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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
The natural modes from Equation 7.166 are s
1
, s
2
¼(13.5022)
1=2
¼j 3.6745, and the frequency
of undamped oscillations is v
n
¼3.6745 rad=s (see Figures 7.63 and 7.64). Furthermore, the two
remaining characteristic roots are, from Equation 7.165, both zero. Laplace transforming Equations
7.165 and 7.166 and solving for Du(s) and DX(s) result in
Du(s) ¼
0:444
s
2
þ 13:5022
DU(s)(7:167)
DX( s) ¼ 0:333
s
2
þ 13:0666
s
2
(s
2
þ 13:5022)

DU( s)(7:168)
The inverted pendulum is often used as an example of an inherently (open-loop) unstable system,
and numerous linear controls texts demonstrate techniques for designing linear controllers to
balance the pendulum in the upright ...
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Publisher Resources

ISBN: 9781439836736