Testbook Logo
Exams SuperCoaching Test Series Skill Academy
More

Question

Download Solution PDF

Consider the closed-loop system shown in the figure. What is the critical value of K for stability by the use of the Nyquist stability criterion?

F1 Madhuri Engineering 03.02.2023 D2

This question was previously asked in
UPSC IES Electrical 2022 Prelims Official Paper
Download PDF Attempt Online
View all UPSC IES Papers >
  1. 0.1
  2. 0.2
  3. 1
  4. 0.5

Answer (Detailed Solution Below)

Option 3 : 1
Free Tests
View all Free tests >
Free
ST 1: UPSC ESE (IES) Civil - Building Materials
6.2 K Users
20 Questions 40 Marks 24 Mins
Start Now

Detailed Solution

Download Solution PDF

Concept:

Enclosed:

A point or region is enclosed, if it lies to the right of the path (polar plot direction is from ω = 0 to ω = ∞)

  • If the plot is intersecting the negative real axis, therefore the stability of a system (-1, j0) critical point should not be enclosed by its plot.

 

F1 Madhuri Engineering 03.02.2023 D3

In this figure, if we take the value K as equal to, then it will be its critical value.

Reason:

By taking the K = 1, the circle center will be -K/2 ie -1/2, and the boundary point will be - k ie - 1.

 

F1 Madhuri Engineering 03.02.2023 D2

Download Solution PDF
Latest UPSC IES Updates

Last updated on May 28, 2025

->  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.

More Nyquist Plot Questions

Q1.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
Q2.In the Nyquist plot of the open-loop transfer function \(\rm G(s)H(s)=\frac{3s+5}{s-1}\) corresponding to the feedback loop shown in the figure, the infinite semi-circular arc of the Nyquist contour in s-plane is mapped into a point at
Q3.If the Nyquist plot cuts the negative real axis at a distance of 0.8, then the gain margin of the system is
Q4.The figure shows the Nyquist plot of the open-loop transfer function G(s)H(s) of a system. If G(s)H(s) has one right-hand pole, the closed-loop system is -
Q5.Consider the closed-loop system shown in the figure. What is the critical value of K for stability by the use of the Nyquist stability criterion?
Q6.Consider a closed-loop control system with unity negative feedback and KG(s) in the forward path, where the gain K = 2. The complete Nyquist plot of the transfer function G(s) is shown in the figure. Note that the Nyquist contour has been chosen to have the clockwise sense. Assume G(s) has no poles on the closed right-half of the complex plane. The number of poles of the closed-loop transfer function in the closed right-half of the complex plane is ___________.
Q7.The open loop transfer function of unity gain negative feedback system is given as \(\rm G(s) = \frac{1}{s(s + 1)}\) The Nyquist contour in the 𝑠-plane encloses the entire right half plane and a small neighborhood around the origin in the left half plane, as shown in the figure below. The number of encirclements of the point (−1 + j0) by the Nyquist plot of G(s), corresponding to the Nyquist contour, is denoted as N. Then N equals to
Q8.In Nyquist plot of a system on adding a pole at s = 0, then plot will -
Q9.The critical point (-1, j0) is mapped to ________ on the Nichols chart.
Q10.Which of the following is a powerful frequency-domain method of extracting the information regarding stability as well as the relative stability of a system without the need to evaluate the roots of the characteristic equation?

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) Prelims Paper 1 Mock Test Series
54 Total Tests with   1 Free Tests
Start Free Test

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
Important Exams
Super Coaching
Exams
Test Series
Previous Year Papers
Objective Questions
Testbook USA SAT Exam
Testbook USA ACT Exam
US College Admissions Guide
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
[email protected]
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
Our Apps
Follow us on
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Get Free Access Now
Hot Links： teen patti master gold apk teen patti comfun card online teen patti master gold teen patti bonus teen patti lucky