# Performance Improvement of a Vehicle Equipped with Active Aerodynamic Surfaces Using Anti-Jerk Preview Control Strategy

^{*}

## Abstract

**:**

## 1. Introduction

- A comprehensive case study for the control of half-car model equipped with active aerodynamics surfaces is presented.
- We consider an anticipation of future values of deterministically known road disturbances in the design problem.
- To reduce the effect of jerk related to the ride comfort of a vehicle, a weighted norm of jerk control input is included in the pre-specified performance index. The minimization of the performance index accounts for improvisation of ride comfort and road holding capability.
- The feed-forward controller is designed based on the formulation for the preview control subjected to oncoming measured road disturbances.
- Simulations were carried using MATLAB that demonstrates the effectiveness of the proposed scheme in terms of minimizing control jerk, and assuring ride comfort and road holding capabilities. It was also demonstrated that the designed control algorithm has a proclivity to anticipate future measured disturbances and to take remedial action accordingly ahead of the occurrence of disturbances.

## 2. Mathematical Modeling of Vehicle

#### 2.1. Aerodynamic Forces

#### Road Excitation Model

## 3. Problem Formulation

#### 3.1. System Description

**Assumption**

**A1.**

**Assumption**

**A2.**

**Assumption**

**A3.**

#### 3.2. Controller

## 4. Optimal Based Anti-Jerk Preview Control

## 5. Simulation Results and Discussion

#### 5.1. Frequency Domain Characteristics

#### 5.2. Time Domain Characteristics

**Remark**

**1.**

## 6. Conclusions

- The proposed control strategy can be investigated considering the actual model of active aerodynamic surfaces with experimental implementations or with some commercial software such as CarSim or CarMaker.
- More advanced robust, and intelligent control algorithms can be considered in the future to tackle both road as well as air disturbances.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

## References

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**Figure 2.**Block diagram schematic comprised of feed-forward to detect the future road disturbance and feedback controller responsible for tracking error.

**Figure 3.**Comparison based on rms values obtained using different weights in the presence of bump velocity input; (

**a**) vehicle body acceleration (

**b**) vehicle body jerk (

**c**) jerk of active aerodynamic surfaces.

**Figure 4.**Comparison based on rms values obtained using different weights in the presence of bump velocity input; (

**a**) tire deflection (

**b**) roll angle (

**c**) total performance.

**Figure 5.**Frequency response comparison of rolling acceleration between proposed AJPC strategy and OPC strategy without jerk.

**Figure 6.**Frequency response to a rolling input using proposed AJPC strategy and OPC strategy without jerk; (

**a**) right suspension deflection (

**b**) right tire deflection.

**Figure 8.**Time domain response of control jerk to a bump velocity input using proposed AJPC strategy and OPC strategy without jerk.

**Figure 9.**Time domain response of vehicle body jerk to a bump velocity input using proposed AJPC strategy and OPC strategy without jerk; (

**a**) heaving jerk (

**b**) rolling jerk.

**Figure 10.**Time domain response of vehicle body acceleration to a bump velocity input using proposed AJPC strategy and OPC strategy without jerk; (

**a**) heaving acceleration (

**b**) rolling acceleration.

**Figure 11.**Time domain response of tire and suspension deflection to a bump velocity input using proposed AJPC strategy and OPC strategy without jerk; (

**a**) right tire deflection (

**b**) right suspension deflection.

**Figure 12.**Time domain response of roll angle to a bump velocity input using proposed AJPC strategy and OPC strategy without jerk.

**Figure 13.**Time domain response of control jerk to an asphalt road using proposed AJPC strategy and OPC strategy without jerk.

**Figure 14.**Time domain response of vehicle body jerk to an asphal road using proposed AJPC strategy and OPC strategy without jerk; (

**a**) heaving jerk (

**b**) rolling jerk.

**Figure 15.**Time domain response of vehicle body acceleration to an asphalt road using proposed AJPC strategy and OPC strategy without jerk; (

**a**) heaving acceleration (

**b**) rolling acceleration.

**Figure 16.**Time domain comparison of tire and suspension deflection between proposed AJPC strategy and OPC strategy without jerk; (

**a**) right tire deflection (

**b**) right suspension deflection.

Symbol | Description | Value | Unit |
---|---|---|---|

M | Vehicle body mass | 500 | Kg |

I | Moment of inertia | 274 | Kg · m${}^{2}$ |

${m}_{1},{m}_{2}$ | Vehicle unsprung mass | 25 | Kg |

${k}_{{s}_{1}},{k}_{{s}_{2}}$ | Suspension stiffness | 10 | $\mathrm{kN}/\mathrm{m}$ |

${k}_{{t}_{1}},\phantom{\rule{4pt}{0ex}}{k}_{{t}_{2}}$ | Tire stiffness | 1 | $\mathrm{kN}/\mathrm{m}$ |

${b}_{{s}_{1}},{b}_{{s}_{2}}$ | Damping coefficients | 1 | $\mathrm{kN}/\mathrm{m}$ |

a | Distance of C.M from right side | 0.74 | m |

b | Distance of C.M from left side | 0.74 | m |

h | Height of C.M from the ground | 0.70 | m |

Weighting Constants | Targets | AJPC | OPC |
---|---|---|---|

${\rho}_{1}$ | Heaving acceleration | 1 | 1 |

${\rho}_{2}$ | Rolling acceleration | 1 | 1 |

${\rho}_{3}$ | Suspension deflection | ${10}^{4}$ | ${10}^{4}$ |

${\rho}_{5}$ | Tire deflection | ${10}^{6}$ | ${10}^{6}$ |

${\rho}_{7}$ | Jerk controller | ${10}^{-2}$ | ${10}^{-4}$ |

**Table 3.**Root mean square error (RMSE) values of performance parameters of half car subjected to an asphalt road.

Performance Parameters | OPC | AJPC |
---|---|---|

Right jerk control input | 100 | 15 |

Heaving jerk | 100 | 92.88 |

Roll jerk | 100 | 97.6 |

Heaving acceleration | 100 | 86 |

Rolling acceleration | 100 | 98 |

Right tyre deflection | 100 | 96 |

Right suspension deflection | 100 | 89 |

Roll angle | 100 | 96 |

Total performance | 100 | 96 |

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**MDPI and ACS Style**

Ahmad, E.; Youn, I.
Performance Improvement of a Vehicle Equipped with Active Aerodynamic Surfaces Using Anti-Jerk Preview Control Strategy. *Sensors* **2022**, *22*, 8057.
https://doi.org/10.3390/s22208057

**AMA Style**

Ahmad E, Youn I.
Performance Improvement of a Vehicle Equipped with Active Aerodynamic Surfaces Using Anti-Jerk Preview Control Strategy. *Sensors*. 2022; 22(20):8057.
https://doi.org/10.3390/s22208057

**Chicago/Turabian Style**

Ahmad, Ejaz, and Iljoong Youn.
2022. "Performance Improvement of a Vehicle Equipped with Active Aerodynamic Surfaces Using Anti-Jerk Preview Control Strategy" *Sensors* 22, no. 20: 8057.
https://doi.org/10.3390/s22208057