Bode_lecture - Complex numbers Polar form z Bode plot of...

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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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Unformatted text preview: Complex numbers Polar form z Bode plot of 1st order system Bode plot of second order system (real poles) >> G = tf(600,[1 32 60]) Transfer function: 600 --------------- s^2 + 32 s + 60 >> figure;bode(G) Bode plot of second order system (real poles) Bode plot of second order system (complex poles) 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 Second order system 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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