%283%29%20Time%20Response

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

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ime Response 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 nalysis of system transient response Analysis of system transient response Poles of a Transfer Function )The values of the Laplace transform variable, at (1)The values of the Laplace transform variable, s, that cause the transfer function to become infinite (2) Any roots of the denominator of the transfer function that are common to roots of the numerator Zeros of a Transfer Function ) The values of the Laplace transform variable that (1) The values of the Laplace transform variable, s , 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
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System Response A pole of the input function generates the form of the forced response (observation 1) l f t ht f f t i t t hf f t h tl 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 h d l t th lit d 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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Example 1 it step response of the system: Unit step response of the system: Observation 1 Observation 2 Observation 3 (c) 2010 Farrokh Sharifi 4 Observation 4
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Example 2 (c) 2010 Farrokh Sharifi 5
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First-Order Systems Without Zeros (section 4.3 in the book) it t Unit step response: (c) 2010 Farrokh Sharifi 6
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First-Order Systems Without Zeros : i t R P f S i f i t i Transient Response Performance Specifications ime Constant ( = / Time Constant ( τ 1/ a ) The time for to decay to 37% of its initial value The time it takes for the step response to rise to 63% of its final value Related to the speed at which the system responds to a step put (transient response specification ) input (transient response specification ) The parameter a (the exponential frequency ) is the initial rate of change of the exponential at t=0 The pole is located at the reciprocal of the time constant- farther the pole from the imaginary axis, the faster the ansient response transient response. (c) 2010 Farrokh Sharifi 7
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First-Order Systems Without Zeros : i t R P f S i f i t i Transient Response Performance Specifications Rise Time ( ) The time for the waveform to go from 0.1 to 0.9 of its final value =2.2 x time constant Q: how did we get this? Settling Time ( ) The time for the response to reach, and stay within, 2% of its final value (i.e. 98% of he final value)= 4 x time constant : how did we get this?
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This note was uploaded on 02/20/2011 for the course MEC 709 taught by Professor Sharifi during the Winter '11 term at Ryerson.

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

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