Page 316 - Modern Control Systems

290 Chapter 4 Feedback Control System Characteristics

W
Heater control Electronic circuit
+ i
K
/?(*•) G(s) 1 • >'(-v)
0.U+ 1
+
FIGURE P4.8
Temperature control
system.

P4.9 A useful unidirectional sensing device is the pho- (a) Determine the closed-loop transfer function of the
toemitter sensor [15]. A light source is sensitive to the system, (b) Determine the sensitivity of the system to
emitter current flowing and alters the resistance of the changes in the gain, K.
photosensor. Both the light source and the photocon-
P4.10 For a paper processing plant, it is important to
ductor are packaged in a single four-terminal device.
maintain a constant tension on the continuous sheet
This device provides a large gain and total isolation.
of paper between the wind-off and wind-up rolls. The
A feedback circuit utilizing this device is shown in
tension varies as the widths of the rolls change, and an
Figure P4.9(a), and the nonlinear resistance-current
adjustment in the take-up motor speed is necessary, as
characteristic is shown in Figure P4.9(b) for the
shown in Figure P4.10. If the wind-up motor speed is
Raytheon CK1116. The resistance curve can be repre-
uncontrolled, as the paper transfers from the wind-off
sented by the equation
roll to the wind-up roll, the velocity u 0 decreases and
the tension of the paper drops [10, 14]. The three-
0.175
i
log o * = l/2 roller and spring combination provides a measure of
(/ - 0.005) ' the tension of the paper. The spring force is equal to
where i is the lamp current. The normal operating k ty, and the linear differential transformer, rectifier,
point is obtained when v 0 = 35 V, and v in = 2.0 V. and amplifier may be represented by e () = —k 2y.

/-IN Constant current Dd
^- •/ source = / 0 1 2 3 4 5 6 7 8 9 10
FIGURE P4.9 Lamp current (mA)
Photosensor
system. (a) (b)

Wind-off Wind-up
t'o(')
roll

(o 0U)
Rectifier
J Motor
FIGURE P4.10 Linear Amplifier
Paper tension differential
control. transformer