Hybrid Particle Swarm Optimization Genetic LQR Controller for Active Suspension
Round 1
Reviewer 1 Report
The abstract is difficult to read. There are incomplete sentences.
In the abstract, the main findings are missing. The methodology could be better summarized. Furthermore, the applicability is missing. There are too many abbreviations in the abstract.
Line 16: The introduction is somehow incomplete. Please first define Vehicle suspension systems and the problem corresponding to those systems. Subsequently, formulate the problem you are going to solve.
Line 46: The state of the art is incomplete. Please evaluate the mentioned approaches regarding 1) applicability, 2) advantages, and 3) disadvantages.
Line 59: Please, first of all, define the Random Road Input Model. Describe parameters (assumptions), input variables, and output variables. Subsequently, formulate the required input variables.
Please improve your argumentation for choosing all those models.
Units should not be in math mode, there are spaces missing between number and unit.
Figures 1 and 2: Please add axis labels, and define q.
The results are not perfectly described. The comparison is sometimes difficult to understand, the Figures are not captioned comprehensively and the quantification of the improvement of the method is not clearly visible. The results and the methodology are not critically discussed.
In the conclusion, the results and the methodology are not critically discussed, assumptions are not mentioned, advantages and disadvantages are not explained, the applicability of the approach is not defined, and the next steps are missing.
There are incomplete sentences. The English language quality is low.
Author Response
Comment 1：the abstract is difficult to read. There are incomplete sentences.In the abstract, the main findings are missing. The methodology could be better summarized. Furthermore, the applicability is missing. There are too many abbreviations in the abstract.
RE: Thank you for your comment. We are sorry for the diffficulty in abstract reading. The abstract has been revised.
Comment 2: Line 16: The introduction is somehow incomplete. Please first define Vehicle suspension systems and the problem corresponding to those systems. Subsequently, formulate the problem you are going to solve.
RE: Thank you for your comment. We are sorry for the incomplete. The related part has been rewritten.
Comment 3: Line 46: The state of the art is incomplete. Please evaluate the mentioned approaches regarding 1) applicability, 2) advantages, and 3) disadvantages.
RE: Thank you for your comment. The relerated state has been revised.
Comment 4:Line 59: Please, first of all, define the Random Road Input Model. Describe parameters (assumptions), input variables, and output variables. Subsequently, formulate the required input variables.
RE: Thank you for your comment. The section of road input model has been revised.
Comment 5: Please improve your argumentation for choosing all those models.
RE: Thank you for your comment. The relerated argumentation has been revised.
Comment 6: Units should not be in math mode, there are spaces missing between number and unit.
RE: Thank you for your comment. We are sorry for our mistakes, and, the mistakes has been corrected.
Comment 7: Figures 1 and 2: Please add axis labels, and define q.
RE: Thank you for your comment. Figure 1 and Figure 2 has been redrawn.
Comment 8: The results are not perfectly described. The comparison is sometimes difficult to understand, the Figures are not captioned comprehensively and the quantification of the improvement of the method is not clearly visible. The results and the methodology are not critically discussed.
RE: Thank you for your comment. The section of results has been revised.
Comment 9: In the conclusion, the results and the methodology are not critically discussed, assumptions are not mentioned, advantages and disadvantages are not explained, the applicability of the approach is not defined, and the next steps are missing.
RE: Thank you for your comment. The section of conclusion has been revised and the misssing steps has been added.
Reviewer 2 Report
This paper proposed a hybrid particle swarm optimization method incorporating with LQR controller for active suspension. However, other researchers have explored this topic well, and it lacks novelty. Besides, here are some concerns:
1. How about the computation performance of the proposed method, especially in terms of heuristic algorithm, for example, particle swarm optimization used in this paper? Is this possible for the current onboard processor to implement?
2. The labels in the legend of figures are confusing. The proposed method should be denoted as “LQR + optimization” to be different from conventional “LQR”. Besides, I cannot understand what the “observer” represents. The observer is impossible to achieve control tasks but estimates some necessary states. On the other hand, I cannot find any reference about these comparisons.
Here are some typos and grammar mistakes.
Author Response
Comment 1. How about the computation performance of the proposed method, especially in terms of heuristic algorithm, for example, particle swarm optimization used in this paper? Is this possible for the current onboard processor to implement?
RE: The proposed hybrid method can effectively improve the performance of active suspension. The existing research results have not been applied to heuristic. And there are few experiments in this area. We are sorry that we did not conduct the relevant experiments for the lack of human and financial resources.
Comment 2. The labels in the legend of figures are confusing. The proposed method should be denoted as “LQR + optimization” to be different from conventional “LQR”. Besides, I cannot understand what the “observer” represents. The observer is impossible to achieve control tasks but estimates some necessary states. On the other hand, I cannot find any reference about these comparisons.
RE: We are sorry for the confusing labels. Because of the size of figure, the lines in the figure are given simplified names. “passive” represents the passive suspension. “LQR” represents the active suspenson with LQR control. “optimization” represents the active suspenson with optimization LQR control. “observer” represents the observe state of the suspension systems. The meaning of the lines has been reexplained. The observer has no effect on the control result. And, we are only verify the applicability of the observer to active suspension systems, so no comparison is performed.
Reviewer 3 Report
The paper titled "Hybrid Particle Swarm Optimization Genetic LQR Controller for Active Suspension" presents a method to ensure the optimality of the LQR controller by applying the genetic algorithm. Comments are below:
1) The weakest part of the paper is the experimental validation of the proposed strategy. Experimental validation is necessary to prove the effectiveness of the new closed-loop strategies. The authors should perform the experiments to verify the theoretical framework. Thus, the work seems incomplete.
2) Comparison results between the proposed LQR and traditional LQR should be summarized using a Table. Please add a Table to present the comparison results regarding transient, steady-state performance, computational time, disturbance rejection, and estimation performance.
3) The conventional method of choosing the weighting matrices should be discussed.
4) The other control methods, such as model predictive control, must be addressed in the introduction section. The adjusting weighting factors is problematic in model predictive control strategies, and several practical methods have been proposed to overcome this issue. Please review the reference papers below and discuss the optimality problems in optimal control methods.
[1] Finite control set model predictive control approach of nine switch inverter-based drive systems: Design, analysis and validation, ISA Transactions 2021
5) In full-order observer, please provide more details to explain how poles of (A-LC) matrix are selected. What is the selection criterion of observer gain? The design steps are not clear.
6) The tradeoff between noise cancellation and tracking performance should be discussed for full-order observer.
Author Response
Comment 1) The weakest part of the paper is the experimental validation of the proposed strategy. Experimental validation is necessary to prove the effectiveness of the new closed-loop strategies. The authors should perform the experiments to verify the theoretical framework. Thus, the work seems incomplete.
RE: Thank you for the commet. And we are sorry that we did not conduct the relevant experiments for the lack of human and financial resources. Therefore, we are sorry that we are unable to perform the relevant experiments.
Comment 2) Comparison results between the proposed LQR and traditional LQR should be summarized using a Table. Please add a Table to present the comparison results regarding transient, steady-state performance, computational time, disturbance rejection, and estimation performance.
RE: Than you for you comment. The comparison results between the proposed LQR and traditional LQR has been added in a Table. The focus of this paper is to improve the performance of the vehicle suspension by comparing the control effects of the two different controllers. The performance of the controller itself is not too strongly related to the focus of this paper.
Comment 3) The conventional method of choosing the weighting matrices should be discussed.
RE: Thanks a lot for your comment. Relavant content has been revised, and the discussion about the choosing the weighting matrices has been addressed in the paper.
Comment 4) The other control methods, such as model predictive control, must be addressed in the introduction section. The adjusting weighting factors is problematic in model predictive control strategies, and several practical methods have been proposed to overcome this issue. Please review the reference papers below and discuss the optimality problems in optimal control methods.
[1] Finite control set model predictive control approach of nine switch inverter-based drive systems: Design, analysis and validation, ISA Transactions 2021
RE: Thank you for the comment. The related content has been added to the paper.
Comment 5) In full-order observer, please provide more details to explain how poles of (A-LC) matrix are selected. What is the selection criterion of observer gain? The design steps are not clear.
RE: Thank you for the comment. The related content has been added to the paper.
Comment 5)The tradeoff between noise cancellation and tracking performance should be discussed for full-order observer.
RE: Thank you for the comment. The research in this paper focus on the control effect of the hybrid control method and the applicablity effect of the observer. The study of the performance of the properties of the observer itself is not very strongly relerant to the focus of this paper.
Round 2
Reviewer 1 Report
Thank you for considering my comments.
The English language has been improved.
Author Response
Dear reviewer,
We are so appreciate for your comments and suggestions. These opinions help us to improve academic rigor of our article.
We would like to thank the referee again for taking time to review our manuscript.
Best
Reviewer 2 Report
1) What is the novelty of the method compared with other existing ones? How about the computational efficacy of the proposed method?
2) If the “observer” represents the observed states of the suspension systems, I suggest the author not put the results together with those from other controllers. This is really confusing.
1) What is the novelty of the method compared with other existing ones? How about the computational efficacy of the proposed method?
2) If the “observer” represents the observed states of the suspension systems, I suggest the author not put the results together with those from other controllers. This is really confusing.
Author Response
Dear reviewer,
We are so appreciate for your comments and suggestions. The following is the response to your comments and suggestions.
Comment 1) What is the novelty of the method compared with other existing ones? How about the computational efficacy of the proposed method?
RE: Thank you for your comment. In traditional LQR control, matrix Q and R determined by experience. Current studies usually only use Particle Swarm Optimization or Genetic Algorithm. But Genetic Algorithm is poor in local search ability, and Particle Swarm Optimization is easy to fall into the local optimal solution. This can not guarantee the optimal control effect. The method proposed in this paper combine the advantage of both Particle Swarm Optimization and Genetic Algorithm. According to the simulation results, the hybrid control method can significantly improve the performance of the suspension.
Comment 2) If the “observer” represents the observed states of the suspension systems, I suggest the author not put the results together with those from other controllers. This is really confusing.
RE: Thank you for your suggestion. The observer is mainly used to observe the state of system, and is part of our study. If separately, the main article would seem long-winded.
We would like to thank the referee again for taking time to review our manuscript！
Best
Reviewer 3 Report
The authors have addressed most of the comments. However, several points still need to be clarified.
1) Reviewer understands that the experimental setup requires a research grant. But the experimental validation is an important part of the conducted research.
2) According to the revised paper, "...then the poles of the full-order observer could be arbitrary". This statement is not completely true. The authors have selected pole values as -6. But this selection criterion must be explained. The reviewer does not think that the poles of the observer cannot be selected randomly. The authors should explain why poles are selected as -6.
Author Response
Dear reviewer,
We are so appreciate for your comments and suggestions. The following is the response to your comments and suggestions.
Comment 1) Reviewer understands that the experimental setup requires a research grant. But the experimental validation is an important part of the conducted research
RE: Thank you for your suggestion, the experimental validation is indeed an important part of the conducted research.
However, we really do not have the experimental conditions. Besides, according to the simulations results, the hybrid control method can significantly improve the performance of the suspension compared with other method.
Comment 2) According to the revised paper, "...then the poles of the full-order observer could be arbitrary". This statement is not completely true. The authors have selected pole values as -6. But this selection criterion must be explained. The reviewer does not think that the poles of the observer cannot be selected randomly. The authors should explain why poles are selected as -6.
RE: Thank you for your comments. The relevant parts have been modified.
Best
