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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
Example 8.1
The rst-order system in Equation 8.1 is simulated using trapezoidal integration.
(a) Find an expression for e
l
, the fractional error in characteristic root.
(b) Find an asymptotic formula for e
l
valid for jlTj1.
(c) Over what range of values for lT is the asymptotic formula for e
l
accurate?
(a) The difference equation for trapezoidal integration is based on
x
A
(n þ 1) ¼ x
A
(n) þ
T
2
{f [x
A
(n), u(n)] þ f [x
A
(n þ 1), u(n þ 1)]} (8:25)
where f [x
A
(n), u(n)] and f [x
A
(n þ1), u(n þ1)] refer to the derivative function in Equation 8.1.
Z-transforming the difference equation and then solving for the ratio X(z)=U(z) results in the
z-domain transfer function ...
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Publisher Resources

ISBN: 9781439836736