# Yaw Moment Control Based on Brake-by-Wire for Vehicle Stbility

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Vehicle Stability Control Model

^{2}) is the vehicle yaw moment of inertia; $u$ is the longitudinal speed; $v$ is the lateral speed.

_{1}and C

_{2}are constants, and C = 0.165, C

_{1}= 4.386 and C

_{2}= 2.562 [24]. If Equations (11) and (12) hold at the same time, the vehicle is stable. If either Equation (11) or (12) does not hold, it indicates that the vehicle needs stability control.

## 3. Controller Design

#### 3.1. Fuzzy Control Structure

#### 3.2. Fuzzy Controller Design

#### 3.2.1. Determination of Fuzzy Sets and Discourse Domains

#### 3.2.2. Determination of Quantification and Scale Factors

#### 3.2.3. Determination of the Membership Function

#### 3.2.4. Fuzzy Rules

## 4. Results and Discussions

#### 4.1. Simulation Analysis

#### 4.1.1. Steering Angle Step Input Condition

#### 4.1.2. Double Lane Change Condition

- Referring to the ISO3888-1:2018 standard, the initial speed is set to 120 km/h in CarSim and the road adhesion coefficient is 0.8. The steering angle is shown in Figure 10a. It can be seen from Figure 10b,c that the maximum yaw rate and sideslip angle reach 0.405 rad/s and 0.075 rad without the participation of stability control, respectively, while in the case of stability control, the yaw rate and sideslip angle are 0.281 rad/s and 0.044 rad, down 0.124 rad/s and 0.031 rad, respectively. In a word, there is a better improvement than without the participation of stability control. Figure 10d shows the braking pressure of the wheel with stability control.

#### 4.1.3. Turning Condition

#### 4.2. Vehicle Test

## 5. Conclusions

^{−4}with the control; however, without the control, the yaw rate MSE was 1.125 × 10

^{−4}. In general, the control strategy proposed in this paper can significantly improve the stability of the vehicle.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 9.**Simulation results of steering angle step input condition: (

**a**) steering angle; (

**b**) yaw rate; (

**c**) sideslip angle; (

**d**) brake pressure.

**Figure 10.**Simulation results of double lane change condition: (

**a**) steering angle; (

**b**) yaw rate; (

**c**) sideslip angle; (

**d**) brake pressure.

**Figure 12.**Simulation results of turning condition: (

**a**) steering angle; (

**b**) yaw rate; (

**c**) sideslip angle; (

**d**) brake pressure.

**Figure 16.**Turning condition test results: (

**a**) front wheel steering angle; (

**b**) yaw rate; (

**c**) sideslip angle; (

**d**) brake pressure.

Angle | Deviation of Yaw Rate | Steering Characteristics | Wheel Selection |
---|---|---|---|

$\delta >0$ | $\mathsf{\Delta}\omega <0$ | Understeering | Left rear |

$\delta >0$ | $\mathsf{\Delta}\omega >0$ | Oversteering | Right rear |

$\delta <0$ | $\mathsf{\Delta}\omega <0$ | Oversteering | Left rear |

$\delta <0$ | $\mathsf{\Delta}\omega >0$ | Understeering | Right rear |

Braking Pressure (MPa) | Front Wheel Braking Torque (N·m) | Rear Wheel Braking Torque (N·m) | Total Braking Torque (N·m) |
---|---|---|---|

0.5 | 37 | 99.5 | 136.5 |

1 | 74.5 | 199.5 | 274 |

1.5 | 112 | 299.5 | 411.5 |

2 | 149.5 | 399.5 | 549 |

$\mathbf{E}\left(\mathsf{\omega}\right)$ | ||||||
---|---|---|---|---|---|---|

$\mathrm{M}$ | PB | PS | Z | NS | NB | |

$\mathrm{e}\left(\mathsf{\beta}\right)$ | PB | PS | PS | NM | NB | NB |

PS | PS | PS | PM | PM | PB | |

Z | PM | PM | Z | NS | NM | |

NS | PB | PM | PS | NS | NS | |

NB | PB | PB | PM | NS | NS |

Parameters | Value |
---|---|

Wheelbase (mm) | 2600 |

Distance from front axel to center of mass (mm) | 1040 |

Distance from rear axel to center of mass (mm) | 1560 |

Wheel radius (mm) | 287 |

Centroid height (mm) | 540 |

Vehicle weight (kg) | 1110 |

Front wheel lateral stiffness (N/rad) | −75,783 |

Rear wheel lateral stiffness (N/rad) | −75,783 |

Moment of inertia around the Z-axis (kg/m^{2}) | 1413.1 |

Parameters | Value |
---|---|

Vehicle dimensions (mm) | 1600 × 820 × 520 |

Vehicle weight (kg) | 165 |

Wheelbase (mm) | 850 |

Axel track (mm) | 645 |

Vehicle velocity (km/h) | 0–18 |

Communication interface | CAN |

Type | BWT901CL-TTL |

Size | 51.3 mm × 36 mm × 15 mm |

Weight | 20 g |

Communication method | Bluetooth/Serial |

Measurement range | acceleration: ±16 g; angle velocity: ±2000°/s; angle: ±180° |

Measurement error | acceleration: 0.01 g; angle velocity:0.05°/s; angle:0.1° |

Output frequency | 0.1~200 Hz |

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© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Li, H.; Wang, K.; Hao, H.; Wu, Z.
Yaw Moment Control Based on Brake-by-Wire for Vehicle Stbility. *World Electr. Veh. J.* **2023**, *14*, 256.
https://doi.org/10.3390/wevj14090256

**AMA Style**

Li H, Wang K, Hao H, Wu Z.
Yaw Moment Control Based on Brake-by-Wire for Vehicle Stbility. *World Electric Vehicle Journal*. 2023; 14(9):256.
https://doi.org/10.3390/wevj14090256

**Chicago/Turabian Style**

Li, Hongfang, Kai Wang, Huimin Hao, and Zhifei Wu.
2023. "Yaw Moment Control Based on Brake-by-Wire for Vehicle Stbility" *World Electric Vehicle Journal* 14, no. 9: 256.
https://doi.org/10.3390/wevj14090256