6.20 The dynamics of the turning motion of an automobile are:

CF + CR v +

v

r =

mu

CRLR - CFLF

Ju

(CRLR - CFLF

V

- u)r

+

Vehicle mass m = 1000 kg

Vehicle moment of inertia (yaw axis) J = 15,000 kg-m2

Constant forward speed u = 10 m/s (22 mph)

Front-tire cornering stiffness CF = 55,000 N/rad

Rear-tire cornering stiffness CR= 45,000 N/rad

Moment arm from c.m. to front axle LF= 1 m

Moment arm from c.m. to rear axle LR = 1.5 m

CE SE

m

mu

CRL + CFL CFLF

∙r +

Ju

J

-SF

where u and v are the forward and lateral components of the vehicle's velocity (in m/s), r is the vehicle's

yaw (turning) rate (in rad/s), and SF is the steering angle of the front tire (in rad). The system parameters

of the automobile are [1]

Use MATLAB er Simulink to numerically simulate the turning response to a ramped step input for the

steering angle: SF(t) = t for 0 < t < 0.1 s, 8F(t) = 0.1 rad for t≥ 0.1 s. Let the simulation time be 5 s. Plot

the lateral velocity v(t), yaw rate r(t), and lateral acceleration alat(t) = + ru.