High-performance tape transport systems are designed 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 possible, 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

where p, = +2000 + /2000, and Y(s) is position.
The specifications for the system are (1) settling time of less than 12 ms, (2) an overshoot to a step position command of less than 10%, and (3) a steady state velocity error of less than .5%. Determine a compensator scheme to achieve these stringent specifications.

(s) E() = G(s) = K(s 4000) s(s 1000) (s 3000)(s +pi)(s p)