Consider the open loop transfer function KG(s) 82 K(8+2)2 of a unity negative feedback system. Plot the root locus for K > 0. Specifically, compute: (i) part of root locus on the real axis, (ii) asymptotes as necessary, (iii) break-away/break-in points on the real axis and the break-away/break-in angles, (iv) crossings with the jw-axis (if any), and (v) sketch the complete root locus. (Hint: the polynomial equation for the break-points has two obvious roots that you can readily factor out, leaving a 2nd order polynomial equation that you can solve for any possible remaining break-points.) K(5+2)2 5²5+1)

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Consider the open loop transfer function KG(s)
of a unity negative feedback system. Plot
the root locus for K> 0. Specifically, compute: (i) part of root locus on the real axis, (ii) asymptotes
as necessary, (iii) break-away/break-in points on the real axis and the break-away/break-in angles,
(iv) crossings with the jw-axis (if any), and (v) sketch the complete root locus.
(Hint: the polynomial equation for the break-points has two obvious roots that you can readily
factor out, leaving a 2nd order polynomial equation that you can solve for any possible remaining
break-points.)
K(5+2)²
S²(SH)
K(s+2)²
8² (s+1)
=
Transcribed Image Text:Consider the open loop transfer function KG(s) of a unity negative feedback system. Plot the root locus for K> 0. Specifically, compute: (i) part of root locus on the real axis, (ii) asymptotes as necessary, (iii) break-away/break-in points on the real axis and the break-away/break-in angles, (iv) crossings with the jw-axis (if any), and (v) sketch the complete root locus. (Hint: the polynomial equation for the break-points has two obvious roots that you can readily factor out, leaving a 2nd order polynomial equation that you can solve for any possible remaining break-points.) K(5+2)² S²(SH) K(s+2)² 8² (s+1) =
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