MCQOPTIONS
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MCQOPTIONS
This section includes 49 Mcqs, each offering curated multiple-choice questions to sharpen your Control Systems knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Consider the transfer function\(G(s)H(s)=\frac{K}{(s^3+4s^2+s-6) }\)The root-locus plot of the system passes through s = 0. The value of K at this point will be |
| A. | 10 |
| B. | 0 |
| C. | 6 |
| D. | 8 |
| Answer» D. 8 | |
| 2. |
If a feedback control system has its open-loop transfer function\(G(s)H(s)=\frac{K}{s(s+2)(s^2+2s+5)}\)The coordinates of the centroid of the asymptotes of its root-locus are |
| A. | -1 and 0 |
| B. | 1 and 0 |
| C. | 0 and -1 |
| D. | 0 and 1 |
| Answer» B. 1 and 0 | |
| 3. |
For a 3rd order system given below, what is the frequency of oscillation?\(G(s)H(s) = \frac{K}{{({s^3} + 6{s^2} + 11s + 6)}}\) |
| A. | √6 rad/sec |
| B. | √11 rad/sec |
| C. | ±√11 rad/sec |
| D. | ±√6 rad/sec |
| Answer» C. ±√11 rad/sec | |
| 4. |
If the number of zeros are less than the number of poles, i.e. Z < P, then the value of the transfer function becomes zero for s → ∞. Hence we say that there are zeros at infinity and the order of such zeros is |
| A. | P + Z |
| B. | P - Z |
| C. | Z - P |
| D. | Z |
| Answer» C. Z - P | |
| 5. |
In root locus plot the angle of asymptote is given as __________. |
| A. | 360 degree/number of poles |
| B. | 360 degree/ number of zeroes |
| C. | 360 degree/(number of poles - number of zeroes) |
| D. | 360 degree/ (number of poles+ number of zeroes) |
| Answer» D. 360 degree/ (number of poles+ number of zeroes) | |
| 6. |
It is required that a control system given below has two roots to the right of section S = -2. Pick the possible ‘T’.\(TF\left( s \right)=\frac{1}{{{s}^{2}}\left( s+T \right)}\) |
| A. | 1 |
| B. | 8 |
| C. | 0.5 |
| D. | 0.25 |
| Answer» C. 0.5 | |
| 7. |
An open loop transfer function G(s) of a system is\(G\left( s \right) = \frac{K}{{s\left( {s + 1} \right)\left( {s + 2} \right)}}\)for a unity feedback system, the breakaway point of the root loci on the real axis occurs at. |
| A. | –0 .42 |
| B. | –1.58 |
| C. | –0.42 and 1.58 |
| D. | None of the above |
| Answer» B. –1.58 | |
| 8. |
Consider the following statements about roots locus:1. The root locus is symmetrical about real axis.2. If a root locus branch moves along the real axis from an open-loop pole to zero or to infinity, this root locus branch is called real root branch.3. The breakaway points of the root locus are the solutions of \(\frac{{dK}}{{ds}} = 0\)Which of the above statements are correct? |
| A. | 1 and 2 only |
| B. | 1 and 3 only |
| C. | 2 and 3 only |
| D. | 1, 2 and 3 |
| Answer» E. | |
| 9. |
In root-locus plot, the breakaway points |
| A. | should always be on the real axis alone |
| B. | must lie on the root loci |
| C. | must lie between 0 and -1 |
| D. | must lie outside the root loci |
| Answer» C. must lie between 0 and -1 | |
| 10. |
Consider the following statements:1. Adding a zero to the G(s)H(s) tends to push root locus to the left.2. Adding a pole to the G(s)H(s) tends to push root locus to the right.3. Complementary root locus (CRL) refers to root loci with positive K.4. Adding a zero to the forward path transfer function reduces the maximum overshoot of the system.Which of the above statements are correct? |
| A. | 1, 2 and 3 only |
| B. | 3 and 4 only |
| C. | 1, 2 and 4 only |
| D. | 1, 2, 3 and 4 |
| Answer» D. 1, 2, 3 and 4 | |
| 11. |
A linear time invariant (LTI) system with the transfer function\(G\left( s \right) = \frac{{K\left( {{s^2} + 2s + 2} \right)}}{{\left( {{s^2} - 3s + 2} \right)}}\)Is connected in unity feedback configuration as shown in the figureFor the closed-loop system shown, the root locus for 0 < K < ∞ intersects the imaginary axis for K = 1.5. The closed-loop system is stable for |
| A. | K > 1.5 |
| B. | 1 > K < 1.5 |
| C. | 0 < K < 1 |
| D. | no positive value of K |
| Answer» B. 1 > K < 1.5 | |
| 12. |
A unity feed-back system has open-loop transfer function \(G\left( s \right)H\left( s \right) = \frac{K}{{s\left( {s + 4} \right)\left( {s + 16} \right)}}\)Its root locus plot intersects the jω axis at |
| A. | ± j2 |
| B. | ± j4 |
| C. | ± j8 |
| D. | does not intersect the jω axis |
| Answer» D. does not intersect the jω axis | |
| 13. |
Consider a unity negative feedback system with feed forward gain \(G\left( s \right) = \frac{K}{{s\left( {s + 1} \right)\left( {s + 2} \right)}}\)The root-loci of the system cross the imaginary axis at: |
| A. | \(s = \pm j\sqrt 3 \) |
| B. | s = ± j2 |
| C. | s = ± j3 |
| D. | \(s = \pm \;j\sqrt 2\) |
| Answer» E. | |
| 14. |
In the root locus plot shown in the figure, the pole/zero marks and the arrows have been removed. Which one of the following transfer functions has this root locus? |
| A. | \(\frac{{s + 1}}{{\left( {s + 2} \right)\left( {s + 4} \right)\left( {s + 7} \right)}}\) |
| B. | \(\frac{{s + 4}}{{\left( {s + 1} \right)\left( {s + 2} \right)\left( {s + 7} \right)}}\) |
| C. | \(\frac{{s + 7}}{{\left( {s + 1} \right)\left( {s + 2} \right)\left( {s + 4} \right)}}\) |
| D. | \(\frac{{\left( {s + 1} \right)\left( {s + 2} \right)}}{{\left( {s + 7} \right)\left( {s + 4} \right)}}\) |
| Answer» C. \(\frac{{s + 7}}{{\left( {s + 1} \right)\left( {s + 2} \right)\left( {s + 4} \right)}}\) | |
| 15. |
Form the given system determine the number of loci, starting points, ending points and number of asymptotes. |
| A. | 2, (2,4), (2 + j4, 2 – j4), 0 respectively |
| B. | 1, (-2, -4), (2 + j4, 2 – j4), 0 respectively |
| C. | 2, (-2, -4), (2 + j4,2 – j4),0 respectively |
| D. | 1, (2,4), (2 + j4, 2 – j4), 0 respectively |
| Answer» D. 1, (2,4), (2 + j4, 2 – j4), 0 respectively | |
| 16. |
Direction: It consists of two statements, one labelled as Statement (I) and the other as Statement (II). Examine these two statements carefully and select the answers to these items using the codes given below:Statement (I): A root locus is obtained using the closed-loop poles.Statement (II): A root locus is plotted using the open-loop poles. |
| A. | Both statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I) |
| B. | Both statement (I) and Statement (II) are individually true and Statement (II) is not the correct explanation of Statement (I) |
| C. | Statement (I) is true but Statement (II) is false |
| D. | Statement (I) is false but Statement (II) is true |
| Answer» E. | |
| 17. |
A graphical technique for plotting the closed-loop poles of a rational system functions as a function of the value of gain for both continuous-time and a discrete-time system is |
| A. | Root locus method |
| B. | Nyquist criterion method |
| C. | Bode plot method |
| D. | Routh-Hurwitz criterion method |
| Answer» B. Nyquist criterion method | |
| 18. |
In a control system with unity gain feedback, the plant has the transfer function P(s) = 3/s. Assuming that a controller of the form C(s) = K/ (s + P) is used, where K is a positive constant, the value of P for which the root-locus of the closed-loop system passes through the points \(- 3 \pm j3\sqrt 3\) where \(j = \sqrt { - 1}\), is |
| A. | 3 |
| B. | \(3\sqrt 3\) |
| C. | 6 |
| D. | 9 |
| Answer» D. 9 | |
| 19. |
Find the number of asymptotes of the root locus point for the open-loop transfer function of unity feedback system given by \(G\left( s \right) = \frac{5}{{\left( {s + 1} \right)\left( {s + 2} \right)\left( {s + 3} \right)}}\) |
| A. | 5 |
| B. | 4 |
| C. | 3 |
| D. | 2 |
| Answer» D. 2 | |
| 20. |
Consider a feedback system with the characteristic equation \(1 + K\frac{1}{{s\left( {s + 1} \right)\left( {s + 2} \right)}} = 0\;\)for root locus. The angles of asymptotes ϕA and the centroid of the asymptotes –σA, are respectively |
| A. | 60°, 120°, 180° and -1 |
| B. | 45°, 90°, 300° and 0 |
| C. | 60°, 180°, 300° and -1 |
| D. | 45°, 90°, 180° and 0 |
| Answer» D. 45°, 90°, 180° and 0 | |
| 21. |
Consider a unity feedback system with open loop transfer function \(G(s)=\frac{K}{(s-1)(s^2 + 4s+7)}\)A root locus exist on the real axis between |
| A. | \(s=1 ~\ and~s=-\infty\) |
| B. | \(s=1 ~\ and~s=-2\) |
| C. | \(s=-1 ~\ and~s=-\infty\) |
| D. | \(s=-2 ~\ and~s=-\infty\) |
| Answer» B. \(s=1 ~\ and~s=-2\) | |
| 22. |
A unity feedback system has an open-loop transfer function \(G\left( s \right) = \frac{{K\left( {s + 4} \right)}}{{\left( {s + 1} \right)\left( {s + 2} \right)}}\)The portions of the real axis that lie on the root loci are between |
| A. | s = -2 and s = -4; s = -1 and +∞ |
| B. | s = -1 and s = -2; s = -4 and -∞ |
| C. | s = 0 and s = -2, beyond s = -4 |
| D. | s = 0 and s = -1 |
| Answer» C. s = 0 and s = -2, beyond s = -4 | |
| 23. |
If the open transfer function of a feedback system is given be \(G(s)H(s)=\frac{K}{s(s+2)(s^2+2s+5)}\) then the centroid of the asymptotes will be |
| A. | -1, j0 |
| B. | 1, j0 |
| C. | 0, -j1 |
| D. | 0, j1 |
| Answer» B. 1, j0 | |
| 24. |
If the gain of the system is reduced to zero value, the roots of the system in the s-plane: |
| A. | Coincide with zeros |
| B. | Move away from the zeros |
| C. | Move away from the poles |
| D. | Coincide with the poles |
| Answer» E. | |
| 25. |
Given the root locus of a system \(G(s) = \frac{4K}{(s+1)(s+3)}\)What will be the gain for obtaining the damping ratio of 0.707? |
| A. | 1/4 |
| B. | 5/4 |
| C. | -3/4 |
| D. | 11/4 |
| Answer» C. -3/4 | |
| 26. |
In root locus method, the value of K is obtained as |
| A. | Product of length of vectors from poles / Product of length of vectors from zeros |
| B. | (Product of length of vectors from poles) × (Product of length of vectors from zeros) |
| C. | Product of length of vectors from zeros / Product of length of vectors from poles |
| D. | Product of length of vectors from zeros + Product of length of vectors from poles |
| Answer» B. (Product of length of vectors from poles) × (Product of length of vectors from zeros) | |
| 27. |
Direction: It consists of two statements, one labelled as Statement (I) and the other as Statement (II). Examine these two statements carefully and select the answers to these items using the codes given below:Statement (I): Inverse root locus is the image of the direct root locus.Statement (II): Root locus is symmetrical about the imaginary axis |
| A. | Both statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I) |
| B. | Both statement (I) and Statement (II) are individually true and Statement (II) is not the correct explanation of Statement (I) |
| C. | Statement (I) is true but Statement (II) is false |
| D. | Statement (I) is false but Statement (II) is true |
| Answer» D. Statement (I) is false but Statement (II) is true | |
| 28. |
Consider that in a system loop transfer function, the addition of a pole results in the following :1. Root locus gets pulled to the right-hand side2. Steady-state error is increased3. System response gets slowerWhich of the above is correct? |
| A. | 1, 2 and 3 |
| B. | 1 and 2 only |
| C. | 1 and 3 only |
| D. | 2 and 3 only |
| Answer» D. 2 and 3 only | |
| 29. |
Direction: It consists of two statements, one labelled as Statement (I) and the other as Statement (II). Examine these two statements carefully and select the answers to these items using the codes given below:Statement (I): Centroid is the point where the root loci break from the real axis.Statement (II): Centroid is the point on the real axis where all the asymptotes intersect. |
| A. | Both statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I) |
| B. | Both statement (I) and Statement (II) are individually true and Statement (II) is not the correct explanation of Statement (I) |
| C. | Statement (I) is true but Statement (II) is false |
| D. | Statement (I) is false but Statement (II) is true |
| Answer» E. | |
| 30. |
If root loci plots of a particular control system intersect the imaginary axis at any point, then the gain margin (in dB) of the system will be |
| A. | 0 |
| B. | 0.707 |
| C. | 1.0 |
| D. | Infinite |
| Answer» B. 0.707 | |
| 31. |
Direction: It consists of two statements, one labelled as Statement (I) and the other as Statement (II). Examine these two statements carefully and select the answers to these items using the codes given below:Statement (I): At breakaway point the system is critically damped.Statement (II): At the point where root loci intersect with the imaginary axis, the system is marginally stable. |
| A. | Both statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I) |
| B. | Both statement (I) and Statement (II) are individually true and Statement (II) is not the correct explanation of Statement (I) |
| C. | Statement (I) is true but Statement (II) is false |
| D. | Statement (I) is false but Statement (II) is true |
| Answer» C. Statement (I) is true but Statement (II) is false | |
| 32. |
Consider a feedback control system:The root locus of the system has which of the following characteristics? |
| A. | Root loci exist on the negative real axis between -2 and -1 and between -3 and -∞. When K → ∞, the root loci terminate at s = -2 and s = -3 |
| B. | Root loci exist on the negative real axis between 0 and -1 and between -2 and -3. When K → ∞, two roots are going to - ∞ |
| C. | Root loci exist on the negative real axis between 0 and -1 between -2 and -3. When K → ∞, two roots are going to ∞. |
| D. | Root loci exist on the negative real axis between 0 and -1 and between -2 and -3. When K → ∞, the root loci terminate at s = -2 and s = -3 |
| Answer» E. | |
| 33. |
A unity feedback control system has an open loop transfer function which is given as \(G(s) =\frac{K} {{s(s + 4)}}\). Find the angle of asymptotes. |
| A. | 55°, 56° |
| B. | 90°, 270° |
| C. | 45°, 115° |
| D. | 109°, 34° |
| Answer» C. 45°, 115° | |
| 34. |
A system has its open-loop transfer function of \(\frac{K}{s(s^2+6s+10)}\). The break-points are at s = -1.18 and s = -2.82, the centroid is at s = -2, while the asymptotic angles are ± 60° ± 180°. The value of K for the closed-loop system to be oscillatory and the frequency of oscillations are respectively: |
| A. | 600 and 10 rad / sec |
| B. | 120 and 5 rad / sec |
| C. | 60 and 3.16 rad / sec |
| D. | 30 and 3.16 rad / sec |
| Answer» D. 30 and 3.16 rad / sec | |
| 35. |
Consider a feedback system with the characteristic equation \(1 + K\frac{1}{{s\left( {s + 1} \right)\left( {s + 2} \right)}} = 0\)The asymptotes of the three branches of root locus plot of this system will form the following angles with the real axis |
| A. | 60°, 120° and 300° |
| B. | 60°, 120° and 180° |
| C. | 60°, 180° and 300° |
| D. | 40°, 120° and 200° |
| Answer» D. 40°, 120° and 200° | |
| 36. |
Consider the system with \(G(s)=\frac{K(s+2)}{(s^2+2s+3)}\) and H(s) = 1. The breakaway point(s) of the root loci is / are at |
| A. | – 0.265 only |
| B. | – 3.735 only |
| C. | – 3.735 and -0.265 |
| D. | There is no breakaway point |
| Answer» C. – 3.735 and -0.265 | |
| 37. |
For the open-loop system \(G\left( s \right)H\left( s \right) = \frac{K}{{s\left( {s + 1} \right)\left( {s + 2} \right)}}\) the breakaway point is |
| A. | - 0.23 |
| B. | - 0.42 |
| C. | - 1.47 |
| D. | - 3.47 |
| Answer» C. - 1.47 | |
| 38. |
" 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." |
| Answer» B. " They start from the open loop poles and terminate at the open loop zeroes" | |
| 39. |
Number of roots of characteristic equation is equal to the number of ______________ |
| A. | Branches |
| B. | Root |
| C. | Stem |
| D. | Poles |
| Answer» B. Root | |
| 40. |
" 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. | " Infinite" |
| Answer» E. | |
| 41. |
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-circle |
| Answer» D. Semi-circle | |
| 42. |
" 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. | " -3" |
| Answer» D. " -3" | |
| 43. |
" 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 zeroes" |
| Answer» D. " The sum of the number of poles and the number of the zeroes" | |
| 44. |
" 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 poles" |
| Answer» E. | |
| 45. |
" 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 unstable" |
| Answer» B. " The right and therefore system becomes unstable" | |
| 46. |
" When the number of poles is equal to the number of zeroes, how many branches of root locus tends towards infinity?" |
| A. | " 1" |
| B. | " 2" |
| C. | " 0" |
| D. | " Equal to number of zeroes" |
| Answer» D. " Equal to number of zeroes" | |
| 47. |
" Which one of the following are correct?The root locus is the path of the roots of the characteristic equation traced out in the s-plane?" |
| A. | " As the input of the system is changed" |
| B. | " As the output of the system is changed" |
| C. | " As a system parameter is changed" |
| D. | " As the sensitivity is changed" |
| Answer» D. " As the sensitivity is changed" | |
| 48. |
" Which one of the following applications software's is used to obtain an accurate root locus for?" |
| A. | " LISP" |
| B. | " MATLAB" |
| C. | " dBase" |
| D. | " Oracle" |
| Answer» C. " dBase" | |
| 49. |
" The breakaway point calculated mathematically must always lie on the root locus." |
| A. | " True" |
| B. | " False" |
| Answer» B. " False" | |