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Simulation of Dynamic Systems with MATLAB and Simulink, 2nd Edition
book

Simulation of Dynamic Systems with MATLAB and Simulink, 2nd Edition

by Harold Klee, Randal Allen
April 2016
Intermediate to advanced content levelIntermediate to advanced
815 pages
31h 29m
English
CRC Press
Content preview from Simulation of Dynamic Systems with MATLAB and Simulink, 2nd Edition
In (a), (b), (c), (d), and (e), the poles p
1
and p
2
are real and distinct. From Equation 4.262, the free
response is the linear combination of natural modes e
p
1
t
and e
p
2
t
. Since
lim
t!1
e
pt
¼
0, p < 0
1, p ¼ 0
1, p > 0
8
>
<
>
:
(4:264)
the two natural modes decay to zero in (a), and the limit L ¼0. Therefore, (a) corresponds to an
asymptotically stable system. In (b), one of the natural modes grows monotonically over time and
L fails to exist. Hence, (b) represents an unstable system. A similar analysis of the remaining cases
(c) through (k) leads to the results shown in Table 4.2.
In summary, the second-order system with transfer function in Equation 4.260 is
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Publisher Resources

ISBN: 9781439836736