Crone Ground Hook Suspension

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1. This paper uses the unsprung mass acceleration as an indicator, whereas the common evaluation indicators for vehicle suspension systems are typically sprung mass acceleration, suspension work space, and dynamic tire load. Please further discuss this indicator.
2. The review of skyhook control and hybrid skyhook control is not comprehensive. In fact, there are many previous works on this topic. It is suggested that the authors carefully read and introduce these studies. For example: Analysis of inertance and damping double-skyhook control strategies for a semi-active device combining an adjustable inerter and damper and Experimental study on the double-skyhook controls of semi-active suspension with variable inertance and damping. 
3. In suspension time-domain simulations, should sprung mass acceleration and suspension work space be discussed?
4. For Figures 11-12, it is recommended to use a combination of line styles and symbols for better differentiation.
5. This paper mainly studies skyhook and groundhook control, and the introduction section should further discuss the relevant references and work. Try to avoid consecutive citations of references, such as in reference 24.
6. To make the paper more rigorous, the related formulas for random road profiles should be supplemented.

Comments on the Quality of English Language

The quality of English can be further improved.

Author Response

Q1-R1: This paper uses the unsprung mass acceleration as an indicator, whereas the common evaluation indicators for vehicle suspension systems are typically sprung mass acceleration, suspension work space, and dynamic tire load. Please further discuss this indicator.

R1-R1: Typically, most work on controlled suspension systems proposes an optimal strategy for the entire operational domain of the suspension. These approaches use a global criterion taking into account the three indices which are the vertical acceleration of the sprung mass (for vibration comfort), the travel of the suspension (for the operating limits) and the variation of the dynamic load of the tires (for handling). This type of approach is optimal with respect to the overall criterion but suboptimal with respect to each criterion.

One of the contributions proposed by the authors is to:

1 - Break down the overall operational domain into three operational subdomains:

- ODD1: 100% vibration comfort => indices = vertical acceleration of the sprung mass + suspension travel

- ODD2: road holding => indices = vertical acceleration of the sprung mass + variation in the dynamic load of the tires + suspension travel

- ODD3 emergency situations => indices = variation in the dynamic load of the tires + suspension travel;

2 – Propose for each operational sub-domain an optimal strategy with regard to comfort (ODD1), or with regard to road holding (ODD2) or with regard to emergency situations (ODD3);

3 – Supervise the vehicle and its environment to estimate the operating domain in which the vehicle is located at each moment (ODD1 or ODD2 or ODD3), in order to propose the optimal strategy adapted to the sub-domain.

Since 2010 in the field of Research and Development, the presence of numerous proprioceptive and exteroceptive sensors, but also the connections between, not only vehicles (V2V), but also between vehicles and road infrastructures (V2X) within the framework of the Connected Autonomous Vehicle (CAV) allows us to consider the strategy proposed by the authors. The CAV environment makes it possible to not only consider the proprioceptive sensors initially dedicated solely to suspension control (body and wheel acceleration sensors, suspension travel sensors).

Regarding ODD1 where the vertical acceleration of the sprung mass is used as the performance index retained for vibration comfort with the suspension travel, the authors have already published results of their work with different Crone Sky Hook (CSH) strategies.

Here, in the proposed paper, the authors voluntarily focus only on ODD3 where the objective is to minimize the variation of the dynamic load of the tires. To achieve the objective, the authors use a Crone Ground Hook (CGH) strategy based on the measurement of the vertical acceleration of the unsprung mass (wheel). This is the reason why only the two criteria concerning the vertical acceleration of the unsprung mass and the suspension travel are used for the optimization of the CGH strategies..

Q2-R1: The review of skyhook control and hybrid skyhook control is not comprehensive. In fact, there are many previous works on this topic. It is suggested that the authors carefully read and introduce these studies. For example: Analysis of inertance and damping double-skyhook control strategies for a semi-active device combining an adjustable inerter and damper and Experimental study on the double-skyhook controls of semi-active suspension with variable inertance and damping. 

R2-R1: In order to be as exhaustive as possible, a paragraph on semi-active suspensions has been added to the introduction.

 

Q3-R1: In suspension time-domain simulations, should sprung mass acceleration and suspension work space be discussed?

R3-R1: The field of study presented in this paper being that of ODD3 (emergency situations), vibration comfort (and therefore vertical acceleration of the sprung mass) is not the priority and is not part of the optimized criteria. That being said, the tables in Figures 19 and 20 show the results obtained a posteriori for all the indices of the three ODDs.

 

Q4-R1: For Figures 11-12, it is recommended to use a combination of line styles and symbols for better differentiation.

R4-R1: The changes have been made.

 

Q5-R1: This paper mainly studies skyhook and groundhook control, and the introduction section should further discuss the relevant references and work. Try to avoid consecutive citations of references, such as in reference 24.

R5-R1: Indeed, the heart of the paper concerning ODD3 (emergency situations), the focus in this paper concerns the Ground Hook approach. But in the introduction other approaches are mentioned in terms of control laws. Note that the introduction has been reorganized, in particular in relation to the bibliographic references mentioned.

 

Q6-R1: To make the paper more rigorous, the related formulas for random road profiles should be supplemented.

R6-R1: Details have been added in accordance with the bibliographic reference mentioned in this paragraph.

Reviewer 2 Report

Comments and Suggestions for Authors

This paper is very interesting and looks suitable for publication. This reviewer have the next commentaries for authors. 

1. An abstract is used to give a general introduction about the research topic of the paper, so the reader can be interested in reading the manuscript. This reviewer do not understand why authors have conclusions lines at the abstract. this reviewer kindly suggest the authors to have a look to the abstract and improve it. 

2. Font size in all figures should be improve it to readable. 

3. Figure 1 should be improved, it seems that the car has 16 DoF.

4. ¿Does the measurement noise model is related to the obtained error? 

5. This reviewer do understand that authors separate the dynamics of the vehicle into vertical forces and horizontal forces, but, ¿what about their interaction? ¿some do not disturb the others? 

6. Authors should check figures 11 and 12, these figures have y label in other language. 

7. In 4. 1, ¿What is the "Black-Nichols loci"?

8. In 4.2, authors have a vibration analysis performance, but, ¿What is a good performance (Hz)? ¿Where is the reference?

9. In figure 19 an 20, authors presents a summarizing table for the proposed values of the criteria. Authors should add a comparative table with other control theories to compare their performances. 

Author Response

Qi-R2: Reviewer’s question or comment (in blue).

Ri-R2: Authors’s response (in black).

 

Q1-R2: An abstract is used to give a general introduction about the research topic of the paper, so the reader can be interested in reading the manuscript. This reviewer do not understand why authors have conclusions lines at the abstract. this reviewer kindly suggest the authors to have a look to the abstract and improve it.

R1-R2: The abstract has been edited to reflect this comment.

 

Q2-R2: Font size in all figures should be improve it to readable. 

R2-R2: Wherever possible, figures have been enlarged.

 

Q3-R2. Figure 1 should be improved, it seems that the car has 16 DoF.

R3-R2: Indeed, from a solid mechanics point of view, Figure 1 shows 16 DOF, but the 2 DOF associated with the two steering wheels are considered as two identical degrees of actuation. This is the reason why from a system point of view these two DOFs are considered as controllable inputs coming either from the driver (manual driving mode) or from the supervisor (autonomous driving mode). A phase specifying this aspect has been added to the text.

 

Q4-R2: Does the measurement noise model is related to the obtained error? 

R4-R2: In the absence of measurement noise and in steady state, the acceleration is zero and therefore the error is zero. In the presence of measurement noise and in steady state, the mean value of the measured acceleration is zero and therefore the mean value of the error is zero, but due to the presence of measurement noise the measured instantaneous value is not systematically zero.

 

Q5-R2: This reviewer do understand that authors separate the dynamics of the vehicle into vertical forces and horizontal forces, but, what about their interaction? some do not disturb the others? 

R5-R2: The link between vertical dynamics and horizontal dynamics is made by the tire. Indeed, the longitudinal forces F_x(t) and transverse forces F_y(t) generated at the tire/ground interface which intervene in the dynamic balance of the vehicle depend in particular (but not only) on the vertical forces F_z(t) whose variations f_z(t) are linked to the behavior of the suspension. However, in ODD1 defined by longitudinal and transverse accelerations lower in absolute values than 4 m/s2, the f_z(t) variations have no significant influence on the f_x(t) and f_y(t) variations. This is the reason why all ADAS associated with horizontal dynamics studies (ACC, LK, …) in this ODD1 are done using unsprung four-wheel models.

 

Q6-R2: Authors should check figures 11 and 12, these figures have y label in other language. 

R6-R2: The changes have been made.

 

 

 

Q7-R2: In 4. 1, What is the "Black-Nichols loci"?

R7-R2: The Black-Nichols locus of the open-loop frequency response, denoted b₁(jw), defined by the plot of the response gain in dB as a function of its argument in degree, is used in linear control theory to analyze not only the stability, but also the degree of stability of the control loop.

 

Q8-R2: In 4.2, authors have a vibration analysis performance, but, What is a good performance (Hz)? Where is the reference?

R8-R2: The performance analysis is not done in relation to an absolute reference, but in relative terms in relation to the fault mode of the suspension. This fault mode is defined based on the expertise acquired in the context of work with PSA concerning the Citroën Hydractive suspension, in particular in comfort mode (suspension in soft mode) where the wheel damping factor is only 0.13, while this same factor is 0.35 in road-handling mode (suspension in hard mode). Indeed, the value of the viscous friction coefficient b₂₀ (see figure 6.2) is calculated so that in the event of a failure of the actuator (u_a(t) = 0 => fault mode of the active suspension) the vehicle, while remaining within ODD1, can continue to drive safely until repair.

This clarification has been added to the paper.

 

Q9-R2: In figure 19 and 20, authors present a summarizing table for the proposed values of the criteria. Authors should add a comparative table with other control theories to compare their performances. 

R9-R2: For a comparative study between different strategies to be significant, it must be done with:

- the same vehicle

- and at least with one criterion having the same value for the strategies compared; for example for the control loop at iso-rapidity or at iso-degree of stability,…

To date, the authors have no significant comparative study between different strategies other than those already published (Sky Hook) or proposed in this article (Ground Hook).

 

 

Reviewer 3 Report

Comments and Suggestions for Authors

The paper addresses the development of suspension control strategies for Connected Autonomous Vehicles (CAVs) within their Operational Design Domain (ODD), which is divided into three sub-domains: comfort (ODD1), road behavior (ODD2), and emergency situations (ODD3). It leverages data from vehicle sensors, infrastructure, and other vehicles to determine the specific ODD and apply the most appropriate control strategy. The authors propose three strategies: a comfort-oriented Crone Sky Hook (CSH) strategy for ODD1, a mixed CSH-CGH strategy for ODD2, and a safety-oriented CGH strategy for ODD3. The CGH strategy—nominal CGHN and generalized CGHG—specifically for ODD3 under normal conditions and actuator failure are compared. Results indicate that the CGHG strategy outperforms CGHN in both frequency and time domains, offering better vibration comfort and addressing the trade-off between acceleration and suspension travel. However, for minimizing variations in vertical tire load, the CGHN strategy is more effective.

1. The Crone Ground Hook Suspension (CGH) strategy proposed in the article, especially the CGHG version, has certain innovation in the application of control theory and vehicle dynamics. However, the author needs to further elaborate on the specific innovative points of CGHG strategy compared to existing technologies such as traditional GH strategy and other revised control strategies (Dynamic modelling and analysis of a physics-driven strategy for vibration control of railway vehicles; Phase deviation of semi-active suspension control and its compensation with inertial suspension), especially its unique advantages in addressing the trade-off between vibration comfort and tire load changes.
2. When describing the mathematical model and control architecture of CGH strategy in the article, although detailed formulas and derivations are provided, it may be difficult for non professional readers to understand. Suggest the author to add some intuitive charts OR diagrams OR more details to help readers better understand the implementation process of the control strategy.
3. In the main text, there are some formatting issues with the numbering of certain formulas. The font size and alignment of the numbering are inconsistent.
4. The description of the parameter optimization process of CGH strategy in the article is relatively brief, especially regarding the selection of optimization objective function and the implementation details of optimization algorithm. Suggest the author to provide a detailed explanation of the optimization process, including the definition of the objective function, constraints, and the selection of optimization algorithms.
5. Regarding the modelling of the vehicle and the road profile, some references should be added and discussed, e.g., 10.1007/s11071-024-10641-8.
6. The article mentions the use of noise models in the measurement of noise models section, but does not provide detailed instructions on how to handle the impact of these noises on control effectiveness in the control strategy. Suggest the author to add noise suppression measures in the control strategy and analyze their impact on performance.

Author Response

Q1-R3: The Crone Ground Hook Suspension (CGH) strategy proposed in the article, especially the CGHG version, has certain innovation in the application of control theory and vehicle dynamics. However, the author needs to further elaborate on the specific innovative points of CGHG strategy compared to existing technologies such as traditional GH strategy and other revised control strategies (Dynamic modelling and analysis of a physics-driven strategy for vibration control of railway vehicles; Phase deviation of semi-active suspension control and its compensation with inertial suspension), especially its unique advantages in addressing the trade-off between vibration comfort and tire load changes.

R1-R3: Supplements have been added throughout the paper.

 

Q2-R3: When describing the mathematical model and control architecture of CGH strategy in the article, although detailed formulas and derivations are provided, it may be difficult for non professional readers to understand. Suggest the author to add some intuitive charts OR diagrams OR more details to help readers better understand the implementation process of the control strategy.

R2-R3: One of the originalities of this work is to approach the subject from both a vibration mechanics point of view (global vision of mechanical causes/consequences) and a control theory point of view (criteria concerning the control loop: stability, degree of stability, speed, etc.).

Historically, the initial Sky Hook strategies (force proportional to the vertical speed of the sprung mass) and Ground Hook (force proportional to the vertical speed of the unsprung mass) have been approached and presented in the literature by many authors from a vibration mechanics point of view by considering them as behavior laws at the functional level (no technological constraints for actuators and sensors, no consideration of the estimation of speeds that are not directly available, etc.), i.e. not in a control theory context at the organic (technological) level.

 

Q3-R3: In the main text, there are some formatting issues with the numbering of certain formulas. The font size and alignment of the numbering are inconsistent.

R3- R3: The changes have been made.

 

Q4-R3: The description of the parameter optimization process of CGH strategy in the article is relatively brief, especially regarding the selection of optimization objective function and the implementation details of optimization algorithm. Suggest the author to provide a detailed explanation of the optimization process, including the definition of the objective function, constraints, and the selection of optimization algorithms.

R4-R3: The Crone Ground Hook Nominal (CGHN) strategy is defined by a single parameter (relation (11)), namely the constant b_gh, the order of the controller integrator being v₁ = 1. What differentiates this approach proposed by the authors from the classic Ground Hook approach is the criterion to be optimized. Indeed, in the CGHN case the total criterion normalized with respect to the fault mode (u_a(t) = 0) only concerns ODD3 with two components (tire load variation and suspension travel, no comfort component) to which we give the same weighting. In the classic approach, the total criterion concerns the entire ODD = ODD1+ODD2+ODD3, with the three classic components (comfort, suspension travel and tire load variation). Thus, in the CGHN case, the total criterion (relation (14)) has a global minimum obtained numerically using the Matlab function min(.): result b_gh = - 934 Ns/m. This CGHN strategy provides readers familiar with Ground Hook strategies with a transition between the classic GH strategy and the innovative Generalized Crone Ground Hook (CGHG) strategy presented later.

Indeed, the Generalized Crone Ground Hook (CGHG) strategy is defined by two parameters (relation (11)), namely the constant b_gh and the fractional integration order v₁ between 0 and 2. This strategy is part of the theory of fractional systems which allows with a small number of parameters (here 2 parameters: b_gh and v₁) to cover a wide range of behaviors. Thus, from a behavioral point of view:

- v₁ = 0 => inertial behavior

- 0 < v₁ < 1 => visco-inertial behavior

- v₁ = 1 => viscous behavior

- 1 < v₁ < 2 => visco-elastic behavior

- v₁ = 2 => elastic behavior

This last aspect was added in the paper.

 

Q5-R3: Regarding the modelling of the vehicle and the road profile, some references should be added and discussed, e.g., 10.1007/s11071-024-10641-8.

R5-R3: This recommendation has been considered.

 

Q6-R3: The article mentions the use of noise models in the measurement of noise models section, but does not provide detailed instructions on how to handle the impact of these noises on control effectiveness in the control strategy. Suggest the author to add noise suppression measures in the control strategy and analyze their impact on performance.

R6-R3: From a general point of view in control theory, it is necessary to limit the gain of the controller in high frequencies to limit the sensitivity of the control signal to measurement noise. This sensitivity is quantified using the sensitivity function R₁ defined by relation (8).

In the particular case of the Sky Hook (SH) and Ground Hook (GH) approaches implemented from the measurement of the acceleration (of the sprung mass for SH or of the unsprung mass for GH), the expression of the controller is that of an integrator (relation (11)).

This is the reason why the gain of the sensitivity function R₁ tends towards zero as the frequency tends towards infinity (see figure 14.c), thus minimizing the sensitivity of the control signal to measurement noise. There is therefore no need to add any specific constraint when designing the controller with regard to measurement noise.

This remark was added to the paper.

Reviewer 4 Report

Comments and Suggestions for Authors

Before publication, the authors must clarify the following aspects:

1. It is not clear the number of degrees of freedom considered for the model. If Fig. 1 is analyzed, then the work refers to a system with 14 degrees of freedom. From Fig. 6 it results a system with 2 degrees of freedom. In the conclusions part, the authors state "To achieve this objective, these ... to a 14-DOF vehicle model ..." (last paragraph).

2. It is not clear where certain formulas ((1), (2), etc.) were obtained, nor whether the formulas are original or taken from the literature. In addition, the equations of motion are not shown either.

3. Some notations are changed. See the paragraph after the formula (6) where the force F_z^e has either the upper index e (formula (6)), or e is a value next to F.

4. Sometimes texts appear in French (first line on page 9, the word et before the formula (13)).

5. It is not specified why certain parameter values were chosen (e.g. paragraph after formula (15), paragraph after formula (16)). What characterizes these values? Why are they important?

6. It is not clear what the work brings new compared to the references [18], [19] of the same authors.

In conclusion, the paper requires major revisions.

Comments on the Quality of English Language

Please, translate text which is not in English language.

Author Response

Q1-R4: It is not clear the number of degrees of freedom considered for the model. If Fig. 1 is analyzed, then the work refers to a system with 14 degrees of freedom. From Fig. 6 it results a system with 2 degrees of freedom. In the conclusions part, the authors state "To achieve this objective, these ... to a 14-DOF vehicle model ..." (last paragraph).

R1-R4: Indeed, from a solid mechanics point of view, Figure 1 shows 16 DOFs, but the 2 DOFs associated with the two steered wheels are considered as two identical degrees of actuation. This is the reason why from a system point of view these two DOFs are considered as controllable inputs coming either from the driver (manual driving mode) or from the supervisor (autonomous driving mode). A phase specifying this aspect has been added to the text.

In addition, this paper deliberately focuses on ODD3 (emergency situations) where minimizing the variation of the vertical load of the tire is the priority objective of the suspension control strategy. In this first study, the analysis is done at a local level with a quarter-vehicle model at 2 DOF. In a second step, the short-term perspective is to do the analysis at the global level of the vehicle dynamics using a 16 DOF simulator in an emergency situation (ODD3), such as an avoidance maneuver at a longitudinal speed greater than 50 km/h on a rough road profile (Class C or D of the ISO standard…, with grip between 0.1 (icy road) and 1 (dry road). Only a 16 DOF simulator can analyze in an emergency situation the influence of the suspension on the dynamic behavior of the vehicle using global variables: drift at the center of gravity, yaw rate, etc.

 

Q2-R4: It is not clear where certain formulas ((1), (2), etc.) were obtained, nor whether the formulas are original or taken from the literature. In addition, the equations of motion are not shown either.

R2-R4: Several bibliographic references have been added to the paper to clarify that these relationships have already been published by the authors as part of specific modeling work.

 

Q3-R4: Some notations are changed. See the paragraph after the formula (6) where the force F_z^e has either the upper index e (formula (6)), or e is a value next to F.

R3-R4: The changes have been made.

 

Q4-R4: Sometimes texts appear in French (first line on page 9, the word et before the formula (13)).

R4-R4: The changes have been made.

 

Q5-R4: It is not specified why certain parameter values were chosen (e.g. paragraph after formula (15), paragraph after formula (16)). What characterizes these values? Why are they important?

R5-R4: The values of the parameters after formulas (15) and (16), i.e.:

- for the CGHN strategy, b_gh = - 934 Ns/m and n₁ = 1;

- for the CGHG strategy, b_gh = - 252 Ns0.7/m and n₁ = 0.7,

are the optimal values for the two proposed strategies from subsection 3.3. Optimal parameters of the CGH strategy

For more details, see response R4-R4.

 

Q6-R4:  It is not clear what the work brings new compared to the references [18], [19] of the same authors.

R6-R4: In references [18] and [19], the authors focus only on ODD1 where the vertical acceleration of the sprung mass is used as the indicator retained for vibration comfort with the suspension travel. The comparative studies of the different strategies studied in these references [18] and [19] belong to the Crone Sky Hook (CSH) strategies. In the submitted paper, the authors focus only on ODD3 with the Crone Ground Hook (CGH) strategies.

Furthermore, the conclusion was completed by recalling the main contributions presented in this submitted paper.

 

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

It is recommended to accept the revised paper

Author Response

Thank you for your review.

Reviewer 2 Report

Comments and Suggestions for Authors

This reviewer would like to thank to authors for answering and follow each of the commentaries and questions. The paper is ready for publication. 

Author Response

Thank you for your review.

Reviewer 3 Report

Comments and Suggestions for Authors

Comments have been satisfactorily addressed in general. Regarding the Comment 1, the SH and GH have been discussed. Further discussion on revised control strategies is encouraged.

Author Response

Thank you for your review. Some additional comments have been added regarding control strategies.

Reviewer 4 Report

Comments and Suggestions for Authors

The authors clarified all the issues. The paper may be published in the current form.

Author Response

Thank you for your review.