# Clamping Force Control Strategy of Electro-Mechanical Brake System Using VUF-PID Controller

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Modeling of EMB

#### 2.1. Motor Model

^{2}; ${T}_{L}$ is the load torque, N·m; $B$ is the viscous friction coefficient, N·m (rad/s)

^{−1}; ${\omega}_{m}$ is the mechanical angular velocity, rad/s.

#### 2.2. Motor Friction Model

#### 2.3. Transmission Mechanism Model

#### 2.4. Load Model

#### 2.5. Brake Disc Model

## 3. EMB Clamping Force Control Strategy Based on VUF-PID

## 4. Simulation Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Emadi, A.; Lee, Y.J.; Rajashekara, K. Power Electronics and Motor Drives in Electric, Hybrid Electric, and Plug-In Hybrid Electric Vehicles. IEEE Trans. Ind. Electron.
**2008**, 55, 2237–2245. [Google Scholar] [CrossRef] - Schrade, S.; Nowak, X.; Verhagen, A.; Schramm, D. Short Review of EMB Systems Related to Safety Concepts. Actuators
**2022**, 11, 214. [Google Scholar] [CrossRef] - Saric, S.; Bab-Hadiashar, A.; van der Walt, J. Estimating clamp force for brake-by-wire systems: Thermal considerations. Mechatronics
**2009**, 19, 886–895. [Google Scholar] [CrossRef] - Ki, Y.H.; Lee, K.J.; Cheon, J.S.; Ahn, H.S. Design and implementation of a new clamping force estimator in Electro-Mechanical Brake systems. Int. J. Automot. Technol.
**2013**, 14, 739–745. [Google Scholar] [CrossRef] - Gong, X.; Ge, W.; Yan, J.; Zhang, Y.; Gongye, X. Review on the Development, Control Method and Application Prospect of Brake-by-Wire Actuator. Actuators
**2020**, 9, 15. [Google Scholar] [CrossRef] [Green Version] - Krishnamurthy, P.; Lu, W.; Khorrami, F.; Keyhani, A. Robust Force Control of an SRM-Based Electromechanical Brake and Experimental Results. IEEE Trans. Control Syst. Technol.
**2009**, 17, 1306–1317. [Google Scholar] [CrossRef] - Han, K.; Kim, M.; Huh, K. Modeling and control of an electronic wedge brake. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci.
**2012**, 226, 2440–2455. [Google Scholar] [CrossRef] - Baek, S.-K.; Oh, H.-K.; Park, J.-H.; Shin, Y.-J.; Kim, S.-W. Evaluation of Efficient Operation for Electromechanical Brake Using Maximum Torque per Ampere Control. Energies
**2019**, 12, 1869. [Google Scholar] [CrossRef] [Green Version] - Park, G.; Choi, S.B. Clamping force control based on dynamic model estimation for electromechanical brakes. Proc. Inst. Mech. Eng. Part D J. Automob. Eng.
**2018**, 232, 2000–2013. [Google Scholar] [CrossRef] - Lee, Y.O.; Jang, M.; Lee, W. Novel clamping force control for electric parking brake systems. Mechatronics
**2011**, 21, 1156–1162. [Google Scholar] [CrossRef] - Line, C.; Manzie, C.; Good, M.C. Electromechanical Brake Modeling and Control: From PI to MPC. IEEE Trans. Control Syst. Technol.
**2008**, 16, 446–457. [Google Scholar] [CrossRef] - Zhao, Y.; Lin, H.; Elahi, H.; Miao, F.; Riaz, S. Clamping Force Sensor Fault Analysis and Fault-Tolerant Control of the Electromechanical Brake System. Arab. J. Sci. Eng.
**2023**, 48, 6011–6023. [Google Scholar] [CrossRef] - Jo, C.; Hwang, S.; Kim, H. Clamping-Force Control for Electromechanical Brake. IEEE Trans. Veh. Technol.
**2010**, 59, 3205–3212. [Google Scholar] [CrossRef] - Park, G.; Choi, S.; Hyun, D. Clamping force estimation based on hysteresis modeling for electro-mechanical brakes. Int. J. Automot. Technol.
**2017**, 18, 883–890. [Google Scholar] [CrossRef] - Lee, C.F.; Manzie, C. Near-time-optimal tracking controller design for an automotive electromechanical brake. Proc. Inst. Mech. Eng. Part I J. Syst. Control Eng.
**2012**, 226, 537–549. [Google Scholar] [CrossRef] - Li, Y.; Shim, T.; Shin, D.-H.; Lee, S.; Jin, S. Control System Design for Electromechanical Brake System Using Novel Clamping Force Model and Estimator. IEEE Trans. Veh. Technol.
**2021**, 70, 8653–8668. [Google Scholar] [CrossRef] - Hoseinnezhad, R.; Bab-Hadiashar, A.; Rocco, T. Real-Time Clamp Force Measurement in Electromechanical Brake Calipers. IEEE Trans. Veh. Technol.
**2008**, 57, 770–777. [Google Scholar] [CrossRef] - Liu, Z.; Chen, Y.; Chen, L. A Gap Control Method for Electromechanical Brakes. Acta Armamentarii
**2022**, 43, 1478–1487. [Google Scholar] - Conker, C.; Baltacioglu, M.K. Fuzzy self-adaptive PID control technique for driving HHO dry cell systems. Int. J. Hydrogen Energy
**2020**, 45, 26059–26069. [Google Scholar] [CrossRef]

**Figure 4.**VUF-PID controller input-output relationship surface: (

**a**) the scale factors K1; (

**b**) the scale factors K2.

**Figure 6.**Clamping force response curve under step braking condition: The target clamping force is (

**a**) 6000N; (

**b**) 12,000 N; (

**c**) 18,000 N; (

**d**) 24,000 N.

**Figure 7.**Clamping force response curve under brake gear switching condition: The target clamping force is (

**a**) 0–12,000–24,000 N; (

**b**) 24,000–12,000–0 N.

e | ec | ||||||
---|---|---|---|---|---|---|---|

NB | NM | NS | ZE | PS | PM | PB | |

NB | NB | NB | NM | NM | NS | ZE | ZE |

NM | NB | NB | NM | NS | NS | ZE | ZE |

NS | NB | NM | NS | NS | ZE | PS | PS |

ZE | NM | NM | NS | ZE | PS | PM | PM |

PS | NM | NS | ZE | PS | PS | PM | PB |

PM | ZE | ZE | PS | PS | PM | PB | PB |

PB | ZE | ZE | PS | PM | PM | PB | PB |

e | ec | ||||||
---|---|---|---|---|---|---|---|

NB | NM | NS | ZE | PS | PM | PB | |

NB | PB | PB | PM | PM | PS | ZE | ZE |

NM | PB | PB | PM | PS | PS | ZE | NS |

NS | PM | PM | PM | PS | ZE | NS | NS |

ZE | PM | PM | PS | ZE | NS | NM | NM |

PS | PS | PS | ZE | NS | NS | NM | NM |

PM | PS | ZE | NS | NM | NM | NM | NB |

PB | ZE | ZE | NM | NM | NM | NB | NB |

e | ec | ||||||
---|---|---|---|---|---|---|---|

NB | NM | NS | ZE | PS | PM | PB | |

NB | PS | NS | NB | NB | NB | NM | PS |

NM | PS | NS | NB | NM | NM | NS | ZE |

NS | ZE | NS | NM | NM | NS | NS | ZE |

ZE | ZE | NS | NS | NS | NS | NS | ZE |

PS | ZE | ZE | ZE | ZE | ZE | ZE | ZE |

PM | PB | NS | PS | PS | PS | PS | PB |

PB | PB | PM | PM | PM | PS | PS | PB |

Parameter | Symbol | Value | Parameter | Symbol | Value |
---|---|---|---|---|---|

Initial parameters of the scale factor | ${K}_{p0}$ | 10 | Quantification factor of $\Delta e$ | ${K}_{ec}$ | 0.0025 |

Initial parameters of the integral factor | ${K}_{i0}$ | 0.02 | Scale factor of $\Delta {K}_{p}$ | ${K}_{up}$ | 0.17 |

Initial parameters of the differential factor | ${K}_{d0}$ | 0.002 | Scale factor of $\Delta {K}_{i}$ | ${K}_{ui}$ | 0.017 |

Quantification factor of $e$ | ${K}_{e}$ | 0.00025 | Scale factor of $\Delta {K}_{d}$ | ${K}_{ud}$ | 0.00033 |

Parameter | Symbol | Value |
---|---|---|

Static friction torque (N·m) | ${T}_{s}$ | 0.0387 |

Coulomb friction torque (N·m) | ${T}_{c}$ | 0.0192 |

Coefficient of viscous friction (N m (rad/s)^{−1}) | $B$ | 1.086 × 10^{−3} |

Ball screw drive efficiency | ${\eta}_{s}$ | 0.92 |

Planetary gearing efficiency | ${\eta}_{p}$ | 0.97 |

Ball Screw Guide (mm) | $L$ | 5 |

Planetary gear ratio | ${i}_{p}$ | 13 |

Target Clamping Force (N) | PID | F-PID | VUF-PID | |||
---|---|---|---|---|---|---|

Adjustment Time | Overshoot | Adjustment Time | Overshoot | Adjustment Time | Overshoot | |

6000 | 0.154 s | 2.28% | 0.191 s | 2.85% | 0.128 s | 0.17% |

12,000 | 0.199 s | 1.57% | 0.229 s | 1.58% | 0.162 s | 0.16% |

18,000 | 0.238 s | 1.33% | 0.246 s | 1.31% | 0.176 s | 0.16% |

24,000 | 0.274 s | 1.06% | 0.272 s | 0.37% | 0.209 s | 0.15% |

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. |

© 2023 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**

Chen, Q.; Lv, Z.; Tong, H.; Xiong, Z.
Clamping Force Control Strategy of Electro-Mechanical Brake System Using VUF-PID Controller. *Actuators* **2023**, *12*, 272.
https://doi.org/10.3390/act12070272

**AMA Style**

Chen Q, Lv Z, Tong H, Xiong Z.
Clamping Force Control Strategy of Electro-Mechanical Brake System Using VUF-PID Controller. *Actuators*. 2023; 12(7):272.
https://doi.org/10.3390/act12070272

**Chicago/Turabian Style**

Chen, Qiping, Zongyu Lv, Haiyang Tong, and Zuqi Xiong.
2023. "Clamping Force Control Strategy of Electro-Mechanical Brake System Using VUF-PID Controller" *Actuators* 12, no. 7: 272.
https://doi.org/10.3390/act12070272