Consider a unity feedback system with forward transfer function given by G(s)=\frac{1}{(s+1)(s+2)} The steady-state error in the output of the system for a unit-step input is ___________(upto 2 decimal places).

GATE Electrical Engineering (EE) 2018 Solved Paper

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Consider a unity feedback system with forward transfer function given by

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

The steady-state error in the output of the system for a unit-step input is ___________(upto 2 decimal places).

Solution:

Steady-state error for type-0 and step input,

e_{s s}=\;{1}/{1+k_{p}}

k_{p}={Lt}↙{s → 0} \;{1}/{(s+1)(s+2)}=\;{1}/{2}

e_{s s}=\;{1}/{1+\;{1}/{2}}=\;{2}/{3}=0.66

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