DP6.5 A traffic control system is designed to control the distance between vehicles, as shown in Figure DP6.5

[15].

(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 jω-axis, then let K K = / m N, where N is to be selected. We want the peak time to be Tp ≤ 2 s and the percent overshoot to be P O. . ≤ 20%. Determine an appropri

ate value for N. 

FIGURE DP6.5 Traffic distance control. R(s) Desired distance Controller S Sensor Throttle, engine, and automobile Y(s) 1 +15s +25 Actual distance