Hierarchical Model Predictive Control for Autonomous Collision Avoidance of Distributed Electric Drive Vehicle with Lateral Stability Analysis in Extreme Scenarios
Round 1
Reviewer 1 Report
This document proposes an active collision avoidance controller based on a predictive control framework of the hierarchical model for the vehicle considering extreme conditions. A comparison is made between a linear MPC and a hybrid one in the hierarchical structure considered.
The paper is well and clearly written in both the exposition both at the vehicle model level (well known in the literature) and in the stability region analysis. In the introduction it is suggested to include, if you deem it appropriate, also paper references in which the instability and saturation of the actuators is managed through a dynamic reference generator, another methodology used for extreme situations, such as:
- Borri, D. Bianchi, M.D. Di Benedetto, S. Di Gennaro, Optimal workload actuator balancing and dynamic reference generation in active vehicle control, Journal of the Franklin Institute, Volume 354, Issue 4, Pages 1722-1740, 2017.
The control structure and the role of the two levels are clear. What could be added to improve the paper is also an analysis and comparison of performance from a computational point of view. In fact, it is well known that to obtain better performance there is a calculation cost that must be taken into account, and therefore it seems appropriate to include considerations on any real-time implementation of complex controllers, as well as a metric that is able to quantify the calculation effort between the two compared algorithms.
Finally, although the problem of formal and theoretical proofs of asymptotic stability with controllers based on MPC is known, it would also be interesting to insert a concept of practical stability linked to the working regions in which one remains as working areas for the system.
Author Response
Dear reviewer:
We gratefully thank the editor and reviewers for your time spend making constructive remarks and precious suggestions. The point-by-point response to the comments are given as follows:
(1) Comment: the supplement and revise of the introduction
(1) Reply: Your suggestion is appropriate and useful, in the introduction, it is necessary to add another methodology using for extreme situations, which manages instability and saturation of the actuators through a dynamic reference generator in vehicle control. As a result, we have cited some relative references (including the one you mentioned) to the introduction of the revised manuscript in the fifth paragraph that describes the methods of dealing with saturation conditions.
(2) Comment: add the analysis and comparison of performance from a computational point of view
(2) Reply: We gratefully appreciate your valuable suggestion. The computational point is truly an important part to analyze the performance of the controller, I add tables2,3 with the computing time of the two compared algorithms in the part of simulation analysis. It is well-known that the MIQP is more difficult to solve than conventional QP, hence the computing time of hybrid MPC is higher but not too much than linear MPC, however, the hybrid method shows better performance in tracking and vehicle stability which is the key point that this paper wants to deliver. Hugely computing load is one of the main reasons that MPC is rarely used for real-time implementation, which will be considered in our future study.
(3) Comment: insert a concept of practical stability linked to the working regions
(3) Reply: Thank you for your comment. The concept of practical stability linked to the working regions is interesting, and I add this concept in the part of stability analysis in which the working areas can be defined by the results of phase portrait analysis.
Sincerely yours
Correspond authors: Cheng Lin, Bowen Wang.
Correspondence: [email protected], [email protected].
Reviewer 2 Report
The reviewed article is of a high scientific level. I am pleased to write that the work can be published in the journal. Work to improve its quality and reception requires minor corrections: - lack of a full description of the axis in figs: 7a, 9, 10a.
Author Response
Dear reviewer:
We gratefully thank the editor and reviewers for your time spend making constructive remarks and precious suggestions. The point-by-point response to the comments are given as follows:
(1) Comment: lack of a full description of the axis in figs: 7a, 9, 10a.
(1) Reply: Thank you so much for your careful check. It is true that figs 7a,9,10a need a more detailed description. Tables2,3 depict the RMSE of tracking errors are added in the part of simulation analysis, quantitative description is supplied to analyze the figs7a,9,10a
Sincerely yours
Correspond authors: Cheng Lin, Bowen Wang.
Correspondence: [email protected], [email protected].
