Chemical Engineering Department
University of Florida
ECH 4323
Process Control Theory
HOMEWORK No. 11 — CLOSEDLOOP DYNAMICS
1.0
Consider the standard feedback loop shown in the figure below.
a)
The closedloop relationship between the output and the setpoint and disturbance
variables is given by the equation
′
Y (s) = G
srv
(s)
¢
R (s) + G
reg
(s)
¢
D (s)
where
G
srv
(s)
and
G
reg
(s)
are respectively the servo and regulation transfer
functions for the loop.
Derive
an expression for
G
reg
(s)
and confirm the result
using the rule of thumb discussed in class.
b)
The closedloop relationship between the feedback error and the setpoint and
disturbance variables is given by the equation
′
E (s) = G
er
(s)
¢
R (s) + G
ed
(s)
¢
D (s)
where
G
er
(s)
and
G
ed
(s)
are respectively the closedloop transfer functions
′
E (s)/
¢
R (s)
and
′
E (s)/
¢
D (s)
.
Derive
an expression for
G
ed
(s)
and confirm the
result using the rule of thumb discussed in class.
R
'(
s
)
E
'(
s
)
U
'(
s
)
P
'(s)
D
'(
s
)
Y
'(
s
)
Y
m
'(
s
)
+
+

+
Χοντρολλερ
Αχτυατορ
Τρανσδυχερ
Προχεσσ
Γ
π
(
σ
29
Γ
μ
(
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 Spring '10
 Crissale
 Kc, closedloop transfer functions, closedloop relationship

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