DP10.5 High-performance tape transport systems are de

signed with a small capstan to pull the tape past the read/write heads and with take-up reels turned by DC motors. The tape is to be controlled at speeds up to 200 inches per second, with start-up as fast as possi

ble, while preventing permanent distortion of the tape.

Since we wish to control the speed and the tension of the tape, we will use a DC tachometer for the speed sensor and a potentiometer for the position sensor. We will use a DC motor for the actuator. Then the linear model for the system is a unity feedback system with

Y(s) = G(s) = E(s) K(s + 4000) s(s+1000)(s+ 3000)(s + 4000s + 8,000,000)' where Y(s) is position. The specifications for the system are (1) settling time of T, 12 ms, (2) a percent overshoot to a step position command of P.O.