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ece580 lecture 05

# ece580 lecture 05 - Lecture 5 ECE 580 Feedback Control...

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Sept. 20, 2011 Feedback Control Systems (I) © Douglas Looze 1 Lecture 5 ECE 580 Feedback Control Systems (I) MIE 444 Automatic Controls Doug Looze

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Sept. 20, 2011 Feedback Control Systems (I) © Douglas Looze 2 Announce Ø PS 2 available Due Thursday Ø Password for PS solutions: feedback Ø Problem 1 (FPE 3.23) circuit
Sept. 20, 2011 Feedback Control Systems (I) © Douglas Looze 3 Last Time Ø Effect of additional pole/zero Dominant (complex) pole pair ( 29 2 2 2 2 n n n G s s s ϖ ζϖ ϖ = + + Additional pole ( 29 ( 29 ( 29 2 1 2 1 1 n n n G s s s s ζ γ = + + + Increased rise time as pole approaches dominant pair Decreased overshoot as pole approaches dominant pair 0 1 ζ < < pole at n ϖ γ - n n s s ϖ =

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Sept. 20, 2011 Feedback Control Systems (I) © Douglas Looze 4 Additional zero Decreased rise time as zero approaches dominant pair Increased overshoot as zero approaches dominant pair Ø Mathematica demonstration of effects Combined as AddedPoleZero.nb On website ( 29 2 1 2 1 z n n n s G s s s τ ζ + = + + zero at n z ϖ τ -
Sept. 20, 2011 Feedback Control Systems (I) © Douglas Looze 5 Stability Ø Idea Apply step input to system Stable: output  steady state Unstable otherwise ( 29 u t ( 29 y t G 1 all poles have negative real parts Ø Routh-Hurwitz test for stability In terms of coefficients of denominator of transfer function Construct Routh array Stable  all elements of 1st column > 0 ( 29 ( 29 ss e t y y t = -

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Sept. 20, 2011 Feedback Control Systems (I) © Douglas Looze 6 Exercise Ø Determine values of k for which a system with the following characteristic polynomial is stable ( 29 ( 29 3 2 3 2 d s s s k s k = + + - +
Sept. 20, 2011 Feedback Control Systems (I) © Douglas Looze 7 3 s 2 s 1 s 0 s ( 29 ( 29 3 2 3 2 d s s s k s k = + + - +

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Sept. 20, 2011 Feedback Control Systems (I) © Douglas Looze 8 1 2– k 3 k 3 s 2 s 1 s 0 s ? ÷ ( 29 3 2 3 k k - - 4 2 3 k - 0 k ( 29 ( 29 3 2 3 2 d s s s k s k = + + - + 4 2 0 3 k - 0 k 3 0 2 k < <
Sept. 20, 2011 Feedback Control Systems (I) © Douglas Looze 9 Today Ø Additional information from Routh-Hurwitz array Ø Begin feedback systems Equations for closed-loop system Benefits of feedback Ø Reading FPE 3.6, 4.1

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Sept. 20, 2011 Feedback Control Systems (I) © Douglas Looze 10 Ø Information from Routh-Hurwitz All roots of d ( s ) are in open LHP if and only if all elements of first column are positive If all 1st column elements are non-zero, the number of RHP roots is the number of sign changes If a 1st column element is zero Investigate further
Sept. 20, 2011

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ece580 lecture 05 - Lecture 5 ECE 580 Feedback Control...

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