GATE 2024 EE – Question 58
Consider the stable closed-loop system shown in the figure. The asymptotic Bode magnitude plot of $G(s)$ has a constant slope of $-20$ dB/decade at least till 100 rad/sec with the gain crossover frequency being 10 rad/sec. The asymptotic Bode phase plot remains constant at $-90^\circ$ at least till $\omega=10$ rad/sec. The steady-state error for a unit ramp input is ______________ (rounded off to 2 decimal places).
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Correct answer: 0.09 to 0.11
Explanation
A constant $-20$ dB/decade slope with a constant $-90^\circ$ phase means $G(s)\approx K/s$ (type 1). Unity gain at 10 rad/s gives $\dfrac{K}{10}=1$, so $K=10$ and the velocity error constant is $K_v=10$. The steady-state error for a unit ramp is $\dfrac1{K_v}=0.10$.