Time Response
CHAPTER 4
(c) 2010 Farrokh Sharifi
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Poles, Zeros
(section 4.2 in the book)
•
Goal of this chapter
Analysis of system transient response
•
Poles of a Transfer Function
(1)The values of the Laplace transform variable,
s,
that
(1)The values of the Laplace transform variable,
that
cause the transfer function to become infinite
(2) Any roots of the denominator of the transfer function
h
f h
that are common to roots of the numerator
•
Zeros of a Transfer Function
(1) The values of the Laplace transform variable
s
that
(1) The values of the Laplace transform variable,
, that
cause the transfer function to become zero
(2) Any roots of the numerator of the transfer function that
are common to roots of the denominator
(c) 2010 Farrokh Sharifi
2

System Response
•
A pole of the input function generates the form of the
forced
response
(observation 1)
A
l
f th
t
f
f
ti
t
th
f
f th
t
l
•
A pole of the transfer function generates the form of the
natural
response
(observation 2)
•
A pole on the real axis
generates an
exponential
response of the form
where
is the pole
location on the real axis.
(observation 3)
Thus, the farther to the left a pole is on the negative real axis, the
faster the exponential transient response will decay to zero
Th
d
l
t
th
lit d
f
b th th
f
d
d
•
The zeros and poles generate the
amplitudes
for both the forced and
natural responses
(observation 4)
(c) 2010 Farrokh Sharifi
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