# Optimizing Energy Harvesting: A Gain-Scheduled Braking System for Electric Vehicles with Enhanced State of Charge and Efficiency

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Methodology

#### 3.1. Vehicle Dynamics

- Vehicle mass is distributed equally on each wheel.
- Lateral, yawing, pitch, and roll dynamics are omitted.

_{d}is the coefficient of air resistance, A

_{f}is the windward area, $\rho $ is the air density, $\Delta V$ is the difference in speed between the vehicle and the air, and $\alpha $ is the road surface’s angle of inclination. Rolling resistance is caused by the energy lost from tire deformation and adhesion to the surface [19]. The tire rolling resistance can be calculated using the following equation:

_{r}is the coefficient of rolling resistance, and m is the total weight. Next, gradient resistance appears due to the component of gravity. When a vehicle goes up or down a slope, the weight component is always directed downward. A weight component operates in the opposite direction of motion and is proportional to the road surface’s angle of inclination. The equation for gradient resistance is formulated below [20]:

#### 3.2. Overall Efficiency

- P
_{1}= Input power - P
_{0}= Output power - P
_{loss}_{1}= Power losses in battery - P
_{loss}_{2}= Power losses in converter and electric motor - P
_{loss}_{3}= Power losses in gear box - ${\eta}_{1}$ = Battery efficiency
- ${\eta}_{2}$ = Power converter and electric motor efficiency
- ${\eta}_{3}$ = Gearbox efficiency.

#### 3.3. Driving Cycle

#### 3.4. State of Charge

_{0}is constant voltage (V), A

_{0}is the exponential voltage (V), B

_{0}is the exponential capacity (Ah)

^{−1}, K

_{0}is the polarisation resistance (Ω), i is the battery’s current (A), it is the extraction capacity (Ah), and i

^{*}is the low-frequency dynamic current (A). The SOC is used to indicate the remaining capacity of the battery, and it is the ratio of the remaining capacity of the battery to its total capacity [25,26].

_{res}represents the remaining battery capacity, Q is the total capacity, and Q

_{used}is the battery capacity that has been used. For a fully charged battery (100%), the SOC is equal to 1, while the SOC is equal to 0 for a depleted battery [13]. During high SOC, the charging should be limited to avoid overcharging. When the SOC drops below 80%, the battery accommodates high current. Therefore, when the SOC is higher than 0.8, appropriate regenerative braking is necessary to prevent the battery from overcharging.

#### 3.5. Braking Force Distribution

_{tot}is the total braking torque request, T

_{fric}is the friction braking force of the front and rear axles, and T

_{reg}is the regenerative braking force of the rear axle.

_{r_fric}and T

_{r_reg}represent the friction braking torque requested for friction and regenerative braking of the rear axle, respectively, and ratio

_{fric}and ratio

_{reg}denote the braking distribution coefficient for friction and regenerative braking, respectively.

#### 3.6. Slip Ratio

_{d}is tire–road friction, and F

_{z}is the wheel’s normal force.

#### 3.7. Sliding Mode Control

## 4. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Kuntanapreeda, S. Traction control of electric vehicles using sliding-mode controller with tractive force observer. Int. J. Veh. Technol.
**2014**, 2014, 829097. [Google Scholar] [CrossRef] [Green Version] - Fajri, P.; Lee, S.; Prabhala, V.A.K.; Ferdowsi, M. Modeling and Integration of Electric Vehicle Regenerative and Friction Braking for Motor/Dynamometer Test Bench Emulation. IEEE Trans. Veh. Technol.
**2016**, 65, 4264–4273. [Google Scholar] [CrossRef] - Kumar, C.S.N.; Subramanian, S.C. Cooperative control of regenerative braking and friction braking for a hybrid electric vehicle. Proc. Inst. Mech. Eng. Part D J. Automob. Eng.
**2016**, 230, 103–116. [Google Scholar] [CrossRef] - Khorsravinia, K.; Hassan, M.K.; Rahman, R.Z.A.; Al-Haddad, S.A.R. Integrated OBD-II and mobile application for electric vehicle (EV) monitoring system. In Proceedings of the 2017 IEEE 2nd International Conference on Automatic Control and Intelligent System, Kota Kinabalu, Malaysia, 21 October 2017; Volume 2017, pp. 202–206. [Google Scholar] [CrossRef]
- Chen, J.; Liu, K.; Lan, F.; Liu, M. Braking Stability-Oriented Regenerative Braking Control Strategy of Twin Motor 4WD Electric Vehicle. DEStech Trans. Eng. Technol. Res.
**2017**, 2017, 58–65. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Lv, C.; Zhang, J.; Li, Y.; Yuan, Y. Regenerative Braking Control Algorithm for an Electrified Vehicle Equipped with a by-Wire brake System; SAE International: Warrendale, PA, USA, 2014; Volume 1. [Google Scholar] [CrossRef]
- Zheng, L.; Shi, Z.; Luo, Y.; Kang, J. A Study of Energy Recovery System during Braking for Electric Vehicle. In 2016 6th International Conference on Applied Science, Engineering and Technology; Atlantis Press: Amsterdam, The Netherlands, 2016; pp. 8–13. [Google Scholar] [CrossRef] [Green Version]
- Shewate, S.; Kumbhalkar, M.A.; Sonawane, Y.; Salunkhe, T.; Savant, S. Modelling And Simulation of Regenerative Braking System for Light Commercial Vehicle—A Review. IOSR J. Mech. Civ. Eng.
**2018**, 8, 52–56. [Google Scholar] - Bai, Z.F.; Li, S.X.; Cao, B.G. H∞ Control Applied to Electric Torque Control for Regenerative Braking of an Electric Vehicle. J. Appl. Sci.
**2005**, 5, 1103–1107. [Google Scholar] [CrossRef] [Green Version] - Palanivel, P.; Alemayehu, H.; Chandramouli, B.; Hiremath, R. Design and Analysis of BLDC Motor Drive Based on Fuzzy-PID Controller. Int. J. Electr. Eng. Technol.
**2020**, 11, 281–290. [Google Scholar] [CrossRef] - Zhang, H.; Xu, G.; Li, W.; Zhou, M. Fuzzy logic control in regenerative braking system for electric vehicle. In Proceedings of the 2012 IEEE International Conference on Information and Automation, Shenyang, China, 6–8 June 2012; pp. 588–591. [Google Scholar] [CrossRef]
- Mei, P.; Yang, S.; Xu, B.; Sun, K. A Fuzzy Sliding-Mode Control for Regenerative Braking System of Electric Vehicle. In Proceedings of the 2021 7th International Conference on Control, Automation and Robotics (ICCAR), Singapore, 23–26 April 2021; pp. 397–401. [Google Scholar] [CrossRef]
- Canciello, G.; Russo, A.; Guida, B.; Cavallo, A. Supervisory Control for Energy Storage System Onboard Aircraft. In Proceedings of the 2018 IEEE International Conference on Environment and Electrical Engineering and 2018 IEEE Industrial and Commercial Power Systems Europe (EEEIC/I&CPS Europe), Palermo, Italy, 12–15 June 2018; pp. 1–6. [Google Scholar] [CrossRef]
- Cavallo, A.; Canciello, G.; Russo, A. Supervised Energy Management in Advanced Aircraft Applications. In Proceedings of the 2018 European Control Conference (ECC), Limassol, Cyprus, 12–15 June 2018; pp. 2769–2774. [Google Scholar] [CrossRef]
- Chu, S.; Xie, Z.; Wong, P.K.; Li, P.; Li, W.; Zhao, J. Observer-based gain scheduling path following control for autonomous electric vehicles subject to time delay. Veh. Syst. Dyn.
**2022**, 60, 1602–1626. [Google Scholar] [CrossRef] - Allagui, N.Y.; Salem, F.A.; Aljuaid, A.M. Artificial Fuzzy-PID Gain Scheduling Algorithm Design for Motion Control in Differential Drive Mobile Robotic Platforms. Comput. Intell. Neurosci.
**2021**, 2021, 5542888. [Google Scholar] [CrossRef] - Mehrdad, E.; Yimin, G.; Sebastian, E.G.; Ali, E. Modern Electric, Hybrid Electric, and Fuel Cell Vehicles; CRC Press: Boca Raton, FL, USA, 2005. [Google Scholar]
- Nam, K.; Hori, Y.; Lee, C. Wheel slip control for improving traction-ability and energy efficiency of a personal electric vehicle. Energies
**2015**, 8, 6820–6840. [Google Scholar] [CrossRef] [Green Version] - Eckert, J.J.; Silva, L.C.A.; Costa, E.S.; Santiciolli, F.M.; Dedini, F.G.; Corrêa, F.C. Electric vehicle drivetrain optimisation. IET Electr. Syst. Transp.
**2017**, 7, 32–40. [Google Scholar] [CrossRef] - Yamsani, A. Gradeability for Automobiles. IOSR J. Mech. Civ. Eng.
**2014**, 11, 35–41. [Google Scholar] [CrossRef] - Niksa, Ć.; Damir, V.; Vraži, M. Overall Efficiency in Electric Road Vehicles. Safety Eng.
**2011**, 8, 51–56. [Google Scholar] [CrossRef] - Josef, B.; Zvolský, T. Experimental study of electric vehicle gearbox efficiency. In MATEC Web of Conferences; EDP Sciences: Les Ulis, France, 2018; Volume 4, p. 02004. [Google Scholar]
- Rajendran, S.; Spurgeon, S.; Tsampardoukas, G.; Hampson, R. Intelligent Sliding Mode Scheme for Regenerative Braking Control. IFAC PapersOnLine
**2018**, 51, 334–339. [Google Scholar] [CrossRef] - Zhang, Z.; Xu, G.; Li, W.; Zheng, L. Regenerative Braking for Electric Vehicle based on Fuzzy Logic Control Strategy. In Proceedings of the 2010 2nd International Conference on Mechanical and Electronics Engineering, Kyoto, Japan, 1–3 August 2010; Volume 1, pp. 319–323. [Google Scholar] [CrossRef]
- Anowar, M.H.; Roy, P. A Modified Incremental Conductance Based Photovoltaic MPPT Charge Controller. In Proceedings of the 2019 International Conference on Electrical, Computer and Communication Engineering (ECCE), Cox’sBazar, Bangladesh, 7–9 February 2019. [Google Scholar] [CrossRef]
- Vyroubal, P.; Maxa, J.; Kazda, T. Simulation of the behavior of the lithium ion battery. Adv. Mil. Technol.
**2014**, 9, 107–115. [Google Scholar] - Gao, Y.; Chen, L.; Ehsani, M. Investigation of the Effectiveness of Regenerative Braking for EV and HEV. SAE Trans.
**2018**, 108, 3184–3190. [Google Scholar] - Sangtarash, F.; Esfahanian, V.; Nehzati, H.; Haddadi, S.; Bavanpour, M.A.; Haghpanah, B. Effect of Different Regenerative Braking Strategies on Braking Performance and Fuel Economy in a Hybrid Electric Bus Employing CRUISE Vehicle Simulation. SAE Int. J. Fuels Lubr.
**2009**, 1, 828–837. [Google Scholar] [CrossRef] [Green Version] - Guo, J.; Wang, J.; Cao, B. Regenerative braking strategy for electric vehicles. In Proceedings of the 2009 IEEE Intelligent Vehicles Symposium, Xi’an, China, 3–5 June 2009; pp. 864–868. [Google Scholar] [CrossRef]
- Zhao, X. Braking torque distribution for hybrid electric vehicles based on nonlinear disturbance observer. Proc. Inst. Mech. Eng. Part D J. Automob. Eng.
**2019**, 233, 3327–3341. [Google Scholar] [CrossRef] - Xu, G.; Xu, K.; Zheng, C.; Zhang, X.; Zahid, T. Fully Electrified Regenerative Braking Control for Deep Energy Recovery and Maintaining Safety of Electric Vehicles. IEEE Trans. Veh. Technol.
**2016**, 65, 1186–1198. [Google Scholar] [CrossRef] - Zhao, Y.; Zhang, J.; Li, C.; He, C. Sliding Mode Control Algorithm for Regenerative Braking of an Electric Bus with a Pneumatic Anti-lock Braking System. In IOP Conference Series: Materials Science and Engineering; IOP Publishing: Bristol, UK, 2019. [Google Scholar] [CrossRef]
- Zheng, Y.; Liu, J.; Liu, X.; Fang, D.; Wu, L. Adaptive Second-Order Sliding Mode Control Design for a Class of Nonlinear Systems with Unknown Input. Math. Probl. Eng.
**2015**, 2015, 319495. [Google Scholar] [CrossRef] [Green Version] - Heng, C.T.; Jamaludin, Z.; Hashim, A.Y.B.; Rafan, N.A.; Abdullah, L.; Salleh, M.R.; Arep, H. Desing and Analysis of Super Twisting Sliding Mode Control for Machine Tools. J. Teknol.
**2016**, 3, 25–29. [Google Scholar] - Kruse, O.; Mukhamejanova, A.; Mercorelli, P. Super-Twisting Sliding Mode Control for Differential Steering Systems in Vehicular Yaw Tracking Motion. Electronics
**2022**, 11, 1330. [Google Scholar] [CrossRef] - Fallaha, C.J.; Saad, M.; Kanaan, H.Y.; Al-Haddad, K. Sliding-mode robot control with exponential reaching law. IEEE Trans. Ind. Electron.
**2011**, 58, 600–610. [Google Scholar] [CrossRef] - Ghazali, A.K.; Hassan, M.K.; Radzi, M.A.M.; As’arry, A. Electric vehicle with sliding mode control super-twisting control strategy. J. Phys. Conf. Ser.
**2020**, 1432, 012023. [Google Scholar] [CrossRef] - Alkharasani, B.A.; Hassan, M.K.; Akmeliawati, R.; Zafira, R.; Ahmed, S.A. PID-sliding surface based sliding mode controller for anti-lock braking system of electric vehicle. Adv. Sci. Lett.
**2016**, 22, 2734–2737. [Google Scholar] [CrossRef] [Green Version] - Ghazali, A.K.; Hassan, M.K.; Radzi, M.A.M.; As’arry, A. Integrated braking force distribution for electric vehicle regenerative braking system. Pertanika J. Sci. Technol.
**2020**, 28, 173–182. [Google Scholar] [CrossRef] - Ghazali, A.K.; Hassan, M.K.; Mohd Radzi, M.A.; As’arry, A. Sliding mode control optimization method using fuzzy-gain scheduling for rgenerative braking system. J. Adv. Res. Dyn. Control Syst.
**2020**, 12, 1504–1509. [Google Scholar] [CrossRef]

**Figure 1.**Individual components of the EV propulsion system’s efficiency [22].

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

Distance | 10.93 km |

Maximum speed | 120 km/h |

Average speed | 33.21 km/h |

Maximum acceleration | 1.06 m/s^{2} |

Maximum deceleration | −1.39 m/s^{2} |

Number of stops | 13 |

**Table 2.**Comparison between default and integrated braking force distributions (without controller).

Parameters | Default | Integrated | Improvement |
---|---|---|---|

Overall efficiency | 0.433 | 0.433 | - |

Motor efficiency | 0.8 | 0.8 | - |

Distance (km) | 32.8 | 32.8 | - |

Energy transmitted (kJ) | 4573 | 5069 | 10.8% |

Energy loss during driving (kJ) | 2550 | 2535 | 15 kJ |

Parameters | Default | Integrated | Improvement |
---|---|---|---|

Overall efficiency | 0.485 | 0.546 | 12.58% |

Motor efficiency | 0.83 | 0.83 | - |

Distance (km) | 33 | 33 | - |

Energy transmitted (kJ) | 119 × 10^{5} | 121 × 10^{5} | 1.68% |

Energy loss during driving (kJ) | 72,813 | 66,207 | 6606 kJ |

Parameters | Default | Integrated | Improvement |
---|---|---|---|

Overall efficiency | 0.74 | 0.83 | 12.16% |

Motor efficiency | 0.86 | 0.86 | - |

Distance (km) | 32.6 | 32.6 | - |

Energy transmitted (kJ) | 4977 | 5687 | 14.27% |

Energy loss during driving (kJ) | 2770 | 2857 | 87 kJ |

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**MDPI and ACS Style**

Ghazali, A.K.; Hassan, M.K.; Radzi, M.A.M.; As’arry, A.
Optimizing Energy Harvesting: A Gain-Scheduled Braking System for Electric Vehicles with Enhanced State of Charge and Efficiency. *Energies* **2023**, *16*, 4561.
https://doi.org/10.3390/en16124561

**AMA Style**

Ghazali AK, Hassan MK, Radzi MAM, As’arry A.
Optimizing Energy Harvesting: A Gain-Scheduled Braking System for Electric Vehicles with Enhanced State of Charge and Efficiency. *Energies*. 2023; 16(12):4561.
https://doi.org/10.3390/en16124561

**Chicago/Turabian Style**

Ghazali, Anith Khairunnisa, Mohd Khair Hassan, Mohd Amran Mohd Radzi, and Azizan As’arry.
2023. "Optimizing Energy Harvesting: A Gain-Scheduled Braking System for Electric Vehicles with Enhanced State of Charge and Efficiency" *Energies* 16, no. 12: 4561.
https://doi.org/10.3390/en16124561