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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
(c) The continuous-time response y(t) to the input u(t) ¼2 sin 3t, t 0 is obtained from the transfer
function of the continuous-time system
H(s) ¼
Y(s)
U(s)
¼
1
ts þ 1
¼
1
0:25s þ 1
(4:666)
Y(s) ¼ H(s)U(s) ¼
1
0:25s þ 1
2
3
s
2
þ 9

(4:667)
¼
24
(s þ 4)(s
2
þ 9)
(4:668)
Inverting Y(s) by partial fractions leads to
y(t) ¼
24
25
e
t=0:25
þ
4
3
sin 3t cos 3t

(4:669)
The transient and steady-state components of y(t) are
y
tr
¼
24
25
e
t=0:25
, y
ss
¼
24
25
4
3
sin 3t cos 3t

(4:670)
(d) The magnitude and phase of the discrete-time frequency response function at v ¼3 rad=s and
T ¼0.025 s are obtained from Equations 4.664 and 4.665, respectively.
jH(e
j3(0:025)
)
0:1
[1:81 1:8 cos 3(0:025)] ...
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Publisher Resources

ISBN: 9781439836736