36 + Interview Questions in Stability And Algebraic Criteria in Control Systems Page 1 InterviewSolution

1.	Consider a negative feedback system where G(s) =1/(s+1) and H(s) =K/s(s+2). The closed loop system is stable for(a) K>6(b) 0
Answer» RIGHT option is (d) 0 For EXPLANATION: Using ROUTH array, for STABILITY k<6.

Discussion

2.	Consider a characteristic equation, s^4+3s^3+5s^2+6s+k+10=0. The condition for stability is(a) K>5(b) -10-4(d) -10
Answer» The correct ANSWER is (d) -10 To elaborate: Solve Roth ARRAY for the system STABLE, -10

Discussion

3.	A system with unity feedback having open loop transfer function as G(s) = K(s+1)/s3+as2+2s+1. What values of ‘K’ and ’a’ should be chosen so that the system oscillates ?(a) K =2, a =1(b) K =2, a =0.75(c) K =4, a =1(d) K =4, a =0.75I had been asked this question during an online exam.My question is taken from Relative Stability Analysis in portion Stability and Algebraic Criteria of Control Systems
Answer» The correct OPTION is (b) K =2, a =0.75 Easiest explanation: Solving Routh Hurwitz table whenever row of zero OCCURS, the roots are located symmetrically on the IMAGINARY AXIS then the system RESPONSE oscillates, a =1+K/2+K. If K =2 is consider then a =0.75.

Discussion

4.	The necessary condition for the stability of the linear system is that all the coefficients of characteristic equation 1+G(s)H(s) =0, be real and have the :(a) Positive sign(b) Negative sign(c) Same sign(d) Both positive and negativeI have been asked this question in an online interview.My question is from Routh-Hurwitz Stability Criterion topic in chapter Stability and Algebraic Criteria of Control Systems
Answer» CORRECT option is (c) Same SIGN For explanation: The necessary condition for the stability of the linear SYSTEM is that all the coefficients of characteristic equation 1+G(s)H(s) =0, is they must have same sign.

Discussion

5.	Determine the value of K such that roots of characteristic equation given below lies to the left of the line s = -1. s^3+10s^2+18s+K.(a) K>16 and K
Answer» The CORRECT answer is (C) 9 The explanation: In Routh array ANALYSIS the first column must be positive and after SOLVING K<16 and K>9.

Discussion

6.	Consider the following statement:(a) A system is said to be stable if its output is bounded for any input(b) A system is said to be stable if all the roots of the characteristic equation lie on the left half of the s plane.(c) A system is said to be stable if all the roots of the characteristic equation have negative real parts.(d) A second order system is always stable for finite values of open loop gainThe question was asked in an online interview.Query is from Routh-Hurwitz Stability Criterion in division Stability and Algebraic Criteria of Control Systems
Answer» CORRECT OPTION is (a) A system is said to be stable if its output is bounded for any input Best EXPLANATION: A system is stable if its output is bounded for bounded input.

Discussion

7.	The characteristic equation of a feedback control system is s^3+Ks^2+9s+18. When the system is marginally stable, the frequency of the sustained oscillation:(a) 1(b) 1.414(c) 1.732(d) 3This question was posed to me by my school teacher while I was bunking the class.My doubt stems from Relative Stability Analysis in portion Stability and Algebraic Criteria of Control Systems
Answer» RIGHT choice is (d) 3 The explanation: Solve using Routh ARRAY and for the system to be marginally stable, K = -2. Polynomial for SUSTAINED OSCILLATION w = 3 rad/s.

Discussion

8.	The polynomial s^4+Ks^3+s^2+s+1=0 the range of K for stability is _____________(a) K>5(b) -10-4(d) K-1>0This question was posed to me in unit test.Query is from Relative Stability Analysis topic in division Stability and Algebraic Criteria of Control Systems
Answer» Right option is (d) K-1>0 For explanation I would say: Solving using Routh ARRAY we GET K-1>0 and is ALWAYS NEGATIVE for K>1.

Discussion

9.	The characteristic equation of a system is given ass3+25s2+10s+50=0. What is the number of the roots in the right half s-plane and the imaginary axis respectively?(a) 1,1(b) 0,0(c) 2,1(d) 1,2The question was posed to me in unit test.Origin of the question is Routh-Hurwitz Stability Criterion topic in chapter Stability and Algebraic Criteria of Control Systems
Answer» The correct option is (B) 0,0 To elaborate: The CHARACTERISTIC equation has no SIGN changes so number of roots on the right HALF of s plane is zero.

Discussion

10.	Consider the following statement regarding Routh Hurwitz criterion:(a) It gives absolute stability(b) It gives gain and phase margin(c) It gives the number of roots lying in RHS of the s-plane(d) It gives gain, phase margin and number of roots lying in RHS of the s-planeI have been asked this question in an online interview.I need to ask this question from Routh-Hurwitz Stability Criterion topic in chapter Stability and Algebraic Criteria of Control Systems
Answer» RIGHT choice is (d) It gives gain, phase margin and NUMBER of roots lying in RHS of the s-plane To explain: ROUTH Hurwitz gives the ABSOLUTE stability and roots on the right of the s plane.

Discussion

11.	The stability of the linear system:(a) Determined by the location of the poles(b) Dependent entirely of whether or the system is driven(c) The stability of the undriven linear system is dependent on the magnitude of the final initial state.(d) Stability cannot be determined by the open loop polesI have been asked this question during an online exam.My query is from Necessary Conditions for Stability and Non-Linear Systems topic in chapter Stability and Algebraic Criteria of Control Systems
Answer» Correct answer is (a) Determined by the location of the POLES To elaborate: Linear system’s stability can be determined by the location of poles and also it is independent entirely of whether or the system is DRIVEN and the stability of the undriven linear system is independent on the magnitude of the final INITIAL STATE.

Discussion

12.	The order of the auxiliary polynomial is always:(a) Even(b) Odd(c) May be even or odd(d) None of the mentionedI have been asked this question in final exam.My question is taken from Routh-Hurwitz Stability Criterion in section Stability and Algebraic Criteria of Control Systems
Answer» CORRECT choice is (a) Even The best explanation: AUXILIARY polynomial DENOTES the derivative of the ODD equation which is always even.

Discussion

13.	If the roots of the have negative real parts then the response is ____________(a) Stable(b) Unstable(c) Marginally stable(d) BoundedThe question was posed to me during an interview for a job.Asked question is from Concept of Stability in portion Stability and Algebraic Criteria of Control Systems
Answer» The correct ANSWER is (d) BOUNDED Best explanation: If the roots of the have negative REAL parts then the response is bounded and EVENTUALLY decreases to ZERO.

Discussion

14.	Routh Hurwitz criterion gives:(a) Number of roots in the right half of the s-plane(b) Value of the roots(c) Number of roots in the left half of the s-plane(d) Number of roots in the top half of the s-planeI had been asked this question in class test.My doubt stems from Routh-Hurwitz Stability Criterion topic in section Stability and Algebraic Criteria of Control Systems
Answer» Right option is (a) NUMBER of roots in the right HALF of the s-plane Easy explanation: Routh Hurwitz criterion GIVES number of roots in the right half of the s-plane.

Discussion

15.	A linear system can be classified as :(a) Absolutely stable(b) Conditionally stable(c) Unstable(d) All of the mentionedI had been asked this question in my homework.My query is from Concept of Stability in portion Stability and Algebraic Criteria of Control Systems
Answer» The CORRECT choice is (d) All of the mentioned For explanation I WOULD say: A system can be STABLE, unstable and conditionally stable ALSO.

Discussion

16.	The __________ of the coefficients of characteristic equation is necessary as well as sufficient condition for the stability of system of first and second order.(a) Negativeness(b) Positiveness(c) Positiveness and Negativeness(d) None of the mentionedI had been asked this question in an online quiz.Question is from Necessary Conditions for Stability and Non-Linear Systems in division Stability and Algebraic Criteria of Control Systems
Answer» The correct choice is (b) Positiveness The BEST EXPLANATION: The Positiveness of the coefficients of CHARACTERISTIC equation is necessary as well as sufficient condition for the stability of system of first and second ORDER.

Discussion

17.	The techniques of linear system can be used in the non-linear system entirely:(a) True(b) FalseI got this question in an international level competition.My question is from Necessary Conditions for Stability and Non-Linear Systems in chapter Stability and Algebraic Criteria of Control Systems
Answer» RIGHT option is (a) True For explanation I would say: The techniques of the LINEAR system cannot be entirely used in the non-linear system as they are differentiated by this way only.

Discussion

18.	The superposition theorem is :(a) Homogeneity(b) Additivity(c) Combination of homogeneity and additivity(d) Applied to non-linear systemsI have been asked this question in a national level competition.My doubt stems from Necessary Conditions for Stability and Non-Linear Systems topic in chapter Stability and Algebraic Criteria of Control Systems
Answer» Correct OPTION is (c) COMBINATION of homogeneity and additivity Easiest explanation: Superposition theorem applies to LINEAR system only and it REFERS to the additivity and homogeneity.

Discussion

19.	The Positiveness of the coefficients of characteristic equation is necessary as well as sufficient condition for:(a) First order system(b) Second order system(c) Third order system(d) None of the mentionedI had been asked this question during an interview for a job.I'd like to ask this question from Necessary Conditions for Stability and Non-Linear Systems topic in section Stability and Algebraic Criteria of Control Systems
Answer» The CORRECT option is (c) Third order system To elaborate: It does not ensure the negativeness of the REAL PARTS of the complex roots of the third or HIGHER order SYSTEMS.

Discussion

20.	The non-linear systems:(a) Do not obey superposition theorem(b) May be highly sensitive to the input amplitude(c) Laplace and z transform are not applicable to the non-linear systems(d) All of the mentionedI have been asked this question by my college professor while I was bunking the class.The query is from Necessary Conditions for Stability and Non-Linear Systems topic in division Stability and Algebraic Criteria of Control Systems
Answer» Correct OPTION is (d) All of the mentioned Explanation: The non-linear systems do not OBEY superposition theorem and also may be HIGHLY SENSITIVE to the input impedance and Laplace and Z transform are only applicable to the linear systems.

Discussion

21.	System non-linearities are taken account by:(a) Analytical(b) Graphical and numerical techniques(c) Both a and b(d) None of the mentionedThe question was asked in an internship interview.This intriguing question comes from Necessary Conditions for Stability and Non-Linear Systems in chapter Stability and Algebraic Criteria of Control Systems
Answer» RIGHT answer is (c) Both a and b Easiest explanation: SYSTEMS non-linearities are taken into account by the analytical, GRAPHICAL and NUMERICAL TECHNIQUES.

Discussion

22.	Routh Hurwitz criterion cannot be applied when the characteristic equation of the system containing coefficient’s which is/are(a) Exponential function of s(b) Sinusoidal function of s(c) Complex(d) Exponential and sinusoidal function of s and complexI got this question in an online interview.My query is from Routh-Hurwitz Stability Criterion in portion Stability and Algebraic Criteria of Control Systems
Answer» Correct option is (d) EXPONENTIAL and sinusoidal FUNCTION of s and complex Easy explanation: Routh HURWITZ criterion cannot be applied when the characteristic EQUATION of the SYSTEM containing coefficient/s which is/are exponential, sinusoidal and complex function of s.

Discussion

23.	The characteristic equation of a system is given as3s4+10s3+5s2+2=0. This system is :(a) Stable(b) Marginally stable(c) Unstable(d) LinearThe question was asked at a job interview.Origin of the question is Routh-Hurwitz Stability Criterion in division Stability and Algebraic Criteria of Control Systems
Answer» RIGHT option is (C) UNSTABLE To explain: There is a missing coefficient so the system is unstable.

Discussion

24.	Roots on the imaginary axis makes the system :(a) Stable(b) Unstable(c) Marginally stable(d) LinearThe question was asked in an internship interview.The doubt is from Concept of Stability in portion Stability and Algebraic Criteria of Control Systems
Answer» Correct answer is (c) Marginally STABLE The explanation: Roots on the imaginary axis makes the SYSTEM marginally stable.

Discussion

25.	Which of the test signals are best utilized by the stability analysis.(a) Impulse(b) Step(c) Ramp(d) ParabolicThis question was posed to me at a job interview.I'm obligated to ask this question of Routh-Hurwitz Stability Criterion topic in division Stability and Algebraic Criteria of Control Systems
Answer» RIGHT OPTION is (a) Impulse To explain: COMPUTATIONAL TASK is REDUCED to much extent.

Discussion

26.	The amplitude of the standard test signal does not matter in linear systems:(a) True(b) FalseThe question was asked during an interview.The origin of the question is Necessary Conditions for Stability and Non-Linear Systems in section Stability and Algebraic Criteria of Control Systems
Answer» Correct answer is (a) True For explanation: The amplitude of the standard test signal is unimportant SINCE any change in input signal amplitude RESULTS SIMPLY change in response scale with no change in the basic response CHARACTERISTICS.

Discussion

27.	The disadvantages of the linear system are:(a) The constraints on the linear operation over wide range demands unnecessarily high quality.(b) The restriction to the linear theory may inhibit the designer’s curiosity to deliberately introduce the non-linear components.(c) Practically systems are non-linear(d) All of the mentionedThis question was addressed to me at a job interview.Asked question is from Necessary Conditions for Stability and Non-Linear Systems topic in chapter Stability and Algebraic Criteria of Control Systems
Answer» Correct OPTION is (d) All of the mentioned To explain: Linear system impose certain restrictions as the COMPONENTS cost is very high and it will cause restriction to OPERATE the OTHERWISE linear components in non-linear region with a view to improve system response.

Discussion

28.	Roots with higher multiplicity on the imaginary axis makes the system :(a) Absolutely stable(b) Unstable(c) Linear(d) StableI got this question at a job interview.The doubt is from Concept of Stability topic in section Stability and Algebraic Criteria of Control Systems
Answer» RIGHT choice is (b) Unstable Easiest explanation: Repetitive ROOTS on the IMAGINARY axis MAKES the SYSTEM unstable.

Discussion

29.	The standard test signal can be applied to give output to:(a) Linear systems(b) Non-linear systems(c) Time variant systems(d) Time invariant systemsThis question was posed to me by my school teacher while I was bunking the class.Query is from Necessary Conditions for Stability and Non-Linear Systems in division Stability and Algebraic Criteria of Control Systems
Answer» Right option is (a) Linear systems For EXPLANATION I WOULD say: For linear systems the STANDARD test signals can be APPLIED to give the desired output.

Discussion

30.	In non-linear system stability is :(a) Dependent on the input(b) Independent on initial state(c) Independent on input(d) Dependent on input and initial state.I got this question in my homework.My doubt is from Necessary Conditions for Stability and Non-Linear Systems topic in chapter Stability and Algebraic Criteria of Control Systems
Answer» Right ANSWER is (d) DEPENDENT on input and INITIAL state. The explanation is: In non-linear system the STABILITY is dependent on the input and initial STATES.

Discussion

31.	If root of the characteristic equation has positive real part the system is :(a) Stable(b) Unstable(c) Marginally stable(d) LinearThe question was posed to me by my college professor while I was bunking the class.Enquiry is from Concept of Stability topic in division Stability and Algebraic Criteria of Control Systems
Answer» Correct ANSWER is (b) Unstable Easiest explanation: The impulse RESPONSE of the system is infinite when the roots of the CHARACTERISTIC equation has positive REAL PART.

Discussion

32.	Linear mathematical model applies to :(a) Linear systems(b) Stable systems(c) Unstable systems(d) Non-linear systemsThis question was addressed to me during an online interview.Query is from Concept of Stability topic in division Stability and Algebraic Criteria of Control Systems
Answer» The correct option is (B) Stable systems To elaborate: As the output exceeds CERTAIN MAGNITUDE then the linear mathematical model no LONGER APPLIES.

Discussion

33.	None of the coefficients can be zero or negative unless one of the following occurs:(a) One or more roots have positive real parts(b) A root at origin(c) Presence of root at the imaginary axis(d) All of the mentionedI had been asked this question during an interview.This question is from Necessary Conditions for Stability and Non-Linear Systems topic in chapter Stability and Algebraic Criteria of Control Systems
Answer» Right ANSWER is (d) All of the mentioned The best I can explain: None of the coefficients can be zero or NEGATIVE unless one or more roots have POSITIVE REAL PARTS, root at origin and presence of root at the imaginary axis.

Discussion

34.	Non-linear elements may exhibit___________(a) Linear systems(b) Non-linear systems(c) Limit cycles(d) Time invariant systemsThis question was addressed to me in an interview.The question is from Necessary Conditions for Stability and Non-Linear Systems topic in division Stability and Algebraic Criteria of Control Systems
Answer» Right OPTION is (c) LIMIT cycles The best explanation: Non-linear elements may exhibit the limit cycles which are self-sustained oscillations of fixed frequency and amplitude. Determination of EXISTENCE of limit cycles is not an EASY task as these may DEPEND upon both the type and amplitude of the excitation signal.

Discussion

35.	The necessary condition of stability are:(a) Coefficient of characteristic equation must be real and have the same sign(b) Coefficient of characteristic equation must be non-zero(c) Both of the mentioned(d) Coefficient of characteristic equation must be zeroThe question was posed to me in an internship interview.Enquiry is from Necessary Conditions for Stability and Non-Linear Systems in portion Stability and Algebraic Criteria of Control Systems
Answer» Correct answer is (c) Both of the mentioned To ELABORATE: The necessary condition of stability are COEFFICIENT of CHARACTERISTIC equation must be REAL, non-zero and have the same sign.

Discussion

36.	Asymptotic stability is concerned with:(a) A system under influence of input(b) A system not under influence of input(c) A system under influence of output(d) A system not under influence of outputI had been asked this question in class test.This question is from Concept of Stability in section Stability and Algebraic Criteria of Control Systems
Answer» CORRECT choice is (b) A system not under INFLUENCE of input To EXPLAIN I would SAY: Asymptotic stability concerns a free system relative to its TRANSIENT behavior.

Discussion

Explore topic-wise InterviewSolutions in .

Consider a negative feedback system where G(s) =1/(s+1) and H(s) =K/s(s+2). The closed loop system is stable for(a) K>6(b) 0

Consider a characteristic equation, s^4+3s^3+5s^2+6s+k+10=0. The condition for stability is(a) K>5(b) -10-4(d) -10

Determine the value of K such that roots of characteristic equation given below lies to the left of the line s = -1. s^3+10s^2+18s+K.(a) K>16 and K

The polynomial s^4+Ks^3+s^2+s+1=0 the range of K for stability is _____________(a) K>5(b) -10-4(d) K-1>0This question was posed to me in unit test.Query is from Relative Stability Analysis topic in division Stability and Algebraic Criteria of Control Systems

The order of the auxiliary polynomial is always:(a) Even(b) Odd(c) May be even or odd(d) None of the mentionedI have been asked this question in final exam.My question is taken from Routh-Hurwitz Stability Criterion in section Stability and Algebraic Criteria of Control Systems

If the roots of the have negative real parts then the response is ____________(a) Stable(b) Unstable(c) Marginally stable(d) BoundedThe question was posed to me during an interview for a job.Asked question is from Concept of Stability in portion Stability and Algebraic Criteria of Control Systems

A linear system can be classified as :(a) Absolutely stable(b) Conditionally stable(c) Unstable(d) All of the mentionedI had been asked this question in my homework.My query is from Concept of Stability in portion Stability and Algebraic Criteria of Control Systems

The techniques of linear system can be used in the non-linear system entirely:(a) True(b) FalseI got this question in an international level competition.My question is from Necessary Conditions for Stability and Non-Linear Systems in chapter Stability and Algebraic Criteria of Control Systems

Roots on the imaginary axis makes the system :(a) Stable(b) Unstable(c) Marginally stable(d) LinearThe question was asked in an internship interview.The doubt is from Concept of Stability in portion Stability and Algebraic Criteria of Control Systems

The amplitude of the standard test signal does not matter in linear systems:(a) True(b) FalseThe question was asked during an interview.The origin of the question is Necessary Conditions for Stability and Non-Linear Systems in section Stability and Algebraic Criteria of Control Systems

Roots with higher multiplicity on the imaginary axis makes the system :(a) Absolutely stable(b) Unstable(c) Linear(d) StableI got this question at a job interview.The doubt is from Concept of Stability topic in section Stability and Algebraic Criteria of Control Systems

Linear mathematical model applies to :(a) Linear systems(b) Stable systems(c) Unstable systems(d) Non-linear systemsThis question was addressed to me during an online interview.Query is from Concept of Stability topic in division Stability and Algebraic Criteria of Control Systems