Bode_lecture_v2 - Transfer function: 600 ---------------...

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S.S. response of LTI BIBO stable systems to sinusoidal inputs (zero I.C.)
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Where
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Where
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recap (In steady state) Same frequency! *) BIBO stable, LTI *)Not true for linear time varying or non-linear systems *) gain and phase at some frequency w is only a function of the value of the T.F. at s = jw gain phase
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sin(wt) -> (.)sin(wt + .) in s.s Gain ~ 0.2, phase ~ - 90
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sin(wt) -> (.)sin(wt + .) in s.s y(t)*10 Gain ~ 0.03, phase ~ - 180
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w = 3 rad/s : mag = -13 dB (I.e.,0.2105), phase = -105 w = 2pi rad/s: mag = - 30 dB (I.e., 0.0316), phase = -163
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G(jw) is G(s) restricted to s = jw Magnitude (dB) of G(s)
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G(jw) is G(s) restricted to s = jw Phase (deg) of G(s)
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Complex numbers Polar form z
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Bode plot of 1st order system
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Bode plot of second order system (real poles) >> G = tf(600,[1 32 60])
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Unformatted text preview: Transfer function: 600 --------------- s^2 + 32 s + 60 >> figure;bode(G) Bode plot of second order system (real poles) Ex 2 (2 nd order, real poles) G ( s ) = 600 s 2 + 1 . 01 s + 0 . 01 = 600 ( s + 0 . 01)( s + 1) G ( j ω ) = 600 ( j ω + 0 . 01)( j ω + 1) Bode plot of second order system (complex poles) Ex 2( 2 nd order, complex poles) Ex 2 G ( s ) = 25 s 2 + 0 . 1 s + 50 Bode plot of second order system (with a zero) Relative degree Relative degree of G = order of denominator of G - order of numerator of G For relative degree is n - m DC gain: G(0), if finite Second order system G ( j ω ) = ω 2 n s 2 + 2 ζω n j + ω 2 n Beam 391 s^2 + 1650 s + 4.291e06 H(s) = --------------------------------------------------- s^4 + 7.14 s^3 + 2.921e04 s^2 + 118482 s + 1.735e08...
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This note was uploaded on 06/06/2011 for the course EML 4312 taught by Professor Dixon during the Fall '07 term at University of Florida.

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Bode_lecture_v2 - Transfer function: 600 ---------------...

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