Poles, Zeros (section 4.2 in the book)•Goal of this chapterAnalysis 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 hf hthat are common to roots of the numerator•Zeros of a Transfer Function(1) The values of the Laplace transform variablesthat(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 Sharifi2
System Response•A pole of the input function generates the form of the forced response (observation 1)Alf thtfftitthff thtl•A pole of the transfer function generates the form of the natural response(observation 2)•A pole on the real axis generates an exponentialresponse 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 zeroThdltthlit dfb th thfdd•The zeros and poles generate the amplitudesfor both the forced and natural responses (observation 4)(c) 2010 Farrokh Sharifi3
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