From Automotive Control Systems: For Engine, Driveline, and Vehicle, Second Edition
10.1 ABS Control Systems
The ABS system aims at minimizing the braking distance while retaining steerability during braking. The shortest braking distance can be reached when the wheels operate at the slip of maximum adhesion co-efficient ? L (Figure 8.17). The tire side slip angle is disregarded here, approximating cos ? ? 1.
10.1.1 Torque Balance at Wheel-Road Contact
By modeling the torque balance at the wheel-road contact, a better understanding can be obtained of how ABS systems are able to operate around maximum friction without sophisticated estimation algorithms. Figure 10.1 shows the forces acting on the wheel.
Figure 10.1: Torque balance at the wheel-road surface contact
In hydraulic brakes, the brake torque at the wheel base depends on the applied braking pressure p Br:
Disregarding the drive torque (at braking), the torque balance is (Equation 9.23):
The respective block diagram is shown in Figure 10.2.
Figure 10.2: Block diagram of torque balance at wheel base
On applying the braking pressure p Br, the brake torque T Br increases. The difference between friction torque T WL and brake torque T Br is negative, resulting in a wheel deceleration. The wheel rotational equivalent velocity v R (after the integrator in Figure 10.2) starts to decrease and yields an increasing slip s L. At first the friction co-efficient ? L( s L) increases as well, building up the friction torque T WL which narrows the torque difference.
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