3
Identification of Nonlinearity
Using Higher-order
7 5
n
14)
s = l
To illustrate
the validity of equation
consider the derivation of
In this
case,
and so
becomes
+
(3-15)
and
upon substitution,
=
[ (a,
+
)(a,
+
r = l
= e
+
+
+
(3-16)
Substituting (3-16) into (3-13) and considering the symmetry property of
equation
13) becomes
(3-17)
Using
this preliminary mathematics, it is now possible to establish an input-output
relationship of a general nonlinear system when the input to
the system is in the form of
sinusoid.
When
then
s = l
where
is given by (3.14). According to the binormial theorem,
I”
n
n!
2”
_
(3-19)
k = O
(3-18)
3
Identification of Nonlinearity Using Higher-order
7 6
Substituting (3-19) into
and using (3-13) for
gives
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