AP7.1 The characteristic equation is 1+ K- 8+6 s(s+4) (82 +48 + 8) = 0. The root locus is shown in Figure AP7.1. The gain at maximum ( is 10 5 -10 0 10 Real Axis FIGURE AP7.1 s(+4) Root locus for 1+ 2+25+2=0. K = 3.7. The roots at K = 3.7 are 81-3.6424 82,3-1.3395 +1.3553j s4= -1.6786. Using Figure 5.13 in Dorf & Bishop, the predicted percent overshoot and settling time are P.O. = 5% and T, = 3 sec. Imag Axis انا -10 s
AP7.1 The characteristic equation is 1+ K- 8+6 s(s+4) (82 +48 + 8) = 0. The root locus is shown in Figure AP7.1. The gain at maximum ( is 10 5 -10 0 10 Real Axis FIGURE AP7.1 s(+4) Root locus for 1+ 2+25+2=0. K = 3.7. The roots at K = 3.7 are 81-3.6424 82,3-1.3395 +1.3553j s4= -1.6786. Using Figure 5.13 in Dorf & Bishop, the predicted percent overshoot and settling time are P.O. = 5% and T, = 3 sec. Imag Axis انا -10 s
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:AP7.1 The characteristic equation is
1+ K-
8+6
s(s+4) (82 +48 + 8).
0.
The root locus is shown in Figure AP7.1. The gain at maximum ( is
10
5
-5
-10
0
10
Real Axis
FIGURE AP7.1
Root locus for 1+ ²+28+2 = 0.
s(s+4)
K = 3.7.
The roots at K = 3.7 are
$13.6424 82,3 = -1.3395 +1.3553j s4= -1.6786.
Using Figure 5.13 in Dorf & Bishop, the predicted percent overshoot and
settling time are
P.O. = 5% and T, = 3 sec,
Imag Axis
O
-10
S
in
5
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