Question

Download Solution PDF

The open-loop transfer function of a unity feedback system is  The gain K that results in a phase margin of 45° is

This question was previously asked in
ESE Electronics 2016 Paper II: Official Paper
Attempt in App
View all UPSC IES Papers >
  1. 35
  2. 30
  3. 25
  4. 20

Answer (Detailed Solution Below)

Option 1 : 35
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:

The phase margin is given by

ωgc is gain crossover frequency.

At gain cross over frequency, the magnitude is unity.

Calculation:

Given that phase margin = 45°

⇒ ωgc = 5 rad/sec

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 Phase Margin Questions

Q1.The phase margin of a system having the loop transfer function \(G(s) H(s)=\frac{2 \sqrt{3}}{s(s+1)}\) is
Q2.Given an open loop transfer function of a control system as G(s).H(s) = \(\frac{k}{s(s^{2}+2 s+5)}\), then find the value of 'k' such that phase margin is 45°-
Q3.Consider the following statements for phase margin: 1. Phase margin is defined as the amount of additional phase lag at the gain crossover frequency required to bring the system to the verge of instability. 2. The phase margin is always positive for stable feedback systems. 3. The phase margin is always negative for stable feedback systems. Which of the above statements is/are correct?
Q4.For a Phase Locked Loop system, the open-loop transfer function is \(G(s) = \frac {1000}{s\left(\frac {s}{1192} + 1\right)}\) The phase margin is 50° and the crossover frequency is approximately 1000 rad / s. A time delay is introduced in the phase detector reducing the phase margin to 40°. The maximum permissible time delay (in seconds) is:
Q5.Which one of the following statements is correct?
Q6.The gain cross-over frequency and phase margin of the transfer function  are  \(G(s)=\frac{1}{s(s+1)}\)
Q7.Phase margin of a system is used to specify
Q8.The loop transfer function of a negative feedback system is \(G\left( s \right)H\left( s \right) = \frac{{2\left( {s\; + \;1} \right)}}{{{s^2}}}\). The phase margin of the system (in degrees, rounded off to one decimal place) is
Q9.The open-loop transfer function of a unity feedback system is \(G\left( s \right) = \frac{K}{{s\left( {s + 5} \right)}}.\) The gain K that results in a phase margin of 45° is

More Frequency Response Analysis Questions

Q1.For a control system having fourteen poles and two zeros, the slope in its magnitude plot for high frequency asymptote will be :
Q2.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
Q3.The phase margin of a system with the open-loop transfer function \(G(s) H(s)=\frac{1-s}{(s+1)(s+2)}\) is
Q4.The phase margin of a system having the loop transfer function \(G(s) H(s)=\frac{2 \sqrt{3}}{s(s+1)}\) is
Q5.By considering standard notations, the peak value of the magnitude in the resonant peak Mr is
Q6.The magnitude of frequency response of an underdamped second-order system is 5 at 0 rad/sec and peaks at \(\frac{10}{\sqrt{3}}\) at 5√2 rad/sec. The transfer function of the system is
Q7.A system has poles at 0.01 Hz, 1 Hz and 80 Hz; zeros at 5 Hz, 100 Hz and 200 Hz. The approximate phase of the system response at 20 Hz is
Q8.Multiplication of magnitudes can be converted into addition in which of the following? 
Q9.Consider a lead compensator of the form \(\rm K(s)=\frac{1+\frac{s}{a}}{1+\frac{s}{β a}}\), β > 1, α > 0 The frequency at which this compensator produces maximum phase lead is 4 rad/s. At this frequency, the gain amplification provided by the controller, assuming asymptotic Bode-magnitude plot of 𝐾(𝑠), is 6 dB. The values of 𝑎, 𝛽, respectively, are
Q10.The magnitude and phase plots of an LTI system are shown in the figure. The transfer function of the system is
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   1 Free Tests
Start Free Test

UPSC IES Important Links

ResultHall TicketEligibilitySalary and Job ProfileExam PatternECE Syllabus

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 cash game teen patti pro teen patti joy official teen patti gold real cash teen patti flush