EEL5173 Fall 2009 Lecture _13

# EEL5173 Fall 2009 Lecture _13 - (2 Nyquist...

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(d) Nyquist path for poles on the unit circle centered at the origin 1 -1 j -j T j e z ω = z -plane Re Im 0 - using semi-circles with small radius ρ to push the poles to the interior of the path. (2) Nyquist Criterion (continue) ω T

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0 , = ρφ ρ ω T j o e z ( )( ) () () L L 1 2 1 ) ( ) ( + = m m T j o p z e z z z z z k z H z G ω π ρ = Δ L L + + = + ) ( ) ( ) ( 1 1 m T j o p z e z m z z k GH φ ρ m m p p m z p p z m z z GH m o o m = × + + = 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 z ϕ ρ ( m ) T j o
( ) ) 3682 . 0 )( 1 ( 264 . 0 368 . 0 + = z z z k GH Ex. (From “Digital Control System Analysis and Design,” 3 rd Ed., by Phillips & Nagle) 0 j ω σ ω T=0+ z -plane GH -plane Im Re 1 ω T 0+ ω T = π -0.0381 k -0.0418 k A B C D

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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 _13 - (2 Nyquist...

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