EEL5173 Fall 2009 Lecture _10

EEL5173 Fall 2009 Lecture _10 - (d) Nyquist Path and...

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(d) Nyquist Path and Diagram for open-loop poles. Figure 10.28 Detouring around open-loop poles: a. poles on contour; b. detour right; c. detour left. N. S. Nise Nyquist Path Modification: Push the poles on the j ω -axis away from the open RFP.
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0 , = ρ φ ω o j s ( )( ) () ( ) L L 1 2 1 ) ( ) ( + = m m o o p s j s z s z s k s H s G π ππ = = Δ 2 2 L L + + = + ) ( ) ( ) ( 1 1 m o o p s j s m z s k GH ρρ m m p p m z p p s m z s GH o o = × + + = Δ Δ + Δ Δ Δ + Δ = Δ L L L L L L 0 0 0 ) ( ) ( ) ( ) ( 1 1 1 1 m : the multiplicity of the pole at j ω o j ω o s ϕ ρ ( m )
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2 ) 2 ( s s GH + = Example 10.5 0 j ω σ ω =+ ω = 0 + (2) s -plane ω =+ 0 + ←ω GH -plane Im Re ω < 0
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2 ) 2 ( s s GH + = Example 10.5 0 j ω σ ω =+ ω = 0 + (2) s -plane ω =+ 0 + ←ω GH -plane Im Re ω < 0 P = 0, N c = 0, Z = P + N c = 0 Hence, the system is stable. π ρ 2 = Δ GH
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Figure 10.31 a. Contour for Example 10.6; b. Nyquist diagram. N. S. Nise ) 5 )( 3 ( 8 1 + + = s s s GH -1 ω 0 + GH -plane -1/120 Im Re ω =+ 0 j ω σ ω =+ ω = 0 + s -plane ω < 0
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Figure 10.31 a. Contour for Example 10.6; b. Nyquist diagram.
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This note was uploaded on 07/15/2011 for the course EEL 5173 taught by Professor Tung during the Fall '09 term at FSU.

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EEL5173 Fall 2009 Lecture _10 - (d) Nyquist Path and...

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