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Unformatted text preview: Root locus H ( s ) = s 3 + s 2 + 3 s 5 s 4 2 s 3 s 2 + 2 s + 10 Root locus H ( s ) = s 3 + s 2 + 3 s 5 s 4 2 s 3 s 2 + 2 s + 10 Rule I: The n branches of the locus start at the poles of H ( s ) and m branches end on the zeros of H ( s ) . Root locus H ( s ) = s 3 + s 2 + 3 s 5 s 4 2 s 3 s 2 + 2 s + 10 Rule I: The n branches of the locus start at the poles of H ( s ) and m branches end on the zeros of H ( s ) . Zeros: 1 , 1 2 j . Poles: 2 j, 1 j Root locus H ( s ) = s 3 + s 2 + 3 s 5 s 4 2 s 3 s 2 + 2 s + 10 Rule I: The n branches of the locus start at the poles of H ( s ) and m branches end on the zeros of H ( s ) . Zeros: 1 , 1 2 j . Poles: 2 j, 1 j Root locus H ( s ) = s 3 + s 2 + 3 s 5 s 4 2 s 3 s 2 + 2 s + 10 Rule II: The loci are on the real axis to the left of an odd number of poles and zeros. Root locus H ( s ) = s 3 + s 2 + 3 s 5 s 4 2 s 3 s 2 + 2 s + 10 Rule II: The loci are on the real axis to the left of an odd number of poles and zeros. Root locus H ( s ) = s 3 + s 2 + 3 s 5 s 4 2 s 3 s 2 + 2 s + 10 Rule III: For large s and K , nm of the loci are asymptotic to lines at angles l radiating out from the center point s = on the real axis, where: l = 180 o + 360 o ( l 1) n m , l = 1 , 2 , . . . , n m, = i p i j z j n m 1 = 180 o + 360 o (1 1) 4 3 = 180 o = (2 + j + 2 j 1 + j 1 j ) (1 1 + 2 j 1 2 j ) 4 3 = 2 ( 1) = 3 Root locus H ( s ) = s 3 + s 2 + 3 s 5 s 4 2 s 3 s 2 + 2 s + 10 Rule III: For large s and K , nm of the loci are asymptotic to lines at angles l radiating out from the center point s = on the real axis, where ... Root locus H ( s ) = s 3 + s 2 + 3 s 5 s 4 2 s 3 s 2 + 2 s + 10 Rule IV: The angle of departure of a branch of the locus from a pole of multiplicity q is given by: q l,dep = X i i X j 6 = l j 180 o 360 o ( l 1) and the angle of arrival of a branch at a zero of multiplicity q is given by: q l,arr = X j j X i 6 = l i + 180 o + 360 o ( l 1) . Root locus...
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This note was uploaded on 02/10/2011 for the course ELEC ENGR 141 taught by Professor Roychowdhury during the Fall '11 term at UCLA.
 Fall '11
 Roychowdhury

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