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In order to research stability of four-wheel independent driving (4WID) electric vehicle, a torque allocation method based on the tire longitudinal forces optimization distribution is adopted. There are two layers in the controller, which includes the upper layer and the lower layer. In the upper layer, according to the demand of the longitudinal force, PID controller is set up to calculate the additional yaw moment created by yaw rate and side-slip angle. In the lower layer, the additional yaw moment is distributed properly to each wheel limited by several constraints. Carsim is used to build up the vehicle model and MATLAB/Simulink is used to build up the control model and both of them are used to simulate jointly. The result of simulation shows that a torque allocation method based on the tire longitudinal forces optimization distribution can ensure the stability of the vehicle.

Four-wheel independent driving electric vehicle removes parts such as engines, clutches, gearboxes. Its structure is simpler than traditional vehicle. Because each wheel has a hub motor, it is more precise and convenient to control the torque on each wheel [

In the stability of 4WID electric vehicle research, there are four-wheel steering system and direct yaw moment control method to improve vehicle stability. However, the four-wheel steering system cannot meet the stability requirements under extreme driving condition, and the direct yaw moment control also has the accuracy problem [

When the vehicle is running at high speed and suddenly turns, it will cause the yaw rate to be too large and cause the vehicle to be unstable. Comparing the accelerator pedal signal and the steering wheel signal actually entered with the ideal linear two-degree-of-freedom model, the strategy calculates the additional yaw moment required and allocated torque rationally to the hub motor and the brakes on the wheels to correct the excessive yaw moment.

According to [

This paper combines the above two methods to design a control strategy. The strategy is divided into two stages. The first stage is reducing the torque on the motor on the outer wheel when the vehicle’s yaw rate is too large and unstable. The second stage is braking the vehicle outside wheels when the torque on the outer wheels cannot guarantee the stability of the vehicle after the reduction of torque (The flow chart of control strategy is shown in

The structure designed is showed in

actuator and vehicle model. The drive torque controller is divided into an upper controller and a lower controller. The upper controller includes a speed controller, a yaw velocity controller, and a sideslip angle controller. The lower controller is the torque distributor. The upper controller calculates the desired additional yaw moment according to the state of the vehicle input and passes the torque to the lower controller. The lower controller reasonably assigns the additional yaw moment transmitted by the upper controller to the actuator according to the constraints. In

According to the speed controller provided in [

where

Since

The linear two-degree-of-freedom model in [

where

The approximate ideal yaw rate can be expressed by Equation (4):

where

ficient,

However, under the ground attachment limit, the lateral acceleration

where

When the sideslip angle is small, ignore the influence of the side angle,

Combining Equations (5) and (6), it can be corrected to the ideal yaw rate

The yaw moment controller uses the PID control method to track the yaw rate and find the additional yaw moment required to maintain the vehicle’s handling stability. The difference between the actual yaw rate

According to the PID control of the mathematical model can be obtained additional yaw moment

where

The role of the torque distributor is reasonably generalized force assigned to an actuator. For 4IWD electric vehicles, the force of each actuator refers to the wheel motor/brake applied to the tire on the longitudinal force.

1) First stage: torque distribution

Taking the left-turn condition as an example, the actual yaw moment

where

As the vehicle in the uniform phase, the torque on each wheel is the same, then

where

2) Torque distribution second stage

In the first stage, when the outside wheels torque is reduced to 0, it is possible to provide the maximum additional yaw moment for the stage

However, due to the actual yaw rate being too large,

The main consideration of this stage is the torque on the inner wheel and the outer wheel braking torque distribution. The expression for the objective function is:

where

In the process of optimizing the distribution, the longitudinal force and yaw moment required for the vehicle are as follows:

where

The limits of the motor torque and ground adhesion to the wheels are as follows:

where

Substituting Equation (17) into the optimal objective function formula (16):

The new objective function (20) is used to derive the

Under the constraints of (21) and (22), the final solution is:

According to Equations (17), (23), and (24), the torque of the second stage can be calculated as:

This paper used Carsim and MATLAB/SIMULINK platform to build a vehicle dynamics model, a double lane change model, and a slalom model. The simulation includes double lane change maneuver and Slalom maneuver. The parameters of the simulation vehicle are shown in the following

To simulate the extreme driving conditions, we take the road friction coefficient of 0.2, equivalent to compaction of the snow road. The simulation is based on the comparison between without control and torque control. The simulation results are shown in Figures 4-8.

Simulation vehicle in situ start, accelerated to 80 km/h and road friction coefficient is 0.8. The simulation results are shown in Figures 9-13.

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

Vehicle mass (m/kg) | 1111 |

Body rotational inertia about the X axis | 288.0 |

Body rotational inertia about the Y axis | 2031.4 |

Body rotational inertia about the Z axis | 2031.4 |

Distance between the front axle and centroid (a/m) | 1.040 |

Distance between the rear axle and centroid (b/m) | 1.560 |

Centroid height (h_{g}/m) | 0.540 |

Front wheel base (B_{f}/m) | 1.481 |

Rear wheel base (B_{r}/m) | 1.481 |

wheel rolling radius (R/m) | 0.311 |

Motor peak torque | 500 |

speed curve changes greatly from the original straight line instability for the lateral sliding. With torque control, the speed fluctuates slightly, but only fluctuates in a very small range. From

curve shows that the vehicle has slipped and lost the ability to return to the normal route. With control, the situation is noticeably improved and can be returned to the normal route and the lateral acceleration which is maintained near 0 (m/s^{2}).

This paper has presented a control strategy to improve stability applied to a 2-DOF vehicle model. The first conclusion is that lateral acceleration, yaw rate and sideslip angle are important parameters of vehicle stability. If the value of these parameters is too large, the vehicle will be unstable.

The second conclusion is that the presented control strategy can make lateral acceleration, yaw rate and sideslip angle within a reasonable range by controlling the torque of each wheel to improve stability.

The authors are grateful to Professor Zhang Huanhuan of this research. She gives me many advices about theoretical knowledge and simulation.

Peng, B., Zhang, H.H. and Zhao, P.T. (2017) Research on the Stability Control Strategy of Four-Wheel Independent Driving Electric Vehicle. Engineering, 9, 338-350. https://doi.org/10.4236/eng.2017.93018