# Robust Clamping Force Control of an Electro-Mechanical Brake System for Application to Commercial City Buses

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## Abstract

**:**

## 1. Introduction

## 2. System Modeling of an EMB System

#### Dynamics Model

## 3. Design of a Sensor-Less Robust Controller

- First, the desired clamping force ${F}^{*}$ is generated by a driver’s brake pedal command. Note that the desired clamping force can be calculated by using the brake pedal stroke sensor.
- Second, the 2-degree-of-freedom position controller is designed based on the defined nominal motor model for improving the position tracking performances and an inner-loop disturbance observer (i.e., called a position-mode DOB) is designed for making the position controller robust against external disturbances.
- Third, a CFO is designed based on a nominal motor model and a reduction gear ratio.
- Forth, the outer-loop disturbance observer (i.e., called a force-mode DOB) is designed to compensate for model variations and to reject undesired disturbances. A F-DOB makes the complicated calmping force dynamics behave as a defined nominal clamping force model.
- Finally, the 2-degree-of-freedom clamping force controller is designed by using the nominal clamping force model.

#### 3.1. Design of a Clamping Force Observer (CFO)

#### 3.2. Design of an Inner-Loop Controller: Position Controller

#### 3.3. Design of an Outer-Loop Controller: Force Controller

## 4. Experiments

#### 4.1. Experimental Setup

#### 4.2. Experimental Results

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

${B}_{m}$ | a damping coefficient in a motor model |

${C}_{f}$ | a force controller |

${C}_{p}$ | a position controller |

${C}_{ff}$ | a force feed-forward controller |

${C}_{fp}$ | a position feed-forward controller |

$d$ | external disturbances |

$\widehat{d}$ | estimated disturbances |

${F}_{cl}$ | a clamping force |

${\widehat{F}}_{cl}$ | an estimated clamping force |

${J}_{m}$ | a moment of inertia for a driving motor |

${K}_{pf}$ | a proportional gain used in the force controller |

${K}_{if}$ | an integral gain used in the force controller |

${K}_{pp}$ | a proportional gain used in the position controller |

${K}_{ip}$ | an integral gain used in the position controller |

${K}_{dp}$ | a derivative gain used in the position controller |

${K}_{t}$ | a force gain |

$k$ | a brake pad coefficient |

$N$ | a residual vibration compensator |

${P}_{n}$ | a nominal model between ${\tau}_{m}$ and ${\omega}_{m}$ |

${P}_{m}$ | a nominal model between ${\theta}_{m}$ and ${\widehat{F}}_{d}$ |

${Q}_{i}$ | a low pass filter used in an inner position control loop |

${Q}_{o}$ | a low pass filter used in an outer force control loop |

${\theta}_{m}$ | an angle of a driving motor |

${\tau}_{m}$ | a torque of a driving motor |

$\tau $ | a time constant |

${\omega}_{m}$ | an angular velocity of a driving motor |

${\omega}_{1}$ | a cutoff frequency of a feedforward filter used in the position control |

${\omega}_{2}$ | a cutoff frequency of a feedforward filter used in the force control |

${\omega}_{c}$ | a bandwidth of the residual vibration compensator, $N$ |

${\omega}_{f}$ | a bandwidth of the force controller |

${\omega}_{i}$ | a cutoff frequency of ${Q}_{i}$ |

${\omega}_{o}$ | a cutoff frequency of ${Q}_{o}$ |

${\omega}_{p}$ | a bandwidth of the position controller |

$x$ | stroke of the brake pad |

$\zeta $ | a damping coefficient used in a residual vibration compensator, $N$ |

## References

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**Figure 5.**Overall structure for a proposed robust clamping force control system: (

**1**) 2-degree-of-freedom clamping force controller; (

**2**) 2-degree-of-freedom position controller; (

**3**) Clamping force observer; (

**4**) Position-mode DOB; (

**5**) Force-mode DOB.

**Figure 8.**Structure of a two-degree-of-freedom position controller with a position-mode disturbance observer (P-DOB).

**Figure 9.**Frequency response function for the closed-loop transfer function with a notch filter: (

**a**) Magnitude plot; (

**b**) Phase plot.

**Figure 12.**Experimental results for braking force apply and release mode: (

**a**) A result for the clamping force tracking control with the 2 Hz force command; (

**b**) A result for the position tracking control with the 2 Hz force command; (

**c**) A result for the clamping force tracking control with the 3 Hz force command; (

**d**) A result for the position tracking control with the 3 Hz force command.

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## Share and Cite

**MDPI and ACS Style**

Eum, S.; Choi, J.; Park, S.-S.; Yoo, C.; Nam, K.
Robust Clamping Force Control of an Electro-Mechanical Brake System for Application to Commercial City Buses. *Energies* **2017**, *10*, 220.
https://doi.org/10.3390/en10020220

**AMA Style**

Eum S, Choi J, Park S-S, Yoo C, Nam K.
Robust Clamping Force Control of an Electro-Mechanical Brake System for Application to Commercial City Buses. *Energies*. 2017; 10(2):220.
https://doi.org/10.3390/en10020220

**Chicago/Turabian Style**

Eum, Sangjune, Jihun Choi, Sang-Shin Park, Changhee Yoo, and Kanghyun Nam.
2017. "Robust Clamping Force Control of an Electro-Mechanical Brake System for Application to Commercial City Buses" *Energies* 10, no. 2: 220.
https://doi.org/10.3390/en10020220