EEL5173 Fall 2009 Lecture _8

# EEL5173 Fall 2009 Lecture _8 - σ j ω R ight H alf P lane...

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Unformatted text preview: σ j ω R ight H alf P lane L eft H alf P lane A sI A sI D B A sI adj C s H − − ⋅ + ⋅ − ⋅ = ) ( ) ( iv. Methods to Determine Stability. – the location of the poles (roots) Three Methods: – Routh-Hurwitz Criterion – Nyquist Criterion – Root-Locus Technique (1) Routh-Hurwitz Criterion- locations of the roots of a given polynomial q (s) 1 2 2 1 1 ... ) ( a s a s a s a s a s q n n n n n n + + + + + = − − − − (a) Routh Table (Array) - n+1 rows- each row represents a polynomial (even or odd) . . 1 . . . . . . . . . . . . . . . . . ) ( . . 1 1 2 1 2 3 2 1 2 5 3 1 1 1 4 2 r m s l l s b b b s a a a s a or a a a a s n n n n n n n n n − − − − − − − ... . ... ... 4 3 2 1 5 4 3 2 1 1 5 4 3 2 1 2 d d d d s c c c c c s b b b b b s i i i + + 1 2 1 2 1 1 c c c b b d − = 1 3 1 3 1 2 c c c b b d − = In general, 1 1 1 1 1 c c c b b d k k k + + − = Ex. 24 50 35 10 ) ( 2 3 4 + + + + = s s s s s q 24 1 42 24 30 50 10 24 35 1 42 42 24 30 30 24 30 50 10 10 10 24 1 10 50 10 35 1 2 3 4 = = = = − − − − s s s s (b) Criterion...
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EEL5173 Fall 2009 Lecture _8 - σ j ω R ight H alf P lane...

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