MCQOPTIONS
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MCQOPTIONS
This section includes 70 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. |
For a unity feedback control system having an open-loop transfer function \(G\left( s \right) = \frac{{25}}{{s\left( {s + 6} \right)}}\), what is the time tp at which the peak of the step input response occurs? |
| A. | 0.52 s |
| B. | 2.75 s |
| C. | 0.79 s |
| D. | 1.57 s |
| Answer» D. 1.57 s | |
| 2. |
A third order system is approximated to an equivalent second order system. The rise time of this approximated system will be |
| A. | Same as the original system for any input |
| B. | Smaller than the original system for any input |
| C. | Larger than the original system for any input |
| D. | Smaller or larger depending on the type of input |
| Answer» C. Larger than the original system for any input | |
| 3. |
For a unity feedback system whose open-loop transfer function is given by \(G\left( s \right) = \frac{{50}}{{\left( {1 + 0.1s} \right)\left( {1 + 2s} \right)}}\) its position error constant is: |
| A. | 50 |
| B. | 25 |
| C. | 0 |
| D. | 1 |
| Answer» B. 25 | |
| 4. |
Consider the following statements regarding poles and zeros of network function.a) The total number of poles is equal to the total number of zeros in a rational network functionb) The poles and zeros of a network function determine the magnitude of the responsec) The poles of a network function determine the waveform of the time variation of the responseWhich of the above statements are correct? |
| A. | (a) and (b) only |
| B. | (a) and (c) only |
| C. | (b) and (c) only |
| D. | (a), (b) and (c) |
| Answer» E. | |
| 5. |
Consider a system with positional constant Kp = 500. The system is _____, Type _____ with error per unit step value of ______. |
| A. | Stable, 0, 1/501 |
| B. | Unstable, 0, 501 |
| C. | Stable, 1, 1/501 |
| D. | Stable, 1, 501 |
| Answer» B. Unstable, 0, 501 | |
| 6. |
In the standard form of closed loop transfer function of second order system is given by C(s)/R(s)= ω2n /s2+2ςωns+ω2n The damping ratio ζ = 0, then the system is |
| A. | undamped system |
| B. | under damped system |
| C. | critically damped system |
| D. | over damped system |
| Answer» B. under damped system | |
| 7. |
If a system is critically damped and the gain is increased, the system |
| A. | become over damped |
| B. | become underdamped |
| C. | become oscillatory |
| D. | remains critically damped |
| Answer» C. become oscillatory | |
| 8. |
For a unity feedback control with \(G\left( s \right) = \frac{9}{{s\left( {s + 3} \right)}}\), the damping ratio is |
| A. | 0.5 |
| B. | 1 |
| C. | 0.707 |
| D. | 0.33 |
| Answer» B. 1 | |
| 9. |
A unity feedback stable control system having \(G\left( s \right) = \frac{k}{{s\left( {s + a} \right)}}\) is critically damped. Now if the gain k is increased, the system will be |
| A. | Overdamped |
| B. | Underdamped |
| C. | Critically damped |
| D. | Undamped |
| Answer» C. Critically damped | |
| 10. |
A unity feedback control system has an open loop transfer function \(G\left( s \right) = \frac{25}{{s\left( {s + 8} \right)}}\). Its damping ratio is |
| A. | 0.2 |
| B. | 0.5 |
| C. | 0.8 |
| D. | 0.99 |
| Answer» D. 0.99 | |
| 11. |
For a second-order differential equation, if the damping ration ζ is unity, then |
| A. | The poles are imaginary and complex conjugate |
| B. | The poles are in the right half of s-plane |
| C. | The poles are equal, negative and real |
| D. | Both the poles are unequal, negative and real |
| Answer» D. Both the poles are unequal, negative and real | |
| 12. |
Consider a system with transfer function \(\frac{{9}}{{{s^2} + 4s + 9}}\) ; The system has _____, _____, and _____ |
| A. | ζ = 0.667, ωn = 3, underdamped |
| B. | ζ = 0.222, ωn = 9, undamped |
| C. | ζ = 0.667, ωn = 9, undamped |
| D. | ζ = 0.222, ωn = 3, underdamped |
| Answer» B. ζ = 0.222, ωn = 9, undamped | |
| 13. |
Consider the following statements regarding the effect of adding a pole in the open-loop transfer function on the closed-loop step response:1. It increases the maximum overshoot.2. It increases the rise time.3. It reduces the bandwidth.Which of the above statements are correct? |
| A. | 1, 2 and 3 |
| B. | 1 and 2 only |
| C. | 2 and 3 only |
| D. | 1 and 3 only |
| Answer» B. 1 and 2 only | |
| 14. |
For a second order dynamic system, if the damping ratio is 1 then the poles are |
| A. | Imaginary and complex conjugate |
| B. | In the right-half of s-plane |
| C. | Equal, negative and real |
| D. | Negative and real |
| Answer» D. Negative and real | |
| 15. |
A unity feedback system is characterized by an open-loop transfer function of \(G\left( s \right) = \frac{K}{{s\left( {s + 10} \right)}}\). Value of K required in order to have a damping ratio of 0.5 is: |
| A. | 50 |
| B. | 10 |
| C. | 20 |
| D. | 100 |
| Answer» E. | |
| 16. |
A system described by the following differential equation is initially at rest and then excited by the input x(t) = 3u(t):\(\frac{d^2 y}{dt^2}+4 \frac{dy}{dt}+3y=x(t)\) The output y(t) is |
| A. | 1 – 1.5e-t + 0.5e-3t |
| B. | 1 – 0.5e-t + 1.5e-3t |
| C. | 1 + 1.5e-t + 0.5e-3t |
| D. | 1 + 0.5e-t – 0.5e-3t |
| Answer» B. 1 – 0.5e-t + 1.5e-3t | |
| 17. |
For type-2 system, the steady state errors for unit step and unit ramp input are |
| A. | 0 & ∞ |
| B. | ∞ & 0 |
| C. | 0 & 0 |
| D. | ∞ & ∞ |
| Answer» D. ∞ & ∞ | |
| 18. |
Consider unity feedback system with forward path transfer function 25/s(s + 5); what are the values of peak time and settling time? |
| A. | 1.6 sec, 0.726 sec |
| B. | 0.726 sec, 1.6 sec |
| C. | 0.5 sec, 0.726 sec |
| D. | 0.726 sec, 1 sec |
| Answer» C. 0.5 sec, 0.726 sec | |
| 19. |
A linear time-invariant system has an impulse response of e2t, t > 0. if the input is e3t, the output for t > 0 is |
| A. | e3t – e2t |
| B. | e5t |
| C. | e3t + e2t |
| D. | et |
| Answer» B. e5t | |
| 20. |
A second-order system is described by the equation\(\frac{d^2 x}{dt^2}+5 \frac{dx}{dt}+7x=7y \)The frequency and damping ratio respectively are: |
| A. | 1 rad / sec and 5 |
| B. | 5 rad / sec and 7 |
| C. | 1 rad / sec and √7 |
| D. | √7 rad / sec and 0.94 |
| Answer» E. | |
| 21. |
A second order has 0 < ζ < 1, the poles of the system are: |
| A. | Real but not repeated |
| B. | Real and repeated |
| C. | Complex conjugate |
| D. | Purely imaginary |
| Answer» D. Purely imaginary | |
| 22. |
If the damping factor of a control system is unity, its response will be: |
| A. | Oscillatory |
| B. | Un-damped |
| C. | Under-damped |
| D. | Critically damped |
| Answer» E. | |
| 23. |
For a unit step input a system with forward path transfer function G(s) = 20 / s2 and feedback path transfer function H(s) = (s + 5), has a steady state output of |
| A. | 2 |
| B. | 0.5 |
| C. | 0.2 |
| D. | 1 |
| Answer» D. 1 | |
| 24. |
In a type-1, second-order system, the first undershoot occurs at a time t (with standard notations) is |
| A. | \(\frac{\pi }{{{\omega _d}}}\) |
| B. | \(\frac{{2\pi }}{{{\omega _d}}}\) |
| C. | \(\frac{\pi }{{2{\omega _d}}}\) |
| D. | \(\frac{{2{\omega _d}}}{\pi }\) |
| Answer» C. \(\frac{\pi }{{2{\omega _d}}}\) | |
| 25. |
A system is described by the transfer function \(G(s)=\frac{(2s+5)}{(s+5)(s+4)}\). The dc gain of the system is |
| A. | 0.25 |
| B. | 0.5 |
| C. | 1 |
| D. | ∞ |
| Answer» B. 0.5 | |
| 26. |
For the system \(\frac{{C\left( s \right)}}{{R\left( s \right)}} = \frac{{16}}{{{s^2} + 8s + 16}}\)The nature of the time response will be |
| A. | Over damped |
| B. | Under damped |
| C. | Critically damped |
| D. | Steady |
| Answer» D. Steady | |
| 27. |
Consider a unity feedback closed loop system with open loop function as \(\frac{{150\left( {s + 3} \right)\left( {s + 4} \right)}}{{s\left( {s + 2} \right)\left( {s + 6} \right)}}\); if the system is excited with unit step, unit ramp and unit parabolic input, steady state errors are ______, _____ and _____ respectively. |
| A. | 0, 1/150, ∞ |
| B. | 0, 0, 1/150 |
| C. | 0, 150, ∞ |
| D. | 0, 1/150, 3/367 |
| Answer» B. 0, 0, 1/150 | |
| 28. |
Match the transfer functions of the second-order systems with the nature of the systemsgiven below.Transfer functionsNature of systemP: \(\frac{{15}}{{{s^2} + 5s + 15}}\)Q: \(\frac{{25}}{{{s^2} + 10s + 25}}\)R: \(\frac{{35}}{{{s^2} + 18s + 35}}\)I: OverdampedII: Critically dampedIII: Underdamped |
| A. | P-I, Q-II, R-III |
| B. | P-II, Q-I, R-III |
| C. | P-III, Q-II, R-I |
| D. | P-III, Q-I, R-II |
| Answer» D. P-III, Q-I, R-II | |
| 29. |
A unity feedback system is characterized by the open-loop transfer function:\(G\left( s \right) = \frac{1}{{s\left( {0.5s + 1} \right)\left( {0.2s + 1} \right)}}\)The steady-state errors for unit-step and unit-ramp inputs are respectively |
| A. | 0 and 0 |
| B. | 0 and 1 |
| C. | 1 and 0 |
| D. | 1 and 1 |
| Answer» C. 1 and 0 | |
| 30. |
Directions: The following quiestion consists of two statements, one labelled as the ‘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): Transfer function approach is inadequate when the time-domain solution is required.Statement (II): All initial conditions of the system are neglected in derivation of transfer function.Codes: |
| 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 but 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» B. Both Statement (I) and Statement (II) are individually true but Statement (II) is not the correct explanation of Statement (I) | |
| 31. |
Consider the unit step response of the system defined as \(G(s) = \frac{g}{s+10}\) and read the following.(i) Kg is the gain of the system(ii) Rt is the transient response of the system(iii) Ess is the steady-state error of the systemArrange the above in increasing order of their numerical values for the given system |
| A. | (i), (ii), (iii) |
| B. | (i), (iii), (ii) |
| C. | (iii), (ii), (i) |
| D. | (ii), (iii), (i) |
| Answer» D. (ii), (iii), (i) | |
| 32. |
In unity feedback system is shown in the figure. What is the magnitude of K so that the system is under-damped? |
| A. | K = 0 |
| B. | \(K = \frac{{{a^2}}}{4}\) |
| C. | \(K < \frac{{{a^2}}}{4}\) |
| D. | \(K > \frac{{{a^2}}}{4}\) |
| Answer» E. | |
| 33. |
In general which of the following system is preferred? |
| A. | Under-damped |
| B. | Over-damped |
| C. | Undamped |
| D. | Critically damped |
| Answer» B. Over-damped | |
| 34. |
Given a unity feedback system with \(G\left( s \right) = \frac{K}{{s\left( {s + 4} \right)}}\), the value of K for damping ratio of 0.5 is |
| A. | 1 |
| B. | 4 |
| C. | 16 |
| D. | 64 |
| Answer» D. 64 | |
| 35. |
In a unity feedback control system, the open-loop transfer function is\(G\left( s \right) = \frac{{K\left( {s + 2} \right)}}{{{s^2}\left( {{s^2} + 7s + 12} \right)}}\)Then the error constants Kp, Kv and Ka, respectively, are |
| A. | \(\infty ,\;\infty \;and\frac{K}{6}\) |
| B. | \(0,\;0\;and\frac{K}{6}\) |
| C. | \(\frac{K}{6},\;0\;and\;0\) |
| D. | \(\frac{K}{6},\;\infty \;and\;\infty \) |
| Answer» B. \(0,\;0\;and\frac{K}{6}\) | |
| 36. |
How can the steady-state error in a system be reduced? |
| A. | By decreasing the type of system |
| B. | By increasing system gain |
| C. | By decreasing the static error constant |
| D. | By increasing the input |
| Answer» C. By decreasing the static error constant | |
| 37. |
A second-order real system has the following properties:The damping ratio \(\xi = 0.5\) and undamped natural frequency \({\omega _n} = 10\;rad/s\), the steady state value at zero is 1.02.The transfer function of the system is |
| A. | \(\frac{{1.02}}{{{s^2} + 5s + 100}}\) |
| B. | \(\frac{{102}}{{{s^2} + 10s + 100}}\) |
| C. | \(\frac{{100}}{{{s^2} + 10s + 100}}\) |
| D. | \(\frac{{102}}{{{s^2} + 5s + 100}}\) |
| Answer» C. \(\frac{{100}}{{{s^2} + 10s + 100}}\) | |
| 38. |
In a system if the poles lie off the real axis then the system is ________ |
| A. | over damped |
| B. | under damped |
| C. | critically damped |
| D. | none of these |
| Answer» C. critically damped | |
| 39. |
A second order system is described by \(2\frac{{{d^2}y}}{{d{t^2}}} + 4\frac{{dy}}{{dt}} + 8y = 8x\). The damping ratio of the system is |
| A. | 0.1 |
| B. | 0.25 |
| C. | 0.333 |
| D. | 0.5 |
| Answer» E. | |
| 40. |
A second order system with no zeros has its poles located at -3 + j4 and -3 – j4 in the s-plane. The undamped natural frequency and the damping ratio of the system are respectively. |
| A. | 4 rad/s and 0.75 |
| B. | 3 rad/s and 0.60 |
| C. | 5 rad/s and 0.80 |
| D. | 5 rad/s and 0.60 |
| Answer» E. | |
| 41. |
Consider the following open-loop transfer function:\(G = \frac{{K\left( {s + 2} \right)}}{{\left( {s + 1} \right)\left( {s + 4} \right)}}\)The characteristic equation of the unity negative feedback will be |
| A. | (s + 1)(s + 4) + K (s + 2) = 0 |
| B. | (s + 2)(s + 1) + K (s + 4) = 0 |
| C. | (s + 1)(s - 2) + K (s + 4) = 0 |
| D. | (s + 2)(s + 4) + K (s + 1) = 0 |
| Answer» B. (s + 2)(s + 1) + K (s + 4) = 0 | |
| 42. |
In a critically damped system, the damping factor of the system is |
| A. | zero |
| B. | less than unity |
| C. | unity |
| D. | greater than unity |
| Answer» D. greater than unity | |
| 43. |
Poles and zeros of a voltage function v(t) are: zero at the origin, simple poles at - 3 and - 1. The scaling factor is 5. The contribution of pole - 3 to v(t) is |
| A. | 2.5 e-3t |
| B. | 7.5 e-3t |
| C. | 2.5 e3t |
| D. | 7.5 e3t |
| Answer» C. 2.5 e3t | |
| 44. |
Consider the time response of a second-order system with damping coefficient less than 1 to a unit step input:1. It is overdamped.2. It is a periodic function.3. Time duration between any two consecutive values of 1 is the same.Which of the above statements is/are correct? |
| A. | 1, 2 and 3 |
| B. | 1 only |
| C. | 2 only |
| D. | 3 only |
| Answer» E. | |
| 45. |
A dominant pole is determined by |
| A. | the highest frequency pole among all poles |
| B. | the lowest frequency pole at least two octaves lower than other poles |
| C. | the lowest pole among all poles |
| D. | the highest frequency pole at least two octaves higher than the other poles |
| Answer» C. the lowest pole among all poles | |
| 46. |
Damping ratio \(\xi\) and peak overshoot Mp are measures of |
| A. | relative stability |
| B. | absolute stability |
| C. | speed of response |
| D. | steady state error |
| Answer» B. absolute stability | |
| 47. |
For a closed-loop system shown in the figure, what is the settling time for ± 2% settling of the steady-state condition, assuming unit-step input? |
| A. | 0.33 s |
| B. | 1.33 s |
| C. | 2.33 s |
| D. | 3.33 s |
| Answer» C. 2.33 s | |
| 48. |
A system having G(s) = 1/(s + 2)(s + 5) and H(s) = 10/s is of type |
| A. | N = 0 |
| B. | N = 1 |
| C. | N = 2 |
| D. | N = 3 |
| Answer» C. N = 2 | |
| 49. |
A unity feedback system has the forward path transfer function G(s). The steady-state error is zero if |
| A. | G(s) is Type-1 and input is unit-ramp |
| B. | G(s) is Type-0 and input is unit-step |
| C. | G(s) is Type-1 and input is unit-step |
| D. | G(s) is Type-0 and input is unit-ramp |
| Answer» D. G(s) is Type-0 and input is unit-ramp | |
| 50. |
In time domain specification, decay ratio is the ratio of the |
| A. | amplitude of the first peak and the steady-state value |
| B. | amplitude of the first two successive peaks |
| C. | peak value to the steady-state value |
| D. | None of the above |
| Answer» C. peak value to the steady-state value | |