Page 101 - Practical Control Engineering a Guide for Engineers, Managers, and Practitioners

DDDI\1\DI\1\DDD
v v vrv vvrvlVlV v v

Y DDDI\1\DI\1\DDI\
V4V v v v \Tv v vlV v

Put in a sinusoidal flow rate U of given amplitude and frequency
-what does the output flow rate Y do?

fKiun 4-2. Frequency response of tank of liquid.

that if the input varies sinusoidally so will the level (and the output
flow rate, too). Assume that the input flow rate is described by

U(t) = Uc +Au sin(21r ft)

The input flow rate has a nominal value of Uc. The flow rate is
varying about the nominal value with an amplitude Au and a fre-
quency f which often has units of hertz or cycles per second. Another
frequency represented by m is the radian frequency, usually having
units of radians per second. It is related to the other frequency by
m = 21r f . Therefore, the input flow rate could also be written as

U(t) = Uc +Au sin(mt)

For the time being, consider the output flow rate F as the process
0
output. In Chap. 3 the level L was the process output. The simple
equations describing these quantities were
dL
1'-+L=RF
df I
L
F=-
o R
or, after combining,

R-rdf, +RF =RF
df 0 I
or (4-1)