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.

Fig: 1