# Research on Multi-Mode Drive Optimization Control Strategy of Four-Wheel-Drive Electric Vehicles with Multiple Motors

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

- The first category of research methods is based on physical models of the drive system. For example, Li Liang established the efficiency loss model of the in-wheel motor under consideration of the iron loss, then obtained the optimized motor torque distribution by identifying the parameters of the motor online based on the MAR theory, thereby improving the energy utilization efficiency of the vehicle [9]. Yuan Xi-bo studied the torque distribution of the front and rear motors at different vehicle velocities based on the loss model of the dual-motor drive system and verified the performance of the control strategy through the motor test bench [10]. These types of methods mainly optimize the torque distribution of the drive system by the system loss model based on the physical characteristics of the motor and controller, so they can obtain accurate and reliable optimization results because the characteristics of the drive system are accurately described. However, due to the complex structure of the physical model and a large amount of calculation, the real-time performance of this research method is poor.
- The second category is based on the efficiency map of the drive system. For instance, Pennycott Andrew optimized the steady-state and transient energy consumption of a dual-motor 4WD electric vehicle based on the motor efficiency loss map [11]. Yang Yee-Pien used the particle swarm algorithm to optimize the efficiency map of the driving motor of a 4WD electric vehicle, then established a real-time optimization allocation strategy of the driving torque, thereby effectively reducing the motor energy loss [12]. Wang Jun-min took the minimization of the weighted sum of the vehicle speed error and the power consumption of the actuators as the objective function, and globally optimized the torque distribution of the four wheels to reduce the power loss of the system for a 4WD electric vehicle [13]. Yu Zhuo-ping adopted the efficiency maximization method to optimize the torque distribution coefficient matrix of the 4WD electric vehicle, and the overall energy efficiency of the vehicle was improved by about 3% due to the reduction in the in-wheel motor heat generation and the increase in feedback braking energy recovery [14]. The methods of the second category mainly use the efficiency map of the motor or the drive system to optimize the torque distribution of the drive system. They have some advantages such as fast calculation speed and good real-time performance, which are easy to deploy in the real vehicle controller. However, since the motor efficiency map depends on the test calibration, the quality of the calibration data will have a significant impact on the control strategy.

## 2. Architecture of Multi-Mode Drive Optimization Control Strategy for the Multi-Motor Electric Vehicle

## 3. Reference Torque Distribution Strategy for Front and Rear Axle Motors Based on Optimal Instantaneous Energy Consumption Power

_{d}is the torque load coefficient, which is determined by the relationship between the accelerator pedal opening and the external characteristics of the drive motor, and α

_{ap}is the accelerator pedal opening in %. As a result, the initial demand torque of the multi-motor-driven electric vehicle in this paper is:

_{i}(L

_{d},n

_{i}) is the torque of the i-th motor in N∙m; T

_{i}

_{max}is the peak torque of the i-th motor in N∙m; n

_{0i}is the base speed of the i-th motor in r/min; and n

_{i}is the speed of the i-th motor in r/min.

_{mech}is the total mechanical power of the driving motor in kW, P

_{mech,i}is the mechanical power of the i-th motor in kW, and ω

_{i}is the rotational speed of the i-th motor by international standards in rad/s:

_{t}is the total power of the drive motor in kW, P

_{loss}is the total loss of power of the drive motor in kW, and P

_{loss,i}is the mechanical power of the i-th motor in kW; the motor loss power is mainly composed of iron loss, copper loss, and friction loss. The motor loss energy is dissipated into air in the form of heat. In motor mode, the motor power loss is:

_{i}

_{0}and ω

_{i}

_{0}are the torque and speed corresponding to the minimum data point of the i-th motor map characteristic, respectively, and η

_{i}(T

_{i}, ω

_{i}) is the efficiency of the i-th motor at a specific speed and torque, which is generally obtained through the motor calibration test.

_{t}(κ) is the total power of all drive motors under κ in kW; i

_{f}and i

_{r}represent the front transmission and rear transmission ratio, respectively; and P

_{loss,i}(κ) is the loss power of the i-th motor under κ in kW.

_{0max}(ω

_{0}) is the maximum external characteristic torque of the rear motor at the speed of ω

_{0}in N∙m and T

_{1max}(ω

_{1}) is the maximum external characteristic torque of the front motor at the speed of ω

_{1}in N∙m. In addition, it is necessary to ensure that the wheels’ adhesion on each axle is not greater than the road adhesion, or else it will cause a dangerous wheel slip. Thus, the constraint of wheel adhesion obtained from the theoretical knowledge of automobiles are as follows:

_{φ}

_{1}and C

_{φ}

_{2}are the adhesion coefficient of the front wheels and rear wheels, respectively; a and b are the distances from the mass center to the front axle and rear axle in m, respectively; h

_{g}is the height of the mass center in m; q is the road equivalent slope; and φ is the road adhesion coefficient.

## 4. Torque Compensation Strategy Based on Fuzzy Control for High Power Demand Conditions

^{3}, i is the transmission ratio, m is the vehicle mass in kg, and η

_{T}is the drive system efficiency. It can be deduced from the formula that the greater change rate of the acceleration is, the bigger the jerk will be. Hence, Formula (12) can be transferred to:

^{−3}[24]. The degree of jerk is proportional to the change rate of the motor driving torque. Therefore, the change rate of the motor torque should satisfy the requirement of driving comfort.

## 5. Hardware-in-the-Loop Simulation Results and Analysis

#### 5.1. Results for WLTC

#### 5.2. Variable Acceleration Conditions

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**The input and output membership functions of the torque compensation controller: (

**a**) velocity; (

**b**) accelerator pedal opening variation rate; (

**c**) compensation torque of front motor; (

**d**) compensation torque of rear motor.

**Figure 8.**Motor torque distribution in WLTC: (

**a**) motor torque of the control strategy proposed in this paper; (

**b**) motor torque of the comparison strategy.

**Figure 9.**Comparison of working points of motors in WLTC: (

**a**) working point of the front motor; (

**b**) working point of the rear motor.

Parameter | Value | Unit | |
---|---|---|---|

Vehicle parameters | Curb weight m_{0} | 1520 | kg |

Max. weight M | 1895 | kg | |

wind resistance coefficient C_{d} | 0.29 | - | |

Windward area A | 2.27 | m^{2} | |

Tire radius R | 0.307 | m | |

Rolling resistance coefficient f | 0.0165 | - | |

Rotational mass conversion factor δ | 1.0425 | - | |

Wheelbase L | 2700 | mm | |

Front motor | Rated speed | 3000 | r∙min^{−1} |

Rated torque | 57 | N∙m | |

Peak power | 30 | kW | |

Peak speed | 7000 | r∙min^{−1} | |

Rear motor | Rated speed | 2500 | r∙min^{−1} |

Rated torque | 120 | N∙m | |

Peak power | 60 | kW | |

Peak speed | 9500 | r∙min^{−1} |

**Table 2.**Fuzzy rules of the torque compensation module. (

**a**) Fuzzy rules of torque compensation for front motors. (

**b**) Fuzzy rules of torque compensation for rear motor.

(a) | |||

Velocity | Accelerator Pedal Opening Variation Rate | ||

S | M | B | |

S | - | - | - |

M | - | - | S |

SH | M | B | B |

H | B | B | B |

(b) | |||

Velocity | Accelerator Pedal Opening Variation Rate | ||

S | M | B | |

S | S | M | B |

M | M | B | B |

SH | - | - | M |

H | S | S | M |

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**MDPI and ACS Style**

Xu, S.; Wei, L.; Zhang, X.; Bai, Z.; Jiao, Y.
Research on Multi-Mode Drive Optimization Control Strategy of Four-Wheel-Drive Electric Vehicles with Multiple Motors. *Sustainability* **2022**, *14*, 7378.
https://doi.org/10.3390/su14127378

**AMA Style**

Xu S, Wei L, Zhang X, Bai Z, Jiao Y.
Research on Multi-Mode Drive Optimization Control Strategy of Four-Wheel-Drive Electric Vehicles with Multiple Motors. *Sustainability*. 2022; 14(12):7378.
https://doi.org/10.3390/su14127378

**Chicago/Turabian Style**

Xu, Shiwei, Lulu Wei, Xiaopeng Zhang, Zhifeng Bai, and Yuan Jiao.
2022. "Research on Multi-Mode Drive Optimization Control Strategy of Four-Wheel-Drive Electric Vehicles with Multiple Motors" *Sustainability* 14, no. 12: 7378.
https://doi.org/10.3390/su14127378