# Energy-Saving Optimization for Electric Vehicles in Car-Following Scenarios Based on Model Predictive Control

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## Abstract

**:**

## 1. Introduction

#### 1.1. Background

#### 1.2. Literature Review

#### 1.3. Original Contributions

- A nonlinear multi-objective model predictive control framework is developed for a FRIDEV under car-following scenarios, in which safety, car-following performance, ride comfort and energy economy are optimized simultaneously;
- The demand power of the host vehicle is used as an indicator to accurately reflect the energy consumption and incorporated in the cost function to achieve enhanced energy economy.

#### 1.4. Outline of the Paper

## 2. System Modeling

#### 2.1. Vehicle Longitudinal Dynamics

#### 2.2. Electric Drive System

## 3. Economy-Oriented Car-Following Control Strategy

#### 3.1. Control Objectives

- A.
- Car-following performance

- B.
- Ride comfort

- C.
- Energy consumption

#### 3.2. Overall Cost Function

#### 3.3. Model Predictive Optimization Problem

- The discrete system state Equation (5);
- The constraints (31)–(33).

## 4. Simulation Results

#### 4.1. Car-Following and Ride Comfort Performance

#### 4.2. Energy Economy

## 5. Conclusions and Future Work

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Rajashekara, K. Present status and future trends in electric vehicle propulsion technologies. IEEE J. Emerg. Sel. Top. Power Electron.
**2013**, 1, 3–10. [Google Scholar] [CrossRef] - Mutoh, N. Front-and-rear-wheel-independent-drive-type electric vehicle (FRID EV) with compatible driving performance and safety. World Electr. Veh. J.
**2009**, 3, 17–26. [Google Scholar] [CrossRef] - Barkenbus, J.N. Eco-driving: An overlooked climate change initiative. Energy Policy
**2010**, 38, 762–769. [Google Scholar] [CrossRef] - Kamal, M.; Mukai, M.; Murata, J.; Kawabe, T. Ecological driver assistance system using model-based anticipation of vehicle–road–traffic information. IET Intell. Transp. Syst.
**2010**, 4, 244–251. [Google Scholar] [CrossRef] - Guo, C.; Fu, C.; Luo, R.; Yang, G. Energy-oriented car-following control for a front-and rear-independent-drive electric vehicle platoon. Energy
**2022**, 257, 124732. [Google Scholar] [CrossRef] - Li, S.; Xu, S.; Wang, W.; Cheng, B. Overview of ecological driving technology and application for ground vehicles. J. Automot. Saf. Energy
**2014**, 5, 121–131. [Google Scholar] - Beusen, B.; Broekx, S.; Denys, T.; Beckx, C.; Degraeuwe, B.; Gijsbers, M.; Scheepers, K.; Govaerts, L.; Torfs, R.; Panis, L.I. Using on-board logging devices to study the longer-term impact of an eco-driving course. Transp. Res. Part D Transp. Environ.
**2009**, 14, 514–520. [Google Scholar] [CrossRef] - Gilbert, E.G. Vehicle cruise: Improved fuel economy by periodic control. Automatica
**1976**, 12, 159–166. [Google Scholar] [CrossRef] - Chen, X.; Yang, J.; Zhai, C.; Lou, J.; Yan, C. Economic adaptive cruise control for electric vehicles based on ADHDP in a car-following scenario. IEEE Access
**2021**, 9, 74949–74958. [Google Scholar] [CrossRef] - Li, S.E.; Peng, H.; Li, K.; Wang, J. Minimum fuel control strategy in automated car-following scenarios. IEEE Trans. Veh. Technol.
**2012**, 61, 998–1007. [Google Scholar] [CrossRef] - Li, S.E.; Peng, H. Strategies to minimize the fuel consumption of passenger cars during car-following scenarios. Proc. Inst. Mech. Eng. Part D J. Automob. Eng.
**2012**, 226, 419–429. [Google Scholar] [CrossRef] - Ioannou, P.A.; Stefanovic, M. Evaluation of ACC vehicles in mixed traffic: Lane change effects and sensitivity analysis. IEEE Trans. Intell. Transp. Syst.
**2005**, 6, 79–89. [Google Scholar] [CrossRef] - Zhang, J.; Ioannou, P.A. Longitudinal control of heavy trucks in mixed traffic: Environmental and fuel economy considerations. IEEE Trans. Intell. Transp. Syst.
**2006**, 7, 92–104. [Google Scholar] [CrossRef] - Wu, C.; Zhao, G.; Ou, B. A fuel economy optimization system with applications in vehicles with human drivers and autonomous vehicles. Transp. Res. Part D Transp. Environ.
**2011**, 16, 515–524. [Google Scholar] [CrossRef] - Li, S.; Li, K.; Rajamani, R.; Wang, J. Model predictive multi-objective vehicular adaptive cruise control. IEEE Trans. Control. Syst. Technol.
**2010**, 19, 556–566. [Google Scholar] [CrossRef] - Eben Li, S.; Li, K.; Wang, J. Economy-oriented vehicle adaptive cruise control with coordinating multiple objectives function. Veh. Syst. Dyn.
**2013**, 51, 1–17. [Google Scholar] [CrossRef] - Luo, L.-h.; Liu, H.; Li, P.; Wang, H. Model predictive control for adaptive cruise control with multi-objectives: Comfort, fuel-economy, safety and car-following. J. Zhejiang Univ. SCIENCE A
**2010**, 11, 191–201. [Google Scholar] [CrossRef] - Schmied, R.; Waschl, H.; Del Re, L. Extension and experimental validation of fuel efficient predictive adaptive cruise control. In Proceedings of the 2015 American Control Conference (ACC), Chicago, IL, USA, 1–3 July 2015; pp. 4753–4758. [Google Scholar]
- Jia, Y.; Jibrin, R.; Itoh, Y.; Görges, D. Energy-optimal adaptive cruise control for electric vehicles in both time and space domain based on model predictive control. IFAC-PapersOnLine
**2019**, 52, 13–20. [Google Scholar] [CrossRef] - Jia, Y.; Saito, T.; Itoh, Y.; Nukezhanov, Y.; Görges, D. Energy-optimal adaptive cruise control in time domain based on model predictive control. IFAC-PapersOnLine
**2018**, 51, 846–853. [Google Scholar] [CrossRef] - Madhusudhanan, A.K. A method to improve an electric vehicle’s range: Efficient Cruise Control. Eur. J. Control.
**2019**, 48, 83–96. [Google Scholar] [CrossRef] - He, H.; Xiong, R.; Fan, J. Evaluation of lithium-ion battery equivalent circuit models for state of charge estimation by an experimental approach. Energies
**2011**, 4, 582–598. [Google Scholar] [CrossRef] - Moon, S.; Yi, K. Human driving data-based design of a vehicle adaptive cruise control algorithm. Veh. Syst. Dyn.
**2008**, 46, 661–690. [Google Scholar] [CrossRef] - Martinez, J.-J.; Canudas-de-Wit, C. A safe longitudinal control for adaptive cruise control and stop-and-go scenarios. IEEE Trans. Control. Syst. Technol.
**2007**, 15, 246–258. [Google Scholar] [CrossRef] - Li, L.; Wang, X.; Song, J. Fuel consumption optimization for smart hybrid electric vehicle during a car-following process. Mech. Syst. Signal Process.
**2017**, 87, 17–29. [Google Scholar] [CrossRef] - Cao, K.; Hu, M.; Wang, D.; Qiao, S.; Guo, C.; Fu, C.; Zhou, A. All-wheel-drive torque distribution strategy for electric vehicle optimal efficiency considering tire slip. IEEE Access
**2021**, 9, 25245–25257. [Google Scholar] [CrossRef]

**Figure 8.**Speed profile of the host vehicle resulting from the MO-ACC strategy and the EOCFC strategy under the WLTC test cycle.

**Figure 9.**Inter-vehicle spacing resulting from the MO-ACC strategy (

**a**) and the EOCFC strategy (

**b**) under the WLTC test cycle.

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

m | kg | 2270 |

A | m^{2} | 3.0 |

C_{D} | - | 0.3 |

f | - | 0.008 |

r | m | 0.393 |

i_{0} | - | 10.885 |

α | deg | 0 |

th | s | 1.5 |

th_{min} | s | 1.2 |

th_{max} | s | 2.5 |

d_{0} | m | 5 |

d_{0_min} | m | 3 |

d_{0_max} | m | 6 |

Δv_{min} | m/s | −3.5 |

Δv_{max} | m/s | 4 |

TTC | s | −2.5 |

d_{s} | m | 3 |

a_{min} | m/s^{2} | −2.8 |

a_{max} | m/s^{2} | 1.2 |

j_{min} | m/s^{3} | −6 |

j_{max} | m/s^{3} | 6 |

Control Scheme | Energy Consumption (kWh) | ||
---|---|---|---|

NEDC | UDDS | WLTC | |

MO-ACC | 1.3687 | 1.3762 | 3.5537 |

EOCFC | 1.3614 | 1.3304 | 3.5000 |

Improvement | 0.53% | 3.33% | 1.51% |

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## Share and Cite

**MDPI and ACS Style**

Liu, Y.; Yao, C.; Guo, C.; Yang, Z.; Fu, C.
Energy-Saving Optimization for Electric Vehicles in Car-Following Scenarios Based on Model Predictive Control. *World Electr. Veh. J.* **2023**, *14*, 42.
https://doi.org/10.3390/wevj14020042

**AMA Style**

Liu Y, Yao C, Guo C, Yang Z, Fu C.
Energy-Saving Optimization for Electric Vehicles in Car-Following Scenarios Based on Model Predictive Control. *World Electric Vehicle Journal*. 2023; 14(2):42.
https://doi.org/10.3390/wevj14020042

**Chicago/Turabian Style**

Liu, Yang, Chuyang Yao, Cong Guo, Zhong Yang, and Chunyun Fu.
2023. "Energy-Saving Optimization for Electric Vehicles in Car-Following Scenarios Based on Model Predictive Control" *World Electric Vehicle Journal* 14, no. 2: 42.
https://doi.org/10.3390/wevj14020042