Feedback Properties
•
Consider a feedback system
•
and define
•
S
i
=(I+KP)
-1
,
S
o
=(I+PK)
-1
•
T
i
=I-S
i
=KP(I+KP)
-1
, T
o
=I-S
o
=PK(I+PK)
-1
•
Y=T
o
(r-n)+S
o
Pd
i
+S
o
d
•
U=KS
o
(r-n)-KS
o
d-T
i
d
i
U
p
=KS
o
(r-n)-KS
o
d+S
i
d
i
q
Disturbance rejection at the plant output (low frequency):
K
P
-
r
u
d
y
n
u
p
d
i