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 and the settling time is less than 3 seconds. Sketch the root locus, and select K so that all of the complex roots have a ζ greater than 0.6. Determine the actual response for the selected K and the percent overshoot.
Figure AP7.2
(a) Magnetically levitated high-speed train.
(b) Feedback control system.

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