(Solution) - Magnetic levitation maglev trains may replace airplanes on routes shorter -(2025 Original AI-Free Solution)

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Magnetic levitation (maglev) trains may replace airplanes on routes shorter than 200 miles. The maglev train developed by a German firm uses electromagnetic attraction to propel and levitate heavy vehicles, carrying up to 400 passengers at 300-mph speeds. But the j-inch gap between car and track is difficult to maintain [7,12,17].
The block diagram of the air-gap control system is shown in Figure P12.3.The compensator is

(a) Find the range of K for a stable system, (b) Select a gain so that the steady-state error of the system is less than 0.1 for a step input command, (c) Find y(t) for the gain of part (b). (d) Find y (t) when K varies ±15% from the gain of part (b).