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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 8.9
Obtain difference equations for simulating the unit step response of the system
dx
dt
¼ lx þ u, l ¼0:25 (8:339)
using the real-time compatible integrators
(a) Modied Euler.
(b) AB-2.
(c) Real-time predictorcorrector.
(d) Choose the step size T, so that lT ¼0.25, 1 for the modied Euler and real-time
predictorcorrector and lT ¼0.125, 0.5 for the AB-2 integrator. Graph the step
responses along with the exact solution and comment on the results.
(a) From Equation 8.323 for modied Euler, the estimated state at the halfway point is
^
x
nþ1=2
¼ x
n
þ 0:5Tf
n
(8:340)
¼ x
n
þ 0:5T(lx
n
þ u
n
)(8:341)
¼ (1 þ 0:5lT)x
n
þ 0:5Tu
n
(8:342)
and the second pass produces ...
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Publisher Resources

ISBN: 9781439836736