EEL5173 Fall 2009 Lecture _11

EEL5173 Fall 2009 Lecture _11 - ? ) 10 )( 3 )( 1 ( 500 + +...

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Unformatted text preview: ? ) 10 )( 3 )( 1 ( 500 + + + = s s s k GH = 0 GH-plane 50/3-1-0.874 < 0 Example 10.4 ) 10 )( 3 )( 1 ( 500 + + + = s s s GH What happens when = 0 GH-plane 50 k /3-1-0.874 k < 0 Find the range of k for BIBO stability. if k > 0 (2) Nyquist Criterion (continue) (e) Design with Nyquist Criterion GH-plane-1 = 0 50 k /3-0.874 k < 0 Im Re A B If k > 0 Case A: P =0, N c =0, Z = P + N c =0; stable, when -1 < -0.874 k,-1/(-0.874) > k, or 0 < k < 1.144 Case B: P =0, N c =2, Z = P + N c =2; unstable What if k < 0?-kGH GH-plane-1 = 0 50 k /3-0.874 k < 0 Im Re A B kGH kGH 1-kGH 1 = 0 50 k /3-0.874 k < 0 C D Re D C Case C: P =0, N c =1, Z = P + N c =1; unstable. Case D: P =0, N c =0, Z = P + N c =0; stable, when -1 < 50 k /3 ,-3/50 < k, or -3/50 < k < 0 When k < 0 =+ + GH-plane Im Re < 2 ) 2 ( s s GH + = Example 10.5 2 ) 2 ( s s k GH + = If find the range of k for a stable system....
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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 _11 - ? ) 10 )( 3 )( 1 ( 500 + +...

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