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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
If we let x and y be the real and imaginary parts of lT, respectively, that is, lT ¼x þjy, then
x ¼ cos u 1, y ¼ sin u (8:151)
) (x þ 1)
2
þ y
2
¼ cos
2
u þ sin
2
u ¼ 1 (8:152)
and the AB-1 stability boundary is therefore a circle with center at (1, 0) and radius 1 in the lT or
xy plane.
AB-1 integration is inappropriate for simulation of an undamped second-order system, a result
we observed earlier in Section 3.6. The charact eristic roots of a second-order system with z ¼0 are
l ¼jv
n
, and hence lT ¼jv
n
T, which corresponds to the imaginary axis in the lT plane. From
Figure 8.21, it is clear that the imaginary axis lies outside the AB-1 stability region ...
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Publisher Resources

ISBN: 9781439836736