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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
k
3
¼ fx(n) þ
2T
3
k
2
, unþ
2
3

(8:211)
x(n þ 1) ¼ x(n) þ
T
4
(k
1
þ 3k
3
)(8:212)
Using this RK-3 integrator with a sampling interval
^
T ¼ T=3 to simulate the rst-order continuous-
time system dx=dt ¼lx þu results in the third-order difference equation (see Exercise 8.27)
x(n þ 3) ¼ 1 þ lT þ
(lT)
2
2
þ
(lT)
3
6

x(n) þ
T
4
þ
l
2
T
3
6

u(n)
þ
lT
2
2
u(n þ 1) þ
3T
4
u(n þ 2), n ¼ 0, 1, 2, 3, ... (8:213)
where x( n ), n ¼0, 3, 6, 9, . . . are the RK-3 states updated once every T(s).
z-Transforming Equation 8.213 leads to the z-domain transfer function
H(z) ¼
(3T=4)z
2
þ ( lT
2
=2)z þ (T=4) þ (l
2
T
3
=6)
z
3
[ 1 þ lT þ (lT)
2
=2 þ (lT)
3
=6
(8:214)
Consider the RK-4 integrator presented in Section
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Publisher Resources

ISBN: 9781439836736