A magnetically levitated train operated in Berlin, Germany from 1989–1991. Fully automated trains can run at short intervals and operate with excellent energy efficiency. The control system for the levitation of the car is shown in Figure P10.34.Select a compensator so that the phase margin of the system is  45° ≤ P.M. ≤ 55°. Predict the response of the system to a step command, and determine the actual step response for comparison.

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FIGURE P10.34 R(s) Input command Compensator Ge(s) Process 1 s²(s+12) Y(s) Levitation distance