# Research on the Stability Control Strategy of Distributed Electric Vehicles Based on Cooperative Reconfiguration Allocation

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## Abstract

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## 1. Introduction

## 2. Controller Structure Design

#### 2.1. Vehicle Modeling

#### 2.1.1. Vehicle Dynamics Model

#### 2.1.2. Tire Model

#### 2.1.3. Motor Model

#### 2.2. Upper Controller

#### 2.2.1. Predictive Model

#### 2.2.2. Constrained Optimization Solution

#### 2.3. Lower Controller

#### 2.3.1. Optimize the Objective Function

#### 2.3.2. Tire Force Constraint

#### 2.3.3. Calculated Wheel Angle

#### 2.3.4. Failure Mode Control Strategy

## 3. Simulation and Analysis

#### 3.1. Double Wheel Failure on a Straight Road

#### 3.2. Single-Wheel Fail-in-Step Steering

#### 3.3. Double Wheel Failure in Sine Steering

## 4. HIL Verification and Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**Results of two failed wheels on a straight road: (

**a**) Yaw rate; (

**b**) Lateral force; (

**c**) Wheel angle; (

**d**) Drive torque.

**Figure 6.**Results of the single-wheel failure in the angular step steering: (

**a**) Yaw rate; (

**b**) Lateral force; (

**c**) Sideslip angle; (

**d**) Drive torque.

**Figure 7.**Results of the two failed wheels in sinusoidal steering: (

**a**) Yaw rate; (

**b**) Lateral speed; (

**c**) Motion trajectory; (

**d**) Drive torque.

**Figure 9.**Results of the single failed wheel in sinusoidal steering: (

**a**) Yaw rate; (

**b**) Lateral speed; (

**c**) Lateral force; (

**d**) Drive torque; (

**e**) Motion trajectory.

Failure Mode | Failure Constraints (Example) | Controllable or Not |
---|---|---|

A single drive motor failure | ${F}_{xfl}=0$ | Controllable |

Two diagonal drive motors failure | ${F}_{xfl}=0,{F}_{xrr}=0$ | Controllable |

Two coaxial drive motors failure | ${F}_{xrl}=0,{F}_{xrr}=0$ | Controllable |

Two ipsilateral drive motors failure | ${F}_{xfl}=0,{F}_{xrl}=0$ | Uncontrollable |

Three drive motors failure | ${F}_{xfl}=0,{F}_{xfr}=0,{F}_{xrl}=0$ | Uncontrollable |

Four drive motors failure | ${F}_{xfl}=0,{F}_{xfr}=0,{F}_{xrl}=0,{F}_{xrr}=0$ | Uncontrollable |

Vehicle Parameters | Values |
---|---|

Vehicle mass $(m/\mathrm{kg})$ | 870 |

Distance from front axle to center of mass $(a/\mathrm{m})$ | 1.013 |

Distance from rear axle to center of mass $(b/\mathrm{m})$ | 0.702 |

Centroid height $(h/\mathrm{m})$ | 0.51 |

Moment of inertia $({I}_{z}/(\mathrm{kg}\cdot {\mathrm{m}}^{2}))$ | 617 |

Wheel pitch $(d/\mathrm{m})$ | 1.3 |

Wheel radius $(r/\mathrm{m})$ | 0.302 |

Peak power $({P}_{\mathrm{max}}/\mathrm{W})$ | 6900 |

Rated power $({P}_{e}/\mathrm{W})$ | 4700 |

Maximum speed $({n}_{\mathrm{max}}/(\mathrm{r}\cdot {\mathrm{min}}^{-1}))$ | 1055 |

Rated speed $({n}_{e}/(\mathrm{r}\cdot {\mathrm{min}}^{-1}))$ | 440 |

Peak torque $({T}_{\mathrm{max}}/(\mathrm{N}\cdot \mathrm{m}))$ | 150 |

Time constant $(\tau /\mathrm{s})$ | 0.01 |

Road adhesion coefficient $(\mu )$ | 0.8 |

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## Share and Cite

**MDPI and ACS Style**

Ou, J.; Yan, D.; Zhang, Y.; Yang, E.; Huang, D.
Research on the Stability Control Strategy of Distributed Electric Vehicles Based on Cooperative Reconfiguration Allocation. *World Electr. Veh. J.* **2023**, *14*, 31.
https://doi.org/10.3390/wevj14020031

**AMA Style**

Ou J, Yan D, Zhang Y, Yang E, Huang D.
Research on the Stability Control Strategy of Distributed Electric Vehicles Based on Cooperative Reconfiguration Allocation. *World Electric Vehicle Journal*. 2023; 14(2):31.
https://doi.org/10.3390/wevj14020031

**Chicago/Turabian Style**

Ou, Jian, Dehai Yan, Yong Zhang, Echuan Yang, and Dong Huang.
2023. "Research on the Stability Control Strategy of Distributed Electric Vehicles Based on Cooperative Reconfiguration Allocation" *World Electric Vehicle Journal* 14, no. 2: 31.
https://doi.org/10.3390/wevj14020031