GATE 2026 IN – Question 59
A linear time-invariant (LTI) system has transfer function $$G(s)=\frac{10(s+1)}{s(s^2+2s+5)}.$$
The system is placed in a unity negative-feedback configuration. For a unit-ramp reference, the steady-state error is ________. (Rounded off to two decimal places.)
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Correct answer: 0.49 to 0.51
Explanation
The velocity error constant is $K_v=\lim_{s\to0}sG(s)=10/5=2$. For a stable type-1 unity-feedback system, the unit-ramp error is $e_{ss}=1/K_v$.
The closed-loop characteristic polynomial is $s^3+2s^2+15s+10$; its Routh first column is $1,2,10,10$, all positive, so the stability requirement holds. Therefore $e_{ss}=1/2=$ **0.50**.