ece580 lecture 12

ece580 lecture 12 - Oct. 18, 2011 Feedback Control Systems...

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Unformatted text preview: Oct. 18, 2011 Feedback Control Systems (I) Douglas Looze 1 Lecture 12 ECE 580 Feedback Control Systems (I) MIE 444 Automatic Controls Doug Looze Oct. 18, 2011 Feedback Control Systems (I) Douglas Looze 2 Announce PS 5 available Due Oct. 25 Midterm exam Wednesday, Oct. 26 7-9 PM Hasbrouck Lab Add 124 Open book, notes No electronic devices Oct. 18, 2011 Feedback Control Systems (I) Douglas Looze 3 Last Time 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. 18, 2011 Feedback Control Systems (I) Douglas Looze 4 Re s Im s- 1 x x x- 2 Nyquist D-contour for systems with poles on j -axis r R Re L Im L + = - = < = Oct. 18, 2011 Feedback Control Systems (I) Douglas Looze 5 ( 29 ( 29 ( 29 1 j j L s G r e G e r - = = Loop transfer function on small circle ( 29 ( 29 ( 29 1 j j j L r e G r e G e r - = Equation of circle Center 0 Radius Motion is CW At s = r ( = 0) ( 29 G r Approaches as r 1 ( 29 ( 29 G L r = Positive real axis Re L Im L + = - = < = Oct. 18, 2011 Feedback Control Systems (I) Douglas Looze 6 Nyquist plot Re s Im s- 1 x x x- 2 r R Re L Im L + = - = < = 1 ~ r Oct. 18, 2011 Feedback Control Systems (I) Douglas Looze 7 Today Continue Nyquist analysis for stability Robust stability Gain margins Definition and concept Margins from Nyquist locus Phase margins Definition and concept Margins from Nyquist locus Reading: FPE p. 634 Oct. 18, 2011 Feedback Control Systems (I) Douglas Looze 8 Nyquist Loci Example (29 ( 29 ( 29 (29 ( 29 ( 29 2 1 2 1 2 1 2 k Ls Ls ss s k ss s = = + + + + Why divide by k ?...
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ece580 lecture 12 - Oct. 18, 2011 Feedback Control Systems...

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