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Unformatted text preview: 1 Lecture 21 From Lecture 20 âŽ¥ âŽ¥ âŽ¥ âŽ¥ âŽ¥ âŽ¥ âŽ¦ âŽ¤ âŽ¢ âŽ¢ âŽ¢ âŽ¢ âŽ¢ âŽ¢ âŽ£ âŽ¡ Î” Î” Î” Î” Î” = Î” m R R S S i i i i x Ï‰ Î´ Î³ Î´ Î³ (8) and âŽ¥ âŽ¥ âŽ¥ âŽ¥ âŽ¥ âŽ¥ âŽ¦ âŽ¤ âŽ¢ âŽ¢ âŽ¢ âŽ¢ âŽ¢ âŽ¢ âŽ£ âŽ¡ Î” Î” Î” Î” = Î” Î´ Î³ Î´ Î³ R R S S i i i i i (9) equations (6) and (7) can be rewritten as âŽ¥ âŽ¦ âŽ¤ âŽ¢ âŽ£ âŽ¡ Î” Î” âŽ¥ âŽ¦ âŽ¤ âŽ¢ âŽ£ âŽ¡ = âŽ¥ âŽ¦ âŽ¤ âŽ¢ âŽ£ âŽ¡ Î” Î” m m i A A A A i p Ï‰ Ï‰ 22 21 12 11 (10) where the 4x4 [A 11 ] matrix is: ]} [ ] [ ] {[ ] [ ] [ 1 11 F G n R L A m Ï‰ + Î© + âˆ’ = âˆ’ (11) where the 4x1 matrix [A 12 ] is: Î³Î´ I G L n A m ] [ ] [ ] [ 1 12 âˆ’ Î© âˆ’ = (12) where the 1x4 [A 21 ] matrix is: ] , , , [( ] [ 1 12 Î³ Î´ Î³ Î´ S S R R I I I I J nM A âˆ’ âˆ’ = ( 1 3 ) and the 1x1 matrix [A 22 ] is: ] [ ] [ 1 1 22 J f A âˆ’ = 2 In Project 3, students have presented eigenvalue loci of [A 11 ] in the Î³ Î´ frame. In the dq frame, the eigenvalue loci of [A 11 ] is of the form shown in Fig. 1....
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 Spring '09
 BonTekOoi
 Howard Staunton, complex conjugate, Î”i SÎ³, dq frame, eigenvalue loci

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