# An Anti-Skid Control System Based on the Energy Method for Decentralized Electric Vehicles

^{*}

## Abstract

**:**

## 1. Introduction

- In turning conditions that are prone to loss of control, the control methods fail to ensure stable driving of the vehicle;
- The performance of these control methods is susceptible to variations in motor parameters, which cannot be avoided in real vehicles.

## 2. Wheel Slip Control Approach

#### 2.1. Control Strategy

^{th}wheel ($i$ = 1, 2, 3, and 4). In Equation (2), $\frac{1}{2}m{u}_{i}^{2}$ represents the translational kinetic energy of the wheel, and $\frac{1}{2}{J}_{\omega}{\omega}_{i}^{2}$ denotes the rotational kinetic energy of each wheel.

#### 2.2. Controller Design

## 3. EV Modelling

^{™}/Simulink coupled with CarSim, which is driven by four independently controlled PMSM motors. The chassis layout is shown in Figure 3. The controller receives power and rotation speed signals from four motors, and then sends the power command signals to them.

#### 3.1. Vehicle Dynamic Model

#### 3.2. Motor Model

## 4. Simulation and Results

^{2}. The noise for the yaw rate reaches 1 deg/s. The noise effect for the wheel speed occurs up to 15 rpm.

#### 4.1. Straight Line

#### 4.2. Sine with Dwell Simulation

## 5. Discussion

#### 5.1. The Variations in Motor Parameters

_{c}due to the drop in motor flux linkage, which causes the decrease of control accuracy and the loss of vehicle power performance. As for the method proposed here, it controls the motor power tracking command power value inside the motor. It indirectly controls the output torque ${T}_{i}$ of the motor so that ${T}_{i}$ is in the internal cycle of power following, thus eliminating the effect of variation in the motor magnetic chain.

#### 5.2. Vehicle Starting from Standstill

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 7.**Comparison of the vehicle’s front left wheel without control, with MTTE and with proposed approach: (

**a**) wheel speed and chassis speed; (

**b**) slip ratio; (

**c**) longitudinal force.

**Figure 8.**Sine with dwell simulation results on a high-adhesion road: (

**a**) the yaw rate and steering wheel angle; (

**b**) lateral displacement.

**Figure 9.**Sine with dwell simulation results on a low-adhesion road: (

**a**) yaw rate and steering wheel angle; (

**b**) lateral displacement.

**Figure 10.**Comparison of intermediate results for sine with dwell: (

**a**) front-right wheel speed and chassis speed; (

**b**) rear-left wheel speed and chassis speed; (

**c**) front-right wheel slip ratio; (

**d**) rear-left wheel slip ratio; (

**e**) front-right wheel longitudinal force; (

**f**) rear-left wheel longitudinal force; (

**g**) front-right wheel lateral force; (

**h**) rear-left wheel lateral force; (

**i**) yaw moment from longitudinal force; (

**j**) yaw moment from lateral force.

**Figure 11.**Comparison of wheel speed and chassis speed under the change of flux linkage: (

**a**) vehicle with MTTE; (

**b**) vehicle with proposed control strategy.

**Figure 12.**Comparison of the yaw rate between the vehicle with MTTE and with proposed control strategy under the change of flux linkage.

**Figure 13.**Simulation results of vehicle starting from standstill: (

**a**) front-left wheel speed and chassis speed; (

**b**) slip ratio of front-left wheel.

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

Vehicle mass $M$ | 1230 kg |

Sprung mass ${M}_{b}$ | 1110 kg |

Wheel mass $m$ | 30 kg |

Half-wheelbase $b$ | 1.300 m |

Front wheelbase ${l}_{f}$ | 1.040 m |

Rear wheelbase ${l}_{r}$ | 1.560 m |

Vehicle yaw inertia $J$ | 1343.1 kg·m² |

Wheel inertia ${J}_{\omega}$ | 0.6 kg·m² |

Wheel radius $r$ | 0.31 m |

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

Stator resistance ${R}_{s}$ | 0.958 Ω |

Number of pole pairs ${p}_{n}$ | 8 |

D-axis inductance ${L}_{d}$ | 5.25 mH |

Q-axis inductance ${L}_{q}$ | 5.25 mH |

Permanent-magnet flux linkage ${\psi}_{f}$ | 0.287 Wb |

DC-link voltage ${U}_{\mathrm{d}c}$ | 560 V |

Rated power ${P}_{N}$ | 45 kW |

Rated current ${I}_{A}$ | 99 A |

Rated torque ${T}_{eN}$ | 340 N · m |

Maximum power ${P}_{m}$ | 110 kW |

Peak current ${I}_{peak}$ | 280 A |

Maximum torque ${T}_{m}$ | 850 N · m |

Torque coefficient ${K}_{T}$ | 3.44 Nm/A |

Back-electromotive force coefficient ${K}_{e}$ | 170 V/krpm |

Yaw Rate | Proposed Control | MTTE |
---|---|---|

Peak value | −0.475 rad/s | −0.645 rad/s |

35% of the peak value | −0.166 rad/s | −0.226 rad/s |

1 s after completing steering | −0.003 rad/s | −0.256 rad/s |

20% of the peak value | −0.095 rad/s | −0.129 rad/s |

1.75 s after completing steering | −0.002 rad/s | −0.133 rad/s |

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**MDPI and ACS Style**

Ci, L.; Zhou, Y.; Yin, D.
An Anti-Skid Control System Based on the Energy Method for Decentralized Electric Vehicles. *World Electr. Veh. J.* **2023**, *14*, 49.
https://doi.org/10.3390/wevj14020049

**AMA Style**

Ci L, Zhou Y, Yin D.
An Anti-Skid Control System Based on the Energy Method for Decentralized Electric Vehicles. *World Electric Vehicle Journal*. 2023; 14(2):49.
https://doi.org/10.3390/wevj14020049

**Chicago/Turabian Style**

Ci, Longtao, Yan Zhou, and Dejun Yin.
2023. "An Anti-Skid Control System Based on the Energy Method for Decentralized Electric Vehicles" *World Electric Vehicle Journal* 14, no. 2: 49.
https://doi.org/10.3390/wevj14020049