# Hierarchical Coordinated Control Method of In-Wheel Motor Drive Electric Vehicle Based on Energy Optimization

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## Abstract

**:**

## 1. Introduction

## 2. Driving Architecture and Dynamic Model of an Electric Vehicle

#### 2.1. Driving Architecture and Simulation Modeling

#### 2.2. Vehicle Dynamic Model

_{x}represents the longitudinal vehicle speed, γ is the yaw rate of the vehicle, m is the vehicle mass, β denotes the vehicle sideslip angle, I

_{z}stands for the moment of inertia, l

_{f}and l

_{r}are the distances from vehicle gravity center to the front and rear axle, respectively, and F

_{yf}and F

_{yr}are the generalized front and rear lateral forces, respectively, i.e., F

_{yf}= F

_{y1}+ F

_{y2}, F

_{yr}= F

_{y3}+ F

_{y4}. $\Delta {M}_{z}$ is the external yaw moment generated by four in-wheel motors, which can be expressed as:

_{f,r}is the half tread of the wheel base, δ is the steering angle of the front wheels, F

_{xj}(j = 1, 2, 3, 4) represents the longitudinal force of the ith tire. Assuming that the steering angle of the front wheel is small and the tire operates in a linear area, F

_{yf}and F

_{yr}can be given by:

_{f}expresses the cornering stiffness of the front tires, C

_{r}expresses the cornering stiffness of the rear tires, α

_{f}represents the slip angle of the front tires, α

_{r}represents the slip angle of the rear tires, and the tire slip angle can be obtained as:

## 3. Analysis of Energy-Saving Feasibility

## 4. Hierarchical Coordinated Control Method Based on Energy Optimization

#### 4.1. Overall Control Strategy

#### 4.2. Upper Layer Controller: Driving Mode Decision

_{d}is the total torque requirement, n is the motor speed, ${\lambda}_{r}$ is the torque distribution coefficient of the rear axle, $\eta \left({T}_{f},n\right)$ is the motor driving efficiency of the front axle, and $\eta \left({T}_{r},n\right)$ is the motor driving efficiency of the rear axle. The constraint condition can be expressed as: 0 ≤ λ

_{r}≤ 0.5, 0 ≤ 0.5λ

_{r}T

_{d}≤ T

_{max}, and 0 ≤ 0.5(1 − λ

_{r})T

_{d}≤ T

_{max}, where T

_{max}represents the maximum motor torque. It can be found that when the result of torque optimization is single-axle drive, the front-axle drive is adopted by default, which contributes to the design of vehicle stability control, and the related methods will be introduced in the next section.

#### 4.3. Middle Layer Controller: Vehicle Stability Control

#### 4.4. Lower Layer Controller: Optimal Torque Distribution Method in Different Driving Modes

## 5. Simulation Results

#### 5.1. Double Lane Change Manoeuvre

_{d}represents the air drag coefficient, and F

_{f}represents the rolling resistance. By calculation, the vehicle torque demand is obtained and can be shown in Figure 8. It can be found that when the vehicle is accelerating, because of the existence of vehicle acceleration, the vehicle torque demand is relatively larger. When the vehicle drives at a uniform speed, the vehicle torque demand is relatively smaller.

#### 5.2. J-Turn Manoeuver

#### 5.3. ECE Manoeuver

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 7.**Simulation condition in case study 1. (

**a**) Planned vehicle speed; (

**b**) Planned double lane change trajectory.

**Figure 13.**Simulation condition in case study 2. (

**a**) Planned vehicle speed; (

**b**) Steering wheel angle.

Symbol | Parameters | Value and Units |
---|---|---|

m | Vehicle mass | 850 kg |

r | Effective radius of wheel | 0.25 m |

l_{f} | Distances from vehicle gravity center to the front axle | 0.815 m |

l_{r} | Distances from vehicle gravity center to the rear axle | 0.985 m |

b_{f}, b_{r} | Half treads of the front(rear) wheels | 0.78 m |

C_{f} | Equivalent cornering stiffness of front wheel | 65,000 N/rad |

C_{r} | Equivalent cornering stiffness of rear wheel | 45,000 N/rad |

I_{z} | Moment of inertia | 1000 kg·m^{2} |

R | Equivalent resistance of winding | 0.675 Ω |

K_{a} | Inverse electromotive force coefficient | 0.065 Nm/A |

K_{t} | Motor torque constant | 11.425 Nm/A |

J | Sum of inertia moment of wheel and motor | 7.165 kg·m^{2} |

b | Damping coefficient | 0.645 Nm·sec/rad |

L | Equivalent inductance of winding | 0.125H |

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**MDPI and ACS Style**

Wang, J.; Li, J.
Hierarchical Coordinated Control Method of In-Wheel Motor Drive Electric Vehicle Based on Energy Optimization. *World Electr. Veh. J.* **2019**, *10*, 15.
https://doi.org/10.3390/wevj10020015

**AMA Style**

Wang J, Li J.
Hierarchical Coordinated Control Method of In-Wheel Motor Drive Electric Vehicle Based on Energy Optimization. *World Electric Vehicle Journal*. 2019; 10(2):15.
https://doi.org/10.3390/wevj10020015

**Chicago/Turabian Style**

Wang, Junchang, and Junmin Li.
2019. "Hierarchical Coordinated Control Method of In-Wheel Motor Drive Electric Vehicle Based on Energy Optimization" *World Electric Vehicle Journal* 10, no. 2: 15.
https://doi.org/10.3390/wevj10020015