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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 need to solve four simultaneous equations for the unknown constants c
1
, c
2
, d
1
, and d
2
.
Substituting the values for c
1
, c
2
, d
1
, and d
2
into Equation 4.99 yields
Y(s) ¼
1=15
s
þ
1=12
s þ 3
þ
(3=20)s 1=20
s
2
þ 2s þ 5
(4:104)
¼
1
15
1
s

þ
1
12
1
s þ 3

1
20
3s þ 1
s
2
þ 2s þ 5

(4:105)
The last term is inverted using Equation 4.97 with d
1
¼3, d
2
¼1, a ¼1, and b ¼2.
Y(t) ¼
1
15
þ
1
12
e
3t
1
20
e
t
3 cos 2t þ
3(1) þ 1
2

sin 2t

(4:106)
¼
1
15
þ
1
12
e
3t
1
20
e
t
(3 cos 2t sin 2t)(4:107)
The second method for inverse Laplace transforming terms like the one in Equation 4.97 is based on
decomposing it into two terms that can be readily inverted. Starting with an expression containing
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Publisher Resources

ISBN: 9781439836736