ece580 lecture 16

ece580 lecture 16 - Nov 3 2011 Feedback Control Systems(I...

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Unformatted text preview: Nov. 3, 2011 Feedback Control Systems (I) © Douglas Looze 1 Lecture 16 ECE 580 Feedback Control Systems (I) MIE 444 Automatic Controls Doug Looze Nov. 3, 2011 Feedback Control Systems (I) © Douglas Looze 2 Announce Ø PS 6 available – Due Thursday, Nov. 17 Nov. 3, 2011 Feedback Control Systems (I) © Douglas Looze 3 Last Time Ø Bode plots can be constructed from individual factors ( 29 ( 29 ( 29 1 1 m n zi pi i i G j q j q j ϖ ϖ ϖ = = =- ∑ ∑ R R R ( 29 ( 29 ( 29 1 1 log log log log m n zi pi i i G j K q j q j ϖ ϖ ϖ = = = +- ∑ ∑ ( 29 ( 29 ( 29 1 1 m zi i n pi i q s G s K q s = = = ∏ ∏ Nov. 3, 2011 Feedback Control Systems (I) © Douglas Looze 4 Ø Individual factors – Gain factor – Pole/zero factor at origin – 1st order factor (real pole/zero) – 2nd order factor (complex pole/zero) Ø Gain factor log constant for all frequencies K ϖ ≡ 0 for all frequencies K ϖ = R Note: K < 0 K π = - R K Nov. 3, 2011 Feedback Control Systems (I) © Douglas Looze 5 Ø Zero/pole at origin ( 29 q s s = ( 29 log log q j ϖ ϖ = ( 29 90 2 q j π ϖ = ± = ± ° R – Line with • slope ±1 • 0 db intercept 1 – Magnitude 1 at 1 rad/s – Horizontal line at ±90° Nov. 3, 2011 Feedback Control Systems (I) © Douglas Looze 6 Ø First order factors (real zeros/poles): magnitude ( 29 1 q s s τ = + – Corner frequency – Low frequency asymptote 0 db – High frequency asymptote • Line with – slope ±1 – 0 db intercept at corner frequency – Magnitude difference is 3 db at corner frequency ( 29 ( 29 ( 29 log log ϖ τ = ± + 1 τ Ø First order factor: phase – Low frequency asymptote 0° – High frequency asymptote ±90° – Step at corner frequency Nov. 3, 2011 Feedback Control Systems (I) © Douglas Looze 7 Ø Second order factors (complex poles/zeros): magnitude – Corner frequency ϖ n – Low frequency asymptote 0 – High frequency asymptote • Line with – slope ±2 – 0 db intercept at corner frequency – Possible notch/peak near corner frequency...
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ece580 lecture 16 - Nov 3 2011 Feedback Control Systems(I...

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