ece580 lecture 13

ece580 lecture 13 - Oct. 20, 2011 Feedback Control Systems...

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Unformatted text preview: Oct. 20, 2011 Feedback Control Systems (I) © Douglas Looze 1 Lecture 13 ECE 580 Feedback Control Systems (I) MIE 444 Automatic Controls Doug Looze Oct. 20, 2011 Feedback Control Systems (I) © Douglas Looze 2 Announce Ø PS 5 available – Due Tuesday, Oct. 25 Ø Midterm exam – Wednesday, Oct. 26 – 7-9 PM – Hasbrouck Lab Add 124 – Open book, notes – No electronic devices – Material through lecture 12 – Practice exam available Oct. 20, 2011 Feedback Control Systems (I) © Douglas Looze 3 Nyquist Plot Analysis Ø Nyquist criterion Then the closed loop system is stable if and only if – The locus does not pass through - 1 – ( 29 ( 29 # open loop ORHP poles of # CW encirclements of 1 by locus P L s N L s ≡ ≡- D ( 29 L s D N P = -- ( 29 L s Oct. 20, 2011 Feedback Control Systems (I) © Douglas Looze 4 – Nyquist plot Re s Im s- 1 x x x- 2 r R Re L Im L ϖ + = ϖ- = ϖ ϖ < ϖ = ±∞ 1 ~ r Oct. 20, 2011 Feedback Control Systems (I) © Douglas Looze 5 Last Time Ø Gain and phase margins m M γ γ γ < < Gain decrease margin Gain increase margin M φ φ ≤ < Phase margin – Margins from Nyquist diagram ( 29 G s ( 29 D s- j e φ- γ Oct. 20, 2011 Feedback Control Systems (I) © Douglas Looze 6- 1 Ø Information from Nyquist locus Re L ( s ) Im L (s) gL gR Assumed stable M φ 1 m L g γ = - 1 M R g γ = - m M γ γ γ < < M φ φ ≤ < Unit circle Oct. 20, 2011 Feedback Control Systems (I) © Douglas Looze 7 Today Ø Example Ø Transient response objectives – Step response of unity feedback system – Measures of response – Two-dominant pole model Oct. 20, 2011 Feedback Control Systems (I) © Douglas Looze 8 Ø Example: ( 29 ( 29 ( 29 ( 29 2 25 1 2 2 16 s L s s s s s + = + + + – Construct Nyquist: ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 2 2 16 2 25 1 2 2 16 2 16 2 j j j j Lj j j j j j j ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ- - +- - + = +- + +- - +- - g ( 29 ( 29 ( 29 ( 29 ( 29 2 2 2 2 2 25 1 2 16 2 4 16 4 j j j j ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ- +- +-- = +- + ÷ ( 29 ( 29 ( 29 ( 29 2 2 2 4 2 25 2 16 2 4 28 256 j j j ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ- + +-- = +- + ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 2 216 2 25 1 2 2 16 216 2 j j j j Lj j j j j j j ϖ ϖ ϖ ϖ ϖ ϖϖ ϖ ϖ ϖ ϖ ϖ- - +- - + = +- + +- - +- - g- ( 29 L s Oct. 20, 2011 Feedback Control Systems (I) © Douglas Looze 9 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 4 2 4 2 2 4 2 2 5 1 2 3 R e 4 2 8 2 5 6 2 5 4 0 0 8 0 0 I m 4 2 8 2 5 6 L j L j ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ- = + - +- - = + - + ( 29 ( 29 ( 29 ( 29 ( 29 2 2 4 2 4 2 25 12 3 800 400 25 4 28 256 j L j ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ-- +- = +- + ( 29 ( 29 ( 29 ( 29 4 2 2 4 2 25 400 800 Im 4 28 256 L j ϖ ϖ ϖ ϖ ϖ ϖ ϖ-- = +- + Oct. 20, 2011 Feedback Control Systems (I) © Douglas Looze 10 – Quantitative analysis • Limits ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 3 0 0 l i m R e 0 . 2 9 3 4 2 5 6 8 0 0 l i m I m 4 2 5 6 8 0 0 l i m I m 4 2 5 6...
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ece580 lecture 13 - Oct. 20, 2011 Feedback Control Systems...

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