141_1_RootLocus

141_1_RootLocus - Root locus H ( s ) = s 3 + s 2 + 3 s- 5 s...

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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 , n-m 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 , n-m 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.

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141_1_RootLocus - Root locus H ( s ) = s 3 + s 2 + 3 s- 5 s...

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