An automatically guided vehicle is shown in Figure P12.4(a) and its control system is shown in Figure P12.4(b). The goal is to track the guide wire accurately, to be insensitive to changes in the gain K1, and to reduce the effect of the disturbance [15, 22]. The gain K1 is normally equal to 1 and T1 = 1/25 second.
(a) Select a compensator Gc{s) so that the percent overshoot to a step input is less than or equal to 10%, the settling time (with a 2% criterion) is less than 100 ms, and the velocity constant Kv for a ramp input is 100.
(b) For the compensator selected in part (a), determine the sensitivity of the system to small changes in K1 by determining Sr Ki or STK1.
(c) If K1 changes to 2 while Gc(s) of part (a) remains unchanged, find the step response of the system and compare selected performance figures with those obtained in part (a).
(d) Determine the effect of Td l/(s) = / s by plotting y(t) when R(s) = 0.

il Ta(s) Actuator and wheels Controller Y(s) Direction of travel R(s) Er s(Ts1) wire signal