The elevator in Yokohama's 70-story Landmark Tower operates at a peak speed of 45 km/hr. To reach such a speed without inducing discomfort in passengers, the elevator accelerates for longer periods, rather than more precipitously. Going up, it reaches full speed only at the 27th floor; it begins decelerating 15 floors later. The result is a peak acceleration similar to that of other skyscraper elevators-a bit less than a tenth of the force of gravity. Admirable ingenuity has gone into making this safe and comfortable. Special ceramic brakes had to be developed; iron ones would melt. Computer-controlled systems damp out vibrations. The lift has been streamlined to reduce the wind noise as it speeds up and down [19]. One proposed control system for the elevator's vertical position is shown in Figure P6.17. Determine the range of K for a stable system.
Figure P6.17
Elevator control system.

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Elevator dynamics R(s) Desired t vertical position Y(s) Veriical position K + 1 s(33)Vertcal