1 Introduction
2 System Description and Modeling
2.1 System Outline
2.2 Leveling Control Problem
2.3 System Modeling
2.3.1 Thermodynamic Behaviors of the Air Spring
2.3.2 Solenoid Valve Airflow Properties
2.3.3 Full-car Dynamic Model
3 Controller Design
3.1 Linearization of the System Model
3.2 SMC Design
3.3 FSMC Design
4 Simulation Study
Parameter | Value |
---|---|
Mass of the vehicle body m
s
(kg) | 11560 |
Roll moment of inertia I
θ
(kg·m2) | 16750 |
Pitch moment of inertia I
φ
(kg·m2) | 85036 |
Unsprung mass of front wheel m
fr
, m
fl
(kg) | 435 |
Unsprung mass of rear wheel m
rl
, m
rr
(kg) | 845 |
Distance from the centre of gravity to front axis l
f
(m) | 3.32 |
Distance from the centre of gravity to front axis l
r
(m) | 2.38 |
Half of the wheel-track l
a
(m) | 1.21 |
Front wheel damping coefficients cd1, cd2 (N·s·m−1) | 11085 |
Rear wheel damping coefficients cd3, cd4 (N·s·m−1) | 13900 |
Tyre stiffness k
tf
, k
tr
(kN/m) | 650 |
Cross-sectional area of the air spring A
asi
(m2) | 0.042 |
Cross-sectional area of the solenoid valve s (m2) | 7 × 10‒6 |
Volume of the pipeline V
pi
(m3) | 1.7 × 10‒4 |
Air pressure of the air reservoir P
h
(MPa) | 1.8 |
Air pressure of the environment P
e
(Pa) | 1.01 × 105 |
Air temperature T (K) | 293.15 |
Universal gas constant R (J·kg‒1·K‒1) | 287.1 |
Polytropic index k | 1.4 |
Critical pressure ratio b | 0.528 |
Control performance | Simulation scenarios | ||||||
---|---|---|---|---|---|---|---|
During standstill | During driving | ||||||
Vehicle height | Desired value | Actual value | Precision (%) | Desired value | Actual value | Precision (%) | |
Height lifting | h
fr
(m) | 0.270 | 0.2698 | 99.92 | 0.270 | 0.2693 | 99.74 |
h
fl
(m) | 0.270 | 0.2697 | 99.89 | 0.270 | 0.2691 | 99.67 | |
h
rl
(m) | 0.270 | 0.2696 | 99.85 | 0.270 | 0.2685 | 99.44 | |
h
rr
(m) | 0.270 | 0.2696 | 99.85 | 0.270 | 0.2690 | 99.63 | |
Height lowering | h
fr
(m) | 0.250 | 0.2502 | 99.92 | 0.250 | 0.2493 | 99.72 |
h
fl
(m) | 0.250 | 0.2503 | 99.88 | 0.250 | 0.2505 | 99.80 | |
h
rl
(m) | 0.250 | 0.2502 | 99.92 | 0.250 | 0.2491 | 99.64 | |
h
rr
(m) | 0.250 | 0.2503 | 99.88 | 0.250 | 0.2506 | 99.76 |
Posture | Without control | With control | Decrease (%) | Without control | With control | Decrease (%) | |
---|---|---|---|---|---|---|---|
Height lifting | θ (rad) | 0.022 | 0.013 | 40.91 | 0.040 | 0.029 | 27.50 |
φ (rad) | 0.035 | 0.022 | 37.14 | 0.053 | 0.042 | 20.75 | |
Height lowering | θ (rad) | 0.019 | 0.011 | 42.11 | 0.028 | 0.017 | 39.29 |
φ (rad) | 0.023 | 0.016 | 30.43 | 0.054 | 0.036 | 33.33 |