The loop transfer function of a negative feedback system is G(s) H(s)=\frac{K(s+11)}{s(s+2)(s+8)} The value of {K}, for which the system is marginally stable, is .........

GATE Electronics and Communications (EC) 2020 Solved Papers

Question : 20 of 65

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The loop transfer function of a negative feedback system is

G(s) H(s)=\;{K(s+11)}/{s(s+2)(s+8)}

The value of

{K}

, for which the system is marginally stable, is .........

Solution:

Closed loop characteristic equations

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

1+\;{K(s+11)}/{s(s+2)(s+8)}=0

s^{3}+10 s^{2}+16 s+K s+11 K=0

s^{3}+10 s^{2}+(16+k) s+11 K=0

For marginal stable system

\;{10(16+ {k})-11 {K}}/{10}=0

160+10 K-11 K=0

{K}=160

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