72 6. ROLLOVER CONTROL STRATEGIES AND ALGORITHMS
1/w
1
G
1
8
6
4
2
0
-2
-4
-6
-8
-10
10
-2
10
-1
10
0
10
1
10
2
Frequency (rad/s)
(a) Singular value plot of the sensitivity function
Gain (dB)
1/w
3
G
3
100
50
0
-50
-100
10
-5
10
0
10
5
Frequency (rad/s)
(b) Singular value plot of the complementary sensitivity function
Gain (dB)
Figure 6.8: Singular value plot of the system with H-infinity control.
6.2. H-INFINITY CONTROL METHOD 73
Without Control
Traditional PID Control
Optimized H∞ Control
1
0.5
0
-0.5
-1
-1.5
0 2 4 6 8 10
Time (s)
Rollover Index
Figure 6.9: Rollover indices of the vehicle under the Fishhook case.
the vehicle with the optimized H-infinity control method is lower and varies more smoothly
than that with the traditional PID control method.
Figure 6.10 show the results when the vehicle moves under the double-lane change ma-
neuver. e similar conclusions can be drawn as under the Fishhook case. So, this rollover avoid-
ance control system has a good robustness for different untripped driving situations.
To demonstrate the performance of the rollover avoidance control system when vehicle
runs on a road with bumps, two rollover cases are selected, as follows.
Case I
In a tripped rollover situation, the vehicle rollover happens due to external road input, such as
an unpredictable road bump under the right wheel when vehicle moves on a straight lane. e
maximum height of the road bump is 0.15 m, and the vehicle speed is 100 km/h.
Case II
In this case a combined untripped and tripped rollover due to an unpredictable road bump under
the right wheel while driving in a step steering is studied. e final value of the steering angle
of the front wheel is ı D 2
ı
, the maximum height of the road bump is 0.15 m.
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