Research on Ride Comfort Control of Air Suspension Based on Genetic Algorithm Optimized Fuzzy PID
Abstract
:1. Introduction
2. Dynamic Modeling of Air Suspension Systems
2.1. Vehicle Model Construction
- (1)
- During vehicle operation, the road surface unevenness excitation experienced by the left and right tires is identical;
- (2)
- The effects of the engine, steering, and drivetrain systems on vibrations are neglected in the modeling process;
- (3)
- The damping of the tires is significantly less than that of the suspension dampers; hence, only the stiffness of the tires is considered, and tire damping is ignored in the modeling;
- (4)
- The time delay effect of the suspension is neglected in the modeling.
2.2. Road Input Model
2.3. Selection of Simulation Parameters
3. Control Algorithm
3.1. PID Controller
3.2. Fuzzy PID Controller
3.2.1. Input and Output of Fuzzy Controller
3.2.2. Selection of Input and Output Variable Domains
3.2.3. Membership Functions of Fuzzy Variables
3.2.4. Establishment of Fuzzy Control Rules
- (1)
- When |e| undergoes significant changes, choose a larger ∆Kp and smaller ∆Ki, ∆Kd to ensure system stability and effectively control the instantaneous deviation;
- (2)
- If there are no significant changes in |e| and |ec|, reduce ∆Kp appropriately and select suitable ∆Ki, ∆Kd based on system requirements to ensure minimal overshoot and effectively reduce system response time;
- (3)
- When |e| changes minimally, increase the values of ∆Kp and ∆Ki, adjusting ∆Kd based on the variation in |ec|. For small |ec|, choose a larger ∆Kd; for large |ec|, choose a smaller ∆Kd;
- (4)
- When e and ec change in the same direction, indicating an increasing error trend, increase ∆Kp; conversely, decrease ∆Kp.
3.3. GA F-PID Controller
3.3.1. Selection of Objective Function
3.3.2. Controller GA Optimization Algorithm
4. Experimental Research
4.1. Air Suspension System Bench Test
4.2. Model Validation
5. Simulation Analysis
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Name | Notation | Value |
---|---|---|
Sprung mass | m2/kg | 500 |
Unsprung mass | m1/kg | 50 |
Suspension damping | c/N·s·m−1 | 1700 |
Tire stiffness | kt/N·m−1 | 200,000 |
Parameters | Rise Time | Overshoot | Setting Time | Steady-State Error |
---|---|---|---|---|
Kp | Decrease | Increase | Slight Change | Decrease |
Ki | Decrease | Increase | Increase | Eliminate |
Kd | Slight Change | Decrease | Decrease | Slight Change |
e | ec | ||||||
---|---|---|---|---|---|---|---|
NB | NM | NS | ZO | PS | PM | PB | |
NB | PB | PB | PM | PM | PS | ZO | ZO |
NM | PB | PB | PM | PS | PS | ZO | NS |
NS | PM | PM | PM | PS | ZO | NS | NS |
ZO | PM | PM | PS | ZO | NS | NM | NM |
PS | PS | PS | ZO | NS | NS | NM | NM |
PM | PS | ZO | NS | NM | NM | NM | NB |
PB | ZO | ZO | NM | NM | NM | NB | NB |
e | ec | ||||||
---|---|---|---|---|---|---|---|
NB | NM | NS | ZO | PS | PM | PB | |
NB | NB | NB | NM | NM | NS | ZO | ZO |
NM | NB | NB | NM | NS | NS | ZO | ZO |
NS | NB | NM | NS | NS | ZO | PS | PS |
ZO | NM | NM | NS | ZO | PS | PM | PM |
PS | NM | NS | ZO | PS | PS | PM | PB |
PM | ZO | ZO | PS | PS | PM | PB | PB |
PB | ZO | ZO | PS | PM | PM | PB | PB |
e | ec | ||||||
---|---|---|---|---|---|---|---|
NB | NM | NS | ZO | PS | PM | PB | |
NB | PS | NS | NB | NB | NB | NM | PS |
NM | PS | NS | NB | NM | NM | NS | ZO |
NS | ZO | NS | NM | NM | NS | NS | ZO |
ZO | ZO | NS | NS | NS | NS | NS | ZO |
PS | ZO | ZO | ZO | ZO | ZO | ZO | ZO |
PM | PB | PS | PS | PS | PS | PS | PB |
PB | PB | PM | PM | PM | PS | PS | PB |
Parameters | Explanation | Parameters | Explanation |
---|---|---|---|
Encoding Method | Binary Encoding | Mutation Function | Constrained Adaptive Mutation |
Initial Population | Randomly Generate Within Specified Bounds | Crossover Probability | 0.9 |
Population Size | 30 | Mutation Function | 0.1 |
Selection Function | Random Uniform Selection | Maximum Evolution Generations | 100 |
Crossover Function | Diversified Crossover | Stopping Generation | 100 |
Evaluation Criteria | Passive Suspension | Fuzzy PID | GA-Fuzzy PID | Percentage of Fuzzy PID Optimization | Percentage of GA-Fuzzy PID Optimization |
---|---|---|---|---|---|
Vehicle Vertical Acceleration (m/s2) | 1.0473 | 0.8169 | 0.7541 | 22% | 28% |
Suspension Wheel Travel (m) | 0.0156 | 0.0129 | 0.0117 | 17% | 25% |
Dynamic Tire Load (kN) | 4.3454 | 4.1281 | 4.0412 | 5% | 7% |
Evaluation Criteria | Passive Suspension | Fuzzy PID | GA-Fuzzy PID | Percentage of Fuzzy PID Optimization | Percentage of GA-Fuzzy PID Optimization |
---|---|---|---|---|---|
Vehicle Vertical Acceleration (m/s2) | 1.8062 | 1.3908 | 1.2643 | 23% | 30% |
Suspension Wheel Travel (m) | 0.0337 | 0.0276 | 0.0249 | 18% | 26% |
Dynamic Tire Load (kN) | 6.0895 | 5.7241 | 5.5414 | 6% | 9% |
Evaluation Criteria | Passive Suspension | Fuzzy PID | GA-Fuzzy PID | Percentage of Fuzzy PID Optimization | Percentage of GA-Fuzzy PID Optimization |
---|---|---|---|---|---|
Vehicle Vertical Acceleration (m/s2) | 2.7638 | 2.0729 | 1.9070 | 25% | 31% |
Suspension Wheel Travel (m) | 0.0611 | 0.0489 | 0.0446 | 20% | 27% |
Dynamic Tire Load (kN) | 8.8378 | 8.3959 | 8.1308 | 5% | 8% |
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Zhang, S.; Li, M.; Li, J.; Xu, J.; Wang, Z.; Liu, S. Research on Ride Comfort Control of Air Suspension Based on Genetic Algorithm Optimized Fuzzy PID. Appl. Sci. 2024, 14, 7787. https://doi.org/10.3390/app14177787
Zhang S, Li M, Li J, Xu J, Wang Z, Liu S. Research on Ride Comfort Control of Air Suspension Based on Genetic Algorithm Optimized Fuzzy PID. Applied Sciences. 2024; 14(17):7787. https://doi.org/10.3390/app14177787
Chicago/Turabian StyleZhang, Shaobo, Mei Li, Jinsong Li, Jie Xu, Zelong Wang, and Shuaihang Liu. 2024. "Research on Ride Comfort Control of Air Suspension Based on Genetic Algorithm Optimized Fuzzy PID" Applied Sciences 14, no. 17: 7787. https://doi.org/10.3390/app14177787