Chemical Engineering Department
University of Florida
ECH 4323
Process Control Theory
HOMEWORK No. 11 — CLOSED-LOOP DYNAMICS
1.0
Consider the standard feedback loop shown in the figure below.
a)
The closed-loop relationship between the output and the set-point 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 closed-loop relationship between the feedback error and the set-point 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 closed-loop 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, closed-loop transfer functions, closed-loop relationship
-
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