Page 342 - Modern Control Systems

3 1 6 Chapter 5 The Performance of Feedback Control Systems

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I
5.0 .
! <f \ i
-• : \ \ \ ^
v
2.0

i s J
1.0
£»* . : p ^ - ^ \XX
-T "Tti-^x%
1
,
!
0.5 - • • \ \ \ i \ X:
, I s^ iXJ>
" ' i i ' "i
0.2 - i
01 i i i 1 1 1:1:1 , ! ' ' ' I
10 20 50 100 200 500 1000
Percent overshoot
(a)

Time (&>„/)
(b)
FIGURE 5.13 (a) Percent overshoot as a function of £ and &>„ when a second-order transfer
function contains a zero. Redrawn with permission from R. N. Clark, Introduction to Automatic
Control Systems (New York: Wiley, 1962). (b) The response for the second-order transfer function
with a zero for four values of the ratio a/£<o n: A = 5, B = 2, C = 1, and D = 0.5 when £ = 0.45.