Magnetic levitation systems are now used to elevate and propel trains along tracks. A diagram of a demonstration magnetic levitation system is shown in Figure 1(a). Action between a permanent magnet attached to the Ping Pong ball, the object to be levitated and electromagnet provides the lift. The amount of the elevation can be controlled through voltage Va applied to the electromagnet as shown in Figure1 (a). The elevation is controlled by using a photo-detector pair to detect the elevation of the Ping Pong ball. Assume that the elevation control system is represented by Figure 1(b). Design a compensator, Gc(s) to yield a settling time of 0.1 second or less if the step response is to have no more than 1% overshoot. Specify the compensator's poles, zeros and gain. a) b) Cascade another compensator to minimize the steady state error and have the total settling time not the exceed 0.5 second. This compensator should not appreciably the transient response designed in part a. Specify the poles and zeros. c) Simulate the system both for unit step and ramp inputs. Anpiter Blectmnagnet cirult Antlog Control compuler bond Fleredeseesce Fhote entie Compensator Plant Permuneat magret Zgeres () Vs) (2-4551)(s + 286) Ping-Pang bal 10 10 GAS) m Daian line (4) 10 Phoocell (b) Figure 1. Magnetic levitation system