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;

Question

Question

Download Solution PDF

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;

This question was previously asked in

DFCCIL Executive S&T 2018 Official Paper

Download PDF Attempt Online

View all DFCCIL Executive Papers >

0.01
1
0.5
0.2

Answer 1

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 : $e s s = \frac{1}{1 + K_{p}}$

For system type 1 : $e s s = \frac{1}{K_{v}}$

For system type 2 : $e s s = \frac{1}{K_{a}}$

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

F3 Neha B Shraddha 05.05.2021. D 2

F3 Neha B Shraddha 05.05.2021. D 3

F3 Neha B Shraddha 05.05.2021. D 4

From the given bode plot initial slope = $\frac{M (j ω_{2}) - M (j ω_{1})}{\log ω_{2} - \log ω_{1}}$

$s l o p e = \frac{- 6.02}{\log 2 - \log 1} = - 20$ 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

$e s s = \frac{1}{K_{v}} = \frac{1}{2} = 0.5$

Download Solution PDF

Question

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;

Answer (Detailed Solution Below)

Detailed Solution

More Bode Plot Questions

More Frequency Response Analysis Questions

More Control Systems Questions