AP7.2 A magnetically levitated high-speed train “flies”

on an air gap above its rail system, as shown in Figure AP7.2

(a) [24]. The air gap control system has a unity feedback system with a loop transfer function

The feedback control system is illustrated in Figure AP7.2(b). The goal is to select K so that the response for a unit step input is reasonably damped. Sketch the root locus, and select K so that the Ts ≤ 3 s and

P.O. ≤ 20%. Determine the actual response for the selected K and the percent overshoot.

= L(s) G(s)G(s) K(s+1)(s+2) = s(s-0.5)(s+5)(s+10)