6.5. SLIDING MODE CONTROL METHOD 91
So
u
d
D ı D
Ry
d
C Py
d
"sgn."/
.
a
1
C
/
Py C a
2
Pr
a
3
: (6.63)
And then, a fuzzy control is used to optimized these two sliding mode controllers.
J-turn manueuver is used to verify the effectiveness of the sliding mode controllers. Vehicle
speed in the simulations is set to 80 km/h and the default front-wheel steering angle in
J-turn manueuver is set to 4.8
ı
/s, which induces rollover easily. e dynamic responses of
uncontrolled, first, and second kind of sliding mode control and the optimized controllers
are shown in Figure 6.17.
Figure 6.17a shows that the trace under the first kind of control is far away from the desired
trace and the trace under the second kind of control is almost consistent with the desired trace.
e trace under the optimized control is between the traces under the first and second kind
of control. e responses of rollover dynamic index LTR in Figure 6.17b shows that all three
control methods can prevent the vehicle rollover. However, the value of LTR in the second kind
of control is nearly reaching 0.9, which means the vehicle is unstable. Instead, the value of LTR
can be reduced to about 0.5 in 3 s under the first kind of control. And the value of LTR can
be reduced under 0.8 through the optimized control method. From these two figures, it can
be concluded that the first kind of control method can prevent the vehicle rollover effectively
but cannot track the desired trace. e second kind of control method have good track tracking
effect, but the response of LTR shows that this method is under the risk of rollover. e optimized
control does combine the advantages of the first two controls. e tracking error is reduced more
than 30 m, and the tracking error is stabilized within 10 m. e value of LTR reaches about 0.6,
and rises slowly to about 0.78, so as to track the desired trace.
Figure 6.17c shows the front-wheel steering angle under the three-control method com-
paring the steering angle without control. e steering angle of the first kind of control varies
greatly, while the shimmy appears in the second kind of control. ough this two-control
method can reach the designed purpose separately, these situations can cause occupant dis-
comfort and adverse factors to steering system. e optimized control reduces the front-wheel
angle variation, eliminate the shimmy, avoid the disadvantages of the first two control methods.
Figures 6.17d–f show the dynamic responses of roll state which includes roll angle and roll
rate and yaw rate. e response of roll rate is similar with the response of the LTR. e first kind
of control method shows its advantages, and the performance of optimized control method is
between the first and second kind of control method. e response of yaw rate of the first kind of
control is little, but it cannot support the need of trace tracking, as the steering angle is less than
the default value in Figure 6.17f. e response of yaw rate of the second kind of control changes
greatly, which will bring discomfort to the occupant. e value and variation of the response of
yaw rate of the optimized control are between the first two kinds of control.
92 6. ROLLOVER CONTROL STRATEGIES AND ALGORITHMS
Desired Trace
Control-1
Control-2
Optimized Control
0 20 40 60 80 100 120 140 160
140
120
100
80
60
40
20
0
X Coordinate (m)
Y Coordinate (m)
(a)
0 2 4 6 8 10
1
0.8
0.6
0.4
0.2
0
Time (s)
LTR
(b)
No Control
Control-1
Control-2
Optimized Control
Figure 6.17: e control performance verification under J-turn maneuver. (Continues.)
6.5. SLIDING MODE CONTROL METHOD 93
0 2 4 6 8 10
7
6
5
4
3
2
1
0
Time (s)
Front Wheel Steering Angle (deg)
(c)
No Control
Control-1
Control-2
Optimized Control
0 2 4 6 8 10
15
10
5
0
Time (s)
Roll Angle (deg)
(d)
No Control
Control-1
Control-2
Optimized Control
Figure 6.17: (Continued.) e control performance verification under J-turn maneuver. (Contin-
ues.)
94 6. ROLLOVER CONTROL STRATEGIES AND ALGORITHMS
0 2 4 6 8 10
20
15
10
5
0
T
ime (s)
Roll Rate (deg)
(e)
No Control
Control-1
Control-2
Optimized Control
0 2 4 6 8 10
25
20
15
10
5
0
Time (s)
Yaw Rate (deg/s)
(f )
No Control
Control-1
Control-2
Optimized Control
Figure 6.17: (Continued.) e control performance verification under J-turn maneuver.
6.6. SUMMARY 95
6.6 SUMMARY
To sum up, there are many kinds of rollover control strategies and algorithms used to prevent
vehicle rollover such as PID control, LQR control, H-infinity control controller, sliding mode
control, and MPC control. To achieve better control effect, it is better to optimize the controller
for different vehicles or employ the combination of one or more controller to complement each
other.
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