lecture12

# lecture12 - MAE 171A Dynamic Systems Control Lecture 12...

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Unformatted text preview: MAE 171A: Dynamic Systems Control Lecture 12: Bode and Nyquist Plot Goele Pipeleers Recall From Lecture 1 Frequency Response Function (FRF) • the FRF G ( jω ) of a system G with impulse response g ( t ) and transfer function G ( s ) equals – Fourier transform of impulse response: G ( jω ) = F{ g ( t ) } – transfer function evaluated on imaginary axis: G ( jω ) = G ( s ) s = jω • G ( jω ) determines the steady-state response to a harmonic input – set u ( t ) = sin( ωt ) – then y ss ( t ) = | G ( jω ) | sin ( ωt + φ ( G ( jω ) )) 1 In This Lecture • representation of a system’s FRF in Bode and Nyquist plots • sketching rules for asymptotic Bode plot 2 Two Ways To Represent an FRF • for a given ω , G ( jω ) is a complex number • Bode plot: plot modulus | G ( jω ) | and argument ∠ G ( jω ) as a function of ω – logaritmic ω scale – modulus in dB: 20log 10 ( G ( jω )) , and argument in degrees • Nyquist plot: plot G ( jω ) for ω : 0 → ∞ in the complex plane – curve in the complex plane, parameterized by ω 3 ω...
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lecture12 - MAE 171A Dynamic Systems Control Lecture 12...

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