# Steering Control in Electric Power Steering Autonomous Vehicle Using Type-2 Fuzzy Logic Control and PI Control

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## Abstract

**:**

## 1. Introduction

## 2. Lateral Vehicle Model

## 3. System Design

## 4. Simulation and Discussion

## 5. Experimental and Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Glossary

${\mathit{\delta}}_{\mathit{f}}$ | front wheel steering angle [rad] |

${\mathit{\delta}}_{\mathit{r}}$ | rear wheel steering angle [rad] |

$\mathit{C}$ | c.g. = center of gravity |

$\mathit{L}$ | total wheel base (l_{f} + l_{r}) [m] |

${\mathit{l}}_{\mathit{f}}$ | longitudinal distance from c.g. to front tires [m] |

${\mathit{l}}_{\mathit{r}}$ | longitudinal distance from c.g. to rear tires [m] |

$\mathit{\beta}$ | slip angle at vehicle c.g. [rad] |

$\mathit{R}$ | turn radius of the vehicle or radius of road [m] |

$\mathit{\psi}$ | yaw rate of vehicle [rad/s] |

$\mathit{a}$ | inertial acceleration [ms^{−2}] |

${\mathit{F}}_{\mathit{y}\mathit{f}}$ | the lateral tire force on front tires [kg m s^{−2}] |

${\mathit{F}}_{\mathit{y}\mathit{r}}$ | the lateral tire force on rear tires [kg m s^{−2}] |

${\mathit{C}}_{\mathit{a}}$ | cornering stiffness of tire [kN rad^{−1}] |

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**Figure 4.**Membership function of (

**a**) speed input; (

**b**) navigation input; (

**c**) distance input; and (

**d**) steering direction output.

**Figure 6.**(

**a**) Input of system; (

**b**) system output at speed 10 km/h; (

**c**) system output at speed 20 km/h; (

**d**) system output at speed 30 km/h; and (

**e**) system output at speed 40 km/h.

**Figure 11.**Comparison between simulation and experiment output signal generated at speeds of (

**a**) 10 km/h; (

**b**) 20 km/h; (

**c**) 30 km/h; and (

**d**) 40 km/h.

**Figure 13.**System output (

**a**) using type-1 FLC and PI control and (

**b**) using type-2 FLC and PI control.

Control | Kp | Ti | Td |
---|---|---|---|

PI | 0.45 K | Pu/1.2 | 0 |

PD | 0.8 K | 0 | Pu/8 |

PID | 0.6 K | Pu/2 | Pu/8 |

Control | Kp | Ti | Td |
---|---|---|---|

PI | 2.7 | 0.0053 | 0 |

PD | 4.8 | 0 | 0.0008 |

PID | 3.6 | 0.0032 | 0.0008 |

**Table 3.**Comparison between simulation and experiment output signal generated at a speed of 10 up to 40 km/h. (Dir = direction; Sim = simulation; Exp = Experiment).

Distance(m) | 3.5 | 7 | 10 | |||||
---|---|---|---|---|---|---|---|---|

Speed (km/h) | FLC | Dir | Sim | Exp | Sim | Exp | Sim | Exp |

10 | Type-1 | Left | −22,995 | −21,176 | −17,739 | −17,731 | −17,082 | −17,062 |

Right | 22,995 | 21,539 | 17,739 | 17,598 | 17,082 | 16,959 | ||

Type-2 | Left | −20,367 | −19,641 | −15,111 | −15,108 | −14,454 | −14,450 | |

Right | 20,367 | 19,639 | 15,111 | 15,097 | 14,454 | 14,431 | ||

20 | Type-1 | Left | −22,995 | −20,691 | −18,396 | −18,376 | −11,169 | −11,169 |

Right | 22,995 | 21,469 | 18,396 | 18,170 | 11,169 | 11,166 | ||

Type-2 | Left | −20,367 | −19,242 | −15,768 | −15,764 | −11,169 | −11,169 | |

Right | 20,367 | 19,604 | 15,768 | 15,702 | 11,169 | 11,163 | ||

30 | Type-1 | Left | −17,082 | −17,044 | −17,082 | −16,185 | −11,169 | −11,169 |

Right | 17,082 | 16,906 | 17,082 | 16,803 | 11,169 | 11,162 | ||

Type-2 | Left | −14,454 | −14,443 | −14,454 | −14,441 | −11,169 | −11,169 | |

Right | 14,454 | 14,430 | 14,454 | 14,424 | 11,169 | 11,164 | ||

40 | Type-1 | Left | −11,169 | −11,169 | −11,169 | −11,169 | −11,169 | −11,166 |

Right | 11,169 | 11,164 | 11,169 | 11,163 | 11,169 | 11,155 | ||

Type-2 | Left | −11,169 | −11,168 | −11,169 | −11,169 | −11,169 | −11,169 | |

Right | 11,169 | 11,160 | 11,169 | 11,164 | 11,169 | 11,158 |

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**MDPI and ACS Style**

Arifin, B.; Suprapto, B.Y.; Prasetyowati, S.A.D.; Nawawi, Z.
Steering Control in Electric Power Steering Autonomous Vehicle Using Type-2 Fuzzy Logic Control and PI Control. *World Electr. Veh. J.* **2022**, *13*, 53.
https://doi.org/10.3390/wevj13030053

**AMA Style**

Arifin B, Suprapto BY, Prasetyowati SAD, Nawawi Z.
Steering Control in Electric Power Steering Autonomous Vehicle Using Type-2 Fuzzy Logic Control and PI Control. *World Electric Vehicle Journal*. 2022; 13(3):53.
https://doi.org/10.3390/wevj13030053

**Chicago/Turabian Style**

Arifin, Bustanul, Bhakti Yudho Suprapto, Sri Arttini Dwi Prasetyowati, and Zainuddin Nawawi.
2022. "Steering Control in Electric Power Steering Autonomous Vehicle Using Type-2 Fuzzy Logic Control and PI Control" *World Electric Vehicle Journal* 13, no. 3: 53.
https://doi.org/10.3390/wevj13030053