English
Hindi

Question

Download Solution PDF

The D.C. gain and steady state error for step input for  are:

This question was previously asked in
ESE Electronics 2013 Paper 2: Official Paper
Attempt in App
View all UPSC IES Papers >
  1. 1 and 1
  2. 0 and 1
  3. 1 and 0.5
  4. 0 and 0

Answer (Detailed Solution Below)

Option 3 : 1 and 0.5
Free Tests
View all Free tests >
Free
ST 1: UPSC ESE (IES) Civil - Building Materials
20 Qs. 40 Marks 24 Mins
Start Now

Detailed Solution

Download Solution PDF

Concept:

DC gain:

The DC gain is the ratio of the magnitude of the steady-state step response to the magnitude of step input.

DC Gain of a system is the gain at the steady-state which is at t tending to infinity i.e., s tending to zero.

DC gain is nothing but the error coefficients.

For type 0 system: 

For type 1 system: 

For type 2 system: 

Steady state error for different inputs is given by

Input

Type -0

Type - 1

Type -2

Unit step

0

0

Unit ramp

∞

0

Unit parabolic

∞

∞

Calculation:

Given:

It is a type 0 system, so:

Kp = 1 = DC Gain

Steady-state error for unit step input is given as:

ess = 0.5

Download Solution PDF
Latest UPSC IES Updates

Last updated on Jul 2, 2025

-> ESE Mains 2025 exam date has been released. As per the schedule, UPSC IES Mains exam 2025 will be conducted on August 10. 

-> UPSC ESE result 2025 has been released. Candidates can download the ESE prelims result PDF from here.

->  UPSC ESE admit card 2025 for the prelims exam has been released. 

-> The UPSC IES Prelims 2025 will be held on 8th June 2025.

-> The selection process includes a Prelims and a Mains Examination, followed by a Personality Test/Interview.

-> Candidates should attempt the UPSC IES mock tests to increase their efficiency. The UPSC IES previous year papers can be downloaded here.

Exams Tests Super Practice

More Steady State Error Questions

Q1.Steady state error is the value of error signal when:
Q2.A closed loop system is shown in the figure where k > 0 and α > 0. The steady state error due to a ramp input (R(s) = α/s2) is given by 
Q3.The steady state error of a stable ‘type 1’ unity feedback system for a unit step function is equal to:
Q4.The steady-state error for the type 0 unity feedback stable control system for unit step signal is equal to
Q5.A unity feedback system has a forward path transfer function G(s) = \(\frac{10(1+4\text{s})}{\text{s}^{2}(1+\text{s})}\). If the system is subjected to an input r(t) = 1 + t + \(\frac{\text{t}^{2}}{2}\), the steady state error of the system will be
Q6.What is the other name for the unit impulse function?
Q7.The steady-state error due to the ramp input for a type two system is equal to-
Q8.The velocity error constant of a system is measured when the input to the system is a-
Q9.Consider the following statements related to steady state error for a control system: 1. Steady-state error can be calculated from a system’s closed-loop transfer function for a unity feedback system. 2. Steady-state error can be calculated from a system’s open-loop transfer function for a unity feedback system. 3. Steady-state error is the difference between the input and the output for a prescribed test input as time tends to infinity. 4. Many steady-state errors in control systems can arise from non-linear sources. Which of the above statements are correct?
Q10.In the feedback control system shown in the figure, D(s) is step disturbance, R(s) is input and C(s) is output : The steady-state error component due to a step disturbance for the system is

More Time Response Analysis Questions

Q1.A unity feedback system is characterized by the open-loop transfer function \(G(s)=\frac{100}{s(5 s+10)(2 s+10)}\) The steady-state errors for unit-step and unit-ramp inputs are :
Q2.In the circuit shown switch is closed at t = 0. The time constant of the circuit is :
Q3.Consider a causal second-order system with the transfer function \(G(s)=\frac{1}{s^2+2 s+1}\) with a unit-step \(R(s)=\frac{1}{s}\) as an input. Let c(s) be the corresponding output. The time taken by the system output c(t) to reach 94% of its steady-state value \(\displaystyle \lim _{t \rightarrow \infty} c(t)\), rounded off to two decimal places, is
Q4.The output of a standard second-order system for a unit-step input is given as \(y(t)=1-\frac{2}{\sqrt{3}} e^{-t} \cos \left(\sqrt{3} t-\frac{\pi}{6}\right)\). What is the transfer function of the system?
Q5.A second-order system has a closed-loop transfer function given by \(G(s)=\frac{25}{s^2+8 s+25}\). The settling time for 5 percentage band in tolerance error is
Q6.A second-order system has a transfer function given by \(G(s)=\frac{25}{s^2+8 s+25}\). If the system, initially at rest, is subjected to a unit-step input at t = 0, the second peak in the response will occur at
Q7.Steady state error is the value of error signal when:
Q8.A closed loop system is shown in the figure where k > 0 and α > 0. The steady state error due to a ramp input (R(s) = α/s2) is given by 
Q9.The nature of the response shown below is:
Q10.When the damping ratio ζ (zeta) lies in between 0 < ζ < 1, then the circuit classification comes under:
Suggested Test Series
View All >
UPSC ESE (IES) Civil Mock Test Series
116 Total Tests with 1 Free Tests
Start Free Test
UPSC ESE (IES) Electrical Mock Test Series
68 Total Tests with   0 Free Tests
Start Free Test

ISRO Scientist EC Important Links

Previous Year PapersAdmit CardResultEligibility CriteriaCut-OffBooks

More Control Systems Questions

Q1.A unity feedback system is characterized by the open-loop transfer function \(G(s)=\frac{100}{s(5 s+10)(2 s+10)}\) The steady-state errors for unit-step and unit-ramp inputs are :
Q2.In the circuit shown switch is closed at t = 0. The time constant of the circuit is :
Q3.The loop transfer function of a closed-loop control system is given as : \(G(s) H(s)=\frac{k(s+1)}{s(s+2)(s+3)}\) The centroid of the asymptotes in root locus is :
Q4.For a control system having fourteen poles and two zeros, the slope in its magnitude plot for high frequency asymptote will be :
Q5.The Routh Array is as below : \(\begin{array}{lllll} \mathrm{S}^{6} & 1 & 8 & 20 & 16 \\ \mathrm{S}^{5} & 2 & 12 & 16 & \\ \mathrm{S}^{4} & 2 & 12 & 16 & \\ \mathrm{S}^{3} & 0 & 0 & & \end{array}\) The row of zero of this array will be replaced by coefficients of 
Q6.The number of roots in the left half of the s-plane for a system having characteristic equations : s3 + 5s2 + 7s + 3 = 0 is : 
Q7.Explain the pattern and trend of public expenditure on social services in the post reforms period in India. To what extent this has been in consonance with achieving objective of inclusive growth? 
Q8.The Nyquist criterion for stability states that an amplifier is unstable if the Nyquist curve encloses the -1 + j0 point, and the amplifier is stable if the curve does not enclose this point. If Aβ
Q9.The phase margin of a system with the open-loop transfer function \(G(s) H(s)=\frac{1-s}{(s+1)(s+2)}\) is
Q10.The phase margin of a system having the loop transfer function \(G(s) H(s)=\frac{2 \sqrt{3}}{s(s+1)}\) is
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
support@testbook.com
Toll Free:1800 833 0800
Office Hours: 10 AM to 7 PM (all 7 days)
Company
About usCareers We are hiringTeach Online on TestbookPartnersMediaSitemap
Products
Test SeriesTestbook PassOnline CoursesOnline VideosPracticeBlogRefer & EarnBooks
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Hot Links： teen patti master new version teen patti lotus teen patti joy 51 bonus real cash teen patti lucky teen patti