A computer system requires a high-performance magnetic tape transport system [17]. The environmental conditions imposed on the system result in a severe test of control engineering design. A direct-drive DC motor system for the magnetic tape reel system is shown in Figure P7.11, where r equals the reel radius, and J equals the reel and rotor inertia. A complete reversal of the tape reel direction is required in 6 ms, and the tape reel must follow a step command in 3 ms or less. The tape is normally operating at a speed of 100 in/s. The motor and components selected for this system possess the following characteristics:
Kb = 0.40
KP = 1
Ñ‚1 = Ñ‚a = 1ms
KT/(LJ) = 2.0
r = 0.2
K1 = 2.0
K2 is adjustable.
The inertia of the reel and motor rotor is 2.5 X 10-3 when the reel is empty, and 5.0 X 10-3 when the reel is full. A series of photocells is used as an error-sensing device. The time constant of the motor is L/R = 0.5 ms.
(a) Sketch the root locus for the system when K2 = 10 and J = 5.0 X 10-3, 0 (b) Determine the gain Ka that results in a well-damped system so that the ζ of all the roots is greater than or equal to 0.60.
(c) With the Ka determined from part (b), sketch a root locus for 0 Figure P7.11
(a) Tape control system
(b) Block diagram.

Tape reels and motors Capslans Photocells Vacuoni Photocell transducer Amplifier Motor Reel 0.SK+ Desired pusition Tape position MeNor back emf Tachometer