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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
Substituting Equation 8.46 into Equation 8.48 results in the asymptotic fractional error as a
linear function of v
n
T, that is,
e
v
n
0:5z(v
n
T), v
n
T 1(8:49)
From Equation 8.45, the damping ratio error e
z
is expressible as
e
z
¼ z* z ¼
ln
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 2
z
v
n
T þ (v
n
T)
2
q

v
n
*
T
z (8:50)
where v
n
*
is given in Equation 8.44. From Equation 8.47, the asymptotic approximation for e
z
is
e
z
0:5(z
2
1)v
n
T, v
n
T 1(8:51)
The asymptotic expressions for e
v
n
in Equation 8.49 and e
z
in Equation 8.51 are of order O(v
n
T)
when using Euler integration to simulate an underdamped second-order system.
A plot of the exact and asymptotic formulas for ...
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Publisher Resources

ISBN: 9781439836736