# Analysis of Active Suspension Control Based on Improved Fuzzy Neural Network PID

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Active Suspension Simulation Model

- The elastic center of the vehicle body coincides with the center of mass;
- The vehicle body is rigid, and the occupants move in the same way as the vehicle body;
- There is no sliding between the tires and the road, and the wheels are always in contact with the ground;
- The vertical vibration characteristics of the wheel are reduced by a spring that does not take into account the damping effect.

#### 2.2. Road Excitation Model

#### 2.2.1. White Noise Road Excitation

#### 2.2.2. Step Noise Road Excitation

#### 2.3. Controller Design Principle

#### 2.3.1. FNN-PID Controller

#### 2.3.2. PID Control

#### 2.3.3. FNN Control

#### 2.3.4. FNN Optimization Algorithm

- Gradient Descent;

- 2.
- Particle swarm algorithm

#### 2.3.5. Hybrid Algorithm Optimization Process

- The fuzzy neural network parameters, ${\mathrm{c}}_{\mathrm{ij}},{\mathrm{b}}_{\mathrm{ij}},{\mathsf{\omega}}_{\mathrm{s}}^{\mathrm{j}}$, are initialized;
- Particle swarm initialization. Parameters such as those of population size, particle dimensions, and initial inertia weight, as well as learning factor, are set first, after which a set of particle positions is generated at random and the particle’s maximum and minimum velocities are determined; between the extremes of highest and minimum velocity, each particle’s velocity is determined randomly;
- After updating the velocity and position of the particle, the fitness value of the particle at each iteration step is calculated, and the individual optimal extremum, ${\mathrm{p}}_{\mathrm{ibest}}$, and the population optimal extremum, ${\mathrm{p}}_{\mathrm{gbest}}$, are updated;
- If the termination condition is satisfied, the corresponding network parameters are passed to the FNN;
- The FNN acquires the initial values of the parameters and then calculates them and updates the network parameters online by back-propagation through the gradient descent method. The final optimal solutions are output.

## 3. Results

## 4. Discussion

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 8.**Plot of vehicle vertical displacement change under step signal. (

**a**) The step signal is 0.01 m. (

**b**) The step signal is 0.05 m. (

**c**) The step signal is 0.08 m.

Road Grade | $\mathbf{Geometric}\mathbf{Mean}\mathbf{of}\mathbf{Power}\mathbf{Spectral}\mathbf{Density}{\mathbf{G}}_{\mathbf{q}}\left({\mathbf{n}}_{0}\right)/{10}^{-6}{\mathbf{m}}^{3}$ |
---|---|

A | 16 |

B | 64 |

C | 256 |

D | 1024 |

Variable | Value |
---|---|

Sprung mass M/kg | 240 |

Unsprung mass m/kg | 30 |

Tire stiffness K_{1}/(N/m) | 160,000 |

Spring rate K_{2}/(N/m) | 16,000 |

Suspension damping c/(N•s)/m | 980 |

Index | Passive | PID Controller | FNN-PID Controller |
---|---|---|---|

SMA (m/s^{2}) | $2.265\times {10}^{-2}$ | $1.838\times {10}^{-2}$ | $1.570\times {10}^{-2}$ |

DDS (m) | $2.896\times {10}^{-4}$ | $2.502\times {10}^{-4}$ | $2.219\times {10}^{-4}$ |

DTD (m) | $3.671\times {10}^{-5}$ | $3.350\times {10}^{-5}$ | $3.074\times {10}^{-5}$ |

Class | Index | Passive | PID Controller | FNN-PID Controller |
---|---|---|---|---|

A | SMA (m/s^{2}) | 0.0490 | 0.0391 | 0.0334 |

DDS (m) | $6.735\times {10}^{-4}$ | $6.286\times {10}^{-4}$ | $5.525\times {10}^{-4}$ | |

DTD (m) | $7.017\times {10}^{-5}$ | $6.701\times {10}^{-5}$ | $5.890\times {10}^{-5}$ | |

B | SMA (m/s^{2}) | 0.0979 | 0.0782 | 0.0681 |

DDS (m) | $1.346\times {10}^{-3}$ | $1.254\times {10}^{-3}$ | $1.107\times {10}^{-3}$ | |

DTD (m) | $1.402\times {10}^{-4}$ | $1.336\times {10}^{-4}$ | $1.185\times {10}^{-4}$ | |

C | SMA (m/s^{2}) | 0.1820 | 0.1440 | 0.1257 |

DDS (m) | $2.515\times {10}^{-3}$ | $2.319\times {10}^{-3}$ | $2.012\times {10}^{-3}$ | |

DTD (m) | $2.576\times {10}^{-4}$ | $2.508\times {10}^{-4}$ | $2.151\times {10}^{-4}$ | |

D | SMA (m/s^{2}) | 0.3476 | 0.2673 | 0.2390 |

DDS (m) | $4.747\times {10}^{-3}$ | $4.354\times {10}^{-3}$ | $3.820\times {10}^{-3}$ | |

DTD (m) | $4.933\times {10}^{-4}$ | $4.602\times {10}^{-4}$ | $4.003\times {10}^{-4}$ |

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**MDPI and ACS Style**

Li, M.; Li, J.; Li, G.; Xu, J.
Analysis of Active Suspension Control Based on Improved Fuzzy Neural Network PID. *World Electr. Veh. J.* **2022**, *13*, 226.
https://doi.org/10.3390/wevj13120226

**AMA Style**

Li M, Li J, Li G, Xu J.
Analysis of Active Suspension Control Based on Improved Fuzzy Neural Network PID. *World Electric Vehicle Journal*. 2022; 13(12):226.
https://doi.org/10.3390/wevj13120226

**Chicago/Turabian Style**

Li, Mei, Jiapeng Li, Guisheng Li, and Jie Xu.
2022. "Analysis of Active Suspension Control Based on Improved Fuzzy Neural Network PID" *World Electric Vehicle Journal* 13, no. 12: 226.
https://doi.org/10.3390/wevj13120226