ece580 lecture 11

ece580 lecture 11 - Oct. 13, 2011 Feedback Control Systems...

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Unformatted text preview: Oct. 13, 2011 Feedback Control Systems (I) Douglas Looze 1 Lecture 11 ECE 580 Feedback Control Systems (I) MIE 444 Automatic Controls Doug Looze Oct. 13, 2011 Feedback Control Systems (I) Douglas Looze 2 Announce PS 4 Due Tomorrow 5 pm in my office PS 5 Available Due Tuesday, Oct. 25 Midterm exam Wednesday, Oct. 26 Hasbrouck Lab Add 124 7-9 PM Open book, notes No electronic devices Oct. 13, 2011 Feedback Control Systems (I) Douglas Looze 3 Last Time Root locus Concept Rules Use of root locus to select PID parameters See FPE, Chapter 5 for details Oct. 13, 2011 Feedback Control Systems (I) Douglas Looze 4 Today Stability Begin Nyquist criterion Reading FPE 6.26.3 Oct. 13, 2011 Feedback Control Systems (I) Douglas Looze 5 Stability Transfer functions ( 29 ( 29 ( 29 ( 29 ( 29 1 1 1 L s S s T s L s L s = = + + Poles ( 29 1 L s + = For stability, need poles of closed loop system in OLHP Re s Im s x x x Stable system x x x x Unstable system s-plane Oct. 13, 2011 Feedback Control Systems (I) Douglas Looze 6 Loop transfer function is ratio of polynomials ( 29 ( 29 ( 29 n s L s d s = Poles satisfy: ( 29 ( 29 ( 29 1 1 n s L s d s + = + = ( 29 ( 29 C h a r a c t e r i s t i c P o l y n o m i a l d s n s + = 1 4 2 4 3 ( 29 ( 29 C h a ra c te ris tic P o ly n o m ia l d s n s + = 1 4 2 4 3 Oct. 13, 2011 Feedback Control Systems (I) Douglas Looze 7 How can you determine stability? Direct computation of poles Compute characteristic polynomial Solve for roots (polynomial equation) Routh-Hurwitz test Root locus ( 29 1 kL s + = Stability: k = 1 Can also be useful for design Nyquist analysis Oct. 13, 2011 Feedback Control Systems (I) Douglas Looze 8 Nyquist Criterion Interested in roots of Want them to be in OLHP Note: L ( s ) is analytic Differentiable almost everywhere Poles are isolated ( 29 1 L s + = Re s Im s x x x Oct. 13, 2011 Feedback Control Systems (I) Douglas...
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ece580 lecture 11 - Oct. 13, 2011 Feedback Control Systems...

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