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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
Equating like powers of z and solving for e
aT
and vT,
e
2aT
¼ 9 ) e
aT
¼ 3(4:435)
2(e
aT
cos vT) ¼3 ) cos (vT) ¼
1
2
) vT ¼
p
3
(4:436)
The quadratic numerator in F(z) in Equation 4.433 must be expressed as a linear combination of
the standard numerator forms in the last two rows of Table 4.4, that is,
2z
2
11z ¼ c
1
(e
aT
sin v T)z þ c
2
[z
2
(e
aT
cos vT)z](4:437)
Solving for c
1
and c
2
in Equation 4.437 leads to c
1
¼16
ffiffiffiffiffiffiffiffi
3=9
p
, c
2
¼ 2: F(z) is now written in a
form where Table 4.4 can be used to nd f
k.
F(z) ¼
1
7
c
1
(e
aT
sin vT)z
z
2
2(e
aT
cos vT)z þ e
2aT
þ
c
2
[z
2
(e
aT
cos vT)z]
z
2
2(e
aT
cos vT)z þ e
2aT

þ
2
7
z
z 1

(4:438)
f (k)
1
7
[c
1
e
akT
sin kvT þ c
2
e
aT
cos k
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Publisher Resources

ISBN: 9781439836736