Testbook Logo
Exams SuperCoaching Test Series Skill Academy
More
Hindi
English

Question

Download Solution PDF

अवस्था चर द्वारा प्रस्तुत एक द्वितीय कोटि प्रणाली में निम्न है।

\(A = \left[ {\begin{array}{*{20}{c}} -2&-4\\ 1&0 \end{array}} \right]\)

प्राकृतिक आवृत्ति और अवमंदन अनुपात के मान क्रमशः _________ हैं।

This question was previously asked in
ESE Electronics 2012 Paper 1: Official Paper
Attempt Online
View all UPSC IES Papers >
  1. 2 और 0.5
  2. 2 और 1
  3. 1 और 2
  4. 0.5 और 2

Answer (Detailed Solution Below)

Option 1 : 2 और 0.5
Free Tests
View all Free tests >
Free
ST 1: UPSC ESE (IES) Civil - Building Materials
6.5 K Users
20 Questions 40 Marks 24 Mins
Start Now

Detailed Solution

Download Solution PDF

\(A = \left[ {\begin{array}{*{20}{c}} -2&-4\\ { 1}&0 \end{array}} \right]\)

\(sI - A = \left[ {\begin{array}{*{20}{c}} s&0\\ 0&s \end{array}} \right] - \left[ {\begin{array}{*{20}{c}} -2&-4\\ {1}&0 \end{array}} \right] \)

\(\\ {\left( {sI - A} \right)^{ - 1}} = \frac{1}{s(s+2)+4}\left[ {\begin{array}{*{20}{c}} {s +2}&4\\ {-1}&{s} \end{array}} \right]\)

विशेषता समीकरण है:

s(s + 2) + 4 = 0

s2 + 2s + 4 = 0

के साथ तुलना करके:

s2 + 2ζ ωn + ωn2 = 0

ωn = 2 rad/s

ζ = 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.

More Transfer Function From State Space Representation Questions

Q1.एक प्रणाली को \(3\dfrac{dy}{dt}+2y=u\) द्वारा दर्शाया जाता है प्रणाली में स्थानांतरण फलन क्या है?
Q2.अवस्था चर द्वारा प्रस्तुत एक द्वितीय कोटि प्रणाली में निम्न है। \(A = \left[ {\begin{array}{*{20}{c}} -2&-4\\ 1&0 \end{array}} \right]\) प्राकृतिक आवृत्ति और अवमंदन अनुपात के मान क्रमशः _________ हैं।
Q3.The system represented by the state-variable model \(\dot{X} = \left[ {\begin{array}{*{20}{c}} 0&-1\\ 1&-2 \end{array}} \right]X+\left[ {\begin{array}{*{20}{c}} 1\\ 2 \end{array}} \right]U\) C = [1 1] is
Q4.The state-variable formulation of a system is ẋ = Ax + Bu; y = [1  0] x where \(A = \left[ {\begin{array}{*{20}{c}} { - 3}&1\\ 0&{ - 2} \end{array}} \right],\;B = \left[ {\begin{array}{*{20}{c}} 2\\ 1 \end{array}} \right]\) The system transfer function would be
Q5.A network is described by the state model as \({{\dot{x}}_{1}}=2{{x}_{1}}-{{x}_{2}}+3u\) \({{\dot{x}}_{2}}=-4{{x}_{2}}-u\) \(y=3{{x}_{1}}-2{{x}_{2}}\) The transfer function H(s) \(\left( { = \frac{{Y\left( s \right)}}{{U\left( s \right)}}} \right)\) is
Q6.A second-order LTI system is described by the following state equations. \(\frac{d}{{dt}}{x_1}\left( t \right) - {x_2}\left( t \right) = 0\) \(\frac{d}{{dt}}{x_2}\left( t \right) + 2{x_1}\left( t \right) + 3{x_2}\left( t \right) = r\left( t \right)\)  where x1(t) and x2(t) are the two state variables and r(t) denotes the input. The output c(t) = x1(t). The system is
Q7.The transfer function of the system \(\frac{{Y\left( s \right)}}{{U\left( s \right)}}\) whose state-space equations are given below is: \(\left[ {\begin{array}{*{20}{c}} {{{\dot x}_1}\left( t \right)}\\ {{{\dot x}_2}\left( t \right)} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 1&2\\ 2&0 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{x_1}\left( t \right)}\\ {{x_2}\left( t \right)} \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} 1\\ 2 \end{array}} \right]u\left( t \right)\) \(y\left( t \right) = \left[ {\begin{array}{*{20}{c}} 1&0 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{x_1}\left( t \right)}\\ {{x_2}\left( t \right)} \end{array}} \right]\)
Q8.Let the state-space representation of an LTI system be ẋ(t) = A x(t) + B u(t), y(t) = C x(t) + d u(t) where A, B, C are matrices, d is a scalar, u(t) is the input to the system, and y(t) is its output. Let B = [0 0 1]T and d = 0. Which one of the following options for A and C will ensure that the transfer function of this LTI system is \(H\left( s \right) = \frac{1}{{{s^3} + 3{s^2} + 2s + 1}} = ?\)
Q9.Consider a state-variable model of a system \(\left[ {\begin{array}{*{20}{c}} {{{\dot x}_1}}\\ {{{\dot x}_2}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 0&1\\ { - \alpha }&{ - 2\beta } \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{x_1}}\\ {{x_2}} \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} 0\\ \alpha \end{array}} \right]r\) \(y = \left[ {\begin{array}{*{20}{c}} 1&0 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{x_1}}\\ {{x_2}} \end{array}} \right]\) where y is the output, and r is the input. The damping ratio ξ and the undamped natural frequency ωn (rad/sec) of the system are given by
Q10.linear time-invariant single-input single-output system has a state space model given by \(\frac{{dx}}{{dt}} = Fx + Gu;y = Hx\) Where, \(F = \left[ {\begin{array}{*{20}{c}} 0&1\\ { - 4}&{ - 2} \end{array}} \right];\;G = \left[ {\begin{array}{*{20}{c}} 0\\ 1 \end{array}} \right];\;H = \left[ {\begin{array}{*{20}{c}} 1&0 \end{array}} \right]\) Here, x is the sate vector, u is the input and y is the output. The damping ratio of the system is

More State Space Analysis Questions

Q1.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? 
Q2.किसी निश्चित प्रणाली में अवस्था प्रतिरूप निम्नानुसार दिया गया है D = 0 के साथ\(\rm\left[\begin{array}{l}\rm X_1 \\\rm X_2\end{array}\right] = \left[\begin{array}{cc}−2 & −3 \\4 & 2\end{array}\right]\left[\begin{array}{l}\rm X_1 \\ \rm X_2\end{array}\right]+\left[\begin{array}{l}3 \\5\end{array}\right] U\) और Y = \(\left[\begin{array}{ll}1 & 1\end{array}\right]\left[\begin{array}{l}\rm X_1 \\ \rm X_2\end{array}\right]\) है। इसका स्थानांतरण फलन ___________ होगा। 
Q3.The transfer function of a system is:  \(\rm \frac{(s+1)(s+3)}{(s+5)(s+7)(s+9)}\) In the state-space representation of the system, the minimum number of state variables (in integer) necessary is _____
Q4.______ helps to expose identified and unidentified vulnerabilities that can be used by the Virus to spread in the system
Q5.Consider the network shown in the following figure. The state equation of the system will be: 
Q6.यदि नियंत्रण प्रणाली का प्रणाली आव्यूह का मान A = \(\begin{bmatrix} -2 & 0\\ 0 & -2 \end{bmatrix}\)और निवेश आव्यूह का मान  B = [ 0 1 ] और निर्गम आव्यूह का मान C = [ 1 3 ] के रूप में दिया गया है, तो अवस्था संक्रमण आव्यूह के लिए दिया गया मान क्या होगा?
Q7.रैखिक समय-अपरिवर्तनीय प्रणाली को अवस्था अन्तराल मॉडल द्वारा दर्शाया गया है: \(\frac{dx}{dt} \) = AX + BU Y = CX + DU n = अवस्था चर की संख्या, m = इनपुट की संख्या, और p = आउटपुट की संख्या पर विचार करें। अवलोकनीयता आव्यूह किसके द्वारा दिया गया है?
Q8.रैखिक समय अपरिवर्ती प्रणाली के अवस्था समष्टि मॉडल निम्न रूप में दर्शाया गया है; \(\frac{dX}{dt}\) = AX + BU Y = CX + DU जहाँ A ________ है। (माना n = अवस्था चर की संख्या, m = इनपुट की संख्या, p = आउटपुट की संख्या)
Q9.रैखिक समय-अपरिवर्तनीय प्रणाली को निम्न रूप में अवस्था अंतराल मॉडल द्वारा दर्शाया गया है \(\frac{dx}{dt}\)= AX + BU Y = CX + DU माना कि n = अवस्था चरों की संख्या, m = इनपुटों की संख्या, p = आउटपुटों की संख्या। तो [SI-A] की सारणिक क्या है?
Q10.रैखिक समय अपरिवर्ती प्रणाली को निम्न रूप में अवस्था अंतराल मॉडल को निम्न के रूप में दर्शाया जाता है, \(\frac{dX}{dt} = A X + B U \)  \(Y = CX + DU\) माना कि n = अवस्था चरों की संख्या, m = इनपुटों की संख्या, p = आउटपुटों की संख्या। तो अवस्था परिपथ आव्यूह Φ( t) को किसके द्वारा ज्ञात किया गया है?
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
Suggested Exams
Exam-Logo
TANGEDCO Assistant Engineer
Exam-Logo
UPSC IES

TANGEDCO Assistant Engineer Important Links

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.लूप स्थानांतरण फलन \(G(s) H(s)=\frac{2 \sqrt{3}}{s(s+1)}\) प्रणाली का फेज मार्जिन है
Important Exam
Super Coaching
Exams
Previous Year Papers
Test Series
Objective Questions
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 game online real cash teen patti teen patti joy 51 bonus teen patti master app teen patti rich