MECH466 - Lecture15-FrequencyResponse-2009W

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Unformatted text preview: (t) What is the output voltage y(t)? What y(t)? -0.8 -1 0 5 10 15 20 25 30 35 40 45 50 At steady-state, rt) and y(t) has same frequency, steadyrt) y(t) 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 How when the input is sinusoidal? y(t) y(t) Inverse Laplace Inverse G(s) G(s) Partial fraction expansion 0 as t goes to infinity. Steady state output Steady Frequency is same as the input frequency Frequency Amplitude is that of input (A) multiplied by Amplitude Gain Gain Phase shifts Phase (Derivation for general G(s) is given at the end of lecture slide.) G(s) 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 For G(s), called frequency response function (FRF). frequency FRF is a complex number, and thus, has an FRF amplitude and a phase. phase. First order example First Im FRF FRF Two graphs representing FRF Two Bode diagram (Bode plot) (Today and next lecture) Bode Nyquist diagram (Nyquist plot) (Next week) Nyquist (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 TF Corner frequency 0 -10 -20 -30 -40 -50 -2 10 -1 10 0 10 1 10 2 10 0 Log-scale Log- -20 -40 -60 -80 -100 -2 10 2008/09 MECH466 : Automatic Control 21 2008/09 Exercises of sketching Bode plot First order system First 200...
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