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%283%29%20Time%20Response

# %283%29%20Time%20Response - Time Response Time Response...

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Time Response CHAPTER 4 (c) 2010 Farrokh Sharifi 1

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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 3

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