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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 4.3
Find the Laplace transform of the signal f(t) shown in Figure 4.4.
The piecewise continuous function f(t)isdened in different intervals by
f(t) ¼
0, t < 1
2(t 1), 1 t < 2
3, 2 t < 4
t þ 7, 4 t < 7
0, 7 t
8
>
>
>
>
>
>
<
>
>
>
>
>
>
:
9
>
>
>
>
>
>
=
>
>
>
>
>
>
;
(4:26)
Next, we write the function f( t) in a single expression using unit step functions. The procedure is
straightforward. The rst nonzero term in Equation 4.26 is multiplied by the appropriate step
function, so that it ‘‘turns on’’ at the correct time. This gives
f(t) ¼ 2(t 1)
^
u(t 1) (4:27)
that is valid for the rst two intervals t < 1 and 1 t <
2. The description of f(t)
changes for t 2
necessitating ...
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Publisher Resources

ISBN: 9781439836736