# A Multi-Source Braking Force Control Method for Electric Vehicles Considering Energy Economy

^{*}

## Abstract

**:**

## 1. Introduction

- The feasibility of using the motor’s energy recovery or power-consuming braking to share part of the braking force for an EMB is theoretically elaborated based on the analysis of motor battery characteristics. This aims to reduce the braking force demand of the EMB system and its size.
- In order to ensure that the braking torque can be easily adjusted using the driving motor, a slip rate controller is designed based on the ENMPC algorithm, which makes the demand torque more stable compared to traditional ABS, thereby improving braking performance.
- In order to achieve a reasonable allocation of the three braking forces, a braking source allocation strategy is developed based on the grey wolf algorithm, which improves the fitness of the braking source allocation and the overall energy efficiency of the vehicle.

## 2. Vehicle and Component Model

#### 2.1. Vehicle Mathematical Model

#### 2.2. EMB Actuator Response Characteristics

#### 2.3. Tire Model

#### 2.4. Drive Motor Model

#### 2.5. Battery Model

## 3. Multi-Source Braking Force System and the Control Strategy

#### 3.1. Enhancements to the Configuration of Multi-Source Braking Power System

#### 3.2. Control Strategies for Multi-Source Braking Power System

#### 3.2.1. Vehicle State Observer

#### 3.2.2. Calculation and Allocation of Required Braking Torque

#### 3.2.3. Distributed Braking Torque Control Strategy

#### 3.2.4. Explicit Control Strategy

#### 3.3. Allocation of Braking Force Sources

## 4. Simulation and Evaluation

#### 4.1. Vehicle State Observer

#### 4.2. ENMPC Braking Torque Control Strategy

^{2}. Figure 17a, Figure 18a, Figure 19a, and Figure 20a show the vehicle speed and wheel speed curves, braking torque curves, slip ratio curves, and deceleration curves, respectively, under the ENMPC strategy. Figure 17b, Figure 18b, Figure 19b, and Figure 20b show the vehicle speed and wheel speed curves, braking torque curves, slip ratio curves, and deceleration curves, respectively, under the rule-based ABS control strategy. Table 3 shows the braking time, average deceleration, and braking distance under both strategies.

^{2}.

^{2}. Figure 21a, Figure 22a, Figure 23a, and Figure 24a show the vehicle speed and wheel speed curves, braking torque curves, slip ratio curves, and deceleration curves, respectively, under the ENMPC strategy. Figure 21b, Figure 22b, Figure 23b, and Figure 24b show the vehicle speed and wheel speed curves, braking torque curves, slip ratio curves, and deceleration curves, respectively, under the rule-based ABS control strategy. Table 4 shows the braking time, average deceleration, and braking distance under both strategies.

^{2}.

#### 4.3. Allocation of Braking Force Sources

^{2}. The front axle braking force is provided solely by the EMB, while the rear axle braking force is provided by the energy recovery of the drive motor, energy-consuming braking of the drive motor, and the EMB. Therefore, the analysis of the braking source allocation focuses on the rear axle.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Gao, Y.; Ehsani, M. Electronic Braking System of EV and HEV—Integration of Regenerative Braking, Automatic Braking Force Control and ABS; SAE Technical Papers; SAE International: Warrendale, PA, USA, 2001. [Google Scholar]
- Nakamura, E.; Soga, M.; Sakai, A.; Otomo, A.; Kobayashi, T. Development of Electronically Controlled Brake System for Hybrid Vehicle; SAE Technical Papers; SAE International: Warrendale, PA, USA, 2002. [Google Scholar]
- Joon, K.S.; Woochul, L.; Jung, D. Electro-Mechanical Brake. KR Patent 102401769B1, 25 May 2022. [Google Scholar]
- Li, C.; Zhuo, G.; Tang, C.; Xiong, L.; Tian, W.; Qiao, L.; Cheng, Y.; Duan, Y. A review of electro-mechanical brake(EMB) system: Structure, control and application. Sustainability
**2023**, 15, 4514. [Google Scholar] [CrossRef] - Maron, C.; Georg, R. Method for Actuating an Electromechanical Parking Brake Device. US Patent 2006131113A1, 22 June 2006. [Google Scholar]
- Michael, H. Bremseinrichtung mit einem Keilmechanismus. DE Patent 102007013421A1, 25 September 2008. [Google Scholar]
- Yang, L.; Sun, S.; Qin, Z.; Shan, G.; Han, Z. Automatic Generation Analysis Method of Automobile Chassis Electronic Control System Based on NLP-intelligent Control Condition. In Proceedings of the 2023 38th Youth Academic Annual Conference of Chinese Association of Automation (YAC), Hefei, China, 27–29 August 2023; pp. 514–519. [Google Scholar]
- Saiteja, P.; Ashok, B.; Wagh, A.S.; Farrag, M.E. Critical review on optimal regenerative braking control system architecture, calibration parameters and development challenges for EVs. Int. J. Energy Res.
**2022**, 46, 20146–20179. [Google Scholar] [CrossRef] - Satzger, C.; de Castro, R. Predictive brake control for electric vehicles. IEEE Trans. Veh. Technol.
**2017**, 67, 977–990. [Google Scholar] [CrossRef] - Lee, C.F. Brake Force Control and Judder Compensation of an Automotive Electromechanical Brake. Doctoral Dissertation, University of Melbourne, Department of Mechanical Engineering, Melbourne, Australia, 2013. [Google Scholar]
- Li, J.; Wu, T.; Fan, T.; He, Y.; Meng, L.; Han, Z. Clamping force control of electro–mechanical brakes based on driver intentions. PLoS ONE
**2020**, 15, e0239608. [Google Scholar] [CrossRef] [PubMed] - Tao, Y.; Xie, X.; Zhao, H.; Xu, W.; Chen, H. A Regenerative Braking System for Electric Vehicle with Four in-Wheel Motors Based on Fuzzy Control. In Proceedings of the Chinese Control Conference, Dalian, China, 26–28 July 2017. [Google Scholar]
- Sun, Y.; Wang, Y.; Zhu, R.; Geng, R.; Zhang, J.; Fan, D.; Wang, H. Study on the Control Strategy of Regenerative Braking for the Hybrid Electric Vehicle under Typical Braking Condition. Iop Conf. Ser. Mater. Sci. Eng.
**2018**, 452, 032092. [Google Scholar] [CrossRef] - Xu, Q.; Wang, F.; Zhang, X. Research on the Efficiency Optimization Control of the Regenerative Braking System of Hybrid Electrical Vehicle Based on Electrical Variable Transmission. IEEE Access
**2019**, 7, 116823–116834. [Google Scholar] [CrossRef] - Gao, H.; Gao, Y.; Ehsani, M. A Neural Network Based SRM Drive Control Strategy for Regenerative Braking in EV and HEV. In Proceedings of the IEMDC 2001, IEEE International Electric Machines and Drives Conference (Cat. No.01EX485), Cambridge, MA, USA, 17–20 June 2001. [Google Scholar]
- Wang, C.; Zhao, W.; Li, W. Braking Sense Consistency Strategy of Electro-Hydraulic Composite Braking System. Mech. Syst. Signal Process.
**2018**, 109, 196–219. [Google Scholar] [CrossRef] - Savaresi, M.S.; Tanelli, M. Active Braking Control System Design for Vehicles; Springer: New York, NY, USA, 2010. [Google Scholar]
- Aly, A.A.; Zeidan, E.-S.; Hamed, A.; Salem, F. An antilock-braking systems (ABS) control: A technical review. Intell. Control Autom.
**2011**, 2, 186–195. [Google Scholar] [CrossRef] - Choi, S.B. Antilock brake system with a continuous wheel slip control to maximize the braking performance and the ride quality. IEEE Trans. Control Syst. Technol.
**2008**, 16, 996–1003. [Google Scholar] [CrossRef] - Yin, D.; Oh, S.; Hori, Y. A novel traction control for EV based on maximum transmissible torque estimation. IEEE Trans. Ind. Electron.
**2009**, 56, 2086–2094. [Google Scholar] - Wang, Y.; Fujimoto, H.; Hara, S. Driving force distribution and control for EV with four in-wheel motors: A case study of acceleration on splitfriction surfaces. IEEE Trans. Ind. Electron.
**2017**, 64, 3380–3388. [Google Scholar] [CrossRef] - Yoo, D.; Wang, L. Model based wheel slip control via constrained optimal algorithm. In Proceedings of the 2007 IEEE International Conference on Control Applications, Singapore, 1–3 October 2007; pp. 1239–1246. [Google Scholar]
- Borrelli, F.; Bemporad, A.; Fodor, M.; Hrovat, D. An MPC/hybrid system approach to traction control. IEEE Trans. Control Syst. Technol.
**2006**, 14, 541–552. [Google Scholar] [CrossRef] - Tavernini, D.; Metzler, M.; Gruber, P.; Sorniotti, A. Explicit nonlinear model predictive control for electric vehicle traction control. IEEE Trans. Contr. Syst. Technol. 2018; to be published. [Google Scholar] [CrossRef]
- von Albrichsfeld, C.; Karner, J. Brake System for Hybrid and Electric Vehicles; SAE Technical Paper; SAE International: Warrendale, PA, USA, 2009. [Google Scholar]
- Conlon, B.M.; Kidston, K.S. Electric Vehicle with Regenerative and Anti-lock Braking. U.S. Patent 5,615,933, 1 April 1997. [Google Scholar]
- Schneider, M.; Shaffer, A. Regenerative Braking Control System and Method. U.S. Patent Application 11/164,195, 14 November 2005. [Google Scholar]
- Hori, Y. Future Vehicle Driven by Electricity and Control research on Four-wheel-motored “UOT Electric March II”. IEEE Trans. Ind. Electron.
**2004**, 51, 954–962. [Google Scholar] [CrossRef] - Hsiao, M.; Lin, C. Antilock Braking Control of Electric Vehicles with Electric Brake; SAE Technical Paper; SAE International: Warrendale, PA, USA, 2005. [Google Scholar]
- Tur, O.; Ustun, O.; Tuncay, R.N. An Introduction to Regenerative Braking of Electric Vehicles as Anti-lock Braking System. In Proceedings of the 2007 Intelligent Vehicles Symposium, Istanbul, Turkey, 13–15 June 2007; pp. 944–948. [Google Scholar]
- Okano, T.; Sakai, S.; Uchida, T.; Hori, Y. Braking Performance Improvement for Hybrid Electric Vehicle Based on Electric Motor’s Quick Torque Response. In Proceedings of the 19th International Electric Vehicle Symposium (EVS19), Busan, Republic of Korea, 19–23 October 1999. [Google Scholar]
- Zhang, J.Z.; Chen, X.; Zhang, P.J. Integrated Control of Braking Energy Regeneration and Pneumatic Anti-lock Braking. J. Automob. Eng.
**2010**, 224, 587–610. [Google Scholar] [CrossRef] - Zhang, J.; Kong, D.; Chen, L.; Chen, X. Optimization of Control Strategy for Regenerative Braking of an Electrified Bus Equipped with an Anti-lock Braking System. J. Automob. Eng.
**2012**, 226, 494–506. [Google Scholar] [CrossRef] - Bayar, K.; Wang, J.; Rizzoni, G. Development of a Vehicle Stability Control Strategy for a Hybrid Electric Vehicle Equipped with Axle Motors. J. Automob. Eng.
**2012**, 226, 795–814. [Google Scholar] [CrossRef] - Liu, Y.; Dou, C. Vehicle State Estimation Based on Unscented Kalman Filtering and a Genetic Algorithm. SAE Int. J. Commer. Veh.
**2020**, 14, 23–37. [Google Scholar] [CrossRef] - Wu, D.; Zeng, C.; Luo, J. Research on Joint Estimation Algorithm of Intelligent Vehicle Mass and Road Grade. In Proceedings of the 2023 4th International Conference on Computer Engineering and Application (ICCEA), Hangzhou, China, 7–9 April 2023. [Google Scholar]
- Rodríguez, A.J.; Sanjurjo, E.; Pastorino, R.; Naya, M.Á. State, parameter and input observers based on multibody models and Kalman filters for vehicle dynamics. Mech. Syst. Signal Process.
**2021**, 155, 107544. [Google Scholar] - Basrah, M.S.; Siampis, E.; Velenis, E.; Cao, D.; Longo, S. Wheel slip control with torque blending using linear and nonlinear model predictive control. Veh. Syst. Dyn.
**2017**, 55, 1665–1685. [Google Scholar] - Yuan, L.; Zhao, H.; Chen, H.; Ren, B. Nonlinear MPC-based slip control for electric vehicles with vehicle safety constraints. Mechatronics
**2016**, 38, 1–15. [Google Scholar] [CrossRef] - Satzger, C.; de Castro, R.; Knoblach, A.; Brembeck, J. Design and validation of anMPC-based torque blending and wheel slip control strategy. In Proceedings of the 2016 IEEE Intelligent Vehicles Symposium (IV), Gothenburg, Sweden, 19–22 June 2016; Volume 2016, pp. 514–520. [Google Scholar]
- Pei, X.; Pan, H.; Chen, Z.; Guo, X.; Yang, B. Coordinated control strategy of electro-hydraulic braking for energy regeneration. Control Eng. Pract.
**2020**, 96, 104324. [Google Scholar] [CrossRef] - Li, N.; Ning, X.; Wang, Q. Genetic Algorithm Optimization of Hydraulic Regenerative Braking System for Electric Vehicles. Bol. Tec.
**2017**, 55, 513–523. [Google Scholar] - Zheng, X.; Gao, X.; Zhao, Z. Simulation Analysis of Tire Dynamic Based on “Magic Formula”. Mach. Electron.
**2012**, 9, 16–20. [Google Scholar]

**Figure 8.**The relationship between deceleration and brake torque for different adhesion coefficients.

**Figure 17.**Vehicle and wheel speed for high adhesion: (

**a**) ENMPC strategy. (

**b**) Rule-based ABS strategy.

**Figure 21.**Vehicle and wheel speed for low adhesion: (

**a**) ENMPC strategy. (

**b**) Rule-based ABS strategy.

**Figure 25.**Brake torque from each sources: (

**a**) Grey wolf strategy. (

**b**) Rule-based distribution strategy.

Definition | Unit | Value |
---|---|---|

Vehicle mass (full) | kg | 4495 |

Vehicle mass (no load) | kg | 3200 |

Front axle load (full) | kg | 2000 |

Front axle load (no load) | kg | 1800 |

Rear axle load (full) | kg | 2495 |

Rear axle load (no load) | kg | 1400 |

Height of vehicle c.g. (full) | mm | 844 |

Height of vehicle c.g. (no load) | mm | 630 |

Distance between two axles | mm | 3300 |

Wheel type | - | 750R16 |

Argument | Value |
---|---|

t | 3 |

q_{1} | $3\times {10}^{8}$ |

q_{2} | $2.8\times {10}^{8}$ |

q_{3} | $1.8\times {10}^{8}$ |

r_{1} | 1 |

r_{2} | 1 |

r_{3} | 1 |

${\chi}_{1}$ | 200 |

${\chi}_{2}$ | 50 |

${\chi}_{3}$ | 150 |

${\chi}_{4}$ | 200 |

Definition | Unit | Value (ENMPC) | Value (Rule-Based) |
---|---|---|---|

Braking time | s | 3.4 | 4 |

Average deceleration | m/s^{2} | 6.96 | 5.56 |

Braking distance | m | 37.2 | 44.6 |

Definition | Unit | Value (ENMPC) | Value (Rule-Based) |
---|---|---|---|

Braking time | s | 6.4 | 10.6 |

Average deceleration | m/s^{2} | 2.67 | 1.73 |

Braking distance | m | 56.4 | 91.2 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2024 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wang, Y.; Zhou, L.; Chu, L.; Zhao, D.; Guo, Z.; Jiang, Z.
A Multi-Source Braking Force Control Method for Electric Vehicles Considering Energy Economy. *Energies* **2024**, *17*, 2032.
https://doi.org/10.3390/en17092032

**AMA Style**

Wang Y, Zhou L, Chu L, Zhao D, Guo Z, Jiang Z.
A Multi-Source Braking Force Control Method for Electric Vehicles Considering Energy Economy. *Energies*. 2024; 17(9):2032.
https://doi.org/10.3390/en17092032

**Chicago/Turabian Style**

Wang, Yinhang, Liqing Zhou, Liang Chu, Di Zhao, Zhiqi Guo, and Zewei Jiang.
2024. "A Multi-Source Braking Force Control Method for Electric Vehicles Considering Energy Economy" *Energies* 17, no. 9: 2032.
https://doi.org/10.3390/en17092032