016, 10 (14), 1641-1652. https://doi.org/10.1049/iet-cta.2015.1030
16. Yang, F.; Zheng, L.-T.;  Wang, J.-Q.; Pan, Q., Double Layer Unscented Kalman Filter. Zidonghua Xuebao. 2019, 45 (7), 1386-1391. https://doi.org/10.16383/j.aas.c180349

 

Comments # 2:

Basically, the ADUKF and the adaptive fuzzy sliding mode controller used in this paper are well known in the control field. This paper only applied these well known methods to the system that can be expressed by (8). There are no any inherent design problems or constraints that is caused from the 7-DOF nonlinear vehicle dynamic model.

Author response:

Thanks for the reviewer’s comments on our work. Although ADUKF, FRBFNN and SMC used in this manuscript have been proposed in the field of control, there is no practical application for the two problems of vehicle slip angle estimation and stability control in this manuscript. This manuscript applies ADUKF and AFRBF-SMC to practical engineering problems, and verifies the feasibility and effectiveness of the above algorithms. It is also an innovation in solving practical engineering problems. In this manuscript, the 7-DOF nonlinear vehicle dynamics model is used to estimate the sideslip angle, and there are no inherent design problems or constraints.

Reviewer 3 Report

Dear Authors,

could you give units - missing units - e.g. 255: "where Cf is the equivalent lateral stiffness of front axle tires; Cr is the equivalent lateral stiffness " etc. 

Table 2. - how did you choose the cornering stiffness value (50000 N/rad)? (it is not mentioned).

Be careful - Mpa but MPa  - see Figure 6 (j) and Figure 8 (j).

 

Reference number 11 is a 60-year-old publication! I understand you, but please change it to a newer publication. Publications should not be older than 20 years (from 2000 to 2021)  No. 19 is similar.

Your article gives new information. Your research is well done.

After the above minor changes, I recommend this manuscript for its publication.

Author Response

Response to Reviewers

Thanks for the insightful comments from the reviewers concerning our manuscript (applsci-1057313) entitled “Design of vehicle stability controller based on fuzzy radial basis neural network sliding mode theory with sideslip angle estimation”. These valuable comments have helped to make this manuscript more rational in term of scientific rigor and clarity. We have addressed all the comments and revised the manuscript as best as we could accordingly.

Comments # 1:

could you give units - missing units - e.g. 255: "where Cf is the equivalent lateral stiffness of front axle tires; Cr is the equivalent lateral stiffness " etc. 

Author response:

Thanks for your advice. We list all the parameters in the appendix at the end of the manuscript. In this way, it is convenient to find the specific information of parameters.

 

Comments # 2:

Table 2. - how did you choose the cornering stiffness value (50000 N/rad)? (it is not mentioned).

Author response:

Thank you very much for your meaningful suggestion. We should state the selection of tire lateral stiffness. We add the selection method of tire side stiffness to the related work section, on page 10 of the manuscript. The details are as follows:

The selection of tire lateral stiffness is based on the tire lateral characteristics. When the tire sideslip angle is small, the lateral force and the cornering angle are linear. It is considered that the ratio of cornering force and cornering angle is the lateral stiffness of vehicle tire under linear condition.

 

Comments # 3:

Be careful - Mpa but MPa  - see Figure 6 (j) and Figure 8 (j).

Author response:

Thanks to the reviewer for pointing out this error due to our carelessness. We replace the units in Figures 6(j) and Figure 8 (j) with MPa instead of Mpa.

 

Comments # 4:

Reference number 11 is a 60-year-old publication! I understand you, but please change it to a newer publication. Publications should not be older than 20 years (from 2000 to 2021)  No. 19 is similar.

Author response:

We thank the reviewer for the suggestion and we replaced the original references with new references. The details are as follows:

11. Basar, T., A New Approach to Linear Filtering and Prediction Problems. Wiley-IEEE Press: 2009.

19. Bartolini, G.; Fridman, L.;  Pisano, A.; Usai, E., Modern sliding mode control theory: New perspectives and applications. Springer: 2008; Vol. 375.

 

Round 2

Reviewer 2 Report

This paper was well revised.

Author Response

Response to Reviewers

Thanks for the positive recognition from the reviewer concerning our manuscript (applsci-1057313) entitled “Design of vehicle stability controller based on fuzzy radial basis neural network sliding mode theory with sideslip angle estimation”.

Sincerely

Jing Li and authors

Author Response File: Author Response.docx