Solution: 7.9.3.1
For the system of Figure 1 wehave
R
+ C
G
c
G
p
Σ
-
Figure 1: Cascade Compensation with UnityFeedback
G
p
=
10
s(s +1)
;; and G
c
=
13:8(s+3:26)
s +30
:
The following MATLAB dialogue generates the step response in Figure 2.
EDU>g = zpk([-3.26],[0 -1 -30],138)
Zero/pole/gain:
138 (s+3.26)
--------------
s(s+1) (s+30)
EDU>h = 1
h=
1
EDU>tc = feedback(g,h)
Zero/pole/gain:
138 (s+3.26)
----------------------
(s+25) (s^2 + 6s + 18)
EDU>step(tc,2)
EDU>print -deps lead0step.eps
EDU>
1
Time (sec.)
Amplitude
Step Response
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Figure 2: Step Response for G
c
=
13:8(s+3:26)
s+30
2