Electrical Engineering (EE) Exam  >  Electrical Engineering (EE) Notes  >  Control Systems  >  Previous Year Questions- Root Locus Techniques

Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE) PDF Download

Q1: Consider the closed-loop system shown in the figure with
Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE) The root locus for the closed-loop system is to be drawn for 0 ≤ K 

lt ∞. The angle of departure (between 0° and 360°) of the root locus branch drawn from the pole (−1 + j2), in degree, is ______ (rounded off to the nearest integer).  (2024)
Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)(a) 2
(b) 9
(c) 7
(d) 11
Ans:
(c)
Sol: Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)
Q2: The open loop transfer function of a unity gain negative feedback system is given by Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)
The range of k for which the system is stable, is  (2022)
(a) k > 3
(b) k < 3
(c) k > 5
(d) k < 5
Ans:
(c)
Sol: Characteristic equation:
Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)R-H criteria:
Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)Hence, for stable system,
k−5>0 ⇒ k>5

Q3: The root locus of the feedback control system having the characteristic equation s+ 6Ks + 2s + 5 = 0 where K > 0, enters into the real axis at  (SET-2 (2017))
(a) s = -1
(b) s = −√5
(c) s = -5
(d) s = √5
Ans: 
(b)
Sol: Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)The point at which root locus enters real axis (break away point) is given by
Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)
Q4: The gain at the breakaway point of the root locus of a unity feedback system with open loop transfer function Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE) is  (SET-2(2016))
(a) 1
(b) 2
(c) 5
(d) 9
Ans:
(a)
Sol: Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)Now, characteristic equation,
Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)For break away point: dK/ds = 0
Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)Therefore valid break away point is s = 2
Now gain at s = 2 is
K = (Product of distances from all the poles to break away point)/(Product of distances from all the zero to break away point)
Gain, Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)

Q5: An open loop transfer function G(s) of a system is Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE) For a unity feedback system, the breakaway point of the root loci on the real axis occurs at,   (SET-2 (2015))
(a) -0.42
(b) -1.58
(c) -0.42 and -1.58
(d) none of the above
Ans: 
(a)
Sol: Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)Only s = -0.422 lie on root locus. Therefore brakaway point is s = -0.42.

Q6: The open loop poles of a third order unity feedback system are at 0, -1, -2. Let the frequency corresponding to the point where the root locus of the system transits to unstable region be K. Now suppose we introduce a zero in the open loop transfer function at -3, while keeping all the earlier open loop poles intact. Which one of the following is TRUE about the point where the root locus of the modified system transits to unstable region?  (SET-1(2015))
(a) It corresponds to a frequency greater than K
(b) It corresponds to a frequency less than K
(c) It corresponds to a frequency K
(d) Root locus of modified system never transits to unstable region
Ans:
(d)
Sol: Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)as root locus never cross asymptotes so, will remain in left sideof x-axis.

Q7: The root locus of a unity feedback system is shown in the figure.
Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)The closed loop transfer function of the system is  (SET-1(2014))
(a) Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)

(b) Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)
(c) Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)
(d) Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)
Ans: (c)
Sol: This is converse root locus having no zero.
As, its G(s) H(s) Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)
Its converse root locus only valid when K < 0
So, C.L.T.F. Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)

=G(s)H(s)1G(s)H(s)=K(s+1)(s+2)1K(s+1)(s+2)=K(s+1)(s+2)KQ8: The open loop transfer function G(s) of a unity feedback control system is given as
Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE) From the root locus, at can be inferred that when k tends to positive infinity,  (2011)
(a) Three roots with nearly equal real parts exist on the left half of the s-plane
(b) One real root is found on the right half of the s-plane
(c) The root loci cross the jωjω axis for a finite value of k; k ≠ 0
(d) Three real roots are found on the right half of the s-plane
Ans:
(a)
Sol: Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)Characteristic equation, 1 + G(s)H(s) = 0
Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)Routh array:
Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)As k > 0, there is no sign change in the 1st column of routh array. So the system is stable and all the three roots lie on LHS of s-plane.
For k > 0 (k ≠ 0), none of the row of Routh array becomes zero. So root loci does not cross the jω-axis.
Number of Zero = Z = 1
Number of poles = P =3
Number of branches terminating at infinity = P - Z = 3 - 1 =2
Angle of asymptotes  = Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)Since, all the three branches terminates at Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE) So, all the three roots have nearly equal real parts.

Q9: The characteristic equation of a closed-loop system is s(s+1)(s+3)k(s+2) = 0, k > 0. Which of the following statements is true?  (2010)
(a) Its root are always real
(b) It cannot have a breakaway point in the range −1< Re[s] < 0
(c) Two of its roots tend to infinity along the asymptotes Re[s] = -1
(d) It may have complex roots in the right half plane.
Ans: 
(c)
Sol: Characteristic equation,
Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)G(s)H(s) = open-loop transfer function (OLTF) = k(s+2)/s(s+1)(s+2)
Number of zeros = Z = 1 zero at -2
Number of poles = P = 3 poles at 0, -1 and -3
Number of branches terminating at infinity
= P − Z = 3 − 1 = 2
Angle of asymptotes  
Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)Breakaway point lies in the range −1 < Re[s] < 0  and two branches terminates at infinityalong the asymptotes Re(s) = −1.

Q10: A closed-loop system has the characteristic function (s− 4)(s + 1) + K(s − 1) = 0. Its root locus plot against K is  (2006)
(a) Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)(b) Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)(c) Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)(d) Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)Ans: 
(b)
Sol: Characteristic function
Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE) Zero of OLTF s = 1; z = 1
Poles of OLTS s = -1, -2, +2, P = 3
Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)The root locus starts from open-loop poles and terminates either on open-loop zero or infinity.
Root locus exist on section of real axis it the sum of the open-loop poles and zeros to the right of the section is odd.
Number of branches teminating on infinity.
= P - Z = 3 - 1 = 2
Angle of asymptotes
Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)Intersection of asymptotes on real axis (centroid)
Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)Option (B) is correct on the basic of above analysis.

Q11: Figure shows the root locus plot (location of poles not given) of a third order system whose open loop transfer function is (2005)
Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)(a) K/s3
(b) Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)

(c) Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)
(d) Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)
Ans: (a)
Sol: Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)These are three asymptotes with angle 60°, 180° and 300°
Angle of asymptotes Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)
Where, k = 0, 1, 2 up to (P-Z)-1 as angle are 60°, 180° and 300°
it means P - Z = 3
Intersection of asymptotes on real axis
Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)Since, system does not have zeroes
Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)As asymptotes intersect at origin, it means all the three poles are on right
Hence, Option (A) is correct.

Q12: A unity feedback system has an open loop transfer function, G(s) = K/s2. The root locus plot is  (2002)
(a) Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)(b) Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)(c) Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)(d) Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)Ans:
(b)
Sol: Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)Angle of asymptotes = 90°, 270°
∴ Option (B) is correct.

Q13: In case of an armature controlled separately excited dc motor drive with closedloop speed control, an inner current loop is useful because it  (2001)
(a) limits the speed of the motor to a safe value
(b) helps in improving the drive energy efficiency
(c) limits the peak current of the motor to the permissible value
(d) reduces the steady state speed error
Ans:
(c)
Sol: Closed loop system limits the peak value.

The document Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE) is a part of the Electrical Engineering (EE) Course Control Systems.
All you need of Electrical Engineering (EE) at this link: Electrical Engineering (EE)
53 videos|73 docs|40 tests

Top Courses for Electrical Engineering (EE)

FAQs on Previous Year Questions- Root Locus Techniques - Control Systems - Electrical Engineering (EE)

1. What is the root locus technique in control systems?
Ans. The root locus technique is a graphical method used in control theory to analyze and design control systems. It provides a way to visualize how the roots of the characteristic equation (poles of the closed-loop transfer function) change as a system parameter, typically the gain, varies. This helps engineers understand system stability and performance as they modify the gain.
2. How do you construct a root locus plot?
Ans. To construct a root locus plot, follow these steps: 1. Identify the open-loop transfer function of the system. 2. Determine the poles and zeros of the transfer function. 3. Plot the poles (X) and zeros (O) on the complex plane. 4. Use the root locus rules, such as symmetry about the real axis, to draw the paths that the poles will follow as gain changes from 0 to infinity. 5. Mark the breakaway and break-in points, if necessary, and identify any asymptotes if the number of poles exceeds the number of zeros.
3. What are the rules for root locus construction?
Ans. The main rules for root locus construction include: 1. The locus starts at the open-loop poles and ends at the open-loop zeros. 2. The number of branches of the locus equals the number of open-loop poles. 3. The locus is symmetrical about the real axis. 4. At points where the angle of the locus is 180 degrees, the gain is infinite. 5. The loci will break away from the real axis at breakaway points determined by the derivative of the characteristic equation.
4. What is the significance of the breakaway and break-in points in root locus?
Ans. Breakaway points are locations on the real axis where the root locus leaves the real axis as gain increases, indicating a change in system stability. Break-in points are locations where the root locus returns to the real axis after entering the complex plane. These points are significant as they provide insight into how system stability and transient response change with varying gain, helping engineers design more stable systems.
5. How does the root locus method help in system stability analysis?
Ans. The root locus method aids in stability analysis by allowing engineers to visualize how the location of the closed-loop poles changes with varying gain. If the poles move into the right half of the complex plane, the system becomes unstable. By analyzing the root locus plot, engineers can determine suitable gain values that keep the poles in the left half-plane, ensuring system stability while also achieving desired performance characteristics.
53 videos|73 docs|40 tests
Download as PDF
Explore Courses for Electrical Engineering (EE) exam

Top Courses for Electrical Engineering (EE)

Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

video lectures

,

Objective type Questions

,

Previous Year Questions with Solutions

,

Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)

,

pdf

,

Important questions

,

shortcuts and tricks

,

past year papers

,

Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)

,

Exam

,

Previous Year Questions- Root Locus Techniques | Control Systems - Electrical Engineering (EE)

,

MCQs

,

Free

,

ppt

,

Sample Paper

,

mock tests for examination

,

Viva Questions

,

Extra Questions

,

Summary

,

Semester Notes

,

practice quizzes

,

study material

;