A rover vehicle designed for use on other planets and moons is shown in Figure DP7.12(a) [21]. The block diagram of the steering control is shown in Figure DP7.12(b), where

(a) When Gc(s) = K, sketch the root locus as K varies from 0 to 1000. Find the roots for K equal to 100, 300, and 600.
(b) Predict the overshoot, settling time (with a 2% criterion), and steady-state error for a step input, assuming dominant roots.
(c) Determine the actual time response for a step input for the three values of the gain K, and compare the actual results with the predicted results.

s 1.5 2)(s 4)(s 10) 1 Y(sy R(5)- | G, ( s) -G'(s) Steering angle FIGURE DP7.12 control system. (a) Planetary rover vehicle. (b) Steering