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What is the output voltage y(t)?
-1 0 5 10 15 20 25 30 35 40 45 50 At steady-state, rt) and y(t) has same frequency,
but different amplitude and phase!
2008/09 MECH466 : Automatic Control 15 2008/09 MECH466 : Automatic Control 16 4 An example (cont’d) Response to sinusoidal input Derivation of y(t)
Derivation y(t) How is the steady state output of a linear system
when the input is sinusoidal?
y(t) Inverse Laplace
G(s) Partial fraction expansion 0 as t goes to infinity. Steady state output
Frequency is same as the input frequency
Amplitude is that of input (A) multiplied by
Phase (Derivation for general G(s) is given at the end of lecture slide.)
2008/09 MECH466 : Automatic Control 17 Frequency response function 2008/09 MECH466 : Automatic Control 18 First order example revisited For a stable system G(s), G(jω) (ω is positive) is
called frequency response function (FRF).
FRF is a complex number, and thus, has an
amplitude and a phase.
First order example
FRF Two graphs representing FRF
Bode diagram (Bode plot) (Today and next lecture)
Nyquist diagram (Nyquist plot) (Next week)
(Nyquist Re 2008/09 MECH466 : Automatic Control 19 2008/09 MECH466 : Automatic Control 20 5 Bode diagram (Bode plot) of G(jω)
Bode diagram consists of gain plot & phase plot
Bode Bode plot of a 1st order system
TF Corner frequency
10 -1 10 0 10 1 10 2 10 0 Log-scale
10 2008/09 MECH466 : Automatic Control 21 2008/09 Exercises of sketching Bode plot
First order system
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This document was uploaded on 03/05/2014 for the course MECH 466 at University of British Columbia.
- Fall '08