# Observation of Dynamic State Parameters and Yaw Stability Control of Four-Wheel-Independent-Drive EV

^{*}

## Abstract

**:**

## 1. Introduction

## 2. System Modeling

#### 2.1. Dynamic Model Establishment

_{r}and C

_{f}are the lateral rigidity of the rear axle and the front axle. When the car performs a steady-state circular motion, the tangential acceleration of the car around the circle is zero, which is $\dot{v}=0$.

#### 2.2. Design of Unscented Kalman Filtering Algorithm

#### 2.3. Design of Yaw Stability Control

#### 2.3.1. Model Control Prediction Algorithm Design

#### 2.3.2. The Main Steps of Model Predictive Controller Design

- (1)
- The establishment of the model.

- (2)
- Linearize the dynamic model.

- (3)
- Set the system objective function.

_{p}is the time domain of the prediction; N

_{c}is the time domain of the control; ε is the relaxation factor; ρ is the weighting coefficient.

- (4)
- Predict, solve, and feedback control of the system.

_{min}is the minimum set of control quantities in the control time domain, and U

_{max}is the maximum set of control quantities in the control time domain.

- (5)
- Quadratic programming solution

_{t}is the tracking error in the prediction time domain, y

_{hc}is the hard constraint, y

_{sG}is the soft constraint, and ε is the relaxation factor.

_{d}represents the desired vehicle speed, and ∆v represents the vehicle speed increment.

- (6)
- Lateral following ability test

## 3. Design of Yaw Moment Controller

#### 3.1. Overall Structure Design of Simulation Platform

#### 3.2. Simulation Verification of Yaw Stability

- (1)
- Simulation of double-lane change test

_{p}= 60, control time domain N

_{C}= 30, and control period T = 0.05s. The car first accelerates to 60km/h, and then begins the double-lane change performance test. The steering wheel double-lane change input signal is shown in Figure 5a. Simultaneously observe the vehicle’s yaw rate, side slip angle, and the driving torque of each wheel.

- (2)
- Simulation of snake test

#### 3.3. HIL Experiment

^{−3}°/s, and the standard deviation is 0.47 × 10

^{−2}°/s. The estimation error of the side slip angle of the centroid is 0.3 × 10

^{−3}°/s, and the standard deviation is 0.3 × 10

^{−2}°/s. The deviation between the estimated value and the true value of both are small and can be ignored.

## 4. Conclusions

- (1)
- Based on the HIL simulation platform of the vehicle state parameter, the estimation algorithm is verified, and the simulation results show that the Kalman estimation algorithm under the steering wheel angle step input yawing angular velocity of the average estimated error was 0.5 × 10
^{−3}°/s, the average estimated error of side slip angle was 0.3 × 10^{−3}°, and the simulation result shows that the algorithm can effectively estimate the vehicle state parameter, high estimation precision, and meet the demand of the vehicle online estimate; - (2)
- With the double-lane change condition and snake conditions for electric vehicles, the yawing motion simulation layer is used to verify. The simulation results show that the maximum errors of yaw velocity are 0.4335 °/s and 1.3647 °/s, respectively, in double-lane change and snaking conditions, which can better track the target value of the yaw rate. The maximum errors of the side slip angle of the center of mass are 0.34°and 0.7334°, respectively. The side slip angle of the center of mass is far below the limit range, which ensures that the vehicle has a sufficient yaw stability margin in the course of steering;
- (3)
- In this paper, the four-wheel-independent-drive electric vehicle state parameter observation and yawing stability study comprehensively improve the real-time stability of the vehicle safety. However, this paper still has some shortcomings. The proposed method can only focus on the influence of the stability of the horizontal pendulum on the state parameters, but ignores the multi-parameter state observation to improve the effect of the yaw stability controller. In addition, in the case of drive skid and drive failure, how to maintain the driving capacity of each wheel to ensure the lateral stability of the vehicle, still needs further research.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 5.**Simulation of double-lane change test. (

**a**) Steering wheel angle; (

**b**) Yaw rate; (

**c**) Side slip angle; (

**d**) Driving torque.

**Figure 6.**Simulation of snake test. (

**a**) Steering wheel angle; (

**b**) Yaw rate; (

**c**) Side slip angle; (

**d**) Driving torque.

Turn | Left Limit | Right Limit |
---|---|---|

Steering wheel angle (°) | −497 | 501 |

Front-wheel angle (°) | −35 | 35 |

Time (s) | 5.5 | 5.5 |

Parameter Names | Numerical Value | Parameter Names | Numerical Value |
---|---|---|---|

Width/mm | 1440 | Vehicle height/mm | 1780 |

height of center of mass/mm | 540 | The moment of inertia around the X-axis/kg·m^{2} | 288 |

Total weight/kg | 1000 | The moment of inertia around the Y-axis/kg·m^{2} | 2031.4 |

wheel base/mm | 2600 | The moment of inertia around the Z-axis/kg·m^{2} | 2031.4 |

The distance from the center of mass to the front axis/mm | 1040 | Reference model front shaft cornering stiffness/N·rad-1 | −53,388 |

The distance from the center of mass to the back axis/mm | 1560 | Reference model rear shaft cornering stiffness/N·rad-1 | −35,592 |

The front wheel radius/mm | 311 | Rear wheel radius/mm | 311 |

Wheel base/mm | 1210 | Tire outside diameter/mm | 580 |

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**MDPI and ACS Style**

Zhang, C.; Chang, B.; Zhang, R.; Wang, R.; Wang, J.
Observation of Dynamic State Parameters and Yaw Stability Control of Four-Wheel-Independent-Drive EV. *World Electr. Veh. J.* **2021**, *12*, 105.
https://doi.org/10.3390/wevj12030105

**AMA Style**

Zhang C, Chang B, Zhang R, Wang R, Wang J.
Observation of Dynamic State Parameters and Yaw Stability Control of Four-Wheel-Independent-Drive EV. *World Electric Vehicle Journal*. 2021; 12(3):105.
https://doi.org/10.3390/wevj12030105

**Chicago/Turabian Style**

Zhang, Chuanwei, Bo Chang, Rongbo Zhang, Rui Wang, and Jianlong Wang.
2021. "Observation of Dynamic State Parameters and Yaw Stability Control of Four-Wheel-Independent-Drive EV" *World Electric Vehicle Journal* 12, no. 3: 105.
https://doi.org/10.3390/wevj12030105