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5.4. ACTIVE BRAKING SYSTEM 55
Vehicle Dynamics Control
Information Driver Input
Force and Moment of Vehicle
Lateral and Longitudinal Forces of Tires
Driving Torque, Brake Pressure, Steer Angle
Force and Moment Distribution
Wheel Control
Actuator
(Result)
(Target)
Figure 5.5: Hierarchical vehicle dynamics management algorithm.
Vehicle Dynamics Control: this layer calculates the target force and moment of the vehicle
to achieve a desirable vehicle motion corresponding to the drivers pedal input and steering
wheel angle. e determined target resultant force and moment also satisfy the robust stability
condition.
Force and Moment Distribution: the target resultant force and moment of the vehicle
motion are distributed to target tire forces of each wheel based on the friction circle of each
wheel in this layer.
Wheel Control: this layer controls each wheel motion to achieve the target tire force.
5.4 ACTIVE BRAKING SYSTEM
Diﬀerential braking system applies unequal braking force to the diﬀerent wheels, which gener-
ates a corresponding additional yawing moment to change the yaw rate of the vehicle. On the
other hand, it can also decrease the vehicle speed, thus the anti-rollover property of vehicle is
improved. Some researchers used diﬀerential braking to keep the value of LTR below a certain
level and yield robustness to variations in vehicle speed [29, 55]. More control eﬀort would be
exerted for drivers with poor driving skills, and vice versa. Zhu proposed a sliding mode con-
trol (SMC)-based diﬀerential braking controller which based on a novel driver-adaptive Vehicle
Stability Control (DAVSC) strategy [20].
Figure 5.6 shows the yaw moment change when the braking force is applied at front-inner
wheel, rear-inner wheel, front-outer wheel, and rear-outer wheel, respectively. It is observed that
applying the braking force to the front-outer wheel or rear-inner wheel can better prevent the
vehicle from yaw motion, thus improving the roll stability of the vehicle.
56 5. ACTIVE CONTROL FOR VEHICLE ROLLOVER AVOIDANCE
Inward
Fx
5,000
Br
aking Force: Fx (N)
Rear-Inner
Wheel
Rear-Outner
Wheel
Front-Inner
Wheel
Front-Outner
Wheel
Yaw Moment Change: M (N-m)
5,000
0
-5,000
Outward
M
Figure 5.6: Yaw moment change.
ß
r
ß
f
δ
F
r
F
f
u
r
b
a
y
x
o
Figure 5.7: Bicycle vehicle model.
Although the actuator can provide enough brake torque, its magnitude at each wheel is
still limited by some other factors, such as the coeﬃcient of road adhesion and tires vertical load.
From the bicycle vehicle model shown in Figure 5.7, the brake force at each wheel is constrained
by:
F
b2
mg.1 C LTR/
2.a C b/
; (5.2)
where is the coeﬃcient of road adhesion, and F
b
is the brake force of front-outer wheel.
5.4. ACTIVE BRAKING SYSTEM 57
e yaw torque can be then expressed as:
M
B
D
T
w
2
.
F
b1
F
b2
/
:
(5.3)
As known in the above section, diﬀerential braking is one of the main techniques for
vehicle rollover avoidance. Also, Electro Hydraulic Brake (EHB) systems can produce enough
brake torques fast enough for rollover prevention. e model and dynamic characteristics of an
EHB was studied theoretically and mathematically in Yong et al.s previous research [56].
Figure 5.8 shows a hydraulic scheme of electro hydraulic brake system including two dif-
ferent electro hydraulic valves. e ﬁrst are controlled by Pulse Width Modulation (PWM)
from the Electronic Control Unit (ECU), including inlet valves and outlet valves. e second
are on/oﬀ valves, such as balance valves and cut valves. All the valves are 2/2 solenoid valve.
ECU
PFE
HCU
RL
IV
BV BV
CV
M
CV
CV
OV IV OV IV OV IV OV
FL FRRR
P
U
P
U
P
U
P
U
P
U
P
U
S
U
Figure 5.8: Hydraulic scheme of Electro Hydraulic Brake system.
When the driver brakes, in normal operation, the stroke sensor unit receives the signal of
drivers brake intention and sends it to ECU. For the ECU switching the solenoid valves into
diﬀerent state. ere are three operation modes of EHB system.
(1) Pressure build-up. e inlet valve and cut valve act in opposition state to each other, the
inlet valve is open and the cut valve closed. Since the outlet valve holds initial state closed, the
wheel brake cylinder is connected to a high-pressure accumulator fed by a pump. e brake ﬂuid
ﬂows out of the high-pressure accumulator into the wheel brake cylinder and the brake pressure
increases. (2) Pressure holding. Depending on requirements, as soon as enough pressure has
been obtained in the wheel brake cylinder, the solenoid valves are switched to pressure holding
state. In this state, all three valves are closed with respect to each other. e connections from
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