# Research on Height Adjustment Characteristics of Heavy Vehicle Active Air Suspension Based on Fuzzy Control

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Design of Active Air Suspension System

#### 2.1. Working Principle of Active Air Suspension System

#### 2.2. Structural Design of Active Air Spring System

#### 2.3. Design of Air Suspension Height Adjustment Controller

## 3. Active Air Suspension System Modeling

#### 3.1. Establishment of Pavement Excitation Model

#### 3.1.1. Random Signal Road Excitation

_{0}—reference spatial frequency, and ${G}_{q}\left({n}_{0}\right)$—pavement roughness coefficient, which is the pavement power spectral density in the n

_{0}state, ${\sigma}_{q}$—standard deviation of road roughness, and w—frequency index.

_{0}= 0.1 m

^{−1}and w = 2 in Formula (1), the geometric average value of pavement roughness of each pavement grade is shown in Table 3 [31].

^{−1}, it is more consistent with the real situation. At this time, the expression of the time–frequency power spectral density can be written as Formula (5):

_{min}—time lower limit cut-off frequency.

#### 3.1.2. Construction of Random Signal Pavement Model

#### 3.2. Establishment of Air Suspension Model

#### 3.2.1. Modeling of Single-Axle Four-Airbag Passive Air Suspension System

#### 3.2.2. Modeling of 1/4 Active Air Suspension System

_{s}is the sprung mass, m

_{t}is the unsprung mass, F

_{a}is the active control force of the controller, k

_{t}is the tire stiffness, k

_{s}is the stiffness of the suspension system, c

_{s}is the damping coefficient of the suspension system, q is the road displacement function, x

_{t}is the vertical displacement of the equivalent unsprung mass of the suspension, x

_{s}is the vertical displacement of the unsprung mass of the suspension system, and x

_{r}is the pavement displacement.

_{s}and m

_{t}as the research objects, respectively, the vibration differential equation of the two degree of freedom active air suspension system model can be established using Newton’s second law, as shown in the Equations (10) and (11):

#### 3.3. Design of Fuzzy PID Controller

_{p}, K

_{i}, and K

_{d}) are dynamically adjusted using specific fuzzy control rules.

#### 3.3.1. Fuzzy Quantization of Controller Parameters

_{p}= {NB,NM,NS,Z,PS,PM,PB}

_{i}= {NB,NM,NS,Z,PS,PM,PB}

_{d}= {NB,NM,NS,Z,PS,PM,PB}

#### 3.3.2. Establishment of Fuzzy PID Membership Function

#### 3.3.3. Design of Fuzzy PID Controller

_{p}value is increased, the K

_{i}value is decreased, and to avoid differential saturation and excessive overshoot in the system response, the K

_{d}value is set to 0. (2) When the product of E and EC is greater than 0, it indicates that the absolute value of the system state error is continuously increasing. When the absolute value of E is not significantly different from the absolute value of EC, the system is in the tracking stage. To reduce system overshoot, the values of K

_{p}, K

_{i}, and K

_{d}should not be too large. When the absolute value of E is relatively large, the K

_{p}value can be appropriately increased, the K

_{i}value decreased, and the K

_{d}value set to a medium level to ensure the system’s dynamic and steady-state performance. When the absolute value of E is small, a large K

_{d}value, a large K

_{i}value, and a medium K

_{p}value should be used to prevent system oscillations. (3) When the product of E and EC is less than 0, it indicates that the error is decreasing. When the absolute value of E is relatively large, to ensure the system’s dynamic and steady-state performance, a medium K

_{p}value, a smaller K

_{i}value, and a medium K

_{d}value should be selected. When the absolute value of E is small, to maintain good steady-state performance, both K

_{p}and K

_{i}values should be increased, and a medium K

_{d}value is appropriate.

_{p}, ΔK

_{i}, and ΔK

_{d}, are mainly derived from fuzzy control theory combined with expert experience.

## 4. Simulation Results and Analysis

- (1)
- SMA, which is the difference between the vertical body acceleration and the wheel acceleration, is a crucial parameter that measures the smoothness of heavy vehicle driving and can be utilized to evaluate the driving performance and comfort.
- (2)
- DTL, which is the difference between body displacement and wheel displacement, is a significant indicator of the handling stability of heavy vehicles and can reflect the body attitude. In simulation analyses, it is usually represented by Dynamic Tire Deformation (DTD).
- (3)
- SWS, which is the difference between the wheel displacement and the road input displacement, is a crucial index used to evaluate the grounding stability of heavy vehicles [35].

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**Schematic diagram of body height control of double-axle eight-airbag active air suspension.

**Figure 6.**(

**a**) Road roughness curve under condition 1 (Class A pavement, 30 km/h) and condition 2 (Class A pavement, 60 km/h); (

**b**) Road roughness curve under condition 3 (Class C pavement, 30 km/h) and condition 4 (Class C pavement, 60 km/h).

**Figure 13.**(

**a**) Membership function of input variable E; (

**b**) Membership function of input variable EC.

**Figure 14.**(

**a**) Membership function of output variable Δk

_{p}; (

**b**) Membership function of output variable Δk

_{i}; (

**c**) Membership function of output variable Δk

_{d}.

**Figure 15.**(

**a**) Observation diagram of the membership function of ΔK

_{p}; (

**b**) Observation diagram of the membership function of ΔK

_{i}; (

**c**) Observation diagram of the membership function of ΔK

_{d}.

**Figure 18.**Time-domain comparison of vibration curves for the air suspension system of heavy-duty vehicles on Grade A pavement at 30 km/h. (

**a**) Body acceleration SMA. (

**b**) Suspension dynamic travel DTD. (

**c**) Tire dynamic load SWS.

**Figure 19.**Time-domain comparison of vibration curves for the air suspension system of heavy-duty vehicles on Grade A pavement at 60 km/h. (

**a**) Body acceleration SMA. (

**b**) Suspension dynamic travel DTD. (

**c**) Tire dynamic load SWS.

**Figure 20.**Time-domain comparison of vibration curves for the air suspension system of heavy-duty vehicles on Grade C pavement at 30 km/h. (

**a**) Body acceleration SMA. (

**b**) Suspension dynamic travel DTD. (

**c**) Tire dynamic load SWS.

**Figure 21.**Time-domain comparison of vibration curves for the air suspension system of heavy-duty vehicles on Grade C pavement at 60 km/h. (

**a**) Body acceleration SMA. (

**b**) Suspension dynamic travel DTD. (

**c**) Tire dynamic load SWS.

Name | Numerical Value | Name | Numerical Value |
---|---|---|---|

Wheelbase | 3200 + 1400 mm | Total mass (full load) | 25 t |

Allowable load of front axle | 7000 kg | Vehicle weight (No load) | 8.8 t |

Permissible rear axle load | 18,000 kg | Body length | 6985 mm |

Front track width | 2041 mm | Body width | 2496 mm |

Rear track width | 1830 mm | Body height | 3850 mm |

Name | Numerical Value |
---|---|

Design load (full load) | 18,000 kg |

Suspension height | 210 mm |

Double-axle wheelbase | 1400 mm |

Suspension width | 762 mm |

Drive axle elevation | 3° |

Different Pavement Grades | ${\mathit{G}}_{\mathit{q}}\left({\mathit{n}}_{0}\right)/\left({10}^{-6}{\mathbf{m}}^{3}\right)$ | ${\mathit{\sigma}}_{\mathit{q}}/\left({10}^{-6}{\mathbf{m}}^{3}\right)$ |
---|---|---|

Geometric Mean | Geometric Mean | |

A | 16 | 3.81 |

B | 64 | 7.61 |

C | 256 | 51.23 |

D | 1024 | 30.45 |

E | 4096 | 60.90 |

F | 16,384 | 121.80 |

G | 65,336 | 243.61 |

H | 262,144 | 487.22 |

Working Condition | Description |
---|---|

Condition 1 | Class A pavement, 30 km/h |

Condition 2 | Class A pavement, 60 km/h |

Condition 3 | Class C pavement, 30 km/h |

Condition 4 | Class C pavement, 60 km/h |

ec | NB | NM | NS | Z | PS | PM | PB | |

e | ||||||||

NB | NB | NM | NM | NS | Z | Z | ||

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

NS | NM | Z | PS | |||||

Z | NS | Z | PS | PM | ||||

PS | NS | Z | PS | |||||

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

PB | Z | PM | PB |

ec | NB | NM | NS | Z | PS | PM | PB | |

e | ||||||||

NB | NB | NM | NS | Z | ||||

NM | NS | NS | ||||||

NS | NM | NS | Z | PS | ||||

Z | NS | Z | PS | PM | ||||

PS | NM | NS | Z | PM | PB | |||

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

PB | PS |

ec | NB | NM | NS | Z | PS | PM | PB | |

e | ||||||||

NB | NS | PS | PB | PM | Z | |||

NM | PM | Z | ||||||

NS | Z | PM | PS | |||||

Z | ||||||||

PS | ||||||||

PM | NB | PS | NS | NB | ||||

PB | NM |

Name | Numerical Value | Unit |
---|---|---|

Sprung mass | 5000 | Kg |

Unsprung mass | 602 | Kg |

Suspension vertical stiffness | 241,200 | N/m |

Wheel stiffness | 192,000 | N/m |

Suspension damping | 6875.505 | N × s/m |

RMS | Pavement Grade | Vehicle Speed | Fuzzy PID Control | Uncontrolled | Improvement Rate |
---|---|---|---|---|---|

Body vertical acceleration (SMA) | A | 30 km/h | 0.03950 m/s^{−2} | 0.05082 m/s^{−2} | 22.3% |

A | 60 km/h | 0.05466 m/s^{−2} | 0.0702 m/s^{−2} | 22.1% | |

C | 30 km/h | 0.1580 m/s^{−2} | 0.2033 m/s^{−2} | 22.3% | |

C | 60 km/h | 0.2186 m/s^{−2} | 0.2808 m/s^{−2} | 22.2% | |

Suspension dynamic travel (DTD) | A | 30 km/h | 0.002424 m | 0.002951 m | 17.9% |

A | 60 km/h | 0.003050 m | 0.003821 m | 20.1% | |

C | 30 km/h | 0.009695 m | 0.01180 m | 17.8% | |

C | 60 km/h | 0.01220 m | 0.01528 m | 20.1% | |

Tire dynamic load (SWS) | A | 30 km/h | 0.001957 m | 0.002186 m | 10.5% |

A | 60 km/h | 0.002363 m | 0.002707 m | 12.7% | |

C | 30 km/h | 0.007828 m | 0.008745 m | 10.5% | |

C | 60 km/h | 0.009453 m | 0.010833 m | 11.9% |

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**MDPI and ACS Style**

Bai, X.; Lu, L.; Zhang, C.; Geng, W.
Research on Height Adjustment Characteristics of Heavy Vehicle Active Air Suspension Based on Fuzzy Control. *World Electr. Veh. J.* **2023**, *14*, 210.
https://doi.org/10.3390/wevj14080210

**AMA Style**

Bai X, Lu L, Zhang C, Geng W.
Research on Height Adjustment Characteristics of Heavy Vehicle Active Air Suspension Based on Fuzzy Control. *World Electric Vehicle Journal*. 2023; 14(8):210.
https://doi.org/10.3390/wevj14080210

**Chicago/Turabian Style**

Bai, Xin, Liqun Lu, Can Zhang, and Wenpeng Geng.
2023. "Research on Height Adjustment Characteristics of Heavy Vehicle Active Air Suspension Based on Fuzzy Control" *World Electric Vehicle Journal* 14, no. 8: 210.
https://doi.org/10.3390/wevj14080210