# Design of Auto-Tuning Nonlinear PID Tracking Speed Control for Electric Vehicle with Uncertainty Consideration

## Abstract

**:**

## 1. Introduction

## 2. System Modeling

_{rr}), aerodynamic drag force (F

_{ad}), gravitational force (F

_{g}), and force due to vehicle acceleration (F

_{a}), as shown in Figure 2. Hence, the total traction force (F

_{t}) acting on a vehicle is given by the following:

_{t}= F

_{rr}+ F

_{ad}+ F

_{g}+ F

_{a}= μ

_{rr}mg + 0.5ρAC

_{d}v

^{2}+ mgsinφ + m dv/dt

_{rr}is the rolling resistance coefficient, ρ is the air density, A is the frontal area of the vehicle, C

_{d}is the drag coefficient, and φ is the hill-climbing angle.

## 3. Auto-Tuning Nonlinear PID Control

_{rd}) is the desired rise time and (t

_{r}) is the measured rise time; (O

_{sd}) is the desired maximum overshoot and (OS) is the actual overshoot; (t

_{sd}) is the desired settling time and (t

_{s}is the determining settling time; and (e

_{ssd}) is the desired steady-state error and (e

_{ss}) is the estimated steady-state error.

## 4. Results and Discussion

## 5. Conclusions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Schematic of external obstacles affecting a running EV [7].

**Figure 8.**The corresponding currents of the PID, NPID, and auto-tuning NPID to track the NEDC speed test.

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

${L}_{a}$+${L}_{f}$ | 6.008 mH | $m$ | 800 kg |

${R}_{a}$+${R}_{f}$ | 0.12 $\mathsf{\Omega}$ | $A$ | 1.8 m^{2} |

${L}_{af}$ | 0.001 mH | $\rho $ | 1.25 (kg/m^{3}) |

$i$ | 78 A (250 max) | $\phi $ | 0$\xb0$ |

$V$ | 0:48 V | ${C}_{d}$ | 0.3 |

$B$ | 0.0002 N.M.s | ${\mu}_{rr}$ | 0.015 |

$J$ | 0.05 Kg.m^{2} | $G$ | 11 |

$\omega $ | 25 Km/h | r | 0.25 m |

Parameter | Variation % |
---|---|

Ra + Rf | +10 |

La + Lf | −20 |

r | +25 |

J | −20 |

m | +30 |

Cd | −20 |

μrr | +30 |

Controller Type | Parameter | Value |
---|---|---|

PID control | ${k}_{p}$ | 5.254 |

${k}_{i}$ | 0.05 | |

${k}_{d}$ | 0.02 | |

NPID Control | ${k}_{p}$ | 10.23 |

${k}_{i}$ | 2.23 | |

${k}_{d}$ | 1.58 | |

${w}_{1}$ | 0.25 | |

${w}_{2}$ | 0.34 | |

${w}_{3}$ | 0.01 | |

Auto-Tuning NPID Control | ${k}_{p}$(0) | 6.35 |

${k}_{i}\left(0\right)$ | 0.125 | |

${k}_{d}\left(0\right)$ | 2.31 | |

${w}_{1}\left(0\right)$ | 0.45 | |

${w}_{2}\left(0\right)$ | 0.69 | |

${w}_{3}\left(0\right)$ | 0.78 |

Controller Type | Peak Current (A) | Average Current (A) |
---|---|---|

PID controller | 1.35 | 0.912 |

NPID controller | 1.36 | 0.851 |

Auto-tuning NPID controller | 1.33 | 0.712 |

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**MDPI and ACS Style**

Shamseldin, M.A.
Design of Auto-Tuning Nonlinear PID Tracking Speed Control for Electric Vehicle with Uncertainty Consideration. *World Electr. Veh. J.* **2023**, *14*, 78.
https://doi.org/10.3390/wevj14040078

**AMA Style**

Shamseldin MA.
Design of Auto-Tuning Nonlinear PID Tracking Speed Control for Electric Vehicle with Uncertainty Consideration. *World Electric Vehicle Journal*. 2023; 14(4):78.
https://doi.org/10.3390/wevj14040078

**Chicago/Turabian Style**

Shamseldin, Mohamed A.
2023. "Design of Auto-Tuning Nonlinear PID Tracking Speed Control for Electric Vehicle with Uncertainty Consideration" *World Electric Vehicle Journal* 14, no. 4: 78.
https://doi.org/10.3390/wevj14040078