{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Bode_lecture_v2

# Bode_lecture_v2 - Transfer function 600 s^2 32 s 60>>...

This preview shows pages 1–21. Sign up to view the full content.

S.S. response of LTI BIBO stable systems to sinusoidal inputs (zero I.C.)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Where

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Where
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
sin(wt) -> (.)sin(wt + .) in s.s Gain ~ 0.2, phase ~ - 90
sin(wt) -> (.)sin(wt + .) in s.s y(t)*10 Gain ~ 0.03, phase ~ - 180

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
G(jw) is G(s) restricted to s = jw Magnitude (dB) of G(s)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
G(jw) is G(s) restricted to s = jw Phase (deg) of G(s)
Complex numbers Polar form z

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Bode plot of 1st order system
Bode plot of second order system (real poles) >> G = tf(600,[1 32 60])

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

{[ snackBarMessage ]}