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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
From Equation 2.18, the characteristic roots of the overdamped system are
s
1
, s
2
¼zv
n
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
z
2
1v
n
q
¼1:1381 rad=min, 0:1953 rad=min (2:58)
The time constants in Equation 2.19 are t
1
¼1=s
1
¼0.8787 min and t
2
¼1=s
2
¼ 5.1213 min,
and from the unit step response in Equation 2.20, the response to a step of magnitude
c is
c
2
(t) ¼ Kc 1 þ
t
2
e
t=t
2
t
1
e
t=t
1
t
1
t
2

(2:59)
¼ 0:25 1
5:1213e
t=5:1213
0:8787e
t=0:8787
4:2426

, t 0(2:60)
The second-order differential equation in Equation 2.51 is in standard form; however, the second-
order differential equation for c
1
(t) contains the rst derivative dc=dt on the right-hand side of the
equation
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Publisher Resources

ISBN: 9781439836736