Solution 3.8.3.2
Let
Z
1
=
R
1
C
1
s
R
1
+
1
C
1
s
=
R
1
R
1
C
1
s+1
;;
and
Z
2
= R
2
+
1
C
2
s
=
R
2
C
2
s+1
C
2
s
;;
Then
Z
2
Z
1
=
R
2
C
2
s+1
C
2
s
R
1
R
1
C
1
s+1
(C
2
s)(R
1
C
1
s+1)
(C
2
s)(R
1
C
1
s+1)
=
(R
2
C
2
s+1)(R
1
C
1
s+1)
R
1
C
2
s
=
(R
2
=C
1
)(s+(1=R
1
C
1
)(s+(1=R
2
C
2
)
s
:
We next havetochoose some values. We knowthat
R
2
C
1
= 10
1
R
1
C
1
= 0:1
1
R
2
C
2
= 1:
If wechoose
R
1
=10
5
;; C
1
=10
;4
f;; ;; R
2
=10
5
and C
2
=10
;5
f:
Then
G(s)=
;10(s+0:1)(s+1)
s
;;
and wehaveachieved a PID compensator.
1