# Automatic Longitudinal Regenerative Control of EVs Based on a Driver Characteristics-Oriented Deceleration Model

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## Abstract

**:**

## 1. Introduction

## 2. System Overview

## 3. State Recognition Algorithm

#### 3.1. Driving State Recognition

#### 3.2. Deceleration Condition Recognition

## 4. Parametric Deceleration Model

#### 4.1. Split of Braking Section

- Release the accelerator pedal;
- Push the brake pedal to some extent with a similar ratio;
- Continuously push the brake pedal to keep a safe distance from the leading car;
- Gradually release the brake pedal.

#### 4.2. Driver Parameters

#### 4.3. Deceleration Model Based on Braking Sections

#### 4.3.1. Coasting Section

#### 4.3.2. Initial Section

#### 4.3.3. Adjustment Section

#### 4.3.4. Termination Section

## 5. Online Learning Algorithm

#### 5.1. Learning Vectors

#### 5.1.1. Driver Parameters and Correlated Indices

#### 5.1.2. Learning and Effective Probability Vectors

- Calculate the initial index from the driving data;
- Generate the Gaussian distribution, which has the mean value of the initial index calculated at step 1, as shown in Figure 10, using Equation (18), where $a$ is the value and $\sigma $ is the standard deviation of the initial index;$${f}_{g}\left(x\right)=\frac{1}{\sqrt{2\pi {\sigma}^{2}}}{e}^{-\frac{{\left(x-a\right)}^{2}}{2{\sigma}^{2}}}.$$
- Extract each value matching to the predetermined vector of the initial index, which is shown as blue squares in Figure 10;
- Normalize the eight values extracted in step 3 to make the sum of the eight values equal to 1, as shown in Equation (19), where $Idx\left(i\right)$ is the i-th value of the index vectors shown in Table 4.$${P}_{eff}\left(i\right)=Norm\left(\frac{1}{\sqrt{2\pi {\sigma}^{2}}}{e}^{-\frac{{\left(Idx\left(i\right)-a\right)}^{2}}{2{\sigma}^{2}}}\right).$$

#### 5.1.3. Calculation of the Driver Parameters

#### 5.2. Online Update of Learning Vectors

- Calculate the effective probability vector using the value of the correlated index;
- Calculate the active parameter by the dot product of the effective probability and learning vectors;
- Calculate the reference parameter from the driving data;
- Update the learning vector based on the active and reference parameters.

## 6. Validation

#### 6.1. Acceleration Controller

#### 6.2. Test Vehicle Configuration

#### 6.3. Vehicle Test Environment

#### 6.4. Vehicle Test Results

#### 6.5. Learning Results

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Driving State | Deceleration Model | Online Learning Algorithm | Acceleration Control |
---|---|---|---|

Driving | X | X | X |

Coasting | O | X | O |

Decelerating | O | O | X |

Stopping | X | X | X |

Driver Parameter | Description |
---|---|

Initial distance (${s}_{init})$ | Relative distance at initial point |

Adjustment distance (${s}_{adj})$ | Relative distance at adjustment point |

Initial jerk (${\varphi}_{init})$ | Slope of acceleration in initial section |

Velocity difference (${v}_{diff})$ | Velocity difference with leading car speed at end of deceleration |

Driver Parameter | Correlated Index |
---|---|

Initial distance (${s}_{init})$ | Coasting distance |

Adjustment distance (${s}_{adj})$ | Initial distance |

Initial jerk (${\varphi}_{init})$ | Initial index |

Velocity difference (${v}_{diff})$ | Initial index |

Index Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|

Initial index $\left(\mathrm{m}/{\mathrm{s}}^{2}\right)$ | 0 | 0.3 | 0.6 | 0.9 | 1.2 | 1.5 | 1.8 | 2.1 |

Learning vector for initial jerk $\left(\mathrm{m}/{\mathrm{s}}^{3}\right)$ | −0.6 | −0.76 | −0.86 | −0.96 | −1.16 | −1.45 | −1.77 | −2.09 |

Type of Learning Vector | Initial Distance | Adjustment Distance | Initial Jerk | Velocity Difference |
---|---|---|---|---|

Learning rate | 0.1 | 0.1 | 0.2 | 0.1 |

Index Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|

Initial index | 0 | 0.3 | 0.6 | 0.9 | 1.2 | 1.5 | 1.8 | 2.1 |

Learning degree | 0.70 | 0.70 | 0.70 | 0.70 | 0.76 | 0.89 | 1.09 | 1.05 |

Learning vector before update ($\mathrm{m}/{\mathrm{s}}^{3}$) | −0.91 | −1.04 | −1.19 | −1.37 | −1.57 | −1.80 | −2.08 | −2.38 |

Learning vector after update ($\mathrm{m}/{\mathrm{s}}^{3}$) | −0.99 | −1.13 | −1.28 | −1.46 | −1.67 | −1.92 | −2.22 | −2.52 |

Index | Value |
---|---|

Maximum range | 150 m |

Field of view (FOV) | +/−10° over 60 m |

+/−45° under 60 m | |

Update rate | 50 ms |

**Table 8.**Specifications of the central processing unit (CPU), random access memory (RAM), and flash memory of MPC5674F.

Component | Specification |
---|---|

CPU | Power architecture 200z7 core 265 MHz |

RAM | 256 KB data RAM with error correcting codes (ECC) |

Flash | 4 MB flash memory with ECC |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Sim, G.; Ahn, S.; Park, I.; Youn, J.; Yoo, S.; Min, K.
Automatic Longitudinal Regenerative Control of EVs Based on a Driver Characteristics-Oriented Deceleration Model. *World Electr. Veh. J.* **2019**, *10*, 58.
https://doi.org/10.3390/wevj10040058

**AMA Style**

Sim G, Ahn S, Park I, Youn J, Yoo S, Min K.
Automatic Longitudinal Regenerative Control of EVs Based on a Driver Characteristics-Oriented Deceleration Model. *World Electric Vehicle Journal*. 2019; 10(4):58.
https://doi.org/10.3390/wevj10040058

**Chicago/Turabian Style**

Sim, Gyubin, Seongju Ahn, Inseok Park, Jeamyoung Youn, Seungjae Yoo, and Kyunghan Min.
2019. "Automatic Longitudinal Regenerative Control of EVs Based on a Driver Characteristics-Oriented Deceleration Model" *World Electric Vehicle Journal* 10, no. 4: 58.
https://doi.org/10.3390/wevj10040058