If the given system is connected to a unity negative feedback system, the steady-state error of a closed-loop system to a ramp input is;

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DFCCIL Executive S&T 2018 Official Paper

Option 3 : 0.5

CT 1: Current Affairs (Government Policies and Schemes)

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**Concept- **

For a unity feedback system with an open-loop transfer function G(s), the steady-state errors can be found identify the system type and using the respective formula:

For system type 0 : \(ess = \frac{1}{{1 + {K_p}}}\)

For system type 1 : \(ess = \frac{1}{{{K_v}}}\)

For system type 2 : \(ess = \frac{1}{{{K_a}}}\)

By identifying the system type from the open-loop Bode plot, the steady-state error can be easily found as follows-

From the given bode plot initial slope = \(\frac{{M\left( {j{\omega _2}} \right) - M\left( {j{\omega _1}} \right)}}{{\log {\omega _2} - \log {\omega _1}}}\)

\(slope = \frac{{ - 6.02}}{{\log 2 - \log 1}} = - 20\) dB / dec

So one pole present at the origin

Since it is a type 1 system so it will intersect Real Axis at k_{v}

K_{v} = 2

\(ess = \frac{1}{{{K_v}}} = \frac{1}{2} = 0.5\)