The unit step response y(t) of a unity feedback system with open-loop transfer function G(s) H(s)=\frac{K}{(s+1)^{2}(s+2)} is shown in the figure. The value of K is ____________(upto 2 decimal places).

GATE Electrical Engineering (EE) 2018 Solved Paper

Question : 52 of 65

Marks: +1, -0

The unit step response

y(t)

of a unity feedback system with open-loop transfer function

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

is shown in the figure. The value of

K

is ____________(upto 2 decimal places).

Solution:

From the response steady state value of the function is 0.8. So finding the steady state value
Closed loop transfer function,

\;{C(s)}/{R(s)}=\;{\;{K}/{(s+1)^{2}(s+2)}}/{1+\;{K}/{(s+1)^{2}(s+2)}}

\;{C(s)}/{R(s)}=\;{K}/{(s+1)^{2}(s+2)+K}

Given,

R(s)=\;{1}/{s}

C(s)=\;{K}/{s[(s+1)^{2}(s+2)+K]}

{Lt}↙{s → 0} s C(s)=0.8

(given)

\;{K}/{2+K} \;\; =0.8

⇒K =8

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