26 + Interview Questions in The Root Locus Technique in Control Systems Page 1 InterviewSolution

1.	The angles of asymptotes of the root loci of the equation s^3+5s^2+(K+2)s+K=0 are:(a) 0° and 270°(b) 0° and 180°(c) 90° and 270°(d) 90° and 180°I have been asked this question in a job interview.Question is taken from Construction of Root Loci in portion The Root Locus Technique of Control Systems
Answer» CORRECT CHOICE is (C) 90° and 270° The EXPLANATION: P-Z =2 Angle of ASYMPTOTE = (2q+1)180°/P-Z Angle are 90° and 270°.

Discussion

2.	The OLTF of a unity feedback system is K(s+2)(s+4)/(s+5)(s+6) the angle of arrival of the root loci as s =-2, and s =-4 respectively are:(a) 0°,180°(b) 180°,0°(c) 90°,180°(d) 180°, 90°This question was posed to me during an interview.My doubt is from Construction of Root Loci topic in division The Root Locus Technique of Control Systems
Answer» The CORRECT option is (b) 180°,0° Best explanation: As it is TYPE zero system THEREFORE the angle of arrival can be EITHER 180°, 0°.

Discussion

3.	The intersection of asymptotes of root loci of a system with open loop transfer function G(s)H(s) = K/s(s+1)(s+3) is(a) 1.44(b) 1.33(c) -1.44(d) -1.33The question was posed to me during a job interview.This intriguing question comes from Construction of Root Loci in division The Root Locus Technique of Control Systems
Answer» The correct answer is (d) -1.33 The explanation: The intersection of ASYMPTOTES of root loci of a SYSTEM is same as the centroid which is centroid =Σreal part of OPEN LOOP pole-Σreal part of open loop zeroes/P-Z. Centroid = -4/3=-1.33.

Discussion

4.	The open loop transfer function of the feedback control system is given by G(s) =K(s+3)/s(s+4)^2(s+5)(s+6). The number of asymptotes and the centroid of asymptotes of the root loci of closed loop system is(a) 4 and (-4,0)(b) 3 and (-12,0)(c) -4 and (-4,0)(d) -3 and (-12,0)I got this question during an interview.This interesting question is from Construction of Root Loci topic in division The Root Locus Technique of Control Systems
Answer» The correct choice is (a) 4 and (-4,0) For EXPLANATION: Number of Poles = 5 Zeroes =1 Asymptotes =P-Z =4 Centroid =Σreal PART of OPEN LOOP pole-Σreal part of open loop zeroes/P-Z Centroid = -4-4-5-6+3/4 =-4.

Discussion

5.	Number of roots of characteristic equation is equal to the number of ______________(a) Branches(b) Root(c) Stem(d) PolesI have been asked this question during a job interview.This key question is from The Root Locus Concepts in division The Root Locus Technique of Control Systems
Answer» Right OPTION is (a) Branches The best I can EXPLAIN: Number of roots of characteristic EQUATION is EQUAL to the number of branches.

Discussion

6.	Consider the following statements regarding root loci:(a) All root loci start from the respective poles of G(s) H(s)(b) All root loci end at the respective zeros of G(s) H(s) or go to infinity(c) The root loci are symmetrical about the imaginary axis of the s-plane(d) All root loci start and end from the respective poles of G(s) H(s) or go to infinityI got this question during an interview.I'd like to ask this question from The Root Locus Concepts in chapter The Root Locus Technique of Control Systems
Answer» The correct answer is (b) All root loci end at the respective zeros of G(s) H(s) or GO to infinity To ELABORATE: All the root LOCUS START at respective poles and end at zeroes.

Discussion

7.	The addition of open loop poles pulls the root locus towards:(a) The right and system becomes unstable(b) Imaginary axis and system becomes marginally stable(c) The left and system becomes unstable(d) The right and system becomes unstableThe question was asked in an online interview.Asked question is from The Root Locus Concepts topic in division The Root Locus Technique of Control Systems
Answer» Right option is (d) The right and system becomes unstable Easiest EXPLANATION: The addition of OPEN loop poles PULLS the ROOT locus TOWARDS the right and system becomes unstable.

Discussion

8.	While increasing the value of gain K, the system becomes(a) Less stable(b) More stable(c) Unstable(d) Absolute stableThe question was posed to me in a job interview.This question is from The Root Locus Concepts in division The Root Locus Technique of Control Systems
Answer» RIGHT ANSWER is (a) Less stable The explanation: Damping factor is inversely PROPORTIONAL to GAIN on increasing gain it reduces HENCE makes the system less stable.

Discussion

9.	The main objective of drawing root locus plot is :(a) To obtain a clear picture about the open loop poles and zeroes of the system(b) To obtain a clear picture about the transient response of feedback system for various values of open loop gain K(c) To determine sufficient condition for the value of ‘K’ that will make the feedback system unstable(d) Both b and cI had been asked this question in exam.Question is taken from The Root Locus Concepts topic in chapter The Root Locus Technique of Control Systems
Answer» The correct option is (d) Both b and c For EXPLANATION I would say: The main objective of drawing root locus plot is to obtain a clear picture about the TRANSIENT response of feedback system for various values of open loop gain K and to determine sufficient CONDITION for the value of ‘K’ that will MAKE the feedback system unstable.

Discussion

10.	Which one of the following statements is not correct?(a) Root loci can be used for analyzing stability and transient performance(b) Root loci provide insight into system stability and performance(c) Shape of the root locus gives idea of type of controller needed to meet design specification(d) Root locus can be used to handle more than one variable at a timeI have been asked this question in an online interview.This question is from The Root Locus Concepts in chapter The Root Locus Technique of Control Systems
Answer» Correct answer is (d) ROOT locus can be used to handle more than ONE VARIABLE at a time For EXPLANATION I would say: For more than one variable state space is used.

Discussion

11.	What is the number of the root locus segments which do not terminate on zeroes?(a) The number of poles(b) The number of zeroes(c) The difference between the number of poles and zeroes(d) The sum of the number of poles and the number of the zeroesThis question was posed to me in an internship interview.Enquiry is from The Root Locus in division The Root Locus Technique of Control Systems
Answer» The correct answer is (c) The difference between the number of poles and zeroes To explain I WOULD SAY: The number of the root locus SEGMENTS which do not LIE on the root locus is the difference between the number of the poles and zeroes.

Discussion

12.	If a feedback control system has its open loop transfer function G(s)H(s) = K/(s-2)(s^2+3s+5) has the root locus plot which intersects the imaginary axis at s =0, then the value of K at this point will be(a) -5(b) 10(c) 5(d) -10I have been asked this question in homework.My question comes from Construction of Root Loci in division The Root Locus Technique of Control Systems
Answer» The CORRECT choice is (B) 10 Easiest explanation: The intersection point on the imaginary axis at s =0 is obtained by ROUTH Hurwitz criteria MAKING s^0 row zero and getting the value K = 10.

Discussion

13.	Determine the centroid of the root locus for the system having G(s)H(s) = K/(s+1)(s^2+4s+5)(a) -2.1(b) -1.78(c) -1.66(d) -1.06I have been asked this question in a job interview.My query is from Construction of Root Loci in division The Root Locus Technique of Control Systems
Answer» Correct option is (C) -1.66 To explain I would SAY: Roots of the open LOOP transfer FUNCTION are -1,-2+j, -2-j then centroid =Σreal PART of open loop pole-Σreal part of open loop zeroes/P-Z Centroid =(-1-2-2)-0/3 =-5/3 =-1.66.

Discussion

14.	Consider the loop transfer function K(s+6)/(s+3)(s+5) In the root locus diagram the centroid will be located at:(a) -4(b) -1(c) -2(d) -3I had been asked this question during an online interview.I would like to ask this question from The Root Locus topic in portion The Root Locus Technique of Control Systems
Answer» Correct CHOICE is (c) -2 Best explanation: Centroid =Sum of real PART of OPEN loop pole-sum of real part of open loop zeros/P-Z.

Discussion

15.	With reference to root locus, the complex conjugate roots of the characteristic equation of the O.L.T.F. given below G(s)H(s) =K(s+3)/(s+1)^2, lie on(a) Straight line(b) Parabola(c) Circle(d) Semi-circleI got this question during an online exam.The doubt is from Construction of Root Loci topic in section The Root Locus Technique of Control Systems
Answer» Correct CHOICE is (C) CIRCLE The explanation is: Complex conjugate roots of the CHARACTERISTIC EQUATION of the O.L.T.F.lie on circle.

Discussion

16.	Which one of the following is not the property of root loci?(a) The root locus is symmetrical about imaginary axis(b) They start from the open loop poles and terminate at the open loop zeroes(c) The breakaway points are determined from dK/ds = 0(d) Segments of the real axis are the part of the root locus if and only is the total number of real poles and zeroes to their right is odd.The question was posed to me in an interview for job.This key question is from The Root Locus topic in portion The Root Locus Technique of Control Systems
Answer» RIGHT answer is (a) The root locus is symmetrical about imaginary axis The EXPLANATION: The root locus is the locus traced DUE to the GAIN of the system with changing frequency and need not be symmetrical about ORIGIN.

Discussion

17.	The loop transfer function of an LTI system is G(s)H(s) =K(s+1)(s+5)/s(s+2)(s+3). For K>0, the point on the real axis that does not belong to the root locus of the system is(a) -0.5(b) -2.5(c) -3.5(d) -5.5I got this question by my school principal while I was bunking the class.The origin of the question is Construction of Root Loci in chapter The Root Locus Technique of Control Systems
Answer» CORRECT choice is (c) -3.5 Easiest explanation: The points PRESENT on the root locus are right to the ODD number of poles and zeroes.

Discussion

18.	The breakaway point calculated mathematically must always lie on the root locus.(a) True(b) FalseI got this question during an internship interview.Query is from The Root Locus in division The Root Locus Technique of Control Systems
Answer» RIGHT answer is (a) True The explanation: The BREAKAWAY point of the two branches of the root locus is the point where the two branches either meet or they break and MAY or may not ALWAYS lie on the root locus.

Discussion

19.	Root locus of s(s+2)+K(s+4) =0 is a circle. What are the coordinates of the center of this circle?(a) -2,0(b) -3,0(c) -4,0(d) -5,0I have been asked this question in an online interview.My doubt stems from The Root Locus Concepts topic in division The Root Locus Technique of Control Systems
Answer» The correct answer is (C) -4,0 For EXPLANATION I WOULD SAY: s(s+2)+K(s+4) =0 1+K(s+4)/s(s+2) =0. G(s)H(s) =K(s+b)/s(s+a) Centre =(-b,0) =(-4,0).

Discussion

20.	If root loci plots of a particular control system do not intersect the imaginary axis at any point, then the gain margin of the system will be:(a) 0(b) 0.707(c) 1(d) InfiniteI got this question at a job interview.The question is from The Root Locus topic in portion The Root Locus Technique of Control Systems
Answer» Right option is (d) Infinite For EXPLANATION: The gain MARGIN is the INVERSE of the intersection of the root LOCI PLOT to the imaginary axis and if it does not intersect then the gain margin will be infinite.

Discussion

21.	Routh Hurwitz criterion is better than root locus.(a) True(b) FalseThis question was addressed to me during an internship interview.The question is from The Root Locus Concepts in portion The Root Locus Technique of Control Systems
Answer» Right choice is (b) False Explanation: ROOT LOCUS is BETTER as it require less computation PROCESS.

Discussion

22.	Root locus is used to calculate:(a) Marginal stability(b) Absolute stability(c) Conditional stability(d) Relative stabilityI had been asked this question during an online exam.The question is from The Root Locus Concepts topic in division The Root Locus Technique of Control Systems
Answer» CORRECT option is (d) RELATIVE STABILITY Explanation: Root locus is USED to CALCULATE relative stability.

Discussion

23.	The characteristic equation of a control system is given as 1+ K(s+4)/s(s+7)(s^2+2s+2)=0. The real axis intercept for root locus asymptote is:(a) -2.25(b) -1(c) -1.67(d) 0The question was asked in quiz.Query is from Construction of Root Loci in chapter The Root Locus Technique of Control Systems
Answer» The correct option is (c) -1.67 To elaborate: Real AXIS intercept =centroid Zero =-4 and POLE = -7, -1, -1, 0 Centroid =Σreal part of open loop pole-Σreal part of open loop zeroes/P-Z Centroid = -7-1-1+4/3 = -1.67.

Discussion

24.	The addition of open loop zero pulls the root loci towards:(a) The left and therefore system becomes more stable(b) The right and therefore system becomes unstable(c) Imaginary axis and therefore system becomes marginally stable(d) The left and therefore system becomes unstableThe question was posed to me during an interview for a job.My question is taken from The Root Locus in chapter The Root Locus Technique of Control Systems
Answer» RIGHT CHOICE is (a) The left and therefore SYSTEM becomes more stable The BEST I can EXPLAIN: The system can become stable by reducing the damping and also by adding zeroes in the s plane andmoving left of the s plane system becomes more stable.

Discussion

25.	Which one of the following applications software’s is used to obtain an accurate root locus for?(a) LISP(b) MATLAB(c) dBase(d) OracleThe question was posed to me in an online quiz.The origin of the question is The Root Locus topic in section The Root Locus Technique of Control Systems
Answer» Correct option is (b) MATLAB Easy explanation: MATLAB stands for mathematics LABORATORY in which the INPUT is in the form of the matrix and is the BEST SOFTWARE for drawing root locus.

Discussion

26.	If the gain of the system is reduced to a zero value, the roots of the system in the s-plane,(a) Coincide with zero(b) Move away from zero(c) Move away from poles(d) Coincide with the polesThe question was asked at a job interview.I'm obligated to ask this question of The Root Locus topic in chapter The Root Locus Technique of Control Systems
Answer» Correct answer is (d) COINCIDE with the poles To explain: The roots of the system in s plane coincides with the poles if the gain of the system is reduced to a value ZERO.

Discussion

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Number of roots of characteristic equation is equal to the number of ______________(a) Branches(b) Root(c) Stem(d) PolesI have been asked this question during a job interview.This key question is from The Root Locus Concepts in division The Root Locus Technique of Control Systems

While increasing the value of gain K, the system becomes(a) Less stable(b) More stable(c) Unstable(d) Absolute stableThe question was posed to me in a job interview.This question is from The Root Locus Concepts in division The Root Locus Technique of Control Systems

Determine the centroid of the root locus for the system having G(s)H(s) = K/(s+1)(s^2+4s+5)(a) -2.1(b) -1.78(c) -1.66(d) -1.06I have been asked this question in a job interview.My query is from Construction of Root Loci in division The Root Locus Technique of Control Systems

The breakaway point calculated mathematically must always lie on the root locus.(a) True(b) FalseI got this question during an internship interview.Query is from The Root Locus in division The Root Locus Technique of Control Systems

Root locus of s(s+2)+K(s+4) =0 is a circle. What are the coordinates of the center of this circle?(a) -2,0(b) -3,0(c) -4,0(d) -5,0I have been asked this question in an online interview.My doubt stems from The Root Locus Concepts topic in division The Root Locus Technique of Control Systems

Routh Hurwitz criterion is better than root locus.(a) True(b) FalseThis question was addressed to me during an internship interview.The question is from The Root Locus Concepts in portion The Root Locus Technique of Control Systems

Root locus is used to calculate:(a) Marginal stability(b) Absolute stability(c) Conditional stability(d) Relative stabilityI had been asked this question during an online exam.The question is from The Root Locus Concepts topic in division The Root Locus Technique of Control Systems

The characteristic equation of a control system is given as 1+ K(s+4)/s(s+7)(s^2+2s+2)=0. The real axis intercept for root locus asymptote is:(a) -2.25(b) -1(c) -1.67(d) 0The question was asked in quiz.Query is from Construction of Root Loci in chapter The Root Locus Technique of Control Systems

Which one of the following applications software’s is used to obtain an accurate root locus for?(a) LISP(b) MATLAB(c) dBase(d) OracleThe question was posed to me in an online quiz.The origin of the question is The Root Locus topic in section The Root Locus Technique of Control Systems