# 16.30 - KG s will result in Nyquist plot rules 1 Plot KG s...

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Handout 2: Gain and Phase margins Eric Feron Feb 6, 2004 Nyquist plots and Cauchy’s principle s 2 + s + 1 Let H ( s ) be a transfer function. eg H ( s ) = ( s + 1)( s + 3) Evaluate H on a contour in the s -plane. (your plots here) 1

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s 2 + s + 1 H = ( s + 3)( s 3) Evaluate H on another contour of the s -plane (your plots here) 2
Cauchy’s Principle: Control application: Given KG ( s ), we encircle the entire to get the contour evaluation of Closed-loop roots are poles of They are zeros of If there are no RHPs, then 1 + KG encirclement of 0 means With no RHP poles, KG encirclement of -1 means 3

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With right half plane open-loop poles A clockwise contour enclosing a zero of 1 + KG ( s ) will result in A clockwise contour enclosing a pole of 1 +

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Unformatted text preview: KG ( s ) will result in Nyquist plot rules 1. Plot KG ( s ) for s = − j ∞ to + j ∞ 2. Count number of 3. Determine number of 4. Nunber of unstable closed-loop roots is 4 1 Example: G ( s ) = s 2 + 3 s + 1 Bode plot Nyquist plot 5 1 Example: G ( s ) = s ( s + 1) 2 Bode plot Nyquist plot 6 Gain and Phase margins Nyquist plot for G ( s ). Gain Margin is Phase Margin is 7 1 G ( s ) = s 2 + 3 s + 1 1 G ( s ) = 2 s ( s + 1) 8...
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## This note was uploaded on 11/07/2011 for the course AERO 16.30 taught by Professor Ericferon during the Spring '04 term at MIT.

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16.30 - KG s will result in Nyquist plot rules 1 Plot KG s...

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