# Torque Distribution Strategy of Electric Vehicle with In-wheel Motors Based on the Identification of Driving Intention

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## Abstract

A driver’s intention is recognized accurately by employing fuzzy identification and a logic threshold including acceleration intention and steering intention. Different torque distribution control strategies are developed for different intentions and the driver’s torque demand is amended by fuzzy identification so that the response of the vehicle is more consistent with the driver’s intention of operation. Finally, a simulation model is built using MATLAB/Simulink to validate the control strategy. Simulation results show that the system accurately identifies the driver’s intention and improves the acceleration performance and steering stability of the vehicle.

## Keywords

Fuzzy recognition Torque distribution Driving intention In-wheel motors Steering stability## 1 Introduction

The electric vehicle with in-wheel motors does not have traditional transmission components, such as a clutch. Each wheel is driven by a separate motor and the vehicle thus allocates individual driving torques to the wheels, i.e., it is possible for the vehicle to adopt any driving torque distribution among the wheels [1, 2]. Electric vehicles having in-wheel motors therefore have an advantage over internal combustion engine vehicles and central-motor-driven vehicles [3, 4]. In previous work, a driving force distribution method was developed on the basis of the minimum tire load [5]; a control allocation method was used in a hierarchical structure to optimize the drive and braking torque distribution and thus improve the handling and stability of a vehicle [6]; and a driving force distribution algorithm was developed on the basis of control allocation [7], where the algorithm establishes an objective function and constraints based on economic requirements, optimizing the torque allocation of the vehicle to ensure the best economic performance.

The shortcoming of present torque distribution strategies is that they do not effectively (consider) a driver’s driving intention when achieving driver’s desired performance.

At the same time, the torque distribution usually has only single target. Furthermore, the strategies fail to consider the different conditions of the desired running performance. Finally, the combined driving intention recognition of vehicle control strategies rarely considered the torque distribution. A fuzzy control method has been proposed where the driver’s operation of the accelerator pedal is converted to a target speed of the motor drive in the effective control of the total output torque demand of a plug-in hybrid electric vehicle [8]. Recognition of the driving intention based on hybrid vehicle control strategies has been developed [9], and fuzzy inference identification of the driving intent has been used to amend the demand for automotive torque during acceleration, but the torque distribution has been not addressed. A method directly controlling the yaw moment that adapts to identified driver behavior has been presented [10], where the intention of lane changing is obtained and the yaw moment required to adjust the distribution of the left and right wheel drive torques is determined according to the prediction of the driver behavior.

This paper considers the driver intention and divides the driving intention into linear acceleration intention and steering intention. The linear acceleration intention is further divided into adjustment acceleration and urgent acceleration to improve the vehicle accelerating performance and steering stability.

## 2 Recognition of Driving Intention

### 2.1 Recognition of the Intention of Linear Acceleration

Acceleration is divided into adjustment acceleration and urgent acceleration. Adjustment acceleration is acceleration that is not immediately crucial, with the driver accelerating or decelerating gradually through control of the accelerator pedal. Urgent acceleration is time-crucial acceleration where high speed is required rapidly.

#### 2.1.1 Identification Parameters and Methods

Our aim is to obtain the intention of the driver and to take an appropriate action, such as operation of the steering wheel or pedals, thus changing the running state of the vehicle. Previous operations of the driver can thus be used to obtain identification parameters. The literature has highlighted that the opening of the accelerator pedal and the rate at which the pedal is opened reflects the intention of the driver [8]. This paper thus uses these indicators in the recognition of accelerating intention.

The driver’s intention is difficult to describe accurately with a mathematical model and is thus treated as a fuzzy concept [8]. Fuzzy reasoning is effective in simulating human reasoning. The present paper therefore uses fuzzy reasoning to identify the driver’s acceleration intention. The process of fuzzy inference of the driving intention is shown in Fig. 1. The function of fuzzification is to transform the exact amount of input into a fuzzy quantity, and the input of fuzzy control is usually a deviation and the deviation rate of change. The fuzzy rule includes a series of rules expressed by fuzzy linguistic variables. Fuzzy inference is based on the fuzzy concept. The fuzzy implication and inference rules of fuzzy logic is used to obtain the model control function and simulate the human decision process. The function of defuzzification is to transform the fuzzy variables obtained from fuzzy inference into those of can be used for control.

#### 2.1.2 Construction of the Model for Recognizing the Acceleration Intention

Fuzzy inference rules of acceleration intention

Opening | Opening rate | |||
---|---|---|---|---|

N | S | M | B | |

S | Aa | Aa | Aa | Aa |

M | Aa | Aa | Aa | Ea |

B | Aa | Ea | Ea | Ea |

### 2.2 Recognition of Steering Intention

The steering intention is relatively easy to identify, so it is recognized using a logic threshold. The angle of the steering wheel is taken as the steering intention parameter. A steering intention (i.e., an intention to change direction) is recognized when the steering wheel angle is nonzero. However, the process of straight driving involves small nonzero angles of the steering wheel, and a steering intention is therefore recognized in practice when the steering wheel angle changes by more than a threshold.

## 3 Torque Distribution Strategies

### 3.1 Torque Distribution Strategy for Acceleration Intention

*K*is the accelerator opening, \(T_{\max } \) is the maximum torque that a single motor can provide, \(T_\mathrm{i}\) denotes torques of the driving wheels, and \(i=\hbox {fl},\hbox {fr},\hbox {rl},\hbox {rr}\), respectively, denotes the front-left, front-right, rear-left, and rear-right wheels.

Fuzzy rule base of the compensation torque correction coefficient

AP | DAP | ||
---|---|---|---|

S | M | B | |

S | S | S | S |

M | S | S | M |

B | S | M | B |

During acceleration and especially urgent acceleration, the front-axle load is shifted to the rear axle. This will be accompanied by changes in the adhesion limits of the front and rear wheels. At the same time, to maximize the use of front- and rear-wheel adhesion, the front and rear torques are allocated in proportion. The front and rear torque distribution ratio can be determined by the front and rear load of vehicle, finally improving the emergency acceleration.

*L*is the length of the wheelbase, a and b are, respectively, the distance between the center of mass and the front and rear axes, \(h_\mathrm{g} \) is the vehicle centroid height, \(\alpha \) is the road slope angle,

*U*is the longitudinal speed, \(I_\mathrm{w}\) is the moment of inertia of the wheel, r is the wheel radius, and

*G*is acceleration due to gravity.

### 3.2 Torque Allocation Strategy Based on the Steering Intention

Steering may lead to lateral instability, the occurrence of understeer or flick and other dangerous situations. The yaw rate and sideslip angle are two important parameters characterizing the stability of a vehicle. The torque is therefore distributed to maintain steering stability when a steering intent is recognized. The torque distribution controls the yaw rate and sideslip angle and generates an additional yaw moment. Increasing the yaw moment is beneficial to steering and vehicle stability.

## 4 Simulation

Simulation parameters of the vehicle

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

Vehicle mass ( | 1482.7 | kg |

Body rotational inertia about the | 346.73 | kg m\(^{2}\) |

Body rotational inertia about the | 1675.8 | kg m\(^{2}\) |

Body rotational inertia about the | 1808.8 | kg m\(^{2}\) |

Wheel rotational inertia (\({I}_\mathrm{w})\) | 5.11 | kg m\(^{2}\) |

Distance between the front axle and centroid (a) | 1.225 | m |

Distance between the rear axle and centroid (b) | 1.437 | m |

Centroid height (\({h}_\mathrm{g})\) | 0.49 | m |

Front wheel base (\({B}_\mathrm{f})\) | 1.438 | m |

Rear-wheel base (\({B}_\mathrm{r})\) | 1.438 | m |

Wheel rolling radius ( | 0.285 | m |

Motor peak torque ( | 300 | N m |

The velocity response is shown in Fig. 9. Results of driving intention identification are shown in Fig. 10.

Results of driving intention identification are shown in Fig. 10 as follows: Adjustment acceleration—emergency acceleration—adjustment acceleration—emergency acceleration—adjustment acceleration—emergency acceleration—adjustment acceleration—steering. The opening degree rate of change is initially large, and the acceleration pedal opening then decreases and increases in a cyclic manner. At 16 s, the recognition result is steering travel.

Figure 11 shows that the torque distribution strategy based on driver intention recognition improves the acceleration performance of the car; the time taken to accelerate from 0 to 73 km/h with intention identification reduced by about 1 s, compared to that of without intention identification. This improvement is due to the system recognizing an urgent intention to accelerate and using four-wheel drive to appropriately increase the compensation torque. The torque distribution ratio is determined by the front- and rear-wheel load, and thus greatly improves the dynamic performance of the vehicle.

## 5 Conclusions

By operating the state of driving behaviors to build a recognition model can accurately identify the driver’s intentions. The desired torque distribution is involved in this recognition model. This improves the acceleration performance and steering stability of the vehicle.

Main limitations of the present paper lie in two aspects: the accuracy of fuzzy rules and the formulation of standards, which are worked out depending on plenty of experiments and experience. In future work, we will investigate the identification of driving intention in a full range of driving conditions and develop appropriate torque distribution strategies.

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