A traffic control signal is designed to control the distance between vehicles as shown in the following diagram Throttle, engine, Controller and automobile K 1 Y(s) L -- R(s) +f"?\_~-­

Desired ~ f distance - s s2+ 10s+20 Actual Sensor dis tan A Traffic Control Signal Control

(a) Determine the range of gain K for which the system is stable.

(b) If Km is the maximum value of K so that the characteristic roots are on the jw-axis, then K = Km/N where 6 < N < 7. We desire that the peak time be less than 2 seconds and the percentage overshoot be less than 18%. Determine an appropriate value of N.

Problem