Genetic Optimization of Fuzzy Adaptive Cruise Control for Urban Traffic - Fuzzy Modeling and Control: Theory and Applications - page 250

ω =

T w − T b − T r −

J T d (14.10)

where J is the inertia of the wheel, T w the torque provided by the power train (zero

in the case of rear wheels), T b the braking torque applied by the brake, T r the torque
due to the traction force F x :

T r = F x R (14.11)

and T d the torque due to the viscous friction:

T d = C f ω (14.12)

where C f is the friction coefficient.

14.2.4.4 Brake

The brake model is composed of a servovalve and a calliper. The servovalve is
modelled as a first order system:

1 . 5 br − p b

p b = ˙ (14.13)

τ b

where br is the action on the brake pedal, in the range from 0 to 100, p b is the
hydraulic pressure, and τ b is a time constant. With the factor 1.5, the maximum

pressure in the hydraulic circuit is 150bar.
The calliper is simply modelled as a gain K c that converts the hydraulic pressure
into brake pressure. That pressure is finally converted into brake friction torque under
a linear relationship with the angular speed of the wheel:

T b = K b K c p b ω (14.14)

The value of K b is approximately twice as much for the front wheels than for rear
ones, because they generally support greater loads.

14.2.4.5 Power Train

This provides the traction torque to the front wheels. It is composed of the motor,
the torque converter, the gearbox and the differential.
The acceleration of the motor is given by the torque balance:

J e ω e = T e − T p (14.15)