GATE Electronics and Communications (EC) 2020 Solved Papers

Question : 65 of 65

Marks: +1, -0

Consider the following closed loop control system

Where

{G}( {s})=\;{1}/{ {s}( {s}+1)}

and

{C}( {s})= {K} \;{ {s}+1}/{ {s}+3} .

If the steady state error for a unit ramp is

0.1

, then the value of

{K}

. . . . . .

Solution:

OLTF

=\;{K(s+1)}/{(s+3)} × \;{1}/{s(s+1)}

OLTF

=\;{K}/{s(s+3)}

It is type ‘1’ system
Steady state error for unit ramp input

{e}_{ {ss}}=\;{1}/{ {K}_{ {V}}}

Where

{K}_{ {p}}=\lim ↙{ {s} → ∞} {s} × \;{ {K}}/{ {s}( {s}+3)}=\;{ {K}}/{3}

e_{s s}=\;{1}/{K {/} 3}=\;{3}/{K}

According to question,

{e}_{ {ss}}=0.1

0.1=\;{3}/{ {K}} ⇒ {K}=30

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