P5.1 An important problem for television systems is the jumping or wobbling of the picture due to the movement of the camera. This effect occurs when the camera is mounted in a moving truck or airplane.

The Dynalens system has been designed to reduce the effect of rapid scanning motion; see Figure P5.1.

A maximum scanning motion of 25°/s is expected.

Let K K g t = = 1 and assume that τg is negligi

ble.

(a) Determine the error of the system E s( ).

(b) Determine the necessary loop gain K Ka mKt when a 1°/s steady-state error is allowable.

(c) The motor time constant is τm = 0.40 s. Determine the neces

sary loop gain so that the settling time (to within 2%

of the final value of υb ) is Ts ≤ 0.03 s.