GATE Electronics and Communications (EC) 2020 Solved Papers

Question : 37 of 65

Marks: +1, -0

The characteristic equation of a system is

s^{3}+3 s^{2}+(k+2) s+3 K=0

In the root locus plot for the given system, as

{K}

varies from 0 to

∞

, the break-away or break-in point(s) lie within

Solution:

s^{3}+3 s^{2}+2 s+k(s+3)=0

1+\;{k(s+3)}/{s+(s^{2}+3 s+2)}=0

1+\;{k(s+3)}/{s(s+1)(s+2)}=0

Compare it with

1+ {G}( {s}) {H}( {s})=0

{G}( {s}) {H}( {s})=\;{ {K}( {s}+3)}/{ {s}( {s}+1)( {s}+2)}

Breakaway point is in between

(0, –1)

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