Genetic Optimization of Fuzzy Adaptive Cruise Control for Urban Traffic - Fuzzy Modeling and Control: Theory and Applications - page 251

Fig. 14.5 Torque-speed curve of the motor

where J e is the inertia of the motor, ω e its angular speed, which is the same as

the pump of the torque converter, T e the torque due to the combustion, and T p the
resistant torque from the pump of the torque converter.
The maximum torque delivered by the motor ( T max ) is obtained from its torque-
speed curve, which is modelled as a second order polynomial of its speed, as is shown
in Fig. 14.5 . The actual torque ( T e ) is a fraction of that maximum torque, proportional
to the action on the accelerator pedal ( ac ):

T e =

.

0 01 ac T max (14.16)

For the torque converter, an experimentally obtained staticmodel is used (Kotwicki
1982 ). If T p , T t , ω t are the torques and speeds in the pump and the turbine

respectively, the model provides the torques as functions of the speeds:

ω e and

ω t < 0 . 9 ω e

10 − 3

2

10 − 3 10 − 3

2
t

T p = 3 . 4325 · ω

e +

2 . 221 · ω e ω t − 4 . 6041 · ω

10 − 3

2

10 − 3 10 − 3

2
t

T t = 5 . 7656 · ω

e +

0 . 3107 · ω e ω t − 5 . 4323 · ω

ω t ≥ 0 . 9 ω e

10 − 3

2

10 − 3 10 − 3

2
t
(14.17)

T t = T p =− 6 . 7644 · ω

e +

32 . 0024 · ω e ω t − 25 . 2441 · ω

The torque in the turbine is amplified by the gear ratio in the gearbox, which is
modelled as a map that relates the moment of the change of gear with the wheel
speed and the throttle position, as in Fig. 14.6 . The gear ratios used are 3.56, 2.19,
1.41, 1.0 and 0.83 from first to fifth gear respectively.